| Index: icu46/source/i18n/decNumber.c
|
| ===================================================================
|
| --- icu46/source/i18n/decNumber.c (revision 0)
|
| +++ icu46/source/i18n/decNumber.c (revision 0)
|
| @@ -0,0 +1,8143 @@
|
| +/* ------------------------------------------------------------------ */
|
| +/* Decimal Number arithmetic module */
|
| +/* ------------------------------------------------------------------ */
|
| +/* Copyright (c) IBM Corporation, 2000-2010. All rights reserved. */
|
| +/* */
|
| +/* This software is made available under the terms of the */
|
| +/* ICU License -- ICU 1.8.1 and later. */
|
| +/* */
|
| +/* The description and User's Guide ("The decNumber C Library") for */
|
| +/* this software is called decNumber.pdf. This document is */
|
| +/* available, together with arithmetic and format specifications, */
|
| +/* testcases, and Web links, on the General Decimal Arithmetic page. */
|
| +/* */
|
| +/* Please send comments, suggestions, and corrections to the author: */
|
| +/* mfc@uk.ibm.com */
|
| +/* Mike Cowlishaw, IBM Fellow */
|
| +/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */
|
| +/* ------------------------------------------------------------------ */
|
| +
|
| +/* Modified version, for use from within ICU.
|
| + * Renamed public functions, to avoid an unwanted export of the
|
| + * standard names from the ICU library.
|
| + *
|
| + * Use ICU's uprv_malloc() and uprv_free()
|
| + *
|
| + * Revert comment syntax to plain C
|
| + *
|
| + * Remove a few compiler warnings.
|
| + */
|
| +
|
| +/* This module comprises the routines for arbitrary-precision General */
|
| +/* Decimal Arithmetic as defined in the specification which may be */
|
| +/* found on the General Decimal Arithmetic pages. It implements both */
|
| +/* the full ('extended') arithmetic and the simpler ('subset') */
|
| +/* arithmetic. */
|
| +/* */
|
| +/* Usage notes: */
|
| +/* */
|
| +/* 1. This code is ANSI C89 except: */
|
| +/* */
|
| +/* a) C99 line comments (double forward slash) are used. (Most C */
|
| +/* compilers accept these. If yours does not, a simple script */
|
| +/* can be used to convert them to ANSI C comments.) */
|
| +/* */
|
| +/* b) Types from C99 stdint.h are used. If you do not have this */
|
| +/* header file, see the User's Guide section of the decNumber */
|
| +/* documentation; this lists the necessary definitions. */
|
| +/* */
|
| +/* c) If DECDPUN>4 or DECUSE64=1, the C99 64-bit int64_t and */
|
| +/* uint64_t types may be used. To avoid these, set DECUSE64=0 */
|
| +/* and DECDPUN<=4 (see documentation). */
|
| +/* */
|
| +/* The code also conforms to C99 restrictions; in particular, */
|
| +/* strict aliasing rules are observed. */
|
| +/* */
|
| +/* 2. The decNumber format which this library uses is optimized for */
|
| +/* efficient processing of relatively short numbers; in particular */
|
| +/* it allows the use of fixed sized structures and minimizes copy */
|
| +/* and move operations. It does, however, support arbitrary */
|
| +/* precision (up to 999,999,999 digits) and arbitrary exponent */
|
| +/* range (Emax in the range 0 through 999,999,999 and Emin in the */
|
| +/* range -999,999,999 through 0). Mathematical functions (for */
|
| +/* example decNumberExp) as identified below are restricted more */
|
| +/* tightly: digits, emax, and -emin in the context must be <= */
|
| +/* DEC_MAX_MATH (999999), and their operand(s) must be within */
|
| +/* these bounds. */
|
| +/* */
|
| +/* 3. Logical functions are further restricted; their operands must */
|
| +/* be finite, positive, have an exponent of zero, and all digits */
|
| +/* must be either 0 or 1. The result will only contain digits */
|
| +/* which are 0 or 1 (and will have exponent=0 and a sign of 0). */
|
| +/* */
|
| +/* 4. Operands to operator functions are never modified unless they */
|
| +/* are also specified to be the result number (which is always */
|
| +/* permitted). Other than that case, operands must not overlap. */
|
| +/* */
|
| +/* 5. Error handling: the type of the error is ORed into the status */
|
| +/* flags in the current context (decContext structure). The */
|
| +/* SIGFPE signal is then raised if the corresponding trap-enabler */
|
| +/* flag in the decContext is set (is 1). */
|
| +/* */
|
| +/* It is the responsibility of the caller to clear the status */
|
| +/* flags as required. */
|
| +/* */
|
| +/* The result of any routine which returns a number will always */
|
| +/* be a valid number (which may be a special value, such as an */
|
| +/* Infinity or NaN). */
|
| +/* */
|
| +/* 6. The decNumber format is not an exchangeable concrete */
|
| +/* representation as it comprises fields which may be machine- */
|
| +/* dependent (packed or unpacked, or special length, for example). */
|
| +/* Canonical conversions to and from strings are provided; other */
|
| +/* conversions are available in separate modules. */
|
| +/* */
|
| +/* 7. Normally, input operands are assumed to be valid. Set DECCHECK */
|
| +/* to 1 for extended operand checking (including NULL operands). */
|
| +/* Results are undefined if a badly-formed structure (or a NULL */
|
| +/* pointer to a structure) is provided, though with DECCHECK */
|
| +/* enabled the operator routines are protected against exceptions. */
|
| +/* (Except if the result pointer is NULL, which is unrecoverable.) */
|
| +/* */
|
| +/* However, the routines will never cause exceptions if they are */
|
| +/* given well-formed operands, even if the value of the operands */
|
| +/* is inappropriate for the operation and DECCHECK is not set. */
|
| +/* (Except for SIGFPE, as and where documented.) */
|
| +/* */
|
| +/* 8. Subset arithmetic is available only if DECSUBSET is set to 1. */
|
| +/* ------------------------------------------------------------------ */
|
| +/* Implementation notes for maintenance of this module: */
|
| +/* */
|
| +/* 1. Storage leak protection: Routines which use malloc are not */
|
| +/* permitted to use return for fastpath or error exits (i.e., */
|
| +/* they follow strict structured programming conventions). */
|
| +/* Instead they have a do{}while(0); construct surrounding the */
|
| +/* code which is protected -- break may be used to exit this. */
|
| +/* Other routines can safely use the return statement inline. */
|
| +/* */
|
| +/* Storage leak accounting can be enabled using DECALLOC. */
|
| +/* */
|
| +/* 2. All loops use the for(;;) construct. Any do construct does */
|
| +/* not loop; it is for allocation protection as just described. */
|
| +/* */
|
| +/* 3. Setting status in the context must always be the very last */
|
| +/* action in a routine, as non-0 status may raise a trap and hence */
|
| +/* the call to set status may not return (if the handler uses long */
|
| +/* jump). Therefore all cleanup must be done first. In general, */
|
| +/* to achieve this status is accumulated and is only applied just */
|
| +/* before return by calling decContextSetStatus (via decStatus). */
|
| +/* */
|
| +/* Routines which allocate storage cannot, in general, use the */
|
| +/* 'top level' routines which could cause a non-returning */
|
| +/* transfer of control. The decXxxxOp routines are safe (do not */
|
| +/* call decStatus even if traps are set in the context) and should */
|
| +/* be used instead (they are also a little faster). */
|
| +/* */
|
| +/* 4. Exponent checking is minimized by allowing the exponent to */
|
| +/* grow outside its limits during calculations, provided that */
|
| +/* the decFinalize function is called later. Multiplication and */
|
| +/* division, and intermediate calculations in exponentiation, */
|
| +/* require more careful checks because of the risk of 31-bit */
|
| +/* overflow (the most negative valid exponent is -1999999997, for */
|
| +/* a 999999999-digit number with adjusted exponent of -999999999). */
|
| +/* */
|
| +/* 5. Rounding is deferred until finalization of results, with any */
|
| +/* 'off to the right' data being represented as a single digit */
|
| +/* residue (in the range -1 through 9). This avoids any double- */
|
| +/* rounding when more than one shortening takes place (for */
|
| +/* example, when a result is subnormal). */
|
| +/* */
|
| +/* 6. The digits count is allowed to rise to a multiple of DECDPUN */
|
| +/* during many operations, so whole Units are handled and exact */
|
| +/* accounting of digits is not needed. The correct digits value */
|
| +/* is found by decGetDigits, which accounts for leading zeros. */
|
| +/* This must be called before any rounding if the number of digits */
|
| +/* is not known exactly. */
|
| +/* */
|
| +/* 7. The multiply-by-reciprocal 'trick' is used for partitioning */
|
| +/* numbers up to four digits, using appropriate constants. This */
|
| +/* is not useful for longer numbers because overflow of 32 bits */
|
| +/* would lead to 4 multiplies, which is almost as expensive as */
|
| +/* a divide (unless a floating-point or 64-bit multiply is */
|
| +/* assumed to be available). */
|
| +/* */
|
| +/* 8. Unusual abbreviations that may be used in the commentary: */
|
| +/* lhs -- left hand side (operand, of an operation) */
|
| +/* lsd -- least significant digit (of coefficient) */
|
| +/* lsu -- least significant Unit (of coefficient) */
|
| +/* msd -- most significant digit (of coefficient) */
|
| +/* msi -- most significant item (in an array) */
|
| +/* msu -- most significant Unit (of coefficient) */
|
| +/* rhs -- right hand side (operand, of an operation) */
|
| +/* +ve -- positive */
|
| +/* -ve -- negative */
|
| +/* ** -- raise to the power */
|
| +/* ------------------------------------------------------------------ */
|
| +
|
| +#include <stdlib.h> /* for malloc, free, etc. */
|
| +/* #include <stdio.h> */ /* for printf [if needed] */
|
| +#include <string.h> /* for strcpy */
|
| +#include <ctype.h> /* for lower */
|
| +#include "cmemory.h" /* for uprv_malloc, etc., in ICU */
|
| +#include "decNumber.h" /* base number library */
|
| +#include "decNumberLocal.h" /* decNumber local types, etc. */
|
| +
|
| +/* Constants */
|
| +/* Public lookup table used by the D2U macro */
|
| +const uByte d2utable[DECMAXD2U+1]=D2UTABLE;
|
| +
|
| +#define DECVERB 1 /* set to 1 for verbose DECCHECK */
|
| +#define powers DECPOWERS /* old internal name */
|
| +
|
| +/* Local constants */
|
| +#define DIVIDE 0x80 /* Divide operators */
|
| +#define REMAINDER 0x40 /* .. */
|
| +#define DIVIDEINT 0x20 /* .. */
|
| +#define REMNEAR 0x10 /* .. */
|
| +#define COMPARE 0x01 /* Compare operators */
|
| +#define COMPMAX 0x02 /* .. */
|
| +#define COMPMIN 0x03 /* .. */
|
| +#define COMPTOTAL 0x04 /* .. */
|
| +#define COMPNAN 0x05 /* .. [NaN processing] */
|
| +#define COMPSIG 0x06 /* .. [signaling COMPARE] */
|
| +#define COMPMAXMAG 0x07 /* .. */
|
| +#define COMPMINMAG 0x08 /* .. */
|
| +
|
| +#define DEC_sNaN 0x40000000 /* local status: sNaN signal */
|
| +#define BADINT (Int)0x80000000 /* most-negative Int; error indicator */
|
| +/* Next two indicate an integer >= 10**6, and its parity (bottom bit) */
|
| +#define BIGEVEN (Int)0x80000002
|
| +#define BIGODD (Int)0x80000003
|
| +
|
| +static Unit uarrone[1]={1}; /* Unit array of 1, used for incrementing */
|
| +
|
| +/* Granularity-dependent code */
|
| +#if DECDPUN<=4
|
| + #define eInt Int /* extended integer */
|
| + #define ueInt uInt /* unsigned extended integer */
|
| + /* Constant multipliers for divide-by-power-of five using reciprocal */
|
| + /* multiply, after removing powers of 2 by shifting, and final shift */
|
| + /* of 17 [we only need up to **4] */
|
| + static const uInt multies[]={131073, 26215, 5243, 1049, 210};
|
| + /* QUOT10 -- macro to return the quotient of unit u divided by 10**n */
|
| + #define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17)
|
| +#else
|
| + /* For DECDPUN>4 non-ANSI-89 64-bit types are needed. */
|
| + #if !DECUSE64
|
| + #error decNumber.c: DECUSE64 must be 1 when DECDPUN>4
|
| + #endif
|
| + #define eInt Long /* extended integer */
|
| + #define ueInt uLong /* unsigned extended integer */
|
| +#endif
|
| +
|
| +/* Local routines */
|
| +static decNumber * decAddOp(decNumber *, const decNumber *, const decNumber *,
|
| + decContext *, uByte, uInt *);
|
| +static Flag decBiStr(const char *, const char *, const char *);
|
| +static uInt decCheckMath(const decNumber *, decContext *, uInt *);
|
| +static void decApplyRound(decNumber *, decContext *, Int, uInt *);
|
| +static Int decCompare(const decNumber *lhs, const decNumber *rhs, Flag);
|
| +static decNumber * decCompareOp(decNumber *, const decNumber *,
|
| + const decNumber *, decContext *,
|
| + Flag, uInt *);
|
| +static void decCopyFit(decNumber *, const decNumber *, decContext *,
|
| + Int *, uInt *);
|
| +static decNumber * decDecap(decNumber *, Int);
|
| +static decNumber * decDivideOp(decNumber *, const decNumber *,
|
| + const decNumber *, decContext *, Flag, uInt *);
|
| +static decNumber * decExpOp(decNumber *, const decNumber *,
|
| + decContext *, uInt *);
|
| +static void decFinalize(decNumber *, decContext *, Int *, uInt *);
|
| +static Int decGetDigits(Unit *, Int);
|
| +static Int decGetInt(const decNumber *);
|
| +static decNumber * decLnOp(decNumber *, const decNumber *,
|
| + decContext *, uInt *);
|
| +static decNumber * decMultiplyOp(decNumber *, const decNumber *,
|
| + const decNumber *, decContext *,
|
| + uInt *);
|
| +static decNumber * decNaNs(decNumber *, const decNumber *,
|
| + const decNumber *, decContext *, uInt *);
|
| +static decNumber * decQuantizeOp(decNumber *, const decNumber *,
|
| + const decNumber *, decContext *, Flag,
|
| + uInt *);
|
| +static void decReverse(Unit *, Unit *);
|
| +static void decSetCoeff(decNumber *, decContext *, const Unit *,
|
| + Int, Int *, uInt *);
|
| +static void decSetMaxValue(decNumber *, decContext *);
|
| +static void decSetOverflow(decNumber *, decContext *, uInt *);
|
| +static void decSetSubnormal(decNumber *, decContext *, Int *, uInt *);
|
| +static Int decShiftToLeast(Unit *, Int, Int);
|
| +static Int decShiftToMost(Unit *, Int, Int);
|
| +static void decStatus(decNumber *, uInt, decContext *);
|
| +static void decToString(const decNumber *, char[], Flag);
|
| +static decNumber * decTrim(decNumber *, decContext *, Flag, Flag, Int *);
|
| +static Int decUnitAddSub(const Unit *, Int, const Unit *, Int, Int,
|
| + Unit *, Int);
|
| +static Int decUnitCompare(const Unit *, Int, const Unit *, Int, Int);
|
| +
|
| +#if !DECSUBSET
|
| +/* decFinish == decFinalize when no subset arithmetic needed */
|
| +#define decFinish(a,b,c,d) decFinalize(a,b,c,d)
|
| +#else
|
| +static void decFinish(decNumber *, decContext *, Int *, uInt *);
|
| +static decNumber * decRoundOperand(const decNumber *, decContext *, uInt *);
|
| +#endif
|
| +
|
| +/* Local macros */
|
| +/* masked special-values bits */
|
| +#define SPECIALARG (rhs->bits & DECSPECIAL)
|
| +#define SPECIALARGS ((lhs->bits | rhs->bits) & DECSPECIAL)
|
| +
|
| +/* For use in ICU */
|
| +#define malloc(a) uprv_malloc(a)
|
| +#define free(a) uprv_free(a)
|
| +
|
| +/* Diagnostic macros, etc. */
|
| +#if DECALLOC
|
| +/* Handle malloc/free accounting. If enabled, our accountable routines */
|
| +/* are used; otherwise the code just goes straight to the system malloc */
|
| +/* and free routines. */
|
| +#define malloc(a) decMalloc(a)
|
| +#define free(a) decFree(a)
|
| +#define DECFENCE 0x5a /* corruption detector */
|
| +/* 'Our' malloc and free: */
|
| +static void *decMalloc(size_t);
|
| +static void decFree(void *);
|
| +uInt decAllocBytes=0; /* count of bytes allocated */
|
| +/* Note that DECALLOC code only checks for storage buffer overflow. */
|
| +/* To check for memory leaks, the decAllocBytes variable must be */
|
| +/* checked to be 0 at appropriate times (e.g., after the test */
|
| +/* harness completes a set of tests). This checking may be unreliable */
|
| +/* if the testing is done in a multi-thread environment. */
|
| +#endif
|
| +
|
| +#if DECCHECK
|
| +/* Optional checking routines. Enabling these means that decNumber */
|
| +/* and decContext operands to operator routines are checked for */
|
| +/* correctness. This roughly doubles the execution time of the */
|
| +/* fastest routines (and adds 600+ bytes), so should not normally be */
|
| +/* used in 'production'. */
|
| +/* decCheckInexact is used to check that inexact results have a full */
|
| +/* complement of digits (where appropriate -- this is not the case */
|
| +/* for Quantize, for example) */
|
| +#define DECUNRESU ((decNumber *)(void *)0xffffffff)
|
| +#define DECUNUSED ((const decNumber *)(void *)0xffffffff)
|
| +#define DECUNCONT ((decContext *)(void *)(0xffffffff))
|
| +static Flag decCheckOperands(decNumber *, const decNumber *,
|
| + const decNumber *, decContext *);
|
| +static Flag decCheckNumber(const decNumber *);
|
| +static void decCheckInexact(const decNumber *, decContext *);
|
| +#endif
|
| +
|
| +#if DECTRACE || DECCHECK
|
| +/* Optional trace/debugging routines (may or may not be used) */
|
| +void decNumberShow(const decNumber *); /* displays the components of a number */
|
| +static void decDumpAr(char, const Unit *, Int);
|
| +#endif
|
| +
|
| +/* ================================================================== */
|
| +/* Conversions */
|
| +/* ================================================================== */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* from-int32 -- conversion from Int or uInt */
|
| +/* */
|
| +/* dn is the decNumber to receive the integer */
|
| +/* in or uin is the integer to be converted */
|
| +/* returns dn */
|
| +/* */
|
| +/* No error is possible. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberFromInt32(decNumber *dn, Int in) {
|
| + uInt unsig;
|
| + if (in>=0) unsig=in;
|
| + else { /* negative (possibly BADINT) */
|
| + if (in==BADINT) unsig=(uInt)1073741824*2; /* special case */
|
| + else unsig=-in; /* invert */
|
| + }
|
| + /* in is now positive */
|
| + uprv_decNumberFromUInt32(dn, unsig);
|
| + if (in<0) dn->bits=DECNEG; /* sign needed */
|
| + return dn;
|
| + } /* decNumberFromInt32 */
|
| +
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberFromUInt32(decNumber *dn, uInt uin) {
|
| + Unit *up; /* work pointer */
|
| + uprv_decNumberZero(dn); /* clean */
|
| + if (uin==0) return dn; /* [or decGetDigits bad call] */
|
| + for (up=dn->lsu; uin>0; up++) {
|
| + *up=(Unit)(uin%(DECDPUNMAX+1));
|
| + uin=uin/(DECDPUNMAX+1);
|
| + }
|
| + dn->digits=decGetDigits(dn->lsu, up-dn->lsu);
|
| + return dn;
|
| + } /* decNumberFromUInt32 */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* to-int32 -- conversion to Int or uInt */
|
| +/* */
|
| +/* dn is the decNumber to convert */
|
| +/* set is the context for reporting errors */
|
| +/* returns the converted decNumber, or 0 if Invalid is set */
|
| +/* */
|
| +/* Invalid is set if the decNumber does not have exponent==0 or if */
|
| +/* it is a NaN, Infinite, or out-of-range. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI Int U_EXPORT2 uprv_decNumberToInt32(const decNumber *dn, decContext *set) {
|
| + #if DECCHECK
|
| + if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
|
| + #endif
|
| +
|
| + /* special or too many digits, or bad exponent */
|
| + if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0) ; /* bad */
|
| + else { /* is a finite integer with 10 or fewer digits */
|
| + Int d; /* work */
|
| + const Unit *up; /* .. */
|
| + uInt hi=0, lo; /* .. */
|
| + up=dn->lsu; /* -> lsu */
|
| + lo=*up; /* get 1 to 9 digits */
|
| + #if DECDPUN>1 /* split to higher */
|
| + hi=lo/10;
|
| + lo=lo%10;
|
| + #endif
|
| + up++;
|
| + /* collect remaining Units, if any, into hi */
|
| + for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];
|
| + /* now low has the lsd, hi the remainder */
|
| + if (hi>214748364 || (hi==214748364 && lo>7)) { /* out of range? */
|
| + /* most-negative is a reprieve */
|
| + if (dn->bits&DECNEG && hi==214748364 && lo==8) return 0x80000000;
|
| + /* bad -- drop through */
|
| + }
|
| + else { /* in-range always */
|
| + Int i=X10(hi)+lo;
|
| + if (dn->bits&DECNEG) return -i;
|
| + return i;
|
| + }
|
| + } /* integer */
|
| + uprv_decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */
|
| + return 0;
|
| + } /* decNumberToInt32 */
|
| +
|
| +U_CAPI uInt U_EXPORT2 uprv_decNumberToUInt32(const decNumber *dn, decContext *set) {
|
| + #if DECCHECK
|
| + if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
|
| + #endif
|
| + /* special or too many digits, or bad exponent, or negative (<0) */
|
| + if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0
|
| + || (dn->bits&DECNEG && !ISZERO(dn))); /* bad */
|
| + else { /* is a finite integer with 10 or fewer digits */
|
| + Int d; /* work */
|
| + const Unit *up; /* .. */
|
| + uInt hi=0, lo; /* .. */
|
| + up=dn->lsu; /* -> lsu */
|
| + lo=*up; /* get 1 to 9 digits */
|
| + #if DECDPUN>1 /* split to higher */
|
| + hi=lo/10;
|
| + lo=lo%10;
|
| + #endif
|
| + up++;
|
| + /* collect remaining Units, if any, into hi */
|
| + for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];
|
| +
|
| + /* now low has the lsd, hi the remainder */
|
| + if (hi>429496729 || (hi==429496729 && lo>5)) ; /* no reprieve possible */
|
| + else return X10(hi)+lo;
|
| + } /* integer */
|
| + uprv_decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */
|
| + return 0;
|
| + } /* decNumberToUInt32 */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* to-scientific-string -- conversion to numeric string */
|
| +/* to-engineering-string -- conversion to numeric string */
|
| +/* */
|
| +/* decNumberToString(dn, string); */
|
| +/* decNumberToEngString(dn, string); */
|
| +/* */
|
| +/* dn is the decNumber to convert */
|
| +/* string is the string where the result will be laid out */
|
| +/* */
|
| +/* string must be at least dn->digits+14 characters long */
|
| +/* */
|
| +/* No error is possible, and no status can be set. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI char * U_EXPORT2 uprv_decNumberToString(const decNumber *dn, char *string){
|
| + decToString(dn, string, 0);
|
| + return string;
|
| + } /* DecNumberToString */
|
| +
|
| +U_CAPI char * U_EXPORT2 uprv_decNumberToEngString(const decNumber *dn, char *string){
|
| + decToString(dn, string, 1);
|
| + return string;
|
| + } /* DecNumberToEngString */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* to-number -- conversion from numeric string */
|
| +/* */
|
| +/* decNumberFromString -- convert string to decNumber */
|
| +/* dn -- the number structure to fill */
|
| +/* chars[] -- the string to convert ('\0' terminated) */
|
| +/* set -- the context used for processing any error, */
|
| +/* determining the maximum precision available */
|
| +/* (set.digits), determining the maximum and minimum */
|
| +/* exponent (set.emax and set.emin), determining if */
|
| +/* extended values are allowed, and checking the */
|
| +/* rounding mode if overflow occurs or rounding is */
|
| +/* needed. */
|
| +/* */
|
| +/* The length of the coefficient and the size of the exponent are */
|
| +/* checked by this routine, so the correct error (Underflow or */
|
| +/* Overflow) can be reported or rounding applied, as necessary. */
|
| +/* */
|
| +/* If bad syntax is detected, the result will be a quiet NaN. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberFromString(decNumber *dn, const char chars[],
|
| + decContext *set) {
|
| + Int exponent=0; /* working exponent [assume 0] */
|
| + uByte bits=0; /* working flags [assume +ve] */
|
| + Unit *res; /* where result will be built */
|
| + Unit resbuff[SD2U(DECBUFFER+9)];/* local buffer in case need temporary */
|
| + /* [+9 allows for ln() constants] */
|
| + Unit *allocres=NULL; /* -> allocated result, iff allocated */
|
| + Int d=0; /* count of digits found in decimal part */
|
| + const char *dotchar=NULL; /* where dot was found */
|
| + const char *cfirst=chars; /* -> first character of decimal part */
|
| + const char *last=NULL; /* -> last digit of decimal part */
|
| + const char *c; /* work */
|
| + Unit *up; /* .. */
|
| + #if DECDPUN>1
|
| + Int cut, out; /* .. */
|
| + #endif
|
| + Int residue; /* rounding residue */
|
| + uInt status=0; /* error code */
|
| +
|
| + #if DECCHECK
|
| + if (decCheckOperands(DECUNRESU, DECUNUSED, DECUNUSED, set))
|
| + return uprv_decNumberZero(dn);
|
| + #endif
|
| +
|
| + do { /* status & malloc protection */
|
| + for (c=chars;; c++) { /* -> input character */
|
| + if (*c>='0' && *c<='9') { /* test for Arabic digit */
|
| + last=c;
|
| + d++; /* count of real digits */
|
| + continue; /* still in decimal part */
|
| + }
|
| + if (*c=='.' && dotchar==NULL) { /* first '.' */
|
| + dotchar=c; /* record offset into decimal part */
|
| + if (c==cfirst) cfirst++; /* first digit must follow */
|
| + continue;}
|
| + if (c==chars) { /* first in string... */
|
| + if (*c=='-') { /* valid - sign */
|
| + cfirst++;
|
| + bits=DECNEG;
|
| + continue;}
|
| + if (*c=='+') { /* valid + sign */
|
| + cfirst++;
|
| + continue;}
|
| + }
|
| + /* *c is not a digit, or a valid +, -, or '.' */
|
| + break;
|
| + } /* c */
|
| +
|
| + if (last==NULL) { /* no digits yet */
|
| + status=DEC_Conversion_syntax;/* assume the worst */
|
| + if (*c=='\0') break; /* and no more to come... */
|
| + #if DECSUBSET
|
| + /* if subset then infinities and NaNs are not allowed */
|
| + if (!set->extended) break; /* hopeless */
|
| + #endif
|
| + /* Infinities and NaNs are possible, here */
|
| + if (dotchar!=NULL) break; /* .. unless had a dot */
|
| + uprv_decNumberZero(dn); /* be optimistic */
|
| + if (decBiStr(c, "infinity", "INFINITY")
|
| + || decBiStr(c, "inf", "INF")) {
|
| + dn->bits=bits | DECINF;
|
| + status=0; /* is OK */
|
| + break; /* all done */
|
| + }
|
| + /* a NaN expected */
|
| + /* 2003.09.10 NaNs are now permitted to have a sign */
|
| + dn->bits=bits | DECNAN; /* assume simple NaN */
|
| + if (*c=='s' || *c=='S') { /* looks like an sNaN */
|
| + c++;
|
| + dn->bits=bits | DECSNAN;
|
| + }
|
| + if (*c!='n' && *c!='N') break; /* check caseless "NaN" */
|
| + c++;
|
| + if (*c!='a' && *c!='A') break; /* .. */
|
| + c++;
|
| + if (*c!='n' && *c!='N') break; /* .. */
|
| + c++;
|
| + /* now either nothing, or nnnn payload, expected */
|
| + /* -> start of integer and skip leading 0s [including plain 0] */
|
| + for (cfirst=c; *cfirst=='0';) cfirst++;
|
| + if (*cfirst=='\0') { /* "NaN" or "sNaN", maybe with all 0s */
|
| + status=0; /* it's good */
|
| + break; /* .. */
|
| + }
|
| + /* something other than 0s; setup last and d as usual [no dots] */
|
| + for (c=cfirst;; c++, d++) {
|
| + if (*c<'0' || *c>'9') break; /* test for Arabic digit */
|
| + last=c;
|
| + }
|
| + if (*c!='\0') break; /* not all digits */
|
| + if (d>set->digits-1) {
|
| + /* [NB: payload in a decNumber can be full length unless */
|
| + /* clamped, in which case can only be digits-1] */
|
| + if (set->clamp) break;
|
| + if (d>set->digits) break;
|
| + } /* too many digits? */
|
| + /* good; drop through to convert the integer to coefficient */
|
| + status=0; /* syntax is OK */
|
| + bits=dn->bits; /* for copy-back */
|
| + } /* last==NULL */
|
| +
|
| + else if (*c!='\0') { /* more to process... */
|
| + /* had some digits; exponent is only valid sequence now */
|
| + Flag nege; /* 1=negative exponent */
|
| + const char *firstexp; /* -> first significant exponent digit */
|
| + status=DEC_Conversion_syntax;/* assume the worst */
|
| + if (*c!='e' && *c!='E') break;
|
| + /* Found 'e' or 'E' -- now process explicit exponent */
|
| + /* 1998.07.11: sign no longer required */
|
| + nege=0;
|
| + c++; /* to (possible) sign */
|
| + if (*c=='-') {nege=1; c++;}
|
| + else if (*c=='+') c++;
|
| + if (*c=='\0') break;
|
| +
|
| + for (; *c=='0' && *(c+1)!='\0';) c++; /* strip insignificant zeros */
|
| + firstexp=c; /* save exponent digit place */
|
| + for (; ;c++) {
|
| + if (*c<'0' || *c>'9') break; /* not a digit */
|
| + exponent=X10(exponent)+(Int)*c-(Int)'0';
|
| + } /* c */
|
| + /* if not now on a '\0', *c must not be a digit */
|
| + if (*c!='\0') break;
|
| +
|
| + /* (this next test must be after the syntax checks) */
|
| + /* if it was too long the exponent may have wrapped, so check */
|
| + /* carefully and set it to a certain overflow if wrap possible */
|
| + if (c>=firstexp+9+1) {
|
| + if (c>firstexp+9+1 || *firstexp>'1') exponent=DECNUMMAXE*2;
|
| + /* [up to 1999999999 is OK, for example 1E-1000000998] */
|
| + }
|
| + if (nege) exponent=-exponent; /* was negative */
|
| + status=0; /* is OK */
|
| + } /* stuff after digits */
|
| +
|
| + /* Here when whole string has been inspected; syntax is good */
|
| + /* cfirst->first digit (never dot), last->last digit (ditto) */
|
| +
|
| + /* strip leading zeros/dot [leave final 0 if all 0's] */
|
| + if (*cfirst=='0') { /* [cfirst has stepped over .] */
|
| + for (c=cfirst; c<last; c++, cfirst++) {
|
| + if (*c=='.') continue; /* ignore dots */
|
| + if (*c!='0') break; /* non-zero found */
|
| + d--; /* 0 stripped */
|
| + } /* c */
|
| + #if DECSUBSET
|
| + /* make a rapid exit for easy zeros if !extended */
|
| + if (*cfirst=='0' && !set->extended) {
|
| + uprv_decNumberZero(dn); /* clean result */
|
| + break; /* [could be return] */
|
| + }
|
| + #endif
|
| + } /* at least one leading 0 */
|
| +
|
| + /* Handle decimal point... */
|
| + if (dotchar!=NULL && dotchar<last) /* non-trailing '.' found? */
|
| + exponent-=(last-dotchar); /* adjust exponent */
|
| + /* [we can now ignore the .] */
|
| +
|
| + /* OK, the digits string is good. Assemble in the decNumber, or in */
|
| + /* a temporary units array if rounding is needed */
|
| + if (d<=set->digits) res=dn->lsu; /* fits into supplied decNumber */
|
| + else { /* rounding needed */
|
| + Int needbytes=D2U(d)*sizeof(Unit);/* bytes needed */
|
| + res=resbuff; /* assume use local buffer */
|
| + if (needbytes>(Int)sizeof(resbuff)) { /* too big for local */
|
| + allocres=(Unit *)malloc(needbytes);
|
| + if (allocres==NULL) {status|=DEC_Insufficient_storage; break;}
|
| + res=allocres;
|
| + }
|
| + }
|
| + /* res now -> number lsu, buffer, or allocated storage for Unit array */
|
| +
|
| + /* Place the coefficient into the selected Unit array */
|
| + /* [this is often 70% of the cost of this function when DECDPUN>1] */
|
| + #if DECDPUN>1
|
| + out=0; /* accumulator */
|
| + up=res+D2U(d)-1; /* -> msu */
|
| + cut=d-(up-res)*DECDPUN; /* digits in top unit */
|
| + for (c=cfirst;; c++) { /* along the digits */
|
| + if (*c=='.') continue; /* ignore '.' [don't decrement cut] */
|
| + out=X10(out)+(Int)*c-(Int)'0';
|
| + if (c==last) break; /* done [never get to trailing '.'] */
|
| + cut--;
|
| + if (cut>0) continue; /* more for this unit */
|
| + *up=(Unit)out; /* write unit */
|
| + up--; /* prepare for unit below.. */
|
| + cut=DECDPUN; /* .. */
|
| + out=0; /* .. */
|
| + } /* c */
|
| + *up=(Unit)out; /* write lsu */
|
| +
|
| + #else
|
| + /* DECDPUN==1 */
|
| + up=res; /* -> lsu */
|
| + for (c=last; c>=cfirst; c--) { /* over each character, from least */
|
| + if (*c=='.') continue; /* ignore . [don't step up] */
|
| + *up=(Unit)((Int)*c-(Int)'0');
|
| + up++;
|
| + } /* c */
|
| + #endif
|
| +
|
| + dn->bits=bits;
|
| + dn->exponent=exponent;
|
| + dn->digits=d;
|
| +
|
| + /* if not in number (too long) shorten into the number */
|
| + if (d>set->digits) {
|
| + residue=0;
|
| + decSetCoeff(dn, set, res, d, &residue, &status);
|
| + /* always check for overflow or subnormal and round as needed */
|
| + decFinalize(dn, set, &residue, &status);
|
| + }
|
| + else { /* no rounding, but may still have overflow or subnormal */
|
| + /* [these tests are just for performance; finalize repeats them] */
|
| + if ((dn->exponent-1<set->emin-dn->digits)
|
| + || (dn->exponent-1>set->emax-set->digits)) {
|
| + residue=0;
|
| + decFinalize(dn, set, &residue, &status);
|
| + }
|
| + }
|
| + /* decNumberShow(dn); */
|
| + } while(0); /* [for break] */
|
| +
|
| + if (allocres!=NULL) free(allocres); /* drop any storage used */
|
| + if (status!=0) decStatus(dn, status, set);
|
| + return dn;
|
| + } /* decNumberFromString */
|
| +
|
| +/* ================================================================== */
|
| +/* Operators */
|
| +/* ================================================================== */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberAbs -- absolute value operator */
|
| +/* */
|
| +/* This computes C = abs(A) */
|
| +/* */
|
| +/* res is C, the result. C may be A */
|
| +/* rhs is A */
|
| +/* set is the context */
|
| +/* */
|
| +/* See also decNumberCopyAbs for a quiet bitwise version of this. */
|
| +/* C must have space for set->digits digits. */
|
| +/* ------------------------------------------------------------------ */
|
| +/* This has the same effect as decNumberPlus unless A is negative, */
|
| +/* in which case it has the same effect as decNumberMinus. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberAbs(decNumber *res, const decNumber *rhs,
|
| + decContext *set) {
|
| + decNumber dzero; /* for 0 */
|
| + uInt status=0; /* accumulator */
|
| +
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| + #endif
|
| +
|
| + uprv_decNumberZero(&dzero); /* set 0 */
|
| + dzero.exponent=rhs->exponent; /* [no coefficient expansion] */
|
| + decAddOp(res, &dzero, rhs, set, (uByte)(rhs->bits & DECNEG), &status);
|
| + if (status!=0) decStatus(res, status, set);
|
| + #if DECCHECK
|
| + decCheckInexact(res, set);
|
| + #endif
|
| + return res;
|
| + } /* decNumberAbs */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberAdd -- add two Numbers */
|
| +/* */
|
| +/* This computes C = A + B */
|
| +/* */
|
| +/* res is C, the result. C may be A and/or B (e.g., X=X+X) */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* set is the context */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* ------------------------------------------------------------------ */
|
| +/* This just calls the routine shared with Subtract */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberAdd(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + uInt status=0; /* accumulator */
|
| + decAddOp(res, lhs, rhs, set, 0, &status);
|
| + if (status!=0) decStatus(res, status, set);
|
| + #if DECCHECK
|
| + decCheckInexact(res, set);
|
| + #endif
|
| + return res;
|
| + } /* decNumberAdd */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberAnd -- AND two Numbers, digitwise */
|
| +/* */
|
| +/* This computes C = A & B */
|
| +/* */
|
| +/* res is C, the result. C may be A and/or B (e.g., X=X&X) */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* set is the context (used for result length and error report) */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* */
|
| +/* Logical function restrictions apply (see above); a NaN is */
|
| +/* returned with Invalid_operation if a restriction is violated. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberAnd(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + const Unit *ua, *ub; /* -> operands */
|
| + const Unit *msua, *msub; /* -> operand msus */
|
| + Unit *uc, *msuc; /* -> result and its msu */
|
| + Int msudigs; /* digits in res msu */
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| + #endif
|
| +
|
| + if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
|
| + || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
|
| + decStatus(res, DEC_Invalid_operation, set);
|
| + return res;
|
| + }
|
| +
|
| + /* operands are valid */
|
| + ua=lhs->lsu; /* bottom-up */
|
| + ub=rhs->lsu; /* .. */
|
| + uc=res->lsu; /* .. */
|
| + msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */
|
| + msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */
|
| + msuc=uc+D2U(set->digits)-1; /* -> msu of result */
|
| + msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */
|
| + for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */
|
| + Unit a, b; /* extract units */
|
| + if (ua>msua) a=0;
|
| + else a=*ua;
|
| + if (ub>msub) b=0;
|
| + else b=*ub;
|
| + *uc=0; /* can now write back */
|
| + if (a|b) { /* maybe 1 bits to examine */
|
| + Int i, j;
|
| + *uc=0; /* can now write back */
|
| + /* This loop could be unrolled and/or use BIN2BCD tables */
|
| + for (i=0; i<DECDPUN; i++) {
|
| + if (a&b&1) *uc=*uc+(Unit)powers[i]; /* effect AND */
|
| + j=a%10;
|
| + a=a/10;
|
| + j|=b%10;
|
| + b=b/10;
|
| + if (j>1) {
|
| + decStatus(res, DEC_Invalid_operation, set);
|
| + return res;
|
| + }
|
| + if (uc==msuc && i==msudigs-1) break; /* just did final digit */
|
| + } /* each digit */
|
| + } /* both OK */
|
| + } /* each unit */
|
| + /* [here uc-1 is the msu of the result] */
|
| + res->digits=decGetDigits(res->lsu, uc-res->lsu);
|
| + res->exponent=0; /* integer */
|
| + res->bits=0; /* sign=0 */
|
| + return res; /* [no status to set] */
|
| + } /* decNumberAnd */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberCompare -- compare two Numbers */
|
| +/* */
|
| +/* This computes C = A ? B */
|
| +/* */
|
| +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* set is the context */
|
| +/* */
|
| +/* C must have space for one digit (or NaN). */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompare(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + uInt status=0; /* accumulator */
|
| + decCompareOp(res, lhs, rhs, set, COMPARE, &status);
|
| + if (status!=0) decStatus(res, status, set);
|
| + return res;
|
| + } /* decNumberCompare */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberCompareSignal -- compare, signalling on all NaNs */
|
| +/* */
|
| +/* This computes C = A ? B */
|
| +/* */
|
| +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* set is the context */
|
| +/* */
|
| +/* C must have space for one digit (or NaN). */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompareSignal(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + uInt status=0; /* accumulator */
|
| + decCompareOp(res, lhs, rhs, set, COMPSIG, &status);
|
| + if (status!=0) decStatus(res, status, set);
|
| + return res;
|
| + } /* decNumberCompareSignal */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberCompareTotal -- compare two Numbers, using total ordering */
|
| +/* */
|
| +/* This computes C = A ? B, under total ordering */
|
| +/* */
|
| +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* set is the context */
|
| +/* */
|
| +/* C must have space for one digit; the result will always be one of */
|
| +/* -1, 0, or 1. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompareTotal(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + uInt status=0; /* accumulator */
|
| + decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);
|
| + if (status!=0) decStatus(res, status, set);
|
| + return res;
|
| + } /* decNumberCompareTotal */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberCompareTotalMag -- compare, total ordering of magnitudes */
|
| +/* */
|
| +/* This computes C = |A| ? |B|, under total ordering */
|
| +/* */
|
| +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* set is the context */
|
| +/* */
|
| +/* C must have space for one digit; the result will always be one of */
|
| +/* -1, 0, or 1. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompareTotalMag(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + uInt status=0; /* accumulator */
|
| + uInt needbytes; /* for space calculations */
|
| + decNumber bufa[D2N(DECBUFFER+1)];/* +1 in case DECBUFFER=0 */
|
| + decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */
|
| + decNumber bufb[D2N(DECBUFFER+1)];
|
| + decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */
|
| + decNumber *a, *b; /* temporary pointers */
|
| +
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| + #endif
|
| +
|
| + do { /* protect allocated storage */
|
| + /* if either is negative, take a copy and absolute */
|
| + if (decNumberIsNegative(lhs)) { /* lhs<0 */
|
| + a=bufa;
|
| + needbytes=sizeof(decNumber)+(D2U(lhs->digits)-1)*sizeof(Unit);
|
| + if (needbytes>sizeof(bufa)) { /* need malloc space */
|
| + allocbufa=(decNumber *)malloc(needbytes);
|
| + if (allocbufa==NULL) { /* hopeless -- abandon */
|
| + status|=DEC_Insufficient_storage;
|
| + break;}
|
| + a=allocbufa; /* use the allocated space */
|
| + }
|
| + uprv_decNumberCopy(a, lhs); /* copy content */
|
| + a->bits&=~DECNEG; /* .. and clear the sign */
|
| + lhs=a; /* use copy from here on */
|
| + }
|
| + if (decNumberIsNegative(rhs)) { /* rhs<0 */
|
| + b=bufb;
|
| + needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
|
| + if (needbytes>sizeof(bufb)) { /* need malloc space */
|
| + allocbufb=(decNumber *)malloc(needbytes);
|
| + if (allocbufb==NULL) { /* hopeless -- abandon */
|
| + status|=DEC_Insufficient_storage;
|
| + break;}
|
| + b=allocbufb; /* use the allocated space */
|
| + }
|
| + uprv_decNumberCopy(b, rhs); /* copy content */
|
| + b->bits&=~DECNEG; /* .. and clear the sign */
|
| + rhs=b; /* use copy from here on */
|
| + }
|
| + decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);
|
| + } while(0); /* end protected */
|
| +
|
| + if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
|
| + if (allocbufb!=NULL) free(allocbufb); /* .. */
|
| + if (status!=0) decStatus(res, status, set);
|
| + return res;
|
| + } /* decNumberCompareTotalMag */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberDivide -- divide one number by another */
|
| +/* */
|
| +/* This computes C = A / B */
|
| +/* */
|
| +/* res is C, the result. C may be A and/or B (e.g., X=X/X) */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* set is the context */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberDivide(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + uInt status=0; /* accumulator */
|
| + decDivideOp(res, lhs, rhs, set, DIVIDE, &status);
|
| + if (status!=0) decStatus(res, status, set);
|
| + #if DECCHECK
|
| + decCheckInexact(res, set);
|
| + #endif
|
| + return res;
|
| + } /* decNumberDivide */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberDivideInteger -- divide and return integer quotient */
|
| +/* */
|
| +/* This computes C = A # B, where # is the integer divide operator */
|
| +/* */
|
| +/* res is C, the result. C may be A and/or B (e.g., X=X#X) */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* set is the context */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberDivideInteger(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + uInt status=0; /* accumulator */
|
| + decDivideOp(res, lhs, rhs, set, DIVIDEINT, &status);
|
| + if (status!=0) decStatus(res, status, set);
|
| + return res;
|
| + } /* decNumberDivideInteger */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberExp -- exponentiation */
|
| +/* */
|
| +/* This computes C = exp(A) */
|
| +/* */
|
| +/* res is C, the result. C may be A */
|
| +/* rhs is A */
|
| +/* set is the context; note that rounding mode has no effect */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* */
|
| +/* Mathematical function restrictions apply (see above); a NaN is */
|
| +/* returned with Invalid_operation if a restriction is violated. */
|
| +/* */
|
| +/* Finite results will always be full precision and Inexact, except */
|
| +/* when A is a zero or -Infinity (giving 1 or 0 respectively). */
|
| +/* */
|
| +/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */
|
| +/* almost always be correctly rounded, but may be up to 1 ulp in */
|
| +/* error in rare cases. */
|
| +/* ------------------------------------------------------------------ */
|
| +/* This is a wrapper for decExpOp which can handle the slightly wider */
|
| +/* (double) range needed by Ln (which has to be able to calculate */
|
| +/* exp(-a) where a can be the tiniest number (Ntiny). */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberExp(decNumber *res, const decNumber *rhs,
|
| + decContext *set) {
|
| + uInt status=0; /* accumulator */
|
| + #if DECSUBSET
|
| + decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */
|
| + #endif
|
| +
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| + #endif
|
| +
|
| + /* Check restrictions; these restrictions ensure that if h=8 (see */
|
| + /* decExpOp) then the result will either overflow or underflow to 0. */
|
| + /* Other math functions restrict the input range, too, for inverses. */
|
| + /* If not violated then carry out the operation. */
|
| + if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */
|
| + #if DECSUBSET
|
| + if (!set->extended) {
|
| + /* reduce operand and set lostDigits status, as needed */
|
| + if (rhs->digits>set->digits) {
|
| + allocrhs=decRoundOperand(rhs, set, &status);
|
| + if (allocrhs==NULL) break;
|
| + rhs=allocrhs;
|
| + }
|
| + }
|
| + #endif
|
| + decExpOp(res, rhs, set, &status);
|
| + } while(0); /* end protected */
|
| +
|
| + #if DECSUBSET
|
| + if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */
|
| + #endif
|
| + /* apply significant status */
|
| + if (status!=0) decStatus(res, status, set);
|
| + #if DECCHECK
|
| + decCheckInexact(res, set);
|
| + #endif
|
| + return res;
|
| + } /* decNumberExp */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberFMA -- fused multiply add */
|
| +/* */
|
| +/* This computes D = (A * B) + C with only one rounding */
|
| +/* */
|
| +/* res is D, the result. D may be A or B or C (e.g., X=FMA(X,X,X)) */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* fhs is C [far hand side] */
|
| +/* set is the context */
|
| +/* */
|
| +/* Mathematical function restrictions apply (see above); a NaN is */
|
| +/* returned with Invalid_operation if a restriction is violated. */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberFMA(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, const decNumber *fhs,
|
| + decContext *set) {
|
| + uInt status=0; /* accumulator */
|
| + decContext dcmul; /* context for the multiplication */
|
| + uInt needbytes; /* for space calculations */
|
| + decNumber bufa[D2N(DECBUFFER*2+1)];
|
| + decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */
|
| + decNumber *acc; /* accumulator pointer */
|
| + decNumber dzero; /* work */
|
| +
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| + if (decCheckOperands(res, fhs, DECUNUSED, set)) return res;
|
| + #endif
|
| +
|
| + do { /* protect allocated storage */
|
| + #if DECSUBSET
|
| + if (!set->extended) { /* [undefined if subset] */
|
| + status|=DEC_Invalid_operation;
|
| + break;}
|
| + #endif
|
| + /* Check math restrictions [these ensure no overflow or underflow] */
|
| + if ((!decNumberIsSpecial(lhs) && decCheckMath(lhs, set, &status))
|
| + || (!decNumberIsSpecial(rhs) && decCheckMath(rhs, set, &status))
|
| + || (!decNumberIsSpecial(fhs) && decCheckMath(fhs, set, &status))) break;
|
| + /* set up context for multiply */
|
| + dcmul=*set;
|
| + dcmul.digits=lhs->digits+rhs->digits; /* just enough */
|
| + /* [The above may be an over-estimate for subset arithmetic, but that's OK] */
|
| + dcmul.emax=DEC_MAX_EMAX; /* effectively unbounded .. */
|
| + dcmul.emin=DEC_MIN_EMIN; /* [thanks to Math restrictions] */
|
| + /* set up decNumber space to receive the result of the multiply */
|
| + acc=bufa; /* may fit */
|
| + needbytes=sizeof(decNumber)+(D2U(dcmul.digits)-1)*sizeof(Unit);
|
| + if (needbytes>sizeof(bufa)) { /* need malloc space */
|
| + allocbufa=(decNumber *)malloc(needbytes);
|
| + if (allocbufa==NULL) { /* hopeless -- abandon */
|
| + status|=DEC_Insufficient_storage;
|
| + break;}
|
| + acc=allocbufa; /* use the allocated space */
|
| + }
|
| + /* multiply with extended range and necessary precision */
|
| + /*printf("emin=%ld\n", dcmul.emin); */
|
| + decMultiplyOp(acc, lhs, rhs, &dcmul, &status);
|
| + /* Only Invalid operation (from sNaN or Inf * 0) is possible in */
|
| + /* status; if either is seen than ignore fhs (in case it is */
|
| + /* another sNaN) and set acc to NaN unless we had an sNaN */
|
| + /* [decMultiplyOp leaves that to caller] */
|
| + /* Note sNaN has to go through addOp to shorten payload if */
|
| + /* necessary */
|
| + if ((status&DEC_Invalid_operation)!=0) {
|
| + if (!(status&DEC_sNaN)) { /* but be true invalid */
|
| + uprv_decNumberZero(res); /* acc not yet set */
|
| + res->bits=DECNAN;
|
| + break;
|
| + }
|
| + uprv_decNumberZero(&dzero); /* make 0 (any non-NaN would do) */
|
| + fhs=&dzero; /* use that */
|
| + }
|
| + #if DECCHECK
|
| + else { /* multiply was OK */
|
| + if (status!=0) printf("Status=%08lx after FMA multiply\n", (LI)status);
|
| + }
|
| + #endif
|
| + /* add the third operand and result -> res, and all is done */
|
| + decAddOp(res, acc, fhs, set, 0, &status);
|
| + } while(0); /* end protected */
|
| +
|
| + if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
|
| + if (status!=0) decStatus(res, status, set);
|
| + #if DECCHECK
|
| + decCheckInexact(res, set);
|
| + #endif
|
| + return res;
|
| + } /* decNumberFMA */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberInvert -- invert a Number, digitwise */
|
| +/* */
|
| +/* This computes C = ~A */
|
| +/* */
|
| +/* res is C, the result. C may be A (e.g., X=~X) */
|
| +/* rhs is A */
|
| +/* set is the context (used for result length and error report) */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* */
|
| +/* Logical function restrictions apply (see above); a NaN is */
|
| +/* returned with Invalid_operation if a restriction is violated. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberInvert(decNumber *res, const decNumber *rhs,
|
| + decContext *set) {
|
| + const Unit *ua, *msua; /* -> operand and its msu */
|
| + Unit *uc, *msuc; /* -> result and its msu */
|
| + Int msudigs; /* digits in res msu */
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| + #endif
|
| +
|
| + if (rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
|
| + decStatus(res, DEC_Invalid_operation, set);
|
| + return res;
|
| + }
|
| + /* operand is valid */
|
| + ua=rhs->lsu; /* bottom-up */
|
| + uc=res->lsu; /* .. */
|
| + msua=ua+D2U(rhs->digits)-1; /* -> msu of rhs */
|
| + msuc=uc+D2U(set->digits)-1; /* -> msu of result */
|
| + msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */
|
| + for (; uc<=msuc; ua++, uc++) { /* Unit loop */
|
| + Unit a; /* extract unit */
|
| + Int i, j; /* work */
|
| + if (ua>msua) a=0;
|
| + else a=*ua;
|
| + *uc=0; /* can now write back */
|
| + /* always need to examine all bits in rhs */
|
| + /* This loop could be unrolled and/or use BIN2BCD tables */
|
| + for (i=0; i<DECDPUN; i++) {
|
| + if ((~a)&1) *uc=*uc+(Unit)powers[i]; /* effect INVERT */
|
| + j=a%10;
|
| + a=a/10;
|
| + if (j>1) {
|
| + decStatus(res, DEC_Invalid_operation, set);
|
| + return res;
|
| + }
|
| + if (uc==msuc && i==msudigs-1) break; /* just did final digit */
|
| + } /* each digit */
|
| + } /* each unit */
|
| + /* [here uc-1 is the msu of the result] */
|
| + res->digits=decGetDigits(res->lsu, uc-res->lsu);
|
| + res->exponent=0; /* integer */
|
| + res->bits=0; /* sign=0 */
|
| + return res; /* [no status to set] */
|
| + } /* decNumberInvert */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberLn -- natural logarithm */
|
| +/* */
|
| +/* This computes C = ln(A) */
|
| +/* */
|
| +/* res is C, the result. C may be A */
|
| +/* rhs is A */
|
| +/* set is the context; note that rounding mode has no effect */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* */
|
| +/* Notable cases: */
|
| +/* A<0 -> Invalid */
|
| +/* A=0 -> -Infinity (Exact) */
|
| +/* A=+Infinity -> +Infinity (Exact) */
|
| +/* A=1 exactly -> 0 (Exact) */
|
| +/* */
|
| +/* Mathematical function restrictions apply (see above); a NaN is */
|
| +/* returned with Invalid_operation if a restriction is violated. */
|
| +/* */
|
| +/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */
|
| +/* almost always be correctly rounded, but may be up to 1 ulp in */
|
| +/* error in rare cases. */
|
| +/* ------------------------------------------------------------------ */
|
| +/* This is a wrapper for decLnOp which can handle the slightly wider */
|
| +/* (+11) range needed by Ln, Log10, etc. (which may have to be able */
|
| +/* to calculate at p+e+2). */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberLn(decNumber *res, const decNumber *rhs,
|
| + decContext *set) {
|
| + uInt status=0; /* accumulator */
|
| + #if DECSUBSET
|
| + decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */
|
| + #endif
|
| +
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| + #endif
|
| +
|
| + /* Check restrictions; this is a math function; if not violated */
|
| + /* then carry out the operation. */
|
| + if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */
|
| + #if DECSUBSET
|
| + if (!set->extended) {
|
| + /* reduce operand and set lostDigits status, as needed */
|
| + if (rhs->digits>set->digits) {
|
| + allocrhs=decRoundOperand(rhs, set, &status);
|
| + if (allocrhs==NULL) break;
|
| + rhs=allocrhs;
|
| + }
|
| + /* special check in subset for rhs=0 */
|
| + if (ISZERO(rhs)) { /* +/- zeros -> error */
|
| + status|=DEC_Invalid_operation;
|
| + break;}
|
| + } /* extended=0 */
|
| + #endif
|
| + decLnOp(res, rhs, set, &status);
|
| + } while(0); /* end protected */
|
| +
|
| + #if DECSUBSET
|
| + if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */
|
| + #endif
|
| + /* apply significant status */
|
| + if (status!=0) decStatus(res, status, set);
|
| + #if DECCHECK
|
| + decCheckInexact(res, set);
|
| + #endif
|
| + return res;
|
| + } /* decNumberLn */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberLogB - get adjusted exponent, by 754 rules */
|
| +/* */
|
| +/* This computes C = adjustedexponent(A) */
|
| +/* */
|
| +/* res is C, the result. C may be A */
|
| +/* rhs is A */
|
| +/* set is the context, used only for digits and status */
|
| +/* */
|
| +/* C must have space for 10 digits (A might have 10**9 digits and */
|
| +/* an exponent of +999999999, or one digit and an exponent of */
|
| +/* -1999999999). */
|
| +/* */
|
| +/* This returns the adjusted exponent of A after (in theory) padding */
|
| +/* with zeros on the right to set->digits digits while keeping the */
|
| +/* same value. The exponent is not limited by emin/emax. */
|
| +/* */
|
| +/* Notable cases: */
|
| +/* A<0 -> Use |A| */
|
| +/* A=0 -> -Infinity (Division by zero) */
|
| +/* A=Infinite -> +Infinity (Exact) */
|
| +/* A=1 exactly -> 0 (Exact) */
|
| +/* NaNs are propagated as usual */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberLogB(decNumber *res, const decNumber *rhs,
|
| + decContext *set) {
|
| + uInt status=0; /* accumulator */
|
| +
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| + #endif
|
| +
|
| + /* NaNs as usual; Infinities return +Infinity; 0->oops */
|
| + if (decNumberIsNaN(rhs)) decNaNs(res, rhs, NULL, set, &status);
|
| + else if (decNumberIsInfinite(rhs)) uprv_decNumberCopyAbs(res, rhs);
|
| + else if (decNumberIsZero(rhs)) {
|
| + uprv_decNumberZero(res); /* prepare for Infinity */
|
| + res->bits=DECNEG|DECINF; /* -Infinity */
|
| + status|=DEC_Division_by_zero; /* as per 754 */
|
| + }
|
| + else { /* finite non-zero */
|
| + Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */
|
| + uprv_decNumberFromInt32(res, ae); /* lay it out */
|
| + }
|
| +
|
| + if (status!=0) decStatus(res, status, set);
|
| + return res;
|
| + } /* decNumberLogB */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberLog10 -- logarithm in base 10 */
|
| +/* */
|
| +/* This computes C = log10(A) */
|
| +/* */
|
| +/* res is C, the result. C may be A */
|
| +/* rhs is A */
|
| +/* set is the context; note that rounding mode has no effect */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* */
|
| +/* Notable cases: */
|
| +/* A<0 -> Invalid */
|
| +/* A=0 -> -Infinity (Exact) */
|
| +/* A=+Infinity -> +Infinity (Exact) */
|
| +/* A=10**n (if n is an integer) -> n (Exact) */
|
| +/* */
|
| +/* Mathematical function restrictions apply (see above); a NaN is */
|
| +/* returned with Invalid_operation if a restriction is violated. */
|
| +/* */
|
| +/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */
|
| +/* almost always be correctly rounded, but may be up to 1 ulp in */
|
| +/* error in rare cases. */
|
| +/* ------------------------------------------------------------------ */
|
| +/* This calculates ln(A)/ln(10) using appropriate precision. For */
|
| +/* ln(A) this is the max(p, rhs->digits + t) + 3, where p is the */
|
| +/* requested digits and t is the number of digits in the exponent */
|
| +/* (maximum 6). For ln(10) it is p + 3; this is often handled by the */
|
| +/* fastpath in decLnOp. The final division is done to the requested */
|
| +/* precision. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberLog10(decNumber *res, const decNumber *rhs,
|
| + decContext *set) {
|
| + uInt status=0, ignore=0; /* status accumulators */
|
| + uInt needbytes; /* for space calculations */
|
| + Int p; /* working precision */
|
| + Int t; /* digits in exponent of A */
|
| +
|
| + /* buffers for a and b working decimals */
|
| + /* (adjustment calculator, same size) */
|
| + decNumber bufa[D2N(DECBUFFER+2)];
|
| + decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */
|
| + decNumber *a=bufa; /* temporary a */
|
| + decNumber bufb[D2N(DECBUFFER+2)];
|
| + decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */
|
| + decNumber *b=bufb; /* temporary b */
|
| + decNumber bufw[D2N(10)]; /* working 2-10 digit number */
|
| + decNumber *w=bufw; /* .. */
|
| + #if DECSUBSET
|
| + decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */
|
| + #endif
|
| +
|
| + decContext aset; /* working context */
|
| +
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| + #endif
|
| +
|
| + /* Check restrictions; this is a math function; if not violated */
|
| + /* then carry out the operation. */
|
| + if (!decCheckMath(rhs, set, &status)) do { /* protect malloc */
|
| + #if DECSUBSET
|
| + if (!set->extended) {
|
| + /* reduce operand and set lostDigits status, as needed */
|
| + if (rhs->digits>set->digits) {
|
| + allocrhs=decRoundOperand(rhs, set, &status);
|
| + if (allocrhs==NULL) break;
|
| + rhs=allocrhs;
|
| + }
|
| + /* special check in subset for rhs=0 */
|
| + if (ISZERO(rhs)) { /* +/- zeros -> error */
|
| + status|=DEC_Invalid_operation;
|
| + break;}
|
| + } /* extended=0 */
|
| + #endif
|
| +
|
| + uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */
|
| +
|
| + /* handle exact powers of 10; only check if +ve finite */
|
| + if (!(rhs->bits&(DECNEG|DECSPECIAL)) && !ISZERO(rhs)) {
|
| + Int residue=0; /* (no residue) */
|
| + uInt copystat=0; /* clean status */
|
| +
|
| + /* round to a single digit... */
|
| + aset.digits=1;
|
| + decCopyFit(w, rhs, &aset, &residue, ©stat); /* copy & shorten */
|
| + /* if exact and the digit is 1, rhs is a power of 10 */
|
| + if (!(copystat&DEC_Inexact) && w->lsu[0]==1) {
|
| + /* the exponent, conveniently, is the power of 10; making */
|
| + /* this the result needs a little care as it might not fit, */
|
| + /* so first convert it into the working number, and then move */
|
| + /* to res */
|
| + uprv_decNumberFromInt32(w, w->exponent);
|
| + residue=0;
|
| + decCopyFit(res, w, set, &residue, &status); /* copy & round */
|
| + decFinish(res, set, &residue, &status); /* cleanup/set flags */
|
| + break;
|
| + } /* not a power of 10 */
|
| + } /* not a candidate for exact */
|
| +
|
| + /* simplify the information-content calculation to use 'total */
|
| + /* number of digits in a, including exponent' as compared to the */
|
| + /* requested digits, as increasing this will only rarely cost an */
|
| + /* iteration in ln(a) anyway */
|
| + t=6; /* it can never be >6 */
|
| +
|
| + /* allocate space when needed... */
|
| + p=(rhs->digits+t>set->digits?rhs->digits+t:set->digits)+3;
|
| + needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);
|
| + if (needbytes>sizeof(bufa)) { /* need malloc space */
|
| + allocbufa=(decNumber *)malloc(needbytes);
|
| + if (allocbufa==NULL) { /* hopeless -- abandon */
|
| + status|=DEC_Insufficient_storage;
|
| + break;}
|
| + a=allocbufa; /* use the allocated space */
|
| + }
|
| + aset.digits=p; /* as calculated */
|
| + aset.emax=DEC_MAX_MATH; /* usual bounds */
|
| + aset.emin=-DEC_MAX_MATH; /* .. */
|
| + aset.clamp=0; /* and no concrete format */
|
| + decLnOp(a, rhs, &aset, &status); /* a=ln(rhs) */
|
| +
|
| + /* skip the division if the result so far is infinite, NaN, or */
|
| + /* zero, or there was an error; note NaN from sNaN needs copy */
|
| + if (status&DEC_NaNs && !(status&DEC_sNaN)) break;
|
| + if (a->bits&DECSPECIAL || ISZERO(a)) {
|
| + uprv_decNumberCopy(res, a); /* [will fit] */
|
| + break;}
|
| +
|
| + /* for ln(10) an extra 3 digits of precision are needed */
|
| + p=set->digits+3;
|
| + needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);
|
| + if (needbytes>sizeof(bufb)) { /* need malloc space */
|
| + allocbufb=(decNumber *)malloc(needbytes);
|
| + if (allocbufb==NULL) { /* hopeless -- abandon */
|
| + status|=DEC_Insufficient_storage;
|
| + break;}
|
| + b=allocbufb; /* use the allocated space */
|
| + }
|
| + uprv_decNumberZero(w); /* set up 10... */
|
| + #if DECDPUN==1
|
| + w->lsu[1]=1; w->lsu[0]=0; /* .. */
|
| + #else
|
| + w->lsu[0]=10; /* .. */
|
| + #endif
|
| + w->digits=2; /* .. */
|
| +
|
| + aset.digits=p;
|
| + decLnOp(b, w, &aset, &ignore); /* b=ln(10) */
|
| +
|
| + aset.digits=set->digits; /* for final divide */
|
| + decDivideOp(res, a, b, &aset, DIVIDE, &status); /* into result */
|
| + } while(0); /* [for break] */
|
| +
|
| + if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
|
| + if (allocbufb!=NULL) free(allocbufb); /* .. */
|
| + #if DECSUBSET
|
| + if (allocrhs !=NULL) free(allocrhs); /* .. */
|
| + #endif
|
| + /* apply significant status */
|
| + if (status!=0) decStatus(res, status, set);
|
| + #if DECCHECK
|
| + decCheckInexact(res, set);
|
| + #endif
|
| + return res;
|
| + } /* decNumberLog10 */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberMax -- compare two Numbers and return the maximum */
|
| +/* */
|
| +/* This computes C = A ? B, returning the maximum by 754 rules */
|
| +/* */
|
| +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* set is the context */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberMax(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + uInt status=0; /* accumulator */
|
| + decCompareOp(res, lhs, rhs, set, COMPMAX, &status);
|
| + if (status!=0) decStatus(res, status, set);
|
| + #if DECCHECK
|
| + decCheckInexact(res, set);
|
| + #endif
|
| + return res;
|
| + } /* decNumberMax */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberMaxMag -- compare and return the maximum by magnitude */
|
| +/* */
|
| +/* This computes C = A ? B, returning the maximum by 754 rules */
|
| +/* */
|
| +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* set is the context */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberMaxMag(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + uInt status=0; /* accumulator */
|
| + decCompareOp(res, lhs, rhs, set, COMPMAXMAG, &status);
|
| + if (status!=0) decStatus(res, status, set);
|
| + #if DECCHECK
|
| + decCheckInexact(res, set);
|
| + #endif
|
| + return res;
|
| + } /* decNumberMaxMag */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberMin -- compare two Numbers and return the minimum */
|
| +/* */
|
| +/* This computes C = A ? B, returning the minimum by 754 rules */
|
| +/* */
|
| +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* set is the context */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberMin(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + uInt status=0; /* accumulator */
|
| + decCompareOp(res, lhs, rhs, set, COMPMIN, &status);
|
| + if (status!=0) decStatus(res, status, set);
|
| + #if DECCHECK
|
| + decCheckInexact(res, set);
|
| + #endif
|
| + return res;
|
| + } /* decNumberMin */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberMinMag -- compare and return the minimum by magnitude */
|
| +/* */
|
| +/* This computes C = A ? B, returning the minimum by 754 rules */
|
| +/* */
|
| +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* set is the context */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberMinMag(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + uInt status=0; /* accumulator */
|
| + decCompareOp(res, lhs, rhs, set, COMPMINMAG, &status);
|
| + if (status!=0) decStatus(res, status, set);
|
| + #if DECCHECK
|
| + decCheckInexact(res, set);
|
| + #endif
|
| + return res;
|
| + } /* decNumberMinMag */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberMinus -- prefix minus operator */
|
| +/* */
|
| +/* This computes C = 0 - A */
|
| +/* */
|
| +/* res is C, the result. C may be A */
|
| +/* rhs is A */
|
| +/* set is the context */
|
| +/* */
|
| +/* See also decNumberCopyNegate for a quiet bitwise version of this. */
|
| +/* C must have space for set->digits digits. */
|
| +/* ------------------------------------------------------------------ */
|
| +/* Simply use AddOp for the subtract, which will do the necessary. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberMinus(decNumber *res, const decNumber *rhs,
|
| + decContext *set) {
|
| + decNumber dzero;
|
| + uInt status=0; /* accumulator */
|
| +
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| + #endif
|
| +
|
| + uprv_decNumberZero(&dzero); /* make 0 */
|
| + dzero.exponent=rhs->exponent; /* [no coefficient expansion] */
|
| + decAddOp(res, &dzero, rhs, set, DECNEG, &status);
|
| + if (status!=0) decStatus(res, status, set);
|
| + #if DECCHECK
|
| + decCheckInexact(res, set);
|
| + #endif
|
| + return res;
|
| + } /* decNumberMinus */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberNextMinus -- next towards -Infinity */
|
| +/* */
|
| +/* This computes C = A - infinitesimal, rounded towards -Infinity */
|
| +/* */
|
| +/* res is C, the result. C may be A */
|
| +/* rhs is A */
|
| +/* set is the context */
|
| +/* */
|
| +/* This is a generalization of 754 NextDown. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberNextMinus(decNumber *res, const decNumber *rhs,
|
| + decContext *set) {
|
| + decNumber dtiny; /* constant */
|
| + decContext workset=*set; /* work */
|
| + uInt status=0; /* accumulator */
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| + #endif
|
| +
|
| + /* +Infinity is the special case */
|
| + if ((rhs->bits&(DECINF|DECNEG))==DECINF) {
|
| + decSetMaxValue(res, set); /* is +ve */
|
| + /* there is no status to set */
|
| + return res;
|
| + }
|
| + uprv_decNumberZero(&dtiny); /* start with 0 */
|
| + dtiny.lsu[0]=1; /* make number that is .. */
|
| + dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */
|
| + workset.round=DEC_ROUND_FLOOR;
|
| + decAddOp(res, rhs, &dtiny, &workset, DECNEG, &status);
|
| + status&=DEC_Invalid_operation|DEC_sNaN; /* only sNaN Invalid please */
|
| + if (status!=0) decStatus(res, status, set);
|
| + return res;
|
| + } /* decNumberNextMinus */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberNextPlus -- next towards +Infinity */
|
| +/* */
|
| +/* This computes C = A + infinitesimal, rounded towards +Infinity */
|
| +/* */
|
| +/* res is C, the result. C may be A */
|
| +/* rhs is A */
|
| +/* set is the context */
|
| +/* */
|
| +/* This is a generalization of 754 NextUp. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberNextPlus(decNumber *res, const decNumber *rhs,
|
| + decContext *set) {
|
| + decNumber dtiny; /* constant */
|
| + decContext workset=*set; /* work */
|
| + uInt status=0; /* accumulator */
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| + #endif
|
| +
|
| + /* -Infinity is the special case */
|
| + if ((rhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {
|
| + decSetMaxValue(res, set);
|
| + res->bits=DECNEG; /* negative */
|
| + /* there is no status to set */
|
| + return res;
|
| + }
|
| + uprv_decNumberZero(&dtiny); /* start with 0 */
|
| + dtiny.lsu[0]=1; /* make number that is .. */
|
| + dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */
|
| + workset.round=DEC_ROUND_CEILING;
|
| + decAddOp(res, rhs, &dtiny, &workset, 0, &status);
|
| + status&=DEC_Invalid_operation|DEC_sNaN; /* only sNaN Invalid please */
|
| + if (status!=0) decStatus(res, status, set);
|
| + return res;
|
| + } /* decNumberNextPlus */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberNextToward -- next towards rhs */
|
| +/* */
|
| +/* This computes C = A +/- infinitesimal, rounded towards */
|
| +/* +/-Infinity in the direction of B, as per 754-1985 nextafter */
|
| +/* modified during revision but dropped from 754-2008. */
|
| +/* */
|
| +/* res is C, the result. C may be A or B. */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* set is the context */
|
| +/* */
|
| +/* This is a generalization of 754-1985 NextAfter. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberNextToward(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + decNumber dtiny; /* constant */
|
| + decContext workset=*set; /* work */
|
| + Int result; /* .. */
|
| + uInt status=0; /* accumulator */
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| + #endif
|
| +
|
| + if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) {
|
| + decNaNs(res, lhs, rhs, set, &status);
|
| + }
|
| + else { /* Is numeric, so no chance of sNaN Invalid, etc. */
|
| + result=decCompare(lhs, rhs, 0); /* sign matters */
|
| + if (result==BADINT) status|=DEC_Insufficient_storage; /* rare */
|
| + else { /* valid compare */
|
| + if (result==0) uprv_decNumberCopySign(res, lhs, rhs); /* easy */
|
| + else { /* differ: need NextPlus or NextMinus */
|
| + uByte sub; /* add or subtract */
|
| + if (result<0) { /* lhs<rhs, do nextplus */
|
| + /* -Infinity is the special case */
|
| + if ((lhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {
|
| + decSetMaxValue(res, set);
|
| + res->bits=DECNEG; /* negative */
|
| + return res; /* there is no status to set */
|
| + }
|
| + workset.round=DEC_ROUND_CEILING;
|
| + sub=0; /* add, please */
|
| + } /* plus */
|
| + else { /* lhs>rhs, do nextminus */
|
| + /* +Infinity is the special case */
|
| + if ((lhs->bits&(DECINF|DECNEG))==DECINF) {
|
| + decSetMaxValue(res, set);
|
| + return res; /* there is no status to set */
|
| + }
|
| + workset.round=DEC_ROUND_FLOOR;
|
| + sub=DECNEG; /* subtract, please */
|
| + } /* minus */
|
| + uprv_decNumberZero(&dtiny); /* start with 0 */
|
| + dtiny.lsu[0]=1; /* make number that is .. */
|
| + dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */
|
| + decAddOp(res, lhs, &dtiny, &workset, sub, &status); /* + or - */
|
| + /* turn off exceptions if the result is a normal number */
|
| + /* (including Nmin), otherwise let all status through */
|
| + if (uprv_decNumberIsNormal(res, set)) status=0;
|
| + } /* unequal */
|
| + } /* compare OK */
|
| + } /* numeric */
|
| + if (status!=0) decStatus(res, status, set);
|
| + return res;
|
| + } /* decNumberNextToward */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberOr -- OR two Numbers, digitwise */
|
| +/* */
|
| +/* This computes C = A | B */
|
| +/* */
|
| +/* res is C, the result. C may be A and/or B (e.g., X=X|X) */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* set is the context (used for result length and error report) */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* */
|
| +/* Logical function restrictions apply (see above); a NaN is */
|
| +/* returned with Invalid_operation if a restriction is violated. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberOr(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + const Unit *ua, *ub; /* -> operands */
|
| + const Unit *msua, *msub; /* -> operand msus */
|
| + Unit *uc, *msuc; /* -> result and its msu */
|
| + Int msudigs; /* digits in res msu */
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| + #endif
|
| +
|
| + if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
|
| + || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
|
| + decStatus(res, DEC_Invalid_operation, set);
|
| + return res;
|
| + }
|
| + /* operands are valid */
|
| + ua=lhs->lsu; /* bottom-up */
|
| + ub=rhs->lsu; /* .. */
|
| + uc=res->lsu; /* .. */
|
| + msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */
|
| + msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */
|
| + msuc=uc+D2U(set->digits)-1; /* -> msu of result */
|
| + msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */
|
| + for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */
|
| + Unit a, b; /* extract units */
|
| + if (ua>msua) a=0;
|
| + else a=*ua;
|
| + if (ub>msub) b=0;
|
| + else b=*ub;
|
| + *uc=0; /* can now write back */
|
| + if (a|b) { /* maybe 1 bits to examine */
|
| + Int i, j;
|
| + /* This loop could be unrolled and/or use BIN2BCD tables */
|
| + for (i=0; i<DECDPUN; i++) {
|
| + if ((a|b)&1) *uc=*uc+(Unit)powers[i]; /* effect OR */
|
| + j=a%10;
|
| + a=a/10;
|
| + j|=b%10;
|
| + b=b/10;
|
| + if (j>1) {
|
| + decStatus(res, DEC_Invalid_operation, set);
|
| + return res;
|
| + }
|
| + if (uc==msuc && i==msudigs-1) break; /* just did final digit */
|
| + } /* each digit */
|
| + } /* non-zero */
|
| + } /* each unit */
|
| + /* [here uc-1 is the msu of the result] */
|
| + res->digits=decGetDigits(res->lsu, uc-res->lsu);
|
| + res->exponent=0; /* integer */
|
| + res->bits=0; /* sign=0 */
|
| + return res; /* [no status to set] */
|
| + } /* decNumberOr */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberPlus -- prefix plus operator */
|
| +/* */
|
| +/* This computes C = 0 + A */
|
| +/* */
|
| +/* res is C, the result. C may be A */
|
| +/* rhs is A */
|
| +/* set is the context */
|
| +/* */
|
| +/* See also decNumberCopy for a quiet bitwise version of this. */
|
| +/* C must have space for set->digits digits. */
|
| +/* ------------------------------------------------------------------ */
|
| +/* This simply uses AddOp; Add will take fast path after preparing A. */
|
| +/* Performance is a concern here, as this routine is often used to */
|
| +/* check operands and apply rounding and overflow/underflow testing. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberPlus(decNumber *res, const decNumber *rhs,
|
| + decContext *set) {
|
| + decNumber dzero;
|
| + uInt status=0; /* accumulator */
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| + #endif
|
| +
|
| + uprv_decNumberZero(&dzero); /* make 0 */
|
| + dzero.exponent=rhs->exponent; /* [no coefficient expansion] */
|
| + decAddOp(res, &dzero, rhs, set, 0, &status);
|
| + if (status!=0) decStatus(res, status, set);
|
| + #if DECCHECK
|
| + decCheckInexact(res, set);
|
| + #endif
|
| + return res;
|
| + } /* decNumberPlus */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberMultiply -- multiply two Numbers */
|
| +/* */
|
| +/* This computes C = A x B */
|
| +/* */
|
| +/* res is C, the result. C may be A and/or B (e.g., X=X+X) */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* set is the context */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberMultiply(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + uInt status=0; /* accumulator */
|
| + decMultiplyOp(res, lhs, rhs, set, &status);
|
| + if (status!=0) decStatus(res, status, set);
|
| + #if DECCHECK
|
| + decCheckInexact(res, set);
|
| + #endif
|
| + return res;
|
| + } /* decNumberMultiply */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberPower -- raise a number to a power */
|
| +/* */
|
| +/* This computes C = A ** B */
|
| +/* */
|
| +/* res is C, the result. C may be A and/or B (e.g., X=X**X) */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* set is the context */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* */
|
| +/* Mathematical function restrictions apply (see above); a NaN is */
|
| +/* returned with Invalid_operation if a restriction is violated. */
|
| +/* */
|
| +/* However, if 1999999997<=B<=999999999 and B is an integer then the */
|
| +/* restrictions on A and the context are relaxed to the usual bounds, */
|
| +/* for compatibility with the earlier (integer power only) version */
|
| +/* of this function. */
|
| +/* */
|
| +/* When B is an integer, the result may be exact, even if rounded. */
|
| +/* */
|
| +/* The final result is rounded according to the context; it will */
|
| +/* almost always be correctly rounded, but may be up to 1 ulp in */
|
| +/* error in rare cases. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberPower(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + #if DECSUBSET
|
| + decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */
|
| + decNumber *allocrhs=NULL; /* .., rhs */
|
| + #endif
|
| + decNumber *allocdac=NULL; /* -> allocated acc buffer, iff used */
|
| + decNumber *allocinv=NULL; /* -> allocated 1/x buffer, iff used */
|
| + Int reqdigits=set->digits; /* requested DIGITS */
|
| + Int n; /* rhs in binary */
|
| + Flag rhsint=0; /* 1 if rhs is an integer */
|
| + Flag useint=0; /* 1 if can use integer calculation */
|
| + Flag isoddint=0; /* 1 if rhs is an integer and odd */
|
| + Int i; /* work */
|
| + #if DECSUBSET
|
| + Int dropped; /* .. */
|
| + #endif
|
| + uInt needbytes; /* buffer size needed */
|
| + Flag seenbit; /* seen a bit while powering */
|
| + Int residue=0; /* rounding residue */
|
| + uInt status=0; /* accumulators */
|
| + uByte bits=0; /* result sign if errors */
|
| + decContext aset; /* working context */
|
| + decNumber dnOne; /* work value 1... */
|
| + /* local accumulator buffer [a decNumber, with digits+elength+1 digits] */
|
| + decNumber dacbuff[D2N(DECBUFFER+9)];
|
| + decNumber *dac=dacbuff; /* -> result accumulator */
|
| + /* same again for possible 1/lhs calculation */
|
| + decNumber invbuff[D2N(DECBUFFER+9)];
|
| +
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| + #endif
|
| +
|
| + do { /* protect allocated storage */
|
| + #if DECSUBSET
|
| + if (!set->extended) { /* reduce operands and set status, as needed */
|
| + if (lhs->digits>reqdigits) {
|
| + alloclhs=decRoundOperand(lhs, set, &status);
|
| + if (alloclhs==NULL) break;
|
| + lhs=alloclhs;
|
| + }
|
| + if (rhs->digits>reqdigits) {
|
| + allocrhs=decRoundOperand(rhs, set, &status);
|
| + if (allocrhs==NULL) break;
|
| + rhs=allocrhs;
|
| + }
|
| + }
|
| + #endif
|
| + /* [following code does not require input rounding] */
|
| +
|
| + /* handle NaNs and rhs Infinity (lhs infinity is harder) */
|
| + if (SPECIALARGS) {
|
| + if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { /* NaNs */
|
| + decNaNs(res, lhs, rhs, set, &status);
|
| + break;}
|
| + if (decNumberIsInfinite(rhs)) { /* rhs Infinity */
|
| + Flag rhsneg=rhs->bits&DECNEG; /* save rhs sign */
|
| + if (decNumberIsNegative(lhs) /* lhs<0 */
|
| + && !decNumberIsZero(lhs)) /* .. */
|
| + status|=DEC_Invalid_operation;
|
| + else { /* lhs >=0 */
|
| + uprv_decNumberZero(&dnOne); /* set up 1 */
|
| + dnOne.lsu[0]=1;
|
| + uprv_decNumberCompare(dac, lhs, &dnOne, set); /* lhs ? 1 */
|
| + uprv_decNumberZero(res); /* prepare for 0/1/Infinity */
|
| + if (decNumberIsNegative(dac)) { /* lhs<1 */
|
| + if (rhsneg) res->bits|=DECINF; /* +Infinity [else is +0] */
|
| + }
|
| + else if (dac->lsu[0]==0) { /* lhs=1 */
|
| + /* 1**Infinity is inexact, so return fully-padded 1.0000 */
|
| + Int shift=set->digits-1;
|
| + *res->lsu=1; /* was 0, make int 1 */
|
| + res->digits=decShiftToMost(res->lsu, 1, shift);
|
| + res->exponent=-shift; /* make 1.0000... */
|
| + status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */
|
| + }
|
| + else { /* lhs>1 */
|
| + if (!rhsneg) res->bits|=DECINF; /* +Infinity [else is +0] */
|
| + }
|
| + } /* lhs>=0 */
|
| + break;}
|
| + /* [lhs infinity drops through] */
|
| + } /* specials */
|
| +
|
| + /* Original rhs may be an integer that fits and is in range */
|
| + n=decGetInt(rhs);
|
| + if (n!=BADINT) { /* it is an integer */
|
| + rhsint=1; /* record the fact for 1**n */
|
| + isoddint=(Flag)n&1; /* [works even if big] */
|
| + if (n!=BIGEVEN && n!=BIGODD) /* can use integer path? */
|
| + useint=1; /* looks good */
|
| + }
|
| +
|
| + if (decNumberIsNegative(lhs) /* -x .. */
|
| + && isoddint) bits=DECNEG; /* .. to an odd power */
|
| +
|
| + /* handle LHS infinity */
|
| + if (decNumberIsInfinite(lhs)) { /* [NaNs already handled] */
|
| + uByte rbits=rhs->bits; /* save */
|
| + uprv_decNumberZero(res); /* prepare */
|
| + if (n==0) *res->lsu=1; /* [-]Inf**0 => 1 */
|
| + else {
|
| + /* -Inf**nonint -> error */
|
| + if (!rhsint && decNumberIsNegative(lhs)) {
|
| + status|=DEC_Invalid_operation; /* -Inf**nonint is error */
|
| + break;}
|
| + if (!(rbits & DECNEG)) bits|=DECINF; /* was not a **-n */
|
| + /* [otherwise will be 0 or -0] */
|
| + res->bits=bits;
|
| + }
|
| + break;}
|
| +
|
| + /* similarly handle LHS zero */
|
| + if (decNumberIsZero(lhs)) {
|
| + if (n==0) { /* 0**0 => Error */
|
| + #if DECSUBSET
|
| + if (!set->extended) { /* [unless subset] */
|
| + uprv_decNumberZero(res);
|
| + *res->lsu=1; /* return 1 */
|
| + break;}
|
| + #endif
|
| + status|=DEC_Invalid_operation;
|
| + }
|
| + else { /* 0**x */
|
| + uByte rbits=rhs->bits; /* save */
|
| + if (rbits & DECNEG) { /* was a 0**(-n) */
|
| + #if DECSUBSET
|
| + if (!set->extended) { /* [bad if subset] */
|
| + status|=DEC_Invalid_operation;
|
| + break;}
|
| + #endif
|
| + bits|=DECINF;
|
| + }
|
| + uprv_decNumberZero(res); /* prepare */
|
| + /* [otherwise will be 0 or -0] */
|
| + res->bits=bits;
|
| + }
|
| + break;}
|
| +
|
| + /* here both lhs and rhs are finite; rhs==0 is handled in the */
|
| + /* integer path. Next handle the non-integer cases */
|
| + if (!useint) { /* non-integral rhs */
|
| + /* any -ve lhs is bad, as is either operand or context out of */
|
| + /* bounds */
|
| + if (decNumberIsNegative(lhs)) {
|
| + status|=DEC_Invalid_operation;
|
| + break;}
|
| + if (decCheckMath(lhs, set, &status)
|
| + || decCheckMath(rhs, set, &status)) break; /* variable status */
|
| +
|
| + uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */
|
| + aset.emax=DEC_MAX_MATH; /* usual bounds */
|
| + aset.emin=-DEC_MAX_MATH; /* .. */
|
| + aset.clamp=0; /* and no concrete format */
|
| +
|
| + /* calculate the result using exp(ln(lhs)*rhs), which can */
|
| + /* all be done into the accumulator, dac. The precision needed */
|
| + /* is enough to contain the full information in the lhs (which */
|
| + /* is the total digits, including exponent), or the requested */
|
| + /* precision, if larger, + 4; 6 is used for the exponent */
|
| + /* maximum length, and this is also used when it is shorter */
|
| + /* than the requested digits as it greatly reduces the >0.5 ulp */
|
| + /* cases at little cost (because Ln doubles digits each */
|
| + /* iteration so a few extra digits rarely causes an extra */
|
| + /* iteration) */
|
| + aset.digits=MAXI(lhs->digits, set->digits)+6+4;
|
| + } /* non-integer rhs */
|
| +
|
| + else { /* rhs is in-range integer */
|
| + if (n==0) { /* x**0 = 1 */
|
| + /* (0**0 was handled above) */
|
| + uprv_decNumberZero(res); /* result=1 */
|
| + *res->lsu=1; /* .. */
|
| + break;}
|
| + /* rhs is a non-zero integer */
|
| + if (n<0) n=-n; /* use abs(n) */
|
| +
|
| + aset=*set; /* clone the context */
|
| + aset.round=DEC_ROUND_HALF_EVEN; /* internally use balanced */
|
| + /* calculate the working DIGITS */
|
| + aset.digits=reqdigits+(rhs->digits+rhs->exponent)+2;
|
| + #if DECSUBSET
|
| + if (!set->extended) aset.digits--; /* use classic precision */
|
| + #endif
|
| + /* it's an error if this is more than can be handled */
|
| + if (aset.digits>DECNUMMAXP) {status|=DEC_Invalid_operation; break;}
|
| + } /* integer path */
|
| +
|
| + /* aset.digits is the count of digits for the accumulator needed */
|
| + /* if accumulator is too long for local storage, then allocate */
|
| + needbytes=sizeof(decNumber)+(D2U(aset.digits)-1)*sizeof(Unit);
|
| + /* [needbytes also used below if 1/lhs needed] */
|
| + if (needbytes>sizeof(dacbuff)) {
|
| + allocdac=(decNumber *)malloc(needbytes);
|
| + if (allocdac==NULL) { /* hopeless -- abandon */
|
| + status|=DEC_Insufficient_storage;
|
| + break;}
|
| + dac=allocdac; /* use the allocated space */
|
| + }
|
| + /* here, aset is set up and accumulator is ready for use */
|
| +
|
| + if (!useint) { /* non-integral rhs */
|
| + /* x ** y; special-case x=1 here as it will otherwise always */
|
| + /* reduce to integer 1; decLnOp has a fastpath which detects */
|
| + /* the case of x=1 */
|
| + decLnOp(dac, lhs, &aset, &status); /* dac=ln(lhs) */
|
| + /* [no error possible, as lhs 0 already handled] */
|
| + if (ISZERO(dac)) { /* x==1, 1.0, etc. */
|
| + /* need to return fully-padded 1.0000 etc., but rhsint->1 */
|
| + *dac->lsu=1; /* was 0, make int 1 */
|
| + if (!rhsint) { /* add padding */
|
| + Int shift=set->digits-1;
|
| + dac->digits=decShiftToMost(dac->lsu, 1, shift);
|
| + dac->exponent=-shift; /* make 1.0000... */
|
| + status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */
|
| + }
|
| + }
|
| + else {
|
| + decMultiplyOp(dac, dac, rhs, &aset, &status); /* dac=dac*rhs */
|
| + decExpOp(dac, dac, &aset, &status); /* dac=exp(dac) */
|
| + }
|
| + /* and drop through for final rounding */
|
| + } /* non-integer rhs */
|
| +
|
| + else { /* carry on with integer */
|
| + uprv_decNumberZero(dac); /* acc=1 */
|
| + *dac->lsu=1; /* .. */
|
| +
|
| + /* if a negative power the constant 1 is needed, and if not subset */
|
| + /* invert the lhs now rather than inverting the result later */
|
| + if (decNumberIsNegative(rhs)) { /* was a **-n [hence digits>0] */
|
| + decNumber *inv=invbuff; /* asssume use fixed buffer */
|
| + uprv_decNumberCopy(&dnOne, dac); /* dnOne=1; [needed now or later] */
|
| + #if DECSUBSET
|
| + if (set->extended) { /* need to calculate 1/lhs */
|
| + #endif
|
| + /* divide lhs into 1, putting result in dac [dac=1/dac] */
|
| + decDivideOp(dac, &dnOne, lhs, &aset, DIVIDE, &status);
|
| + /* now locate or allocate space for the inverted lhs */
|
| + if (needbytes>sizeof(invbuff)) {
|
| + allocinv=(decNumber *)malloc(needbytes);
|
| + if (allocinv==NULL) { /* hopeless -- abandon */
|
| + status|=DEC_Insufficient_storage;
|
| + break;}
|
| + inv=allocinv; /* use the allocated space */
|
| + }
|
| + /* [inv now points to big-enough buffer or allocated storage] */
|
| + uprv_decNumberCopy(inv, dac); /* copy the 1/lhs */
|
| + uprv_decNumberCopy(dac, &dnOne); /* restore acc=1 */
|
| + lhs=inv; /* .. and go forward with new lhs */
|
| + #if DECSUBSET
|
| + }
|
| + #endif
|
| + }
|
| +
|
| + /* Raise-to-the-power loop... */
|
| + seenbit=0; /* set once a 1-bit is encountered */
|
| + for (i=1;;i++){ /* for each bit [top bit ignored] */
|
| + /* abandon if had overflow or terminal underflow */
|
| + if (status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */
|
| + if (status&DEC_Overflow || ISZERO(dac)) break;
|
| + }
|
| + /* [the following two lines revealed an optimizer bug in a C++ */
|
| + /* compiler, with symptom: 5**3 -> 25, when n=n+n was used] */
|
| + n=n<<1; /* move next bit to testable position */
|
| + if (n<0) { /* top bit is set */
|
| + seenbit=1; /* OK, significant bit seen */
|
| + decMultiplyOp(dac, dac, lhs, &aset, &status); /* dac=dac*x */
|
| + }
|
| + if (i==31) break; /* that was the last bit */
|
| + if (!seenbit) continue; /* no need to square 1 */
|
| + decMultiplyOp(dac, dac, dac, &aset, &status); /* dac=dac*dac [square] */
|
| + } /*i*/ /* 32 bits */
|
| +
|
| + /* complete internal overflow or underflow processing */
|
| + if (status & (DEC_Overflow|DEC_Underflow)) {
|
| + #if DECSUBSET
|
| + /* If subset, and power was negative, reverse the kind of -erflow */
|
| + /* [1/x not yet done] */
|
| + if (!set->extended && decNumberIsNegative(rhs)) {
|
| + if (status & DEC_Overflow)
|
| + status^=DEC_Overflow | DEC_Underflow | DEC_Subnormal;
|
| + else { /* trickier -- Underflow may or may not be set */
|
| + status&=~(DEC_Underflow | DEC_Subnormal); /* [one or both] */
|
| + status|=DEC_Overflow;
|
| + }
|
| + }
|
| + #endif
|
| + dac->bits=(dac->bits & ~DECNEG) | bits; /* force correct sign */
|
| + /* round subnormals [to set.digits rather than aset.digits] */
|
| + /* or set overflow result similarly as required */
|
| + decFinalize(dac, set, &residue, &status);
|
| + uprv_decNumberCopy(res, dac); /* copy to result (is now OK length) */
|
| + break;
|
| + }
|
| +
|
| + #if DECSUBSET
|
| + if (!set->extended && /* subset math */
|
| + decNumberIsNegative(rhs)) { /* was a **-n [hence digits>0] */
|
| + /* so divide result into 1 [dac=1/dac] */
|
| + decDivideOp(dac, &dnOne, dac, &aset, DIVIDE, &status);
|
| + }
|
| + #endif
|
| + } /* rhs integer path */
|
| +
|
| + /* reduce result to the requested length and copy to result */
|
| + decCopyFit(res, dac, set, &residue, &status);
|
| + decFinish(res, set, &residue, &status); /* final cleanup */
|
| + #if DECSUBSET
|
| + if (!set->extended) decTrim(res, set, 0, 1, &dropped); /* trailing zeros */
|
| + #endif
|
| + } while(0); /* end protected */
|
| +
|
| + if (allocdac!=NULL) free(allocdac); /* drop any storage used */
|
| + if (allocinv!=NULL) free(allocinv); /* .. */
|
| + #if DECSUBSET
|
| + if (alloclhs!=NULL) free(alloclhs); /* .. */
|
| + if (allocrhs!=NULL) free(allocrhs); /* .. */
|
| + #endif
|
| + if (status!=0) decStatus(res, status, set);
|
| + #if DECCHECK
|
| + decCheckInexact(res, set);
|
| + #endif
|
| + return res;
|
| + } /* decNumberPower */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberQuantize -- force exponent to requested value */
|
| +/* */
|
| +/* This computes C = op(A, B), where op adjusts the coefficient */
|
| +/* of C (by rounding or shifting) such that the exponent (-scale) */
|
| +/* of C has exponent of B. The numerical value of C will equal A, */
|
| +/* except for the effects of any rounding that occurred. */
|
| +/* */
|
| +/* res is C, the result. C may be A or B */
|
| +/* lhs is A, the number to adjust */
|
| +/* rhs is B, the number with exponent to match */
|
| +/* set is the context */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* */
|
| +/* Unless there is an error or the result is infinite, the exponent */
|
| +/* after the operation is guaranteed to be equal to that of B. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberQuantize(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + uInt status=0; /* accumulator */
|
| + decQuantizeOp(res, lhs, rhs, set, 1, &status);
|
| + if (status!=0) decStatus(res, status, set);
|
| + return res;
|
| + } /* decNumberQuantize */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberReduce -- remove trailing zeros */
|
| +/* */
|
| +/* This computes C = 0 + A, and normalizes the result */
|
| +/* */
|
| +/* res is C, the result. C may be A */
|
| +/* rhs is A */
|
| +/* set is the context */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* ------------------------------------------------------------------ */
|
| +/* Previously known as Normalize */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberNormalize(decNumber *res, const decNumber *rhs,
|
| + decContext *set) {
|
| + return uprv_decNumberReduce(res, rhs, set);
|
| + } /* decNumberNormalize */
|
| +
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberReduce(decNumber *res, const decNumber *rhs,
|
| + decContext *set) {
|
| + #if DECSUBSET
|
| + decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */
|
| + #endif
|
| + uInt status=0; /* as usual */
|
| + Int residue=0; /* as usual */
|
| + Int dropped; /* work */
|
| +
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| + #endif
|
| +
|
| + do { /* protect allocated storage */
|
| + #if DECSUBSET
|
| + if (!set->extended) {
|
| + /* reduce operand and set lostDigits status, as needed */
|
| + if (rhs->digits>set->digits) {
|
| + allocrhs=decRoundOperand(rhs, set, &status);
|
| + if (allocrhs==NULL) break;
|
| + rhs=allocrhs;
|
| + }
|
| + }
|
| + #endif
|
| + /* [following code does not require input rounding] */
|
| +
|
| + /* Infinities copy through; NaNs need usual treatment */
|
| + if (decNumberIsNaN(rhs)) {
|
| + decNaNs(res, rhs, NULL, set, &status);
|
| + break;
|
| + }
|
| +
|
| + /* reduce result to the requested length and copy to result */
|
| + decCopyFit(res, rhs, set, &residue, &status); /* copy & round */
|
| + decFinish(res, set, &residue, &status); /* cleanup/set flags */
|
| + decTrim(res, set, 1, 0, &dropped); /* normalize in place */
|
| + /* [may clamp] */
|
| + } while(0); /* end protected */
|
| +
|
| + #if DECSUBSET
|
| + if (allocrhs !=NULL) free(allocrhs); /* .. */
|
| + #endif
|
| + if (status!=0) decStatus(res, status, set);/* then report status */
|
| + return res;
|
| + } /* decNumberReduce */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberRescale -- force exponent to requested value */
|
| +/* */
|
| +/* This computes C = op(A, B), where op adjusts the coefficient */
|
| +/* of C (by rounding or shifting) such that the exponent (-scale) */
|
| +/* of C has the value B. The numerical value of C will equal A, */
|
| +/* except for the effects of any rounding that occurred. */
|
| +/* */
|
| +/* res is C, the result. C may be A or B */
|
| +/* lhs is A, the number to adjust */
|
| +/* rhs is B, the requested exponent */
|
| +/* set is the context */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* */
|
| +/* Unless there is an error or the result is infinite, the exponent */
|
| +/* after the operation is guaranteed to be equal to B. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberRescale(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + uInt status=0; /* accumulator */
|
| + decQuantizeOp(res, lhs, rhs, set, 0, &status);
|
| + if (status!=0) decStatus(res, status, set);
|
| + return res;
|
| + } /* decNumberRescale */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberRemainder -- divide and return remainder */
|
| +/* */
|
| +/* This computes C = A % B */
|
| +/* */
|
| +/* res is C, the result. C may be A and/or B (e.g., X=X%X) */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* set is the context */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberRemainder(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + uInt status=0; /* accumulator */
|
| + decDivideOp(res, lhs, rhs, set, REMAINDER, &status);
|
| + if (status!=0) decStatus(res, status, set);
|
| + #if DECCHECK
|
| + decCheckInexact(res, set);
|
| + #endif
|
| + return res;
|
| + } /* decNumberRemainder */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberRemainderNear -- divide and return remainder from nearest */
|
| +/* */
|
| +/* This computes C = A % B, where % is the IEEE remainder operator */
|
| +/* */
|
| +/* res is C, the result. C may be A and/or B (e.g., X=X%X) */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* set is the context */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberRemainderNear(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + uInt status=0; /* accumulator */
|
| + decDivideOp(res, lhs, rhs, set, REMNEAR, &status);
|
| + if (status!=0) decStatus(res, status, set);
|
| + #if DECCHECK
|
| + decCheckInexact(res, set);
|
| + #endif
|
| + return res;
|
| + } /* decNumberRemainderNear */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberRotate -- rotate the coefficient of a Number left/right */
|
| +/* */
|
| +/* This computes C = A rot B (in base ten and rotating set->digits */
|
| +/* digits). */
|
| +/* */
|
| +/* res is C, the result. C may be A and/or B (e.g., X=XrotX) */
|
| +/* lhs is A */
|
| +/* rhs is B, the number of digits to rotate (-ve to right) */
|
| +/* set is the context */
|
| +/* */
|
| +/* The digits of the coefficient of A are rotated to the left (if B */
|
| +/* is positive) or to the right (if B is negative) without adjusting */
|
| +/* the exponent or the sign of A. If lhs->digits is less than */
|
| +/* set->digits the coefficient is padded with zeros on the left */
|
| +/* before the rotate. Any leading zeros in the result are removed */
|
| +/* as usual. */
|
| +/* */
|
| +/* B must be an integer (q=0) and in the range -set->digits through */
|
| +/* +set->digits. */
|
| +/* C must have space for set->digits digits. */
|
| +/* NaNs are propagated as usual. Infinities are unaffected (but */
|
| +/* B must be valid). No status is set unless B is invalid or an */
|
| +/* operand is an sNaN. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberRotate(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + uInt status=0; /* accumulator */
|
| + Int rotate; /* rhs as an Int */
|
| +
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| + #endif
|
| +
|
| + /* NaNs propagate as normal */
|
| + if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
|
| + decNaNs(res, lhs, rhs, set, &status);
|
| + /* rhs must be an integer */
|
| + else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
|
| + status=DEC_Invalid_operation;
|
| + else { /* both numeric, rhs is an integer */
|
| + rotate=decGetInt(rhs); /* [cannot fail] */
|
| + if (rotate==BADINT /* something bad .. */
|
| + || rotate==BIGODD || rotate==BIGEVEN /* .. very big .. */
|
| + || abs(rotate)>set->digits) /* .. or out of range */
|
| + status=DEC_Invalid_operation;
|
| + else { /* rhs is OK */
|
| + uprv_decNumberCopy(res, lhs);
|
| + /* convert -ve rotate to equivalent positive rotation */
|
| + if (rotate<0) rotate=set->digits+rotate;
|
| + if (rotate!=0 && rotate!=set->digits /* zero or full rotation */
|
| + && !decNumberIsInfinite(res)) { /* lhs was infinite */
|
| + /* left-rotate to do; 0 < rotate < set->digits */
|
| + uInt units, shift; /* work */
|
| + uInt msudigits; /* digits in result msu */
|
| + Unit *msu=res->lsu+D2U(res->digits)-1; /* current msu */
|
| + Unit *msumax=res->lsu+D2U(set->digits)-1; /* rotation msu */
|
| + for (msu++; msu<=msumax; msu++) *msu=0; /* ensure high units=0 */
|
| + res->digits=set->digits; /* now full-length */
|
| + msudigits=MSUDIGITS(res->digits); /* actual digits in msu */
|
| +
|
| + /* rotation here is done in-place, in three steps */
|
| + /* 1. shift all to least up to one unit to unit-align final */
|
| + /* lsd [any digits shifted out are rotated to the left, */
|
| + /* abutted to the original msd (which may require split)] */
|
| + /* */
|
| + /* [if there are no whole units left to rotate, the */
|
| + /* rotation is now complete] */
|
| + /* */
|
| + /* 2. shift to least, from below the split point only, so that */
|
| + /* the final msd is in the right place in its Unit [any */
|
| + /* digits shifted out will fit exactly in the current msu, */
|
| + /* left aligned, no split required] */
|
| + /* */
|
| + /* 3. rotate all the units by reversing left part, right */
|
| + /* part, and then whole */
|
| + /* */
|
| + /* example: rotate right 8 digits (2 units + 2), DECDPUN=3. */
|
| + /* */
|
| + /* start: 00a bcd efg hij klm npq */
|
| + /* */
|
| + /* 1a 000 0ab cde fgh|ijk lmn [pq saved] */
|
| + /* 1b 00p qab cde fgh|ijk lmn */
|
| + /* */
|
| + /* 2a 00p qab cde fgh|00i jkl [mn saved] */
|
| + /* 2b mnp qab cde fgh|00i jkl */
|
| + /* */
|
| + /* 3a fgh cde qab mnp|00i jkl */
|
| + /* 3b fgh cde qab mnp|jkl 00i */
|
| + /* 3c 00i jkl mnp qab cde fgh */
|
| +
|
| + /* Step 1: amount to shift is the partial right-rotate count */
|
| + rotate=set->digits-rotate; /* make it right-rotate */
|
| + units=rotate/DECDPUN; /* whole units to rotate */
|
| + shift=rotate%DECDPUN; /* left-over digits count */
|
| + if (shift>0) { /* not an exact number of units */
|
| + uInt save=res->lsu[0]%powers[shift]; /* save low digit(s) */
|
| + decShiftToLeast(res->lsu, D2U(res->digits), shift);
|
| + if (shift>msudigits) { /* msumax-1 needs >0 digits */
|
| + uInt rem=save%powers[shift-msudigits];/* split save */
|
| + *msumax=(Unit)(save/powers[shift-msudigits]); /* and insert */
|
| + *(msumax-1)=*(msumax-1)
|
| + +(Unit)(rem*powers[DECDPUN-(shift-msudigits)]); /* .. */
|
| + }
|
| + else { /* all fits in msumax */
|
| + *msumax=*msumax+(Unit)(save*powers[msudigits-shift]); /* [maybe *1] */
|
| + }
|
| + } /* digits shift needed */
|
| +
|
| + /* If whole units to rotate... */
|
| + if (units>0) { /* some to do */
|
| + /* Step 2: the units to touch are the whole ones in rotate, */
|
| + /* if any, and the shift is DECDPUN-msudigits (which may be */
|
| + /* 0, again) */
|
| + shift=DECDPUN-msudigits;
|
| + if (shift>0) { /* not an exact number of units */
|
| + uInt save=res->lsu[0]%powers[shift]; /* save low digit(s) */
|
| + decShiftToLeast(res->lsu, units, shift);
|
| + *msumax=*msumax+(Unit)(save*powers[msudigits]);
|
| + } /* partial shift needed */
|
| +
|
| + /* Step 3: rotate the units array using triple reverse */
|
| + /* (reversing is easy and fast) */
|
| + decReverse(res->lsu+units, msumax); /* left part */
|
| + decReverse(res->lsu, res->lsu+units-1); /* right part */
|
| + decReverse(res->lsu, msumax); /* whole */
|
| + } /* whole units to rotate */
|
| + /* the rotation may have left an undetermined number of zeros */
|
| + /* on the left, so true length needs to be calculated */
|
| + res->digits=decGetDigits(res->lsu, msumax-res->lsu+1);
|
| + } /* rotate needed */
|
| + } /* rhs OK */
|
| + } /* numerics */
|
| + if (status!=0) decStatus(res, status, set);
|
| + return res;
|
| + } /* decNumberRotate */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberSameQuantum -- test for equal exponents */
|
| +/* */
|
| +/* res is the result number, which will contain either 0 or 1 */
|
| +/* lhs is a number to test */
|
| +/* rhs is the second (usually a pattern) */
|
| +/* */
|
| +/* No errors are possible and no context is needed. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberSameQuantum(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs) {
|
| + Unit ret=0; /* return value */
|
| +
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, lhs, rhs, DECUNCONT)) return res;
|
| + #endif
|
| +
|
| + if (SPECIALARGS) {
|
| + if (decNumberIsNaN(lhs) && decNumberIsNaN(rhs)) ret=1;
|
| + else if (decNumberIsInfinite(lhs) && decNumberIsInfinite(rhs)) ret=1;
|
| + /* [anything else with a special gives 0] */
|
| + }
|
| + else if (lhs->exponent==rhs->exponent) ret=1;
|
| +
|
| + uprv_decNumberZero(res); /* OK to overwrite an operand now */
|
| + *res->lsu=ret;
|
| + return res;
|
| + } /* decNumberSameQuantum */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberScaleB -- multiply by a power of 10 */
|
| +/* */
|
| +/* This computes C = A x 10**B where B is an integer (q=0) with */
|
| +/* maximum magnitude 2*(emax+digits) */
|
| +/* */
|
| +/* res is C, the result. C may be A or B */
|
| +/* lhs is A, the number to adjust */
|
| +/* rhs is B, the requested power of ten to use */
|
| +/* set is the context */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* */
|
| +/* The result may underflow or overflow. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberScaleB(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + Int reqexp; /* requested exponent change [B] */
|
| + uInt status=0; /* accumulator */
|
| + Int residue; /* work */
|
| +
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| + #endif
|
| +
|
| + /* Handle special values except lhs infinite */
|
| + if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
|
| + decNaNs(res, lhs, rhs, set, &status);
|
| + /* rhs must be an integer */
|
| + else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
|
| + status=DEC_Invalid_operation;
|
| + else {
|
| + /* lhs is a number; rhs is a finite with q==0 */
|
| + reqexp=decGetInt(rhs); /* [cannot fail] */
|
| + if (reqexp==BADINT /* something bad .. */
|
| + || reqexp==BIGODD || reqexp==BIGEVEN /* .. very big .. */
|
| + || abs(reqexp)>(2*(set->digits+set->emax))) /* .. or out of range */
|
| + status=DEC_Invalid_operation;
|
| + else { /* rhs is OK */
|
| + uprv_decNumberCopy(res, lhs); /* all done if infinite lhs */
|
| + if (!decNumberIsInfinite(res)) { /* prepare to scale */
|
| + res->exponent+=reqexp; /* adjust the exponent */
|
| + residue=0;
|
| + decFinalize(res, set, &residue, &status); /* .. and check */
|
| + } /* finite LHS */
|
| + } /* rhs OK */
|
| + } /* rhs finite */
|
| + if (status!=0) decStatus(res, status, set);
|
| + return res;
|
| + } /* decNumberScaleB */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberShift -- shift the coefficient of a Number left or right */
|
| +/* */
|
| +/* This computes C = A << B or C = A >> -B (in base ten). */
|
| +/* */
|
| +/* res is C, the result. C may be A and/or B (e.g., X=X<<X) */
|
| +/* lhs is A */
|
| +/* rhs is B, the number of digits to shift (-ve to right) */
|
| +/* set is the context */
|
| +/* */
|
| +/* The digits of the coefficient of A are shifted to the left (if B */
|
| +/* is positive) or to the right (if B is negative) without adjusting */
|
| +/* the exponent or the sign of A. */
|
| +/* */
|
| +/* B must be an integer (q=0) and in the range -set->digits through */
|
| +/* +set->digits. */
|
| +/* C must have space for set->digits digits. */
|
| +/* NaNs are propagated as usual. Infinities are unaffected (but */
|
| +/* B must be valid). No status is set unless B is invalid or an */
|
| +/* operand is an sNaN. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberShift(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + uInt status=0; /* accumulator */
|
| + Int shift; /* rhs as an Int */
|
| +
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| + #endif
|
| +
|
| + /* NaNs propagate as normal */
|
| + if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
|
| + decNaNs(res, lhs, rhs, set, &status);
|
| + /* rhs must be an integer */
|
| + else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
|
| + status=DEC_Invalid_operation;
|
| + else { /* both numeric, rhs is an integer */
|
| + shift=decGetInt(rhs); /* [cannot fail] */
|
| + if (shift==BADINT /* something bad .. */
|
| + || shift==BIGODD || shift==BIGEVEN /* .. very big .. */
|
| + || abs(shift)>set->digits) /* .. or out of range */
|
| + status=DEC_Invalid_operation;
|
| + else { /* rhs is OK */
|
| + uprv_decNumberCopy(res, lhs);
|
| + if (shift!=0 && !decNumberIsInfinite(res)) { /* something to do */
|
| + if (shift>0) { /* to left */
|
| + if (shift==set->digits) { /* removing all */
|
| + *res->lsu=0; /* so place 0 */
|
| + res->digits=1; /* .. */
|
| + }
|
| + else { /* */
|
| + /* first remove leading digits if necessary */
|
| + if (res->digits+shift>set->digits) {
|
| + decDecap(res, res->digits+shift-set->digits);
|
| + /* that updated res->digits; may have gone to 1 (for a */
|
| + /* single digit or for zero */
|
| + }
|
| + if (res->digits>1 || *res->lsu) /* if non-zero.. */
|
| + res->digits=decShiftToMost(res->lsu, res->digits, shift);
|
| + } /* partial left */
|
| + } /* left */
|
| + else { /* to right */
|
| + if (-shift>=res->digits) { /* discarding all */
|
| + *res->lsu=0; /* so place 0 */
|
| + res->digits=1; /* .. */
|
| + }
|
| + else {
|
| + decShiftToLeast(res->lsu, D2U(res->digits), -shift);
|
| + res->digits-=(-shift);
|
| + }
|
| + } /* to right */
|
| + } /* non-0 non-Inf shift */
|
| + } /* rhs OK */
|
| + } /* numerics */
|
| + if (status!=0) decStatus(res, status, set);
|
| + return res;
|
| + } /* decNumberShift */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberSquareRoot -- square root operator */
|
| +/* */
|
| +/* This computes C = squareroot(A) */
|
| +/* */
|
| +/* res is C, the result. C may be A */
|
| +/* rhs is A */
|
| +/* set is the context; note that rounding mode has no effect */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* ------------------------------------------------------------------ */
|
| +/* This uses the following varying-precision algorithm in: */
|
| +/* */
|
| +/* Properly Rounded Variable Precision Square Root, T. E. Hull and */
|
| +/* A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */
|
| +/* pp229-237, ACM, September 1985. */
|
| +/* */
|
| +/* The square-root is calculated using Newton's method, after which */
|
| +/* a check is made to ensure the result is correctly rounded. */
|
| +/* */
|
| +/* % [Reformatted original Numerical Turing source code follows.] */
|
| +/* function sqrt(x : real) : real */
|
| +/* % sqrt(x) returns the properly rounded approximation to the square */
|
| +/* % root of x, in the precision of the calling environment, or it */
|
| +/* % fails if x < 0. */
|
| +/* % t e hull and a abrham, august, 1984 */
|
| +/* if x <= 0 then */
|
| +/* if x < 0 then */
|
| +/* assert false */
|
| +/* else */
|
| +/* result 0 */
|
| +/* end if */
|
| +/* end if */
|
| +/* var f := setexp(x, 0) % fraction part of x [0.1 <= x < 1] */
|
| +/* var e := getexp(x) % exponent part of x */
|
| +/* var approx : real */
|
| +/* if e mod 2 = 0 then */
|
| +/* approx := .259 + .819 * f % approx to root of f */
|
| +/* else */
|
| +/* f := f/l0 % adjustments */
|
| +/* e := e + 1 % for odd */
|
| +/* approx := .0819 + 2.59 * f % exponent */
|
| +/* end if */
|
| +/* */
|
| +/* var p:= 3 */
|
| +/* const maxp := currentprecision + 2 */
|
| +/* loop */
|
| +/* p := min(2*p - 2, maxp) % p = 4,6,10, . . . , maxp */
|
| +/* precision p */
|
| +/* approx := .5 * (approx + f/approx) */
|
| +/* exit when p = maxp */
|
| +/* end loop */
|
| +/* */
|
| +/* % approx is now within 1 ulp of the properly rounded square root */
|
| +/* % of f; to ensure proper rounding, compare squares of (approx - */
|
| +/* % l/2 ulp) and (approx + l/2 ulp) with f. */
|
| +/* p := currentprecision */
|
| +/* begin */
|
| +/* precision p + 2 */
|
| +/* const approxsubhalf := approx - setexp(.5, -p) */
|
| +/* if mulru(approxsubhalf, approxsubhalf) > f then */
|
| +/* approx := approx - setexp(.l, -p + 1) */
|
| +/* else */
|
| +/* const approxaddhalf := approx + setexp(.5, -p) */
|
| +/* if mulrd(approxaddhalf, approxaddhalf) < f then */
|
| +/* approx := approx + setexp(.l, -p + 1) */
|
| +/* end if */
|
| +/* end if */
|
| +/* end */
|
| +/* result setexp(approx, e div 2) % fix exponent */
|
| +/* end sqrt */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberSquareRoot(decNumber *res, const decNumber *rhs,
|
| + decContext *set) {
|
| + decContext workset, approxset; /* work contexts */
|
| + decNumber dzero; /* used for constant zero */
|
| + Int maxp; /* largest working precision */
|
| + Int workp; /* working precision */
|
| + Int residue=0; /* rounding residue */
|
| + uInt status=0, ignore=0; /* status accumulators */
|
| + uInt rstatus; /* .. */
|
| + Int exp; /* working exponent */
|
| + Int ideal; /* ideal (preferred) exponent */
|
| + Int needbytes; /* work */
|
| + Int dropped; /* .. */
|
| +
|
| + #if DECSUBSET
|
| + decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */
|
| + #endif
|
| + /* buffer for f [needs +1 in case DECBUFFER 0] */
|
| + decNumber buff[D2N(DECBUFFER+1)];
|
| + /* buffer for a [needs +2 to match likely maxp] */
|
| + decNumber bufa[D2N(DECBUFFER+2)];
|
| + /* buffer for temporary, b [must be same size as a] */
|
| + decNumber bufb[D2N(DECBUFFER+2)];
|
| + decNumber *allocbuff=NULL; /* -> allocated buff, iff allocated */
|
| + decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */
|
| + decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */
|
| + decNumber *f=buff; /* reduced fraction */
|
| + decNumber *a=bufa; /* approximation to result */
|
| + decNumber *b=bufb; /* intermediate result */
|
| + /* buffer for temporary variable, up to 3 digits */
|
| + decNumber buft[D2N(3)];
|
| + decNumber *t=buft; /* up-to-3-digit constant or work */
|
| +
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| + #endif
|
| +
|
| + do { /* protect allocated storage */
|
| + #if DECSUBSET
|
| + if (!set->extended) {
|
| + /* reduce operand and set lostDigits status, as needed */
|
| + if (rhs->digits>set->digits) {
|
| + allocrhs=decRoundOperand(rhs, set, &status);
|
| + if (allocrhs==NULL) break;
|
| + /* [Note: 'f' allocation below could reuse this buffer if */
|
| + /* used, but as this is rare they are kept separate for clarity.] */
|
| + rhs=allocrhs;
|
| + }
|
| + }
|
| + #endif
|
| + /* [following code does not require input rounding] */
|
| +
|
| + /* handle infinities and NaNs */
|
| + if (SPECIALARG) {
|
| + if (decNumberIsInfinite(rhs)) { /* an infinity */
|
| + if (decNumberIsNegative(rhs)) status|=DEC_Invalid_operation;
|
| + else uprv_decNumberCopy(res, rhs); /* +Infinity */
|
| + }
|
| + else decNaNs(res, rhs, NULL, set, &status); /* a NaN */
|
| + break;
|
| + }
|
| +
|
| + /* calculate the ideal (preferred) exponent [floor(exp/2)] */
|
| + /* [It would be nicer to write: ideal=rhs->exponent>>1, but this */
|
| + /* generates a compiler warning. Generated code is the same.] */
|
| + ideal=(rhs->exponent&~1)/2; /* target */
|
| +
|
| + /* handle zeros */
|
| + if (ISZERO(rhs)) {
|
| + uprv_decNumberCopy(res, rhs); /* could be 0 or -0 */
|
| + res->exponent=ideal; /* use the ideal [safe] */
|
| + /* use decFinish to clamp any out-of-range exponent, etc. */
|
| + decFinish(res, set, &residue, &status);
|
| + break;
|
| + }
|
| +
|
| + /* any other -x is an oops */
|
| + if (decNumberIsNegative(rhs)) {
|
| + status|=DEC_Invalid_operation;
|
| + break;
|
| + }
|
| +
|
| + /* space is needed for three working variables */
|
| + /* f -- the same precision as the RHS, reduced to 0.01->0.99... */
|
| + /* a -- Hull's approximation -- precision, when assigned, is */
|
| + /* currentprecision+1 or the input argument precision, */
|
| + /* whichever is larger (+2 for use as temporary) */
|
| + /* b -- intermediate temporary result (same size as a) */
|
| + /* if any is too long for local storage, then allocate */
|
| + workp=MAXI(set->digits+1, rhs->digits); /* actual rounding precision */
|
| + workp=MAXI(workp, 7); /* at least 7 for low cases */
|
| + maxp=workp+2; /* largest working precision */
|
| +
|
| + needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
|
| + if (needbytes>(Int)sizeof(buff)) {
|
| + allocbuff=(decNumber *)malloc(needbytes);
|
| + if (allocbuff==NULL) { /* hopeless -- abandon */
|
| + status|=DEC_Insufficient_storage;
|
| + break;}
|
| + f=allocbuff; /* use the allocated space */
|
| + }
|
| + /* a and b both need to be able to hold a maxp-length number */
|
| + needbytes=sizeof(decNumber)+(D2U(maxp)-1)*sizeof(Unit);
|
| + if (needbytes>(Int)sizeof(bufa)) { /* [same applies to b] */
|
| + allocbufa=(decNumber *)malloc(needbytes);
|
| + allocbufb=(decNumber *)malloc(needbytes);
|
| + if (allocbufa==NULL || allocbufb==NULL) { /* hopeless */
|
| + status|=DEC_Insufficient_storage;
|
| + break;}
|
| + a=allocbufa; /* use the allocated spaces */
|
| + b=allocbufb; /* .. */
|
| + }
|
| +
|
| + /* copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1 */
|
| + uprv_decNumberCopy(f, rhs);
|
| + exp=f->exponent+f->digits; /* adjusted to Hull rules */
|
| + f->exponent=-(f->digits); /* to range */
|
| +
|
| + /* set up working context */
|
| + uprv_decContextDefault(&workset, DEC_INIT_DECIMAL64);
|
| + workset.emax=DEC_MAX_EMAX;
|
| + workset.emin=DEC_MIN_EMIN;
|
| +
|
| + /* [Until further notice, no error is possible and status bits */
|
| + /* (Rounded, etc.) should be ignored, not accumulated.] */
|
| +
|
| + /* Calculate initial approximation, and allow for odd exponent */
|
| + workset.digits=workp; /* p for initial calculation */
|
| + t->bits=0; t->digits=3;
|
| + a->bits=0; a->digits=3;
|
| + if ((exp & 1)==0) { /* even exponent */
|
| + /* Set t=0.259, a=0.819 */
|
| + t->exponent=-3;
|
| + a->exponent=-3;
|
| + #if DECDPUN>=3
|
| + t->lsu[0]=259;
|
| + a->lsu[0]=819;
|
| + #elif DECDPUN==2
|
| + t->lsu[0]=59; t->lsu[1]=2;
|
| + a->lsu[0]=19; a->lsu[1]=8;
|
| + #else
|
| + t->lsu[0]=9; t->lsu[1]=5; t->lsu[2]=2;
|
| + a->lsu[0]=9; a->lsu[1]=1; a->lsu[2]=8;
|
| + #endif
|
| + }
|
| + else { /* odd exponent */
|
| + /* Set t=0.0819, a=2.59 */
|
| + f->exponent--; /* f=f/10 */
|
| + exp++; /* e=e+1 */
|
| + t->exponent=-4;
|
| + a->exponent=-2;
|
| + #if DECDPUN>=3
|
| + t->lsu[0]=819;
|
| + a->lsu[0]=259;
|
| + #elif DECDPUN==2
|
| + t->lsu[0]=19; t->lsu[1]=8;
|
| + a->lsu[0]=59; a->lsu[1]=2;
|
| + #else
|
| + t->lsu[0]=9; t->lsu[1]=1; t->lsu[2]=8;
|
| + a->lsu[0]=9; a->lsu[1]=5; a->lsu[2]=2;
|
| + #endif
|
| + }
|
| +
|
| + decMultiplyOp(a, a, f, &workset, &ignore); /* a=a*f */
|
| + decAddOp(a, a, t, &workset, 0, &ignore); /* ..+t */
|
| + /* [a is now the initial approximation for sqrt(f), calculated with */
|
| + /* currentprecision, which is also a's precision.] */
|
| +
|
| + /* the main calculation loop */
|
| + uprv_decNumberZero(&dzero); /* make 0 */
|
| + uprv_decNumberZero(t); /* set t = 0.5 */
|
| + t->lsu[0]=5; /* .. */
|
| + t->exponent=-1; /* .. */
|
| + workset.digits=3; /* initial p */
|
| + for (; workset.digits<maxp;) {
|
| + /* set p to min(2*p - 2, maxp) [hence 3; or: 4, 6, 10, ... , maxp] */
|
| + workset.digits=MINI(workset.digits*2-2, maxp);
|
| + /* a = 0.5 * (a + f/a) */
|
| + /* [calculated at p then rounded to currentprecision] */
|
| + decDivideOp(b, f, a, &workset, DIVIDE, &ignore); /* b=f/a */
|
| + decAddOp(b, b, a, &workset, 0, &ignore); /* b=b+a */
|
| + decMultiplyOp(a, b, t, &workset, &ignore); /* a=b*0.5 */
|
| + } /* loop */
|
| +
|
| + /* Here, 0.1 <= a < 1 [Hull], and a has maxp digits */
|
| + /* now reduce to length, etc.; this needs to be done with a */
|
| + /* having the correct exponent so as to handle subnormals */
|
| + /* correctly */
|
| + approxset=*set; /* get emin, emax, etc. */
|
| + approxset.round=DEC_ROUND_HALF_EVEN;
|
| + a->exponent+=exp/2; /* set correct exponent */
|
| + rstatus=0; /* clear status */
|
| + residue=0; /* .. and accumulator */
|
| + decCopyFit(a, a, &approxset, &residue, &rstatus); /* reduce (if needed) */
|
| + decFinish(a, &approxset, &residue, &rstatus); /* clean and finalize */
|
| +
|
| + /* Overflow was possible if the input exponent was out-of-range, */
|
| + /* in which case quit */
|
| + if (rstatus&DEC_Overflow) {
|
| + status=rstatus; /* use the status as-is */
|
| + uprv_decNumberCopy(res, a); /* copy to result */
|
| + break;
|
| + }
|
| +
|
| + /* Preserve status except Inexact/Rounded */
|
| + status|=(rstatus & ~(DEC_Rounded|DEC_Inexact));
|
| +
|
| + /* Carry out the Hull correction */
|
| + a->exponent-=exp/2; /* back to 0.1->1 */
|
| +
|
| + /* a is now at final precision and within 1 ulp of the properly */
|
| + /* rounded square root of f; to ensure proper rounding, compare */
|
| + /* squares of (a - l/2 ulp) and (a + l/2 ulp) with f. */
|
| + /* Here workset.digits=maxp and t=0.5, and a->digits determines */
|
| + /* the ulp */
|
| + workset.digits--; /* maxp-1 is OK now */
|
| + t->exponent=-a->digits-1; /* make 0.5 ulp */
|
| + decAddOp(b, a, t, &workset, DECNEG, &ignore); /* b = a - 0.5 ulp */
|
| + workset.round=DEC_ROUND_UP;
|
| + decMultiplyOp(b, b, b, &workset, &ignore); /* b = mulru(b, b) */
|
| + decCompareOp(b, f, b, &workset, COMPARE, &ignore); /* b ? f, reversed */
|
| + if (decNumberIsNegative(b)) { /* f < b [i.e., b > f] */
|
| + /* this is the more common adjustment, though both are rare */
|
| + t->exponent++; /* make 1.0 ulp */
|
| + t->lsu[0]=1; /* .. */
|
| + decAddOp(a, a, t, &workset, DECNEG, &ignore); /* a = a - 1 ulp */
|
| + /* assign to approx [round to length] */
|
| + approxset.emin-=exp/2; /* adjust to match a */
|
| + approxset.emax-=exp/2;
|
| + decAddOp(a, &dzero, a, &approxset, 0, &ignore);
|
| + }
|
| + else {
|
| + decAddOp(b, a, t, &workset, 0, &ignore); /* b = a + 0.5 ulp */
|
| + workset.round=DEC_ROUND_DOWN;
|
| + decMultiplyOp(b, b, b, &workset, &ignore); /* b = mulrd(b, b) */
|
| + decCompareOp(b, b, f, &workset, COMPARE, &ignore); /* b ? f */
|
| + if (decNumberIsNegative(b)) { /* b < f */
|
| + t->exponent++; /* make 1.0 ulp */
|
| + t->lsu[0]=1; /* .. */
|
| + decAddOp(a, a, t, &workset, 0, &ignore); /* a = a + 1 ulp */
|
| + /* assign to approx [round to length] */
|
| + approxset.emin-=exp/2; /* adjust to match a */
|
| + approxset.emax-=exp/2;
|
| + decAddOp(a, &dzero, a, &approxset, 0, &ignore);
|
| + }
|
| + }
|
| + /* [no errors are possible in the above, and rounding/inexact during */
|
| + /* estimation are irrelevant, so status was not accumulated] */
|
| +
|
| + /* Here, 0.1 <= a < 1 (still), so adjust back */
|
| + a->exponent+=exp/2; /* set correct exponent */
|
| +
|
| + /* count droppable zeros [after any subnormal rounding] by */
|
| + /* trimming a copy */
|
| + uprv_decNumberCopy(b, a);
|
| + decTrim(b, set, 1, 1, &dropped); /* [drops trailing zeros] */
|
| +
|
| + /* Set Inexact and Rounded. The answer can only be exact if */
|
| + /* it is short enough so that squaring it could fit in workp */
|
| + /* digits, so this is the only (relatively rare) condition that */
|
| + /* a careful check is needed */
|
| + if (b->digits*2-1 > workp) { /* cannot fit */
|
| + status|=DEC_Inexact|DEC_Rounded;
|
| + }
|
| + else { /* could be exact/unrounded */
|
| + uInt mstatus=0; /* local status */
|
| + decMultiplyOp(b, b, b, &workset, &mstatus); /* try the multiply */
|
| + if (mstatus&DEC_Overflow) { /* result just won't fit */
|
| + status|=DEC_Inexact|DEC_Rounded;
|
| + }
|
| + else { /* plausible */
|
| + decCompareOp(t, b, rhs, &workset, COMPARE, &mstatus); /* b ? rhs */
|
| + if (!ISZERO(t)) status|=DEC_Inexact|DEC_Rounded; /* not equal */
|
| + else { /* is Exact */
|
| + /* here, dropped is the count of trailing zeros in 'a' */
|
| + /* use closest exponent to ideal... */
|
| + Int todrop=ideal-a->exponent; /* most that can be dropped */
|
| + if (todrop<0) status|=DEC_Rounded; /* ideally would add 0s */
|
| + else { /* unrounded */
|
| + /* there are some to drop, but emax may not allow all */
|
| + Int maxexp=set->emax-set->digits+1;
|
| + Int maxdrop=maxexp-a->exponent;
|
| + if (todrop>maxdrop && set->clamp) { /* apply clamping */
|
| + todrop=maxdrop;
|
| + status|=DEC_Clamped;
|
| + }
|
| + if (dropped<todrop) { /* clamp to those available */
|
| + todrop=dropped;
|
| + status|=DEC_Clamped;
|
| + }
|
| + if (todrop>0) { /* have some to drop */
|
| + decShiftToLeast(a->lsu, D2U(a->digits), todrop);
|
| + a->exponent+=todrop; /* maintain numerical value */
|
| + a->digits-=todrop; /* new length */
|
| + }
|
| + }
|
| + }
|
| + }
|
| + }
|
| +
|
| + /* double-check Underflow, as perhaps the result could not have */
|
| + /* been subnormal (initial argument too big), or it is now Exact */
|
| + if (status&DEC_Underflow) {
|
| + Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */
|
| + /* check if truly subnormal */
|
| + #if DECEXTFLAG /* DEC_Subnormal too */
|
| + if (ae>=set->emin*2) status&=~(DEC_Subnormal|DEC_Underflow);
|
| + #else
|
| + if (ae>=set->emin*2) status&=~DEC_Underflow;
|
| + #endif
|
| + /* check if truly inexact */
|
| + if (!(status&DEC_Inexact)) status&=~DEC_Underflow;
|
| + }
|
| +
|
| + uprv_decNumberCopy(res, a); /* a is now the result */
|
| + } while(0); /* end protected */
|
| +
|
| + if (allocbuff!=NULL) free(allocbuff); /* drop any storage used */
|
| + if (allocbufa!=NULL) free(allocbufa); /* .. */
|
| + if (allocbufb!=NULL) free(allocbufb); /* .. */
|
| + #if DECSUBSET
|
| + if (allocrhs !=NULL) free(allocrhs); /* .. */
|
| + #endif
|
| + if (status!=0) decStatus(res, status, set);/* then report status */
|
| + #if DECCHECK
|
| + decCheckInexact(res, set);
|
| + #endif
|
| + return res;
|
| + } /* decNumberSquareRoot */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberSubtract -- subtract two Numbers */
|
| +/* */
|
| +/* This computes C = A - B */
|
| +/* */
|
| +/* res is C, the result. C may be A and/or B (e.g., X=X-X) */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* set is the context */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberSubtract(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + uInt status=0; /* accumulator */
|
| +
|
| + decAddOp(res, lhs, rhs, set, DECNEG, &status);
|
| + if (status!=0) decStatus(res, status, set);
|
| + #if DECCHECK
|
| + decCheckInexact(res, set);
|
| + #endif
|
| + return res;
|
| + } /* decNumberSubtract */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberToIntegralExact -- round-to-integral-value with InExact */
|
| +/* decNumberToIntegralValue -- round-to-integral-value */
|
| +/* */
|
| +/* res is the result */
|
| +/* rhs is input number */
|
| +/* set is the context */
|
| +/* */
|
| +/* res must have space for any value of rhs. */
|
| +/* */
|
| +/* This implements the IEEE special operators and therefore treats */
|
| +/* special values as valid. For finite numbers it returns */
|
| +/* rescale(rhs, 0) if rhs->exponent is <0. */
|
| +/* Otherwise the result is rhs (so no error is possible, except for */
|
| +/* sNaN). */
|
| +/* */
|
| +/* The context is used for rounding mode and status after sNaN, but */
|
| +/* the digits setting is ignored. The Exact version will signal */
|
| +/* Inexact if the result differs numerically from rhs; the other */
|
| +/* never signals Inexact. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberToIntegralExact(decNumber *res, const decNumber *rhs,
|
| + decContext *set) {
|
| + decNumber dn;
|
| + decContext workset; /* working context */
|
| + uInt status=0; /* accumulator */
|
| +
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| + #endif
|
| +
|
| + /* handle infinities and NaNs */
|
| + if (SPECIALARG) {
|
| + if (decNumberIsInfinite(rhs)) uprv_decNumberCopy(res, rhs); /* an Infinity */
|
| + else decNaNs(res, rhs, NULL, set, &status); /* a NaN */
|
| + }
|
| + else { /* finite */
|
| + /* have a finite number; no error possible (res must be big enough) */
|
| + if (rhs->exponent>=0) return uprv_decNumberCopy(res, rhs);
|
| + /* that was easy, but if negative exponent there is work to do... */
|
| + workset=*set; /* clone rounding, etc. */
|
| + workset.digits=rhs->digits; /* no length rounding */
|
| + workset.traps=0; /* no traps */
|
| + uprv_decNumberZero(&dn); /* make a number with exponent 0 */
|
| + uprv_decNumberQuantize(res, rhs, &dn, &workset);
|
| + status|=workset.status;
|
| + }
|
| + if (status!=0) decStatus(res, status, set);
|
| + return res;
|
| + } /* decNumberToIntegralExact */
|
| +
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberToIntegralValue(decNumber *res, const decNumber *rhs,
|
| + decContext *set) {
|
| + decContext workset=*set; /* working context */
|
| + workset.traps=0; /* no traps */
|
| + uprv_decNumberToIntegralExact(res, rhs, &workset);
|
| + /* this never affects set, except for sNaNs; NaN will have been set */
|
| + /* or propagated already, so no need to call decStatus */
|
| + set->status|=workset.status&DEC_Invalid_operation;
|
| + return res;
|
| + } /* decNumberToIntegralValue */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberXor -- XOR two Numbers, digitwise */
|
| +/* */
|
| +/* This computes C = A ^ B */
|
| +/* */
|
| +/* res is C, the result. C may be A and/or B (e.g., X=X^X) */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* set is the context (used for result length and error report) */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* */
|
| +/* Logical function restrictions apply (see above); a NaN is */
|
| +/* returned with Invalid_operation if a restriction is violated. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberXor(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + const Unit *ua, *ub; /* -> operands */
|
| + const Unit *msua, *msub; /* -> operand msus */
|
| + Unit *uc, *msuc; /* -> result and its msu */
|
| + Int msudigs; /* digits in res msu */
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| + #endif
|
| +
|
| + if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
|
| + || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
|
| + decStatus(res, DEC_Invalid_operation, set);
|
| + return res;
|
| + }
|
| + /* operands are valid */
|
| + ua=lhs->lsu; /* bottom-up */
|
| + ub=rhs->lsu; /* .. */
|
| + uc=res->lsu; /* .. */
|
| + msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */
|
| + msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */
|
| + msuc=uc+D2U(set->digits)-1; /* -> msu of result */
|
| + msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */
|
| + for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */
|
| + Unit a, b; /* extract units */
|
| + if (ua>msua) a=0;
|
| + else a=*ua;
|
| + if (ub>msub) b=0;
|
| + else b=*ub;
|
| + *uc=0; /* can now write back */
|
| + if (a|b) { /* maybe 1 bits to examine */
|
| + Int i, j;
|
| + /* This loop could be unrolled and/or use BIN2BCD tables */
|
| + for (i=0; i<DECDPUN; i++) {
|
| + if ((a^b)&1) *uc=*uc+(Unit)powers[i]; /* effect XOR */
|
| + j=a%10;
|
| + a=a/10;
|
| + j|=b%10;
|
| + b=b/10;
|
| + if (j>1) {
|
| + decStatus(res, DEC_Invalid_operation, set);
|
| + return res;
|
| + }
|
| + if (uc==msuc && i==msudigs-1) break; /* just did final digit */
|
| + } /* each digit */
|
| + } /* non-zero */
|
| + } /* each unit */
|
| + /* [here uc-1 is the msu of the result] */
|
| + res->digits=decGetDigits(res->lsu, uc-res->lsu);
|
| + res->exponent=0; /* integer */
|
| + res->bits=0; /* sign=0 */
|
| + return res; /* [no status to set] */
|
| + } /* decNumberXor */
|
| +
|
| +
|
| +/* ================================================================== */
|
| +/* Utility routines */
|
| +/* ================================================================== */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberClass -- return the decClass of a decNumber */
|
| +/* dn -- the decNumber to test */
|
| +/* set -- the context to use for Emin */
|
| +/* returns the decClass enum */
|
| +/* ------------------------------------------------------------------ */
|
| +enum decClass uprv_decNumberClass(const decNumber *dn, decContext *set) {
|
| + if (decNumberIsSpecial(dn)) {
|
| + if (decNumberIsQNaN(dn)) return DEC_CLASS_QNAN;
|
| + if (decNumberIsSNaN(dn)) return DEC_CLASS_SNAN;
|
| + /* must be an infinity */
|
| + if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_INF;
|
| + return DEC_CLASS_POS_INF;
|
| + }
|
| + /* is finite */
|
| + if (uprv_decNumberIsNormal(dn, set)) { /* most common */
|
| + if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_NORMAL;
|
| + return DEC_CLASS_POS_NORMAL;
|
| + }
|
| + /* is subnormal or zero */
|
| + if (decNumberIsZero(dn)) { /* most common */
|
| + if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_ZERO;
|
| + return DEC_CLASS_POS_ZERO;
|
| + }
|
| + if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_SUBNORMAL;
|
| + return DEC_CLASS_POS_SUBNORMAL;
|
| + } /* decNumberClass */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberClassToString -- convert decClass to a string */
|
| +/* */
|
| +/* eclass is a valid decClass */
|
| +/* returns a constant string describing the class (max 13+1 chars) */
|
| +/* ------------------------------------------------------------------ */
|
| +const char *uprv_decNumberClassToString(enum decClass eclass) {
|
| + if (eclass==DEC_CLASS_POS_NORMAL) return DEC_ClassString_PN;
|
| + if (eclass==DEC_CLASS_NEG_NORMAL) return DEC_ClassString_NN;
|
| + if (eclass==DEC_CLASS_POS_ZERO) return DEC_ClassString_PZ;
|
| + if (eclass==DEC_CLASS_NEG_ZERO) return DEC_ClassString_NZ;
|
| + if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS;
|
| + if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS;
|
| + if (eclass==DEC_CLASS_POS_INF) return DEC_ClassString_PI;
|
| + if (eclass==DEC_CLASS_NEG_INF) return DEC_ClassString_NI;
|
| + if (eclass==DEC_CLASS_QNAN) return DEC_ClassString_QN;
|
| + if (eclass==DEC_CLASS_SNAN) return DEC_ClassString_SN;
|
| + return DEC_ClassString_UN; /* Unknown */
|
| + } /* decNumberClassToString */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberCopy -- copy a number */
|
| +/* */
|
| +/* dest is the target decNumber */
|
| +/* src is the source decNumber */
|
| +/* returns dest */
|
| +/* */
|
| +/* (dest==src is allowed and is a no-op) */
|
| +/* All fields are updated as required. This is a utility operation, */
|
| +/* so special values are unchanged and no error is possible. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopy(decNumber *dest, const decNumber *src) {
|
| +
|
| + #if DECCHECK
|
| + if (src==NULL) return uprv_decNumberZero(dest);
|
| + #endif
|
| +
|
| + if (dest==src) return dest; /* no copy required */
|
| +
|
| + /* Use explicit assignments here as structure assignment could copy */
|
| + /* more than just the lsu (for small DECDPUN). This would not affect */
|
| + /* the value of the results, but could disturb test harness spill */
|
| + /* checking. */
|
| + dest->bits=src->bits;
|
| + dest->exponent=src->exponent;
|
| + dest->digits=src->digits;
|
| + dest->lsu[0]=src->lsu[0];
|
| + if (src->digits>DECDPUN) { /* more Units to come */
|
| + const Unit *smsup, *s; /* work */
|
| + Unit *d; /* .. */
|
| + /* memcpy for the remaining Units would be safe as they cannot */
|
| + /* overlap. However, this explicit loop is faster in short cases. */
|
| + d=dest->lsu+1; /* -> first destination */
|
| + smsup=src->lsu+D2U(src->digits); /* -> source msu+1 */
|
| + for (s=src->lsu+1; s<smsup; s++, d++) *d=*s;
|
| + }
|
| + return dest;
|
| + } /* decNumberCopy */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberCopyAbs -- quiet absolute value operator */
|
| +/* */
|
| +/* This sets C = abs(A) */
|
| +/* */
|
| +/* res is C, the result. C may be A */
|
| +/* rhs is A */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* No exception or error can occur; this is a quiet bitwise operation.*/
|
| +/* See also decNumberAbs for a checking version of this. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopyAbs(decNumber *res, const decNumber *rhs) {
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
|
| + #endif
|
| + uprv_decNumberCopy(res, rhs);
|
| + res->bits&=~DECNEG; /* turn off sign */
|
| + return res;
|
| + } /* decNumberCopyAbs */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberCopyNegate -- quiet negate value operator */
|
| +/* */
|
| +/* This sets C = negate(A) */
|
| +/* */
|
| +/* res is C, the result. C may be A */
|
| +/* rhs is A */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* No exception or error can occur; this is a quiet bitwise operation.*/
|
| +/* See also decNumberMinus for a checking version of this. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopyNegate(decNumber *res, const decNumber *rhs) {
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
|
| + #endif
|
| + uprv_decNumberCopy(res, rhs);
|
| + res->bits^=DECNEG; /* invert the sign */
|
| + return res;
|
| + } /* decNumberCopyNegate */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberCopySign -- quiet copy and set sign operator */
|
| +/* */
|
| +/* This sets C = A with the sign of B */
|
| +/* */
|
| +/* res is C, the result. C may be A */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* No exception or error can occur; this is a quiet bitwise operation.*/
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopySign(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs) {
|
| + uByte sign; /* rhs sign */
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
|
| + #endif
|
| + sign=rhs->bits & DECNEG; /* save sign bit */
|
| + uprv_decNumberCopy(res, lhs);
|
| + res->bits&=~DECNEG; /* clear the sign */
|
| + res->bits|=sign; /* set from rhs */
|
| + return res;
|
| + } /* decNumberCopySign */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberGetBCD -- get the coefficient in BCD8 */
|
| +/* dn is the source decNumber */
|
| +/* bcd is the uInt array that will receive dn->digits BCD bytes, */
|
| +/* most-significant at offset 0 */
|
| +/* returns bcd */
|
| +/* */
|
| +/* bcd must have at least dn->digits bytes. No error is possible; if */
|
| +/* dn is a NaN or Infinite, digits must be 1 and the coefficient 0. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI uByte * U_EXPORT2 uprv_decNumberGetBCD(const decNumber *dn, uByte *bcd) {
|
| + uByte *ub=bcd+dn->digits-1; /* -> lsd */
|
| + const Unit *up=dn->lsu; /* Unit pointer, -> lsu */
|
| +
|
| + #if DECDPUN==1 /* trivial simple copy */
|
| + for (; ub>=bcd; ub--, up++) *ub=*up;
|
| + #else /* chopping needed */
|
| + uInt u=*up; /* work */
|
| + uInt cut=DECDPUN; /* downcounter through unit */
|
| + for (; ub>=bcd; ub--) {
|
| + *ub=(uByte)(u%10); /* [*6554 trick inhibits, here] */
|
| + u=u/10;
|
| + cut--;
|
| + if (cut>0) continue; /* more in this unit */
|
| + up++;
|
| + u=*up;
|
| + cut=DECDPUN;
|
| + }
|
| + #endif
|
| + return bcd;
|
| + } /* decNumberGetBCD */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberSetBCD -- set (replace) the coefficient from BCD8 */
|
| +/* dn is the target decNumber */
|
| +/* bcd is the uInt array that will source n BCD bytes, most- */
|
| +/* significant at offset 0 */
|
| +/* n is the number of digits in the source BCD array (bcd) */
|
| +/* returns dn */
|
| +/* */
|
| +/* dn must have space for at least n digits. No error is possible; */
|
| +/* if dn is a NaN, or Infinite, or is to become a zero, n must be 1 */
|
| +/* and bcd[0] zero. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberSetBCD(decNumber *dn, const uByte *bcd, uInt n) {
|
| + Unit *up=dn->lsu+D2U(dn->digits)-1; /* -> msu [target pointer] */
|
| + const uByte *ub=bcd; /* -> source msd */
|
| +
|
| + #if DECDPUN==1 /* trivial simple copy */
|
| + for (; ub<bcd+n; ub++, up--) *up=*ub;
|
| + #else /* some assembly needed */
|
| + /* calculate how many digits in msu, and hence first cut */
|
| + Int cut=MSUDIGITS(n); /* [faster than remainder] */
|
| + for (;up>=dn->lsu; up--) { /* each Unit from msu */
|
| + *up=0; /* will take <=DECDPUN digits */
|
| + for (; cut>0; ub++, cut--) *up=X10(*up)+*ub;
|
| + cut=DECDPUN; /* next Unit has all digits */
|
| + }
|
| + #endif
|
| + dn->digits=n; /* set digit count */
|
| + return dn;
|
| + } /* decNumberSetBCD */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberIsNormal -- test normality of a decNumber */
|
| +/* dn is the decNumber to test */
|
| +/* set is the context to use for Emin */
|
| +/* returns 1 if |dn| is finite and >=Nmin, 0 otherwise */
|
| +/* ------------------------------------------------------------------ */
|
| +Int uprv_decNumberIsNormal(const decNumber *dn, decContext *set) {
|
| + Int ae; /* adjusted exponent */
|
| + #if DECCHECK
|
| + if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
|
| + #endif
|
| +
|
| + if (decNumberIsSpecial(dn)) return 0; /* not finite */
|
| + if (decNumberIsZero(dn)) return 0; /* not non-zero */
|
| +
|
| + ae=dn->exponent+dn->digits-1; /* adjusted exponent */
|
| + if (ae<set->emin) return 0; /* is subnormal */
|
| + return 1;
|
| + } /* decNumberIsNormal */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberIsSubnormal -- test subnormality of a decNumber */
|
| +/* dn is the decNumber to test */
|
| +/* set is the context to use for Emin */
|
| +/* returns 1 if |dn| is finite, non-zero, and <Nmin, 0 otherwise */
|
| +/* ------------------------------------------------------------------ */
|
| +Int uprv_decNumberIsSubnormal(const decNumber *dn, decContext *set) {
|
| + Int ae; /* adjusted exponent */
|
| + #if DECCHECK
|
| + if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
|
| + #endif
|
| +
|
| + if (decNumberIsSpecial(dn)) return 0; /* not finite */
|
| + if (decNumberIsZero(dn)) return 0; /* not non-zero */
|
| +
|
| + ae=dn->exponent+dn->digits-1; /* adjusted exponent */
|
| + if (ae<set->emin) return 1; /* is subnormal */
|
| + return 0;
|
| + } /* decNumberIsSubnormal */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberTrim -- remove insignificant zeros */
|
| +/* */
|
| +/* dn is the number to trim */
|
| +/* returns dn */
|
| +/* */
|
| +/* All fields are updated as required. This is a utility operation, */
|
| +/* so special values are unchanged and no error is possible. The */
|
| +/* zeros are removed unconditionally. */
|
| +/* ------------------------------------------------------------------ */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberTrim(decNumber *dn) {
|
| + Int dropped; /* work */
|
| + decContext set; /* .. */
|
| + #if DECCHECK
|
| + if (decCheckOperands(DECUNRESU, DECUNUSED, dn, DECUNCONT)) return dn;
|
| + #endif
|
| + uprv_decContextDefault(&set, DEC_INIT_BASE); /* clamp=0 */
|
| + return decTrim(dn, &set, 0, 1, &dropped);
|
| + } /* decNumberTrim */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberVersion -- return the name and version of this module */
|
| +/* */
|
| +/* No error is possible. */
|
| +/* ------------------------------------------------------------------ */
|
| +const char * uprv_decNumberVersion(void) {
|
| + return DECVERSION;
|
| + } /* decNumberVersion */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberZero -- set a number to 0 */
|
| +/* */
|
| +/* dn is the number to set, with space for one digit */
|
| +/* returns dn */
|
| +/* */
|
| +/* No error is possible. */
|
| +/* ------------------------------------------------------------------ */
|
| +/* Memset is not used as it is much slower in some environments. */
|
| +U_CAPI decNumber * U_EXPORT2 uprv_decNumberZero(decNumber *dn) {
|
| +
|
| + #if DECCHECK
|
| + if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn;
|
| + #endif
|
| +
|
| + dn->bits=0;
|
| + dn->exponent=0;
|
| + dn->digits=1;
|
| + dn->lsu[0]=0;
|
| + return dn;
|
| + } /* decNumberZero */
|
| +
|
| +/* ================================================================== */
|
| +/* Local routines */
|
| +/* ================================================================== */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decToString -- lay out a number into a string */
|
| +/* */
|
| +/* dn is the number to lay out */
|
| +/* string is where to lay out the number */
|
| +/* eng is 1 if Engineering, 0 if Scientific */
|
| +/* */
|
| +/* string must be at least dn->digits+14 characters long */
|
| +/* No error is possible. */
|
| +/* */
|
| +/* Note that this routine can generate a -0 or 0.000. These are */
|
| +/* never generated in subset to-number or arithmetic, but can occur */
|
| +/* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234). */
|
| +/* ------------------------------------------------------------------ */
|
| +/* If DECCHECK is enabled the string "?" is returned if a number is */
|
| +/* invalid. */
|
| +static void decToString(const decNumber *dn, char *string, Flag eng) {
|
| + Int exp=dn->exponent; /* local copy */
|
| + Int e; /* E-part value */
|
| + Int pre; /* digits before the '.' */
|
| + Int cut; /* for counting digits in a Unit */
|
| + char *c=string; /* work [output pointer] */
|
| + const Unit *up=dn->lsu+D2U(dn->digits)-1; /* -> msu [input pointer] */
|
| + uInt u, pow; /* work */
|
| +
|
| + #if DECCHECK
|
| + if (decCheckOperands(DECUNRESU, dn, DECUNUSED, DECUNCONT)) {
|
| + strcpy(string, "?");
|
| + return;}
|
| + #endif
|
| +
|
| + if (decNumberIsNegative(dn)) { /* Negatives get a minus */
|
| + *c='-';
|
| + c++;
|
| + }
|
| + if (dn->bits&DECSPECIAL) { /* Is a special value */
|
| + if (decNumberIsInfinite(dn)) {
|
| + strcpy(c, "Inf");
|
| + strcpy(c+3, "inity");
|
| + return;}
|
| + /* a NaN */
|
| + if (dn->bits&DECSNAN) { /* signalling NaN */
|
| + *c='s';
|
| + c++;
|
| + }
|
| + strcpy(c, "NaN");
|
| + c+=3; /* step past */
|
| + /* if not a clean non-zero coefficient, that's all there is in a */
|
| + /* NaN string */
|
| + if (exp!=0 || (*dn->lsu==0 && dn->digits==1)) return;
|
| + /* [drop through to add integer] */
|
| + }
|
| +
|
| + /* calculate how many digits in msu, and hence first cut */
|
| + cut=MSUDIGITS(dn->digits); /* [faster than remainder] */
|
| + cut--; /* power of ten for digit */
|
| +
|
| + if (exp==0) { /* simple integer [common fastpath] */
|
| + for (;up>=dn->lsu; up--) { /* each Unit from msu */
|
| + u=*up; /* contains DECDPUN digits to lay out */
|
| + for (; cut>=0; c++, cut--) TODIGIT(u, cut, c, pow);
|
| + cut=DECDPUN-1; /* next Unit has all digits */
|
| + }
|
| + *c='\0'; /* terminate the string */
|
| + return;}
|
| +
|
| + /* non-0 exponent -- assume plain form */
|
| + pre=dn->digits+exp; /* digits before '.' */
|
| + e=0; /* no E */
|
| + if ((exp>0) || (pre<-5)) { /* need exponential form */
|
| + e=exp+dn->digits-1; /* calculate E value */
|
| + pre=1; /* assume one digit before '.' */
|
| + if (eng && (e!=0)) { /* engineering: may need to adjust */
|
| + Int adj; /* adjustment */
|
| + /* The C remainder operator is undefined for negative numbers, so */
|
| + /* a positive remainder calculation must be used here */
|
| + if (e<0) {
|
| + adj=(-e)%3;
|
| + if (adj!=0) adj=3-adj;
|
| + }
|
| + else { /* e>0 */
|
| + adj=e%3;
|
| + }
|
| + e=e-adj;
|
| + /* if dealing with zero still produce an exponent which is a */
|
| + /* multiple of three, as expected, but there will only be the */
|
| + /* one zero before the E, still. Otherwise note the padding. */
|
| + if (!ISZERO(dn)) pre+=adj;
|
| + else { /* is zero */
|
| + if (adj!=0) { /* 0.00Esnn needed */
|
| + e=e+3;
|
| + pre=-(2-adj);
|
| + }
|
| + } /* zero */
|
| + } /* eng */
|
| + } /* need exponent */
|
| +
|
| + /* lay out the digits of the coefficient, adding 0s and . as needed */
|
| + u=*up;
|
| + if (pre>0) { /* xxx.xxx or xx00 (engineering) form */
|
| + Int n=pre;
|
| + for (; pre>0; pre--, c++, cut--) {
|
| + if (cut<0) { /* need new Unit */
|
| + if (up==dn->lsu) break; /* out of input digits (pre>digits) */
|
| + up--;
|
| + cut=DECDPUN-1;
|
| + u=*up;
|
| + }
|
| + TODIGIT(u, cut, c, pow);
|
| + }
|
| + if (n<dn->digits) { /* more to come, after '.' */
|
| + *c='.'; c++;
|
| + for (;; c++, cut--) {
|
| + if (cut<0) { /* need new Unit */
|
| + if (up==dn->lsu) break; /* out of input digits */
|
| + up--;
|
| + cut=DECDPUN-1;
|
| + u=*up;
|
| + }
|
| + TODIGIT(u, cut, c, pow);
|
| + }
|
| + }
|
| + else for (; pre>0; pre--, c++) *c='0'; /* 0 padding (for engineering) needed */
|
| + }
|
| + else { /* 0.xxx or 0.000xxx form */
|
| + *c='0'; c++;
|
| + *c='.'; c++;
|
| + for (; pre<0; pre++, c++) *c='0'; /* add any 0's after '.' */
|
| + for (; ; c++, cut--) {
|
| + if (cut<0) { /* need new Unit */
|
| + if (up==dn->lsu) break; /* out of input digits */
|
| + up--;
|
| + cut=DECDPUN-1;
|
| + u=*up;
|
| + }
|
| + TODIGIT(u, cut, c, pow);
|
| + }
|
| + }
|
| +
|
| + /* Finally add the E-part, if needed. It will never be 0, has a
|
| + base maximum and minimum of +999999999 through -999999999, but
|
| + could range down to -1999999998 for anormal numbers */
|
| + if (e!=0) {
|
| + Flag had=0; /* 1=had non-zero */
|
| + *c='E'; c++;
|
| + *c='+'; c++; /* assume positive */
|
| + u=e; /* .. */
|
| + if (e<0) {
|
| + *(c-1)='-'; /* oops, need - */
|
| + u=-e; /* uInt, please */
|
| + }
|
| + /* lay out the exponent [_itoa or equivalent is not ANSI C] */
|
| + for (cut=9; cut>=0; cut--) {
|
| + TODIGIT(u, cut, c, pow);
|
| + if (*c=='0' && !had) continue; /* skip leading zeros */
|
| + had=1; /* had non-0 */
|
| + c++; /* step for next */
|
| + } /* cut */
|
| + }
|
| + *c='\0'; /* terminate the string (all paths) */
|
| + return;
|
| + } /* decToString */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decAddOp -- add/subtract operation */
|
| +/* */
|
| +/* This computes C = A + B */
|
| +/* */
|
| +/* res is C, the result. C may be A and/or B (e.g., X=X+X) */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* set is the context */
|
| +/* negate is DECNEG if rhs should be negated, or 0 otherwise */
|
| +/* status accumulates status for the caller */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* Inexact in status must be 0 for correct Exact zero sign in result */
|
| +/* ------------------------------------------------------------------ */
|
| +/* If possible, the coefficient is calculated directly into C. */
|
| +/* However, if: */
|
| +/* -- a digits+1 calculation is needed because the numbers are */
|
| +/* unaligned and span more than set->digits digits */
|
| +/* -- a carry to digits+1 digits looks possible */
|
| +/* -- C is the same as A or B, and the result would destructively */
|
| +/* overlap the A or B coefficient */
|
| +/* then the result must be calculated into a temporary buffer. In */
|
| +/* this case a local (stack) buffer is used if possible, and only if */
|
| +/* too long for that does malloc become the final resort. */
|
| +/* */
|
| +/* Misalignment is handled as follows: */
|
| +/* Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp. */
|
| +/* BPad: Apply the padding by a combination of shifting (whole */
|
| +/* units) and multiplication (part units). */
|
| +/* */
|
| +/* Addition, especially x=x+1, is speed-critical. */
|
| +/* The static buffer is larger than might be expected to allow for */
|
| +/* calls from higher-level funtions (notable exp). */
|
| +/* ------------------------------------------------------------------ */
|
| +static decNumber * decAddOp(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set,
|
| + uByte negate, uInt *status) {
|
| + #if DECSUBSET
|
| + decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */
|
| + decNumber *allocrhs=NULL; /* .., rhs */
|
| + #endif
|
| + Int rhsshift; /* working shift (in Units) */
|
| + Int maxdigits; /* longest logical length */
|
| + Int mult; /* multiplier */
|
| + Int residue; /* rounding accumulator */
|
| + uByte bits; /* result bits */
|
| + Flag diffsign; /* non-0 if arguments have different sign */
|
| + Unit *acc; /* accumulator for result */
|
| + Unit accbuff[SD2U(DECBUFFER*2+20)]; /* local buffer [*2+20 reduces many */
|
| + /* allocations when called from */
|
| + /* other operations, notable exp] */
|
| + Unit *allocacc=NULL; /* -> allocated acc buffer, iff allocated */
|
| + Int reqdigits=set->digits; /* local copy; requested DIGITS */
|
| + Int padding; /* work */
|
| +
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| + #endif
|
| +
|
| + do { /* protect allocated storage */
|
| + #if DECSUBSET
|
| + if (!set->extended) {
|
| + /* reduce operands and set lostDigits status, as needed */
|
| + if (lhs->digits>reqdigits) {
|
| + alloclhs=decRoundOperand(lhs, set, status);
|
| + if (alloclhs==NULL) break;
|
| + lhs=alloclhs;
|
| + }
|
| + if (rhs->digits>reqdigits) {
|
| + allocrhs=decRoundOperand(rhs, set, status);
|
| + if (allocrhs==NULL) break;
|
| + rhs=allocrhs;
|
| + }
|
| + }
|
| + #endif
|
| + /* [following code does not require input rounding] */
|
| +
|
| + /* note whether signs differ [used all paths] */
|
| + diffsign=(Flag)((lhs->bits^rhs->bits^negate)&DECNEG);
|
| +
|
| + /* handle infinities and NaNs */
|
| + if (SPECIALARGS) { /* a special bit set */
|
| + if (SPECIALARGS & (DECSNAN | DECNAN)) /* a NaN */
|
| + decNaNs(res, lhs, rhs, set, status);
|
| + else { /* one or two infinities */
|
| + if (decNumberIsInfinite(lhs)) { /* LHS is infinity */
|
| + /* two infinities with different signs is invalid */
|
| + if (decNumberIsInfinite(rhs) && diffsign) {
|
| + *status|=DEC_Invalid_operation;
|
| + break;
|
| + }
|
| + bits=lhs->bits & DECNEG; /* get sign from LHS */
|
| + }
|
| + else bits=(rhs->bits^negate) & DECNEG;/* RHS must be Infinity */
|
| + bits|=DECINF;
|
| + uprv_decNumberZero(res);
|
| + res->bits=bits; /* set +/- infinity */
|
| + } /* an infinity */
|
| + break;
|
| + }
|
| +
|
| + /* Quick exit for add 0s; return the non-0, modified as need be */
|
| + if (ISZERO(lhs)) {
|
| + Int adjust; /* work */
|
| + Int lexp=lhs->exponent; /* save in case LHS==RES */
|
| + bits=lhs->bits; /* .. */
|
| + residue=0; /* clear accumulator */
|
| + decCopyFit(res, rhs, set, &residue, status); /* copy (as needed) */
|
| + res->bits^=negate; /* flip if rhs was negated */
|
| + #if DECSUBSET
|
| + if (set->extended) { /* exponents on zeros count */
|
| + #endif
|
| + /* exponent will be the lower of the two */
|
| + adjust=lexp-res->exponent; /* adjustment needed [if -ve] */
|
| + if (ISZERO(res)) { /* both 0: special IEEE 754 rules */
|
| + if (adjust<0) res->exponent=lexp; /* set exponent */
|
| + /* 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0 */
|
| + if (diffsign) {
|
| + if (set->round!=DEC_ROUND_FLOOR) res->bits=0;
|
| + else res->bits=DECNEG; /* preserve 0 sign */
|
| + }
|
| + }
|
| + else { /* non-0 res */
|
| + if (adjust<0) { /* 0-padding needed */
|
| + if ((res->digits-adjust)>set->digits) {
|
| + adjust=res->digits-set->digits; /* to fit exactly */
|
| + *status|=DEC_Rounded; /* [but exact] */
|
| + }
|
| + res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
|
| + res->exponent+=adjust; /* set the exponent. */
|
| + }
|
| + } /* non-0 res */
|
| + #if DECSUBSET
|
| + } /* extended */
|
| + #endif
|
| + decFinish(res, set, &residue, status); /* clean and finalize */
|
| + break;}
|
| +
|
| + if (ISZERO(rhs)) { /* [lhs is non-zero] */
|
| + Int adjust; /* work */
|
| + Int rexp=rhs->exponent; /* save in case RHS==RES */
|
| + bits=rhs->bits; /* be clean */
|
| + residue=0; /* clear accumulator */
|
| + decCopyFit(res, lhs, set, &residue, status); /* copy (as needed) */
|
| + #if DECSUBSET
|
| + if (set->extended) { /* exponents on zeros count */
|
| + #endif
|
| + /* exponent will be the lower of the two */
|
| + /* [0-0 case handled above] */
|
| + adjust=rexp-res->exponent; /* adjustment needed [if -ve] */
|
| + if (adjust<0) { /* 0-padding needed */
|
| + if ((res->digits-adjust)>set->digits) {
|
| + adjust=res->digits-set->digits; /* to fit exactly */
|
| + *status|=DEC_Rounded; /* [but exact] */
|
| + }
|
| + res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
|
| + res->exponent+=adjust; /* set the exponent. */
|
| + }
|
| + #if DECSUBSET
|
| + } /* extended */
|
| + #endif
|
| + decFinish(res, set, &residue, status); /* clean and finalize */
|
| + break;}
|
| +
|
| + /* [NB: both fastpath and mainpath code below assume these cases */
|
| + /* (notably 0-0) have already been handled] */
|
| +
|
| + /* calculate the padding needed to align the operands */
|
| + padding=rhs->exponent-lhs->exponent;
|
| +
|
| + /* Fastpath cases where the numbers are aligned and normal, the RHS */
|
| + /* is all in one unit, no operand rounding is needed, and no carry, */
|
| + /* lengthening, or borrow is needed */
|
| + if (padding==0
|
| + && rhs->digits<=DECDPUN
|
| + && rhs->exponent>=set->emin /* [some normals drop through] */
|
| + && rhs->exponent<=set->emax-set->digits+1 /* [could clamp] */
|
| + && rhs->digits<=reqdigits
|
| + && lhs->digits<=reqdigits) {
|
| + Int partial=*lhs->lsu;
|
| + if (!diffsign) { /* adding */
|
| + partial+=*rhs->lsu;
|
| + if ((partial<=DECDPUNMAX) /* result fits in unit */
|
| + && (lhs->digits>=DECDPUN || /* .. and no digits-count change */
|
| + partial<(Int)powers[lhs->digits])) { /* .. */
|
| + if (res!=lhs) uprv_decNumberCopy(res, lhs); /* not in place */
|
| + *res->lsu=(Unit)partial; /* [copy could have overwritten RHS] */
|
| + break;
|
| + }
|
| + /* else drop out for careful add */
|
| + }
|
| + else { /* signs differ */
|
| + partial-=*rhs->lsu;
|
| + if (partial>0) { /* no borrow needed, and non-0 result */
|
| + if (res!=lhs) uprv_decNumberCopy(res, lhs); /* not in place */
|
| + *res->lsu=(Unit)partial;
|
| + /* this could have reduced digits [but result>0] */
|
| + res->digits=decGetDigits(res->lsu, D2U(res->digits));
|
| + break;
|
| + }
|
| + /* else drop out for careful subtract */
|
| + }
|
| + }
|
| +
|
| + /* Now align (pad) the lhs or rhs so they can be added or */
|
| + /* subtracted, as necessary. If one number is much larger than */
|
| + /* the other (that is, if in plain form there is a least one */
|
| + /* digit between the lowest digit of one and the highest of the */
|
| + /* other) padding with up to DIGITS-1 trailing zeros may be */
|
| + /* needed; then apply rounding (as exotic rounding modes may be */
|
| + /* affected by the residue). */
|
| + rhsshift=0; /* rhs shift to left (padding) in Units */
|
| + bits=lhs->bits; /* assume sign is that of LHS */
|
| + mult=1; /* likely multiplier */
|
| +
|
| + /* [if padding==0 the operands are aligned; no padding is needed] */
|
| + if (padding!=0) {
|
| + /* some padding needed; always pad the RHS, as any required */
|
| + /* padding can then be effected by a simple combination of */
|
| + /* shifts and a multiply */
|
| + Flag swapped=0;
|
| + if (padding<0) { /* LHS needs the padding */
|
| + const decNumber *t;
|
| + padding=-padding; /* will be +ve */
|
| + bits=(uByte)(rhs->bits^negate); /* assumed sign is now that of RHS */
|
| + t=lhs; lhs=rhs; rhs=t;
|
| + swapped=1;
|
| + }
|
| +
|
| + /* If, after pad, rhs would be longer than lhs by digits+1 or */
|
| + /* more then lhs cannot affect the answer, except as a residue, */
|
| + /* so only need to pad up to a length of DIGITS+1. */
|
| + if (rhs->digits+padding > lhs->digits+reqdigits+1) {
|
| + /* The RHS is sufficient */
|
| + /* for residue use the relative sign indication... */
|
| + Int shift=reqdigits-rhs->digits; /* left shift needed */
|
| + residue=1; /* residue for rounding */
|
| + if (diffsign) residue=-residue; /* signs differ */
|
| + /* copy, shortening if necessary */
|
| + decCopyFit(res, rhs, set, &residue, status);
|
| + /* if it was already shorter, then need to pad with zeros */
|
| + if (shift>0) {
|
| + res->digits=decShiftToMost(res->lsu, res->digits, shift);
|
| + res->exponent-=shift; /* adjust the exponent. */
|
| + }
|
| + /* flip the result sign if unswapped and rhs was negated */
|
| + if (!swapped) res->bits^=negate;
|
| + decFinish(res, set, &residue, status); /* done */
|
| + break;}
|
| +
|
| + /* LHS digits may affect result */
|
| + rhsshift=D2U(padding+1)-1; /* this much by Unit shift .. */
|
| + mult=powers[padding-(rhsshift*DECDPUN)]; /* .. this by multiplication */
|
| + } /* padding needed */
|
| +
|
| + if (diffsign) mult=-mult; /* signs differ */
|
| +
|
| + /* determine the longer operand */
|
| + maxdigits=rhs->digits+padding; /* virtual length of RHS */
|
| + if (lhs->digits>maxdigits) maxdigits=lhs->digits;
|
| +
|
| + /* Decide on the result buffer to use; if possible place directly */
|
| + /* into result. */
|
| + acc=res->lsu; /* assume add direct to result */
|
| + /* If destructive overlap, or the number is too long, or a carry or */
|
| + /* borrow to DIGITS+1 might be possible, a buffer must be used. */
|
| + /* [Might be worth more sophisticated tests when maxdigits==reqdigits] */
|
| + if ((maxdigits>=reqdigits) /* is, or could be, too large */
|
| + || (res==rhs && rhsshift>0)) { /* destructive overlap */
|
| + /* buffer needed, choose it; units for maxdigits digits will be */
|
| + /* needed, +1 Unit for carry or borrow */
|
| + Int need=D2U(maxdigits)+1;
|
| + acc=accbuff; /* assume use local buffer */
|
| + if (need*sizeof(Unit)>sizeof(accbuff)) {
|
| + /* printf("malloc add %ld %ld\n", need, sizeof(accbuff)); */
|
| + allocacc=(Unit *)malloc(need*sizeof(Unit));
|
| + if (allocacc==NULL) { /* hopeless -- abandon */
|
| + *status|=DEC_Insufficient_storage;
|
| + break;}
|
| + acc=allocacc;
|
| + }
|
| + }
|
| +
|
| + res->bits=(uByte)(bits&DECNEG); /* it's now safe to overwrite.. */
|
| + res->exponent=lhs->exponent; /* .. operands (even if aliased) */
|
| +
|
| + #if DECTRACE
|
| + decDumpAr('A', lhs->lsu, D2U(lhs->digits));
|
| + decDumpAr('B', rhs->lsu, D2U(rhs->digits));
|
| + printf(" :h: %ld %ld\n", rhsshift, mult);
|
| + #endif
|
| +
|
| + /* add [A+B*m] or subtract [A+B*(-m)] */
|
| + res->digits=decUnitAddSub(lhs->lsu, D2U(lhs->digits),
|
| + rhs->lsu, D2U(rhs->digits),
|
| + rhsshift, acc, mult)
|
| + *DECDPUN; /* [units -> digits] */
|
| + if (res->digits<0) { /* borrowed... */
|
| + res->digits=-res->digits;
|
| + res->bits^=DECNEG; /* flip the sign */
|
| + }
|
| + #if DECTRACE
|
| + decDumpAr('+', acc, D2U(res->digits));
|
| + #endif
|
| +
|
| + /* If a buffer was used the result must be copied back, possibly */
|
| + /* shortening. (If no buffer was used then the result must have */
|
| + /* fit, so can't need rounding and residue must be 0.) */
|
| + residue=0; /* clear accumulator */
|
| + if (acc!=res->lsu) {
|
| + #if DECSUBSET
|
| + if (set->extended) { /* round from first significant digit */
|
| + #endif
|
| + /* remove leading zeros that were added due to rounding up to */
|
| + /* integral Units -- before the test for rounding. */
|
| + if (res->digits>reqdigits)
|
| + res->digits=decGetDigits(acc, D2U(res->digits));
|
| + decSetCoeff(res, set, acc, res->digits, &residue, status);
|
| + #if DECSUBSET
|
| + }
|
| + else { /* subset arithmetic rounds from original significant digit */
|
| + /* May have an underestimate. This only occurs when both */
|
| + /* numbers fit in DECDPUN digits and are padding with a */
|
| + /* negative multiple (-10, -100...) and the top digit(s) become */
|
| + /* 0. (This only matters when using X3.274 rules where the */
|
| + /* leading zero could be included in the rounding.) */
|
| + if (res->digits<maxdigits) {
|
| + *(acc+D2U(res->digits))=0; /* ensure leading 0 is there */
|
| + res->digits=maxdigits;
|
| + }
|
| + else {
|
| + /* remove leading zeros that added due to rounding up to */
|
| + /* integral Units (but only those in excess of the original */
|
| + /* maxdigits length, unless extended) before test for rounding. */
|
| + if (res->digits>reqdigits) {
|
| + res->digits=decGetDigits(acc, D2U(res->digits));
|
| + if (res->digits<maxdigits) res->digits=maxdigits;
|
| + }
|
| + }
|
| + decSetCoeff(res, set, acc, res->digits, &residue, status);
|
| + /* Now apply rounding if needed before removing leading zeros. */
|
| + /* This is safe because subnormals are not a possibility */
|
| + if (residue!=0) {
|
| + decApplyRound(res, set, residue, status);
|
| + residue=0; /* did what needed to be done */
|
| + }
|
| + } /* subset */
|
| + #endif
|
| + } /* used buffer */
|
| +
|
| + /* strip leading zeros [these were left on in case of subset subtract] */
|
| + res->digits=decGetDigits(res->lsu, D2U(res->digits));
|
| +
|
| + /* apply checks and rounding */
|
| + decFinish(res, set, &residue, status);
|
| +
|
| + /* "When the sum of two operands with opposite signs is exactly */
|
| + /* zero, the sign of that sum shall be '+' in all rounding modes */
|
| + /* except round toward -Infinity, in which mode that sign shall be */
|
| + /* '-'." [Subset zeros also never have '-', set by decFinish.] */
|
| + if (ISZERO(res) && diffsign
|
| + #if DECSUBSET
|
| + && set->extended
|
| + #endif
|
| + && (*status&DEC_Inexact)==0) {
|
| + if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG; /* sign - */
|
| + else res->bits&=~DECNEG; /* sign + */
|
| + }
|
| + } while(0); /* end protected */
|
| +
|
| + if (allocacc!=NULL) free(allocacc); /* drop any storage used */
|
| + #if DECSUBSET
|
| + if (allocrhs!=NULL) free(allocrhs); /* .. */
|
| + if (alloclhs!=NULL) free(alloclhs); /* .. */
|
| + #endif
|
| + return res;
|
| + } /* decAddOp */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decDivideOp -- division operation */
|
| +/* */
|
| +/* This routine performs the calculations for all four division */
|
| +/* operators (divide, divideInteger, remainder, remainderNear). */
|
| +/* */
|
| +/* C=A op B */
|
| +/* */
|
| +/* res is C, the result. C may be A and/or B (e.g., X=X/X) */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* set is the context */
|
| +/* op is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively. */
|
| +/* status is the usual accumulator */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* */
|
| +/* ------------------------------------------------------------------ */
|
| +/* The underlying algorithm of this routine is the same as in the */
|
| +/* 1981 S/370 implementation, that is, non-restoring long division */
|
| +/* with bi-unit (rather than bi-digit) estimation for each unit */
|
| +/* multiplier. In this pseudocode overview, complications for the */
|
| +/* Remainder operators and division residues for exact rounding are */
|
| +/* omitted for clarity. */
|
| +/* */
|
| +/* Prepare operands and handle special values */
|
| +/* Test for x/0 and then 0/x */
|
| +/* Exp =Exp1 - Exp2 */
|
| +/* Exp =Exp +len(var1) -len(var2) */
|
| +/* Sign=Sign1 * Sign2 */
|
| +/* Pad accumulator (Var1) to double-length with 0's (pad1) */
|
| +/* Pad Var2 to same length as Var1 */
|
| +/* msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round */
|
| +/* have=0 */
|
| +/* Do until (have=digits+1 OR residue=0) */
|
| +/* if exp<0 then if integer divide/residue then leave */
|
| +/* this_unit=0 */
|
| +/* Do forever */
|
| +/* compare numbers */
|
| +/* if <0 then leave inner_loop */
|
| +/* if =0 then (* quick exit without subtract *) do */
|
| +/* this_unit=this_unit+1; output this_unit */
|
| +/* leave outer_loop; end */
|
| +/* Compare lengths of numbers (mantissae): */
|
| +/* If same then tops2=msu2pair -- {units 1&2 of var2} */
|
| +/* else tops2=msu2plus -- {0, unit 1 of var2} */
|
| +/* tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */
|
| +/* mult=tops1/tops2 -- Good and safe guess at divisor */
|
| +/* if mult=0 then mult=1 */
|
| +/* this_unit=this_unit+mult */
|
| +/* subtract */
|
| +/* end inner_loop */
|
| +/* if have\=0 | this_unit\=0 then do */
|
| +/* output this_unit */
|
| +/* have=have+1; end */
|
| +/* var2=var2/10 */
|
| +/* exp=exp-1 */
|
| +/* end outer_loop */
|
| +/* exp=exp+1 -- set the proper exponent */
|
| +/* if have=0 then generate answer=0 */
|
| +/* Return (Result is defined by Var1) */
|
| +/* */
|
| +/* ------------------------------------------------------------------ */
|
| +/* Two working buffers are needed during the division; one (digits+ */
|
| +/* 1) to accumulate the result, and the other (up to 2*digits+1) for */
|
| +/* long subtractions. These are acc and var1 respectively. */
|
| +/* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/
|
| +/* The static buffers may be larger than might be expected to allow */
|
| +/* for calls from higher-level funtions (notable exp). */
|
| +/* ------------------------------------------------------------------ */
|
| +static decNumber * decDivideOp(decNumber *res,
|
| + const decNumber *lhs, const decNumber *rhs,
|
| + decContext *set, Flag op, uInt *status) {
|
| + #if DECSUBSET
|
| + decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */
|
| + decNumber *allocrhs=NULL; /* .., rhs */
|
| + #endif
|
| + Unit accbuff[SD2U(DECBUFFER+DECDPUN+10)]; /* local buffer */
|
| + Unit *acc=accbuff; /* -> accumulator array for result */
|
| + Unit *allocacc=NULL; /* -> allocated buffer, iff allocated */
|
| + Unit *accnext; /* -> where next digit will go */
|
| + Int acclength; /* length of acc needed [Units] */
|
| + Int accunits; /* count of units accumulated */
|
| + Int accdigits; /* count of digits accumulated */
|
| +
|
| + Unit varbuff[SD2U(DECBUFFER*2+DECDPUN)]; /* buffer for var1 */
|
| + Unit *var1=varbuff; /* -> var1 array for long subtraction */
|
| + Unit *varalloc=NULL; /* -> allocated buffer, iff used */
|
| + Unit *msu1; /* -> msu of var1 */
|
| +
|
| + const Unit *var2; /* -> var2 array */
|
| + const Unit *msu2; /* -> msu of var2 */
|
| + Int msu2plus; /* msu2 plus one [does not vary] */
|
| + eInt msu2pair; /* msu2 pair plus one [does not vary] */
|
| +
|
| + Int var1units, var2units; /* actual lengths */
|
| + Int var2ulen; /* logical length (units) */
|
| + Int var1initpad=0; /* var1 initial padding (digits) */
|
| + Int maxdigits; /* longest LHS or required acc length */
|
| + Int mult; /* multiplier for subtraction */
|
| + Unit thisunit; /* current unit being accumulated */
|
| + Int residue; /* for rounding */
|
| + Int reqdigits=set->digits; /* requested DIGITS */
|
| + Int exponent; /* working exponent */
|
| + Int maxexponent=0; /* DIVIDE maximum exponent if unrounded */
|
| + uByte bits; /* working sign */
|
| + Unit *target; /* work */
|
| + const Unit *source; /* .. */
|
| + uInt const *pow; /* .. */
|
| + Int shift, cut; /* .. */
|
| + #if DECSUBSET
|
| + Int dropped; /* work */
|
| + #endif
|
| +
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| + #endif
|
| +
|
| + do { /* protect allocated storage */
|
| + #if DECSUBSET
|
| + if (!set->extended) {
|
| + /* reduce operands and set lostDigits status, as needed */
|
| + if (lhs->digits>reqdigits) {
|
| + alloclhs=decRoundOperand(lhs, set, status);
|
| + if (alloclhs==NULL) break;
|
| + lhs=alloclhs;
|
| + }
|
| + if (rhs->digits>reqdigits) {
|
| + allocrhs=decRoundOperand(rhs, set, status);
|
| + if (allocrhs==NULL) break;
|
| + rhs=allocrhs;
|
| + }
|
| + }
|
| + #endif
|
| + /* [following code does not require input rounding] */
|
| +
|
| + bits=(lhs->bits^rhs->bits)&DECNEG; /* assumed sign for divisions */
|
| +
|
| + /* handle infinities and NaNs */
|
| + if (SPECIALARGS) { /* a special bit set */
|
| + if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */
|
| + decNaNs(res, lhs, rhs, set, status);
|
| + break;
|
| + }
|
| + /* one or two infinities */
|
| + if (decNumberIsInfinite(lhs)) { /* LHS (dividend) is infinite */
|
| + if (decNumberIsInfinite(rhs) || /* two infinities are invalid .. */
|
| + op & (REMAINDER | REMNEAR)) { /* as is remainder of infinity */
|
| + *status|=DEC_Invalid_operation;
|
| + break;
|
| + }
|
| + /* [Note that infinity/0 raises no exceptions] */
|
| + uprv_decNumberZero(res);
|
| + res->bits=bits|DECINF; /* set +/- infinity */
|
| + break;
|
| + }
|
| + else { /* RHS (divisor) is infinite */
|
| + residue=0;
|
| + if (op&(REMAINDER|REMNEAR)) {
|
| + /* result is [finished clone of] lhs */
|
| + decCopyFit(res, lhs, set, &residue, status);
|
| + }
|
| + else { /* a division */
|
| + uprv_decNumberZero(res);
|
| + res->bits=bits; /* set +/- zero */
|
| + /* for DIVIDEINT the exponent is always 0. For DIVIDE, result */
|
| + /* is a 0 with infinitely negative exponent, clamped to minimum */
|
| + if (op&DIVIDE) {
|
| + res->exponent=set->emin-set->digits+1;
|
| + *status|=DEC_Clamped;
|
| + }
|
| + }
|
| + decFinish(res, set, &residue, status);
|
| + break;
|
| + }
|
| + }
|
| +
|
| + /* handle 0 rhs (x/0) */
|
| + if (ISZERO(rhs)) { /* x/0 is always exceptional */
|
| + if (ISZERO(lhs)) {
|
| + uprv_decNumberZero(res); /* [after lhs test] */
|
| + *status|=DEC_Division_undefined;/* 0/0 will become NaN */
|
| + }
|
| + else {
|
| + uprv_decNumberZero(res);
|
| + if (op&(REMAINDER|REMNEAR)) *status|=DEC_Invalid_operation;
|
| + else {
|
| + *status|=DEC_Division_by_zero; /* x/0 */
|
| + res->bits=bits|DECINF; /* .. is +/- Infinity */
|
| + }
|
| + }
|
| + break;}
|
| +
|
| + /* handle 0 lhs (0/x) */
|
| + if (ISZERO(lhs)) { /* 0/x [x!=0] */
|
| + #if DECSUBSET
|
| + if (!set->extended) uprv_decNumberZero(res);
|
| + else {
|
| + #endif
|
| + if (op&DIVIDE) {
|
| + residue=0;
|
| + exponent=lhs->exponent-rhs->exponent; /* ideal exponent */
|
| + uprv_decNumberCopy(res, lhs); /* [zeros always fit] */
|
| + res->bits=bits; /* sign as computed */
|
| + res->exponent=exponent; /* exponent, too */
|
| + decFinalize(res, set, &residue, status); /* check exponent */
|
| + }
|
| + else if (op&DIVIDEINT) {
|
| + uprv_decNumberZero(res); /* integer 0 */
|
| + res->bits=bits; /* sign as computed */
|
| + }
|
| + else { /* a remainder */
|
| + exponent=rhs->exponent; /* [save in case overwrite] */
|
| + uprv_decNumberCopy(res, lhs); /* [zeros always fit] */
|
| + if (exponent<res->exponent) res->exponent=exponent; /* use lower */
|
| + }
|
| + #if DECSUBSET
|
| + }
|
| + #endif
|
| + break;}
|
| +
|
| + /* Precalculate exponent. This starts off adjusted (and hence fits */
|
| + /* in 31 bits) and becomes the usual unadjusted exponent as the */
|
| + /* division proceeds. The order of evaluation is important, here, */
|
| + /* to avoid wrap. */
|
| + exponent=(lhs->exponent+lhs->digits)-(rhs->exponent+rhs->digits);
|
| +
|
| + /* If the working exponent is -ve, then some quick exits are */
|
| + /* possible because the quotient is known to be <1 */
|
| + /* [for REMNEAR, it needs to be < -1, as -0.5 could need work] */
|
| + if (exponent<0 && !(op==DIVIDE)) {
|
| + if (op&DIVIDEINT) {
|
| + uprv_decNumberZero(res); /* integer part is 0 */
|
| + #if DECSUBSET
|
| + if (set->extended)
|
| + #endif
|
| + res->bits=bits; /* set +/- zero */
|
| + break;}
|
| + /* fastpath remainders so long as the lhs has the smaller */
|
| + /* (or equal) exponent */
|
| + if (lhs->exponent<=rhs->exponent) {
|
| + if (op&REMAINDER || exponent<-1) {
|
| + /* It is REMAINDER or safe REMNEAR; result is [finished */
|
| + /* clone of] lhs (r = x - 0*y) */
|
| + residue=0;
|
| + decCopyFit(res, lhs, set, &residue, status);
|
| + decFinish(res, set, &residue, status);
|
| + break;
|
| + }
|
| + /* [unsafe REMNEAR drops through] */
|
| + }
|
| + } /* fastpaths */
|
| +
|
| + /* Long (slow) division is needed; roll up the sleeves... */
|
| +
|
| + /* The accumulator will hold the quotient of the division. */
|
| + /* If it needs to be too long for stack storage, then allocate. */
|
| + acclength=D2U(reqdigits+DECDPUN); /* in Units */
|
| + if (acclength*sizeof(Unit)>sizeof(accbuff)) {
|
| + /* printf("malloc dvacc %ld units\n", acclength); */
|
| + allocacc=(Unit *)malloc(acclength*sizeof(Unit));
|
| + if (allocacc==NULL) { /* hopeless -- abandon */
|
| + *status|=DEC_Insufficient_storage;
|
| + break;}
|
| + acc=allocacc; /* use the allocated space */
|
| + }
|
| +
|
| + /* var1 is the padded LHS ready for subtractions. */
|
| + /* If it needs to be too long for stack storage, then allocate. */
|
| + /* The maximum units needed for var1 (long subtraction) is: */
|
| + /* Enough for */
|
| + /* (rhs->digits+reqdigits-1) -- to allow full slide to right */
|
| + /* or (lhs->digits) -- to allow for long lhs */
|
| + /* whichever is larger */
|
| + /* +1 -- for rounding of slide to right */
|
| + /* +1 -- for leading 0s */
|
| + /* +1 -- for pre-adjust if a remainder or DIVIDEINT */
|
| + /* [Note: unused units do not participate in decUnitAddSub data] */
|
| + maxdigits=rhs->digits+reqdigits-1;
|
| + if (lhs->digits>maxdigits) maxdigits=lhs->digits;
|
| + var1units=D2U(maxdigits)+2;
|
| + /* allocate a guard unit above msu1 for REMAINDERNEAR */
|
| + if (!(op&DIVIDE)) var1units++;
|
| + if ((var1units+1)*sizeof(Unit)>sizeof(varbuff)) {
|
| + /* printf("malloc dvvar %ld units\n", var1units+1); */
|
| + varalloc=(Unit *)malloc((var1units+1)*sizeof(Unit));
|
| + if (varalloc==NULL) { /* hopeless -- abandon */
|
| + *status|=DEC_Insufficient_storage;
|
| + break;}
|
| + var1=varalloc; /* use the allocated space */
|
| + }
|
| +
|
| + /* Extend the lhs and rhs to full long subtraction length. The lhs */
|
| + /* is truly extended into the var1 buffer, with 0 padding, so a */
|
| + /* subtract in place is always possible. The rhs (var2) has */
|
| + /* virtual padding (implemented by decUnitAddSub). */
|
| + /* One guard unit was allocated above msu1 for rem=rem+rem in */
|
| + /* REMAINDERNEAR. */
|
| + msu1=var1+var1units-1; /* msu of var1 */
|
| + source=lhs->lsu+D2U(lhs->digits)-1; /* msu of input array */
|
| + for (target=msu1; source>=lhs->lsu; source--, target--) *target=*source;
|
| + for (; target>=var1; target--) *target=0;
|
| +
|
| + /* rhs (var2) is left-aligned with var1 at the start */
|
| + var2ulen=var1units; /* rhs logical length (units) */
|
| + var2units=D2U(rhs->digits); /* rhs actual length (units) */
|
| + var2=rhs->lsu; /* -> rhs array */
|
| + msu2=var2+var2units-1; /* -> msu of var2 [never changes] */
|
| + /* now set up the variables which will be used for estimating the */
|
| + /* multiplication factor. If these variables are not exact, add */
|
| + /* 1 to make sure that the multiplier is never overestimated. */
|
| + msu2plus=*msu2; /* it's value .. */
|
| + if (var2units>1) msu2plus++; /* .. +1 if any more */
|
| + msu2pair=(eInt)*msu2*(DECDPUNMAX+1);/* top two pair .. */
|
| + if (var2units>1) { /* .. [else treat 2nd as 0] */
|
| + msu2pair+=*(msu2-1); /* .. */
|
| + if (var2units>2) msu2pair++; /* .. +1 if any more */
|
| + }
|
| +
|
| + /* The calculation is working in units, which may have leading zeros, */
|
| + /* but the exponent was calculated on the assumption that they are */
|
| + /* both left-aligned. Adjust the exponent to compensate: add the */
|
| + /* number of leading zeros in var1 msu and subtract those in var2 msu. */
|
| + /* [This is actually done by counting the digits and negating, as */
|
| + /* lead1=DECDPUN-digits1, and similarly for lead2.] */
|
| + for (pow=&powers[1]; *msu1>=*pow; pow++) exponent--;
|
| + for (pow=&powers[1]; *msu2>=*pow; pow++) exponent++;
|
| +
|
| + /* Now, if doing an integer divide or remainder, ensure that */
|
| + /* the result will be Unit-aligned. To do this, shift the var1 */
|
| + /* accumulator towards least if need be. (It's much easier to */
|
| + /* do this now than to reassemble the residue afterwards, if */
|
| + /* doing a remainder.) Also ensure the exponent is not negative. */
|
| + if (!(op&DIVIDE)) {
|
| + Unit *u; /* work */
|
| + /* save the initial 'false' padding of var1, in digits */
|
| + var1initpad=(var1units-D2U(lhs->digits))*DECDPUN;
|
| + /* Determine the shift to do. */
|
| + if (exponent<0) cut=-exponent;
|
| + else cut=DECDPUN-exponent%DECDPUN;
|
| + decShiftToLeast(var1, var1units, cut);
|
| + exponent+=cut; /* maintain numerical value */
|
| + var1initpad-=cut; /* .. and reduce padding */
|
| + /* clean any most-significant units which were just emptied */
|
| + for (u=msu1; cut>=DECDPUN; cut-=DECDPUN, u--) *u=0;
|
| + } /* align */
|
| + else { /* is DIVIDE */
|
| + maxexponent=lhs->exponent-rhs->exponent; /* save */
|
| + /* optimization: if the first iteration will just produce 0, */
|
| + /* preadjust to skip it [valid for DIVIDE only] */
|
| + if (*msu1<*msu2) {
|
| + var2ulen--; /* shift down */
|
| + exponent-=DECDPUN; /* update the exponent */
|
| + }
|
| + }
|
| +
|
| + /* ---- start the long-division loops ------------------------------ */
|
| + accunits=0; /* no units accumulated yet */
|
| + accdigits=0; /* .. or digits */
|
| + accnext=acc+acclength-1; /* -> msu of acc [NB: allows digits+1] */
|
| + for (;;) { /* outer forever loop */
|
| + thisunit=0; /* current unit assumed 0 */
|
| + /* find the next unit */
|
| + for (;;) { /* inner forever loop */
|
| + /* strip leading zero units [from either pre-adjust or from */
|
| + /* subtract last time around]. Leave at least one unit. */
|
| + for (; *msu1==0 && msu1>var1; msu1--) var1units--;
|
| +
|
| + if (var1units<var2ulen) break; /* var1 too low for subtract */
|
| + if (var1units==var2ulen) { /* unit-by-unit compare needed */
|
| + /* compare the two numbers, from msu */
|
| + const Unit *pv1, *pv2;
|
| + Unit v2; /* units to compare */
|
| + pv2=msu2; /* -> msu */
|
| + for (pv1=msu1; ; pv1--, pv2--) {
|
| + /* v1=*pv1 -- always OK */
|
| + v2=0; /* assume in padding */
|
| + if (pv2>=var2) v2=*pv2; /* in range */
|
| + if (*pv1!=v2) break; /* no longer the same */
|
| + if (pv1==var1) break; /* done; leave pv1 as is */
|
| + }
|
| + /* here when all inspected or a difference seen */
|
| + if (*pv1<v2) break; /* var1 too low to subtract */
|
| + if (*pv1==v2) { /* var1 == var2 */
|
| + /* reach here if var1 and var2 are identical; subtraction */
|
| + /* would increase digit by one, and the residue will be 0 so */
|
| + /* the calculation is done; leave the loop with residue=0. */
|
| + thisunit++; /* as though subtracted */
|
| + *var1=0; /* set var1 to 0 */
|
| + var1units=1; /* .. */
|
| + break; /* from inner */
|
| + } /* var1 == var2 */
|
| + /* *pv1>v2. Prepare for real subtraction; the lengths are equal */
|
| + /* Estimate the multiplier (there's always a msu1-1)... */
|
| + /* Bring in two units of var2 to provide a good estimate. */
|
| + mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2pair);
|
| + } /* lengths the same */
|
| + else { /* var1units > var2ulen, so subtraction is safe */
|
| + /* The var2 msu is one unit towards the lsu of the var1 msu, */
|
| + /* so only one unit for var2 can be used. */
|
| + mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2plus);
|
| + }
|
| + if (mult==0) mult=1; /* must always be at least 1 */
|
| + /* subtraction needed; var1 is > var2 */
|
| + thisunit=(Unit)(thisunit+mult); /* accumulate */
|
| + /* subtract var1-var2, into var1; only the overlap needs */
|
| + /* processing, as this is an in-place calculation */
|
| + shift=var2ulen-var2units;
|
| + #if DECTRACE
|
| + decDumpAr('1', &var1[shift], var1units-shift);
|
| + decDumpAr('2', var2, var2units);
|
| + printf("m=%ld\n", -mult);
|
| + #endif
|
| + decUnitAddSub(&var1[shift], var1units-shift,
|
| + var2, var2units, 0,
|
| + &var1[shift], -mult);
|
| + #if DECTRACE
|
| + decDumpAr('#', &var1[shift], var1units-shift);
|
| + #endif
|
| + /* var1 now probably has leading zeros; these are removed at the */
|
| + /* top of the inner loop. */
|
| + } /* inner loop */
|
| +
|
| + /* The next unit has been calculated in full; unless it's a */
|
| + /* leading zero, add to acc */
|
| + if (accunits!=0 || thisunit!=0) { /* is first or non-zero */
|
| + *accnext=thisunit; /* store in accumulator */
|
| + /* account exactly for the new digits */
|
| + if (accunits==0) {
|
| + accdigits++; /* at least one */
|
| + for (pow=&powers[1]; thisunit>=*pow; pow++) accdigits++;
|
| + }
|
| + else accdigits+=DECDPUN;
|
| + accunits++; /* update count */
|
| + accnext--; /* ready for next */
|
| + if (accdigits>reqdigits) break; /* have enough digits */
|
| + }
|
| +
|
| + /* if the residue is zero, the operation is done (unless divide */
|
| + /* or divideInteger and still not enough digits yet) */
|
| + if (*var1==0 && var1units==1) { /* residue is 0 */
|
| + if (op&(REMAINDER|REMNEAR)) break;
|
| + if ((op&DIVIDE) && (exponent<=maxexponent)) break;
|
| + /* [drop through if divideInteger] */
|
| + }
|
| + /* also done enough if calculating remainder or integer */
|
| + /* divide and just did the last ('units') unit */
|
| + if (exponent==0 && !(op&DIVIDE)) break;
|
| +
|
| + /* to get here, var1 is less than var2, so divide var2 by the per- */
|
| + /* Unit power of ten and go for the next digit */
|
| + var2ulen--; /* shift down */
|
| + exponent-=DECDPUN; /* update the exponent */
|
| + } /* outer loop */
|
| +
|
| + /* ---- division is complete --------------------------------------- */
|
| + /* here: acc has at least reqdigits+1 of good results (or fewer */
|
| + /* if early stop), starting at accnext+1 (its lsu) */
|
| + /* var1 has any residue at the stopping point */
|
| + /* accunits is the number of digits collected in acc */
|
| + if (accunits==0) { /* acc is 0 */
|
| + accunits=1; /* show have a unit .. */
|
| + accdigits=1; /* .. */
|
| + *accnext=0; /* .. whose value is 0 */
|
| + }
|
| + else accnext++; /* back to last placed */
|
| + /* accnext now -> lowest unit of result */
|
| +
|
| + residue=0; /* assume no residue */
|
| + if (op&DIVIDE) {
|
| + /* record the presence of any residue, for rounding */
|
| + if (*var1!=0 || var1units>1) residue=1;
|
| + else { /* no residue */
|
| + /* Had an exact division; clean up spurious trailing 0s. */
|
| + /* There will be at most DECDPUN-1, from the final multiply, */
|
| + /* and then only if the result is non-0 (and even) and the */
|
| + /* exponent is 'loose'. */
|
| + #if DECDPUN>1
|
| + Unit lsu=*accnext;
|
| + if (!(lsu&0x01) && (lsu!=0)) {
|
| + /* count the trailing zeros */
|
| + Int drop=0;
|
| + for (;; drop++) { /* [will terminate because lsu!=0] */
|
| + if (exponent>=maxexponent) break; /* don't chop real 0s */
|
| + #if DECDPUN<=4
|
| + if ((lsu-QUOT10(lsu, drop+1)
|
| + *powers[drop+1])!=0) break; /* found non-0 digit */
|
| + #else
|
| + if (lsu%powers[drop+1]!=0) break; /* found non-0 digit */
|
| + #endif
|
| + exponent++;
|
| + }
|
| + if (drop>0) {
|
| + accunits=decShiftToLeast(accnext, accunits, drop);
|
| + accdigits=decGetDigits(accnext, accunits);
|
| + accunits=D2U(accdigits);
|
| + /* [exponent was adjusted in the loop] */
|
| + }
|
| + } /* neither odd nor 0 */
|
| + #endif
|
| + } /* exact divide */
|
| + } /* divide */
|
| + else /* op!=DIVIDE */ {
|
| + /* check for coefficient overflow */
|
| + if (accdigits+exponent>reqdigits) {
|
| + *status|=DEC_Division_impossible;
|
| + break;
|
| + }
|
| + if (op & (REMAINDER|REMNEAR)) {
|
| + /* [Here, the exponent will be 0, because var1 was adjusted */
|
| + /* appropriately.] */
|
| + Int postshift; /* work */
|
| + Flag wasodd=0; /* integer was odd */
|
| + Unit *quotlsu; /* for save */
|
| + Int quotdigits; /* .. */
|
| +
|
| + bits=lhs->bits; /* remainder sign is always as lhs */
|
| +
|
| + /* Fastpath when residue is truly 0 is worthwhile [and */
|
| + /* simplifies the code below] */
|
| + if (*var1==0 && var1units==1) { /* residue is 0 */
|
| + Int exp=lhs->exponent; /* save min(exponents) */
|
| + if (rhs->exponent<exp) exp=rhs->exponent;
|
| + uprv_decNumberZero(res); /* 0 coefficient */
|
| + #if DECSUBSET
|
| + if (set->extended)
|
| + #endif
|
| + res->exponent=exp; /* .. with proper exponent */
|
| + res->bits=(uByte)(bits&DECNEG); /* [cleaned] */
|
| + decFinish(res, set, &residue, status); /* might clamp */
|
| + break;
|
| + }
|
| + /* note if the quotient was odd */
|
| + if (*accnext & 0x01) wasodd=1; /* acc is odd */
|
| + quotlsu=accnext; /* save in case need to reinspect */
|
| + quotdigits=accdigits; /* .. */
|
| +
|
| + /* treat the residue, in var1, as the value to return, via acc */
|
| + /* calculate the unused zero digits. This is the smaller of: */
|
| + /* var1 initial padding (saved above) */
|
| + /* var2 residual padding, which happens to be given by: */
|
| + postshift=var1initpad+exponent-lhs->exponent+rhs->exponent;
|
| + /* [the 'exponent' term accounts for the shifts during divide] */
|
| + if (var1initpad<postshift) postshift=var1initpad;
|
| +
|
| + /* shift var1 the requested amount, and adjust its digits */
|
| + var1units=decShiftToLeast(var1, var1units, postshift);
|
| + accnext=var1;
|
| + accdigits=decGetDigits(var1, var1units);
|
| + accunits=D2U(accdigits);
|
| +
|
| + exponent=lhs->exponent; /* exponent is smaller of lhs & rhs */
|
| + if (rhs->exponent<exponent) exponent=rhs->exponent;
|
| +
|
| + /* Now correct the result if doing remainderNear; if it */
|
| + /* (looking just at coefficients) is > rhs/2, or == rhs/2 and */
|
| + /* the integer was odd then the result should be rem-rhs. */
|
| + if (op&REMNEAR) {
|
| + Int compare, tarunits; /* work */
|
| + Unit *up; /* .. */
|
| + /* calculate remainder*2 into the var1 buffer (which has */
|
| + /* 'headroom' of an extra unit and hence enough space) */
|
| + /* [a dedicated 'double' loop would be faster, here] */
|
| + tarunits=decUnitAddSub(accnext, accunits, accnext, accunits,
|
| + 0, accnext, 1);
|
| + /* decDumpAr('r', accnext, tarunits); */
|
| +
|
| + /* Here, accnext (var1) holds tarunits Units with twice the */
|
| + /* remainder's coefficient, which must now be compared to the */
|
| + /* RHS. The remainder's exponent may be smaller than the RHS's. */
|
| + compare=decUnitCompare(accnext, tarunits, rhs->lsu, D2U(rhs->digits),
|
| + rhs->exponent-exponent);
|
| + if (compare==BADINT) { /* deep trouble */
|
| + *status|=DEC_Insufficient_storage;
|
| + break;}
|
| +
|
| + /* now restore the remainder by dividing by two; the lsu */
|
| + /* is known to be even. */
|
| + for (up=accnext; up<accnext+tarunits; up++) {
|
| + Int half; /* half to add to lower unit */
|
| + half=*up & 0x01;
|
| + *up/=2; /* [shift] */
|
| + if (!half) continue;
|
| + *(up-1)+=(DECDPUNMAX+1)/2;
|
| + }
|
| + /* [accunits still describes the original remainder length] */
|
| +
|
| + if (compare>0 || (compare==0 && wasodd)) { /* adjustment needed */
|
| + Int exp, expunits, exprem; /* work */
|
| + /* This is effectively causing round-up of the quotient, */
|
| + /* so if it was the rare case where it was full and all */
|
| + /* nines, it would overflow and hence division-impossible */
|
| + /* should be raised */
|
| + Flag allnines=0; /* 1 if quotient all nines */
|
| + if (quotdigits==reqdigits) { /* could be borderline */
|
| + for (up=quotlsu; ; up++) {
|
| + if (quotdigits>DECDPUN) {
|
| + if (*up!=DECDPUNMAX) break;/* non-nines */
|
| + }
|
| + else { /* this is the last Unit */
|
| + if (*up==powers[quotdigits]-1) allnines=1;
|
| + break;
|
| + }
|
| + quotdigits-=DECDPUN; /* checked those digits */
|
| + } /* up */
|
| + } /* borderline check */
|
| + if (allnines) {
|
| + *status|=DEC_Division_impossible;
|
| + break;}
|
| +
|
| + /* rem-rhs is needed; the sign will invert. Again, var1 */
|
| + /* can safely be used for the working Units array. */
|
| + exp=rhs->exponent-exponent; /* RHS padding needed */
|
| + /* Calculate units and remainder from exponent. */
|
| + expunits=exp/DECDPUN;
|
| + exprem=exp%DECDPUN;
|
| + /* subtract [A+B*(-m)]; the result will always be negative */
|
| + accunits=-decUnitAddSub(accnext, accunits,
|
| + rhs->lsu, D2U(rhs->digits),
|
| + expunits, accnext, -(Int)powers[exprem]);
|
| + accdigits=decGetDigits(accnext, accunits); /* count digits exactly */
|
| + accunits=D2U(accdigits); /* and recalculate the units for copy */
|
| + /* [exponent is as for original remainder] */
|
| + bits^=DECNEG; /* flip the sign */
|
| + }
|
| + } /* REMNEAR */
|
| + } /* REMAINDER or REMNEAR */
|
| + } /* not DIVIDE */
|
| +
|
| + /* Set exponent and bits */
|
| + res->exponent=exponent;
|
| + res->bits=(uByte)(bits&DECNEG); /* [cleaned] */
|
| +
|
| + /* Now the coefficient. */
|
| + decSetCoeff(res, set, accnext, accdigits, &residue, status);
|
| +
|
| + decFinish(res, set, &residue, status); /* final cleanup */
|
| +
|
| + #if DECSUBSET
|
| + /* If a divide then strip trailing zeros if subset [after round] */
|
| + if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, 1, &dropped);
|
| + #endif
|
| + } while(0); /* end protected */
|
| +
|
| + if (varalloc!=NULL) free(varalloc); /* drop any storage used */
|
| + if (allocacc!=NULL) free(allocacc); /* .. */
|
| + #if DECSUBSET
|
| + if (allocrhs!=NULL) free(allocrhs); /* .. */
|
| + if (alloclhs!=NULL) free(alloclhs); /* .. */
|
| + #endif
|
| + return res;
|
| + } /* decDivideOp */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decMultiplyOp -- multiplication operation */
|
| +/* */
|
| +/* This routine performs the multiplication C=A x B. */
|
| +/* */
|
| +/* res is C, the result. C may be A and/or B (e.g., X=X*X) */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* set is the context */
|
| +/* status is the usual accumulator */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* */
|
| +/* ------------------------------------------------------------------ */
|
| +/* 'Classic' multiplication is used rather than Karatsuba, as the */
|
| +/* latter would give only a minor improvement for the short numbers */
|
| +/* expected to be handled most (and uses much more memory). */
|
| +/* */
|
| +/* There are two major paths here: the general-purpose ('old code') */
|
| +/* path which handles all DECDPUN values, and a fastpath version */
|
| +/* which is used if 64-bit ints are available, DECDPUN<=4, and more */
|
| +/* than two calls to decUnitAddSub would be made. */
|
| +/* */
|
| +/* The fastpath version lumps units together into 8-digit or 9-digit */
|
| +/* chunks, and also uses a lazy carry strategy to minimise expensive */
|
| +/* 64-bit divisions. The chunks are then broken apart again into */
|
| +/* units for continuing processing. Despite this overhead, the */
|
| +/* fastpath can speed up some 16-digit operations by 10x (and much */
|
| +/* more for higher-precision calculations). */
|
| +/* */
|
| +/* A buffer always has to be used for the accumulator; in the */
|
| +/* fastpath, buffers are also always needed for the chunked copies of */
|
| +/* of the operand coefficients. */
|
| +/* Static buffers are larger than needed just for multiply, to allow */
|
| +/* for calls from other operations (notably exp). */
|
| +/* ------------------------------------------------------------------ */
|
| +#define FASTMUL (DECUSE64 && DECDPUN<5)
|
| +static decNumber * decMultiplyOp(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set,
|
| + uInt *status) {
|
| + Int accunits; /* Units of accumulator in use */
|
| + Int exponent; /* work */
|
| + Int residue=0; /* rounding residue */
|
| + uByte bits; /* result sign */
|
| + Unit *acc; /* -> accumulator Unit array */
|
| + Int needbytes; /* size calculator */
|
| + void *allocacc=NULL; /* -> allocated accumulator, iff allocated */
|
| + Unit accbuff[SD2U(DECBUFFER*4+1)]; /* buffer (+1 for DECBUFFER==0, */
|
| + /* *4 for calls from other operations) */
|
| + const Unit *mer, *mermsup; /* work */
|
| + Int madlength; /* Units in multiplicand */
|
| + Int shift; /* Units to shift multiplicand by */
|
| +
|
| + #if FASTMUL
|
| + /* if DECDPUN is 1 or 3 work in base 10**9, otherwise */
|
| + /* (DECDPUN is 2 or 4) then work in base 10**8 */
|
| + #if DECDPUN & 1 /* odd */
|
| + #define FASTBASE 1000000000 /* base */
|
| + #define FASTDIGS 9 /* digits in base */
|
| + #define FASTLAZY 18 /* carry resolution point [1->18] */
|
| + #else
|
| + #define FASTBASE 100000000
|
| + #define FASTDIGS 8
|
| + #define FASTLAZY 1844 /* carry resolution point [1->1844] */
|
| + #endif
|
| + /* three buffers are used, two for chunked copies of the operands */
|
| + /* (base 10**8 or base 10**9) and one base 2**64 accumulator with */
|
| + /* lazy carry evaluation */
|
| + uInt zlhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */
|
| + uInt *zlhi=zlhibuff; /* -> lhs array */
|
| + uInt *alloclhi=NULL; /* -> allocated buffer, iff allocated */
|
| + uInt zrhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */
|
| + uInt *zrhi=zrhibuff; /* -> rhs array */
|
| + uInt *allocrhi=NULL; /* -> allocated buffer, iff allocated */
|
| + uLong zaccbuff[(DECBUFFER*2+1)/4+2]; /* buffer (+1 for DECBUFFER==0) */
|
| + /* [allocacc is shared for both paths, as only one will run] */
|
| + uLong *zacc=zaccbuff; /* -> accumulator array for exact result */
|
| + #if DECDPUN==1
|
| + Int zoff; /* accumulator offset */
|
| + #endif
|
| + uInt *lip, *rip; /* item pointers */
|
| + uInt *lmsi, *rmsi; /* most significant items */
|
| + Int ilhs, irhs, iacc; /* item counts in the arrays */
|
| + Int lazy; /* lazy carry counter */
|
| + uLong lcarry; /* uLong carry */
|
| + uInt carry; /* carry (NB not uLong) */
|
| + Int count; /* work */
|
| + const Unit *cup; /* .. */
|
| + Unit *up; /* .. */
|
| + uLong *lp; /* .. */
|
| + Int p; /* .. */
|
| + #endif
|
| +
|
| + #if DECSUBSET
|
| + decNumber *alloclhs=NULL; /* -> allocated buffer, iff allocated */
|
| + decNumber *allocrhs=NULL; /* -> allocated buffer, iff allocated */
|
| + #endif
|
| +
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| + #endif
|
| +
|
| + /* precalculate result sign */
|
| + bits=(uByte)((lhs->bits^rhs->bits)&DECNEG);
|
| +
|
| + /* handle infinities and NaNs */
|
| + if (SPECIALARGS) { /* a special bit set */
|
| + if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */
|
| + decNaNs(res, lhs, rhs, set, status);
|
| + return res;}
|
| + /* one or two infinities; Infinity * 0 is invalid */
|
| + if (((lhs->bits & DECINF)==0 && ISZERO(lhs))
|
| + ||((rhs->bits & DECINF)==0 && ISZERO(rhs))) {
|
| + *status|=DEC_Invalid_operation;
|
| + return res;}
|
| + uprv_decNumberZero(res);
|
| + res->bits=bits|DECINF; /* infinity */
|
| + return res;}
|
| +
|
| + /* For best speed, as in DMSRCN [the original Rexx numerics */
|
| + /* module], use the shorter number as the multiplier (rhs) and */
|
| + /* the longer as the multiplicand (lhs) to minimise the number of */
|
| + /* adds (partial products) */
|
| + if (lhs->digits<rhs->digits) { /* swap... */
|
| + const decNumber *hold=lhs;
|
| + lhs=rhs;
|
| + rhs=hold;
|
| + }
|
| +
|
| + do { /* protect allocated storage */
|
| + #if DECSUBSET
|
| + if (!set->extended) {
|
| + /* reduce operands and set lostDigits status, as needed */
|
| + if (lhs->digits>set->digits) {
|
| + alloclhs=decRoundOperand(lhs, set, status);
|
| + if (alloclhs==NULL) break;
|
| + lhs=alloclhs;
|
| + }
|
| + if (rhs->digits>set->digits) {
|
| + allocrhs=decRoundOperand(rhs, set, status);
|
| + if (allocrhs==NULL) break;
|
| + rhs=allocrhs;
|
| + }
|
| + }
|
| + #endif
|
| + /* [following code does not require input rounding] */
|
| +
|
| + #if FASTMUL /* fastpath can be used */
|
| + /* use the fast path if there are enough digits in the shorter */
|
| + /* operand to make the setup and takedown worthwhile */
|
| + #define NEEDTWO (DECDPUN*2) /* within two decUnitAddSub calls */
|
| + if (rhs->digits>NEEDTWO) { /* use fastpath... */
|
| + /* calculate the number of elements in each array */
|
| + ilhs=(lhs->digits+FASTDIGS-1)/FASTDIGS; /* [ceiling] */
|
| + irhs=(rhs->digits+FASTDIGS-1)/FASTDIGS; /* .. */
|
| + iacc=ilhs+irhs;
|
| +
|
| + /* allocate buffers if required, as usual */
|
| + needbytes=ilhs*sizeof(uInt);
|
| + if (needbytes>(Int)sizeof(zlhibuff)) {
|
| + alloclhi=(uInt *)malloc(needbytes);
|
| + zlhi=alloclhi;}
|
| + needbytes=irhs*sizeof(uInt);
|
| + if (needbytes>(Int)sizeof(zrhibuff)) {
|
| + allocrhi=(uInt *)malloc(needbytes);
|
| + zrhi=allocrhi;}
|
| +
|
| + /* Allocating the accumulator space needs a special case when */
|
| + /* DECDPUN=1 because when converting the accumulator to Units */
|
| + /* after the multiplication each 8-byte item becomes 9 1-byte */
|
| + /* units. Therefore iacc extra bytes are needed at the front */
|
| + /* (rounded up to a multiple of 8 bytes), and the uLong */
|
| + /* accumulator starts offset the appropriate number of units */
|
| + /* to the right to avoid overwrite during the unchunking. */
|
| + needbytes=iacc*sizeof(uLong);
|
| + #if DECDPUN==1
|
| + zoff=(iacc+7)/8; /* items to offset by */
|
| + needbytes+=zoff*8;
|
| + #endif
|
| + if (needbytes>(Int)sizeof(zaccbuff)) {
|
| + allocacc=(uLong *)malloc(needbytes);
|
| + zacc=(uLong *)allocacc;}
|
| + if (zlhi==NULL||zrhi==NULL||zacc==NULL) {
|
| + *status|=DEC_Insufficient_storage;
|
| + break;}
|
| +
|
| + acc=(Unit *)zacc; /* -> target Unit array */
|
| + #if DECDPUN==1
|
| + zacc+=zoff; /* start uLong accumulator to right */
|
| + #endif
|
| +
|
| + /* assemble the chunked copies of the left and right sides */
|
| + for (count=lhs->digits, cup=lhs->lsu, lip=zlhi; count>0; lip++)
|
| + for (p=0, *lip=0; p<FASTDIGS && count>0;
|
| + p+=DECDPUN, cup++, count-=DECDPUN)
|
| + *lip+=*cup*powers[p];
|
| + lmsi=lip-1; /* save -> msi */
|
| + for (count=rhs->digits, cup=rhs->lsu, rip=zrhi; count>0; rip++)
|
| + for (p=0, *rip=0; p<FASTDIGS && count>0;
|
| + p+=DECDPUN, cup++, count-=DECDPUN)
|
| + *rip+=*cup*powers[p];
|
| + rmsi=rip-1; /* save -> msi */
|
| +
|
| + /* zero the accumulator */
|
| + for (lp=zacc; lp<zacc+iacc; lp++) *lp=0;
|
| +
|
| + /* Start the multiplication */
|
| + /* Resolving carries can dominate the cost of accumulating the */
|
| + /* partial products, so this is only done when necessary. */
|
| + /* Each uLong item in the accumulator can hold values up to */
|
| + /* 2**64-1, and each partial product can be as large as */
|
| + /* (10**FASTDIGS-1)**2. When FASTDIGS=9, this can be added to */
|
| + /* itself 18.4 times in a uLong without overflowing, so during */
|
| + /* the main calculation resolution is carried out every 18th */
|
| + /* add -- every 162 digits. Similarly, when FASTDIGS=8, the */
|
| + /* partial products can be added to themselves 1844.6 times in */
|
| + /* a uLong without overflowing, so intermediate carry */
|
| + /* resolution occurs only every 14752 digits. Hence for common */
|
| + /* short numbers usually only the one final carry resolution */
|
| + /* occurs. */
|
| + /* (The count is set via FASTLAZY to simplify experiments to */
|
| + /* measure the value of this approach: a 35% improvement on a */
|
| + /* [34x34] multiply.) */
|
| + lazy=FASTLAZY; /* carry delay count */
|
| + for (rip=zrhi; rip<=rmsi; rip++) { /* over each item in rhs */
|
| + lp=zacc+(rip-zrhi); /* where to add the lhs */
|
| + for (lip=zlhi; lip<=lmsi; lip++, lp++) { /* over each item in lhs */
|
| + *lp+=(uLong)(*lip)*(*rip); /* [this should in-line] */
|
| + } /* lip loop */
|
| + lazy--;
|
| + if (lazy>0 && rip!=rmsi) continue;
|
| + lazy=FASTLAZY; /* reset delay count */
|
| + /* spin up the accumulator resolving overflows */
|
| + for (lp=zacc; lp<zacc+iacc; lp++) {
|
| + if (*lp<FASTBASE) continue; /* it fits */
|
| + lcarry=*lp/FASTBASE; /* top part [slow divide] */
|
| + /* lcarry can exceed 2**32-1, so check again; this check */
|
| + /* and occasional extra divide (slow) is well worth it, as */
|
| + /* it allows FASTLAZY to be increased to 18 rather than 4 */
|
| + /* in the FASTDIGS=9 case */
|
| + if (lcarry<FASTBASE) carry=(uInt)lcarry; /* [usual] */
|
| + else { /* two-place carry [fairly rare] */
|
| + uInt carry2=(uInt)(lcarry/FASTBASE); /* top top part */
|
| + *(lp+2)+=carry2; /* add to item+2 */
|
| + *lp-=((uLong)FASTBASE*FASTBASE*carry2); /* [slow] */
|
| + carry=(uInt)(lcarry-((uLong)FASTBASE*carry2)); /* [inline] */
|
| + }
|
| + *(lp+1)+=carry; /* add to item above [inline] */
|
| + *lp-=((uLong)FASTBASE*carry); /* [inline] */
|
| + } /* carry resolution */
|
| + } /* rip loop */
|
| +
|
| + /* The multiplication is complete; time to convert back into */
|
| + /* units. This can be done in-place in the accumulator and in */
|
| + /* 32-bit operations, because carries were resolved after the */
|
| + /* final add. This needs N-1 divides and multiplies for */
|
| + /* each item in the accumulator (which will become up to N */
|
| + /* units, where 2<=N<=9). */
|
| + for (lp=zacc, up=acc; lp<zacc+iacc; lp++) {
|
| + uInt item=(uInt)*lp; /* decapitate to uInt */
|
| + for (p=0; p<FASTDIGS-DECDPUN; p+=DECDPUN, up++) {
|
| + uInt part=item/(DECDPUNMAX+1);
|
| + *up=(Unit)(item-(part*(DECDPUNMAX+1)));
|
| + item=part;
|
| + } /* p */
|
| + *up=(Unit)item; up++; /* [final needs no division] */
|
| + } /* lp */
|
| + accunits=up-acc; /* count of units */
|
| + }
|
| + else { /* here to use units directly, without chunking ['old code'] */
|
| + #endif
|
| +
|
| + /* if accumulator will be too long for local storage, then allocate */
|
| + acc=accbuff; /* -> assume buffer for accumulator */
|
| + needbytes=(D2U(lhs->digits)+D2U(rhs->digits))*sizeof(Unit);
|
| + if (needbytes>(Int)sizeof(accbuff)) {
|
| + allocacc=(Unit *)malloc(needbytes);
|
| + if (allocacc==NULL) {*status|=DEC_Insufficient_storage; break;}
|
| + acc=(Unit *)allocacc; /* use the allocated space */
|
| + }
|
| +
|
| + /* Now the main long multiplication loop */
|
| + /* Unlike the equivalent in the IBM Java implementation, there */
|
| + /* is no advantage in calculating from msu to lsu. So, do it */
|
| + /* by the book, as it were. */
|
| + /* Each iteration calculates ACC=ACC+MULTAND*MULT */
|
| + accunits=1; /* accumulator starts at '0' */
|
| + *acc=0; /* .. (lsu=0) */
|
| + shift=0; /* no multiplicand shift at first */
|
| + madlength=D2U(lhs->digits); /* this won't change */
|
| + mermsup=rhs->lsu+D2U(rhs->digits); /* -> msu+1 of multiplier */
|
| +
|
| + for (mer=rhs->lsu; mer<mermsup; mer++) {
|
| + /* Here, *mer is the next Unit in the multiplier to use */
|
| + /* If non-zero [optimization] add it... */
|
| + if (*mer!=0) accunits=decUnitAddSub(&acc[shift], accunits-shift,
|
| + lhs->lsu, madlength, 0,
|
| + &acc[shift], *mer)
|
| + + shift;
|
| + else { /* extend acc with a 0; it will be used shortly */
|
| + *(acc+accunits)=0; /* [this avoids length of <=0 later] */
|
| + accunits++;
|
| + }
|
| + /* multiply multiplicand by 10**DECDPUN for next Unit to left */
|
| + shift++; /* add this for 'logical length' */
|
| + } /* n */
|
| + #if FASTMUL
|
| + } /* unchunked units */
|
| + #endif
|
| + /* common end-path */
|
| + #if DECTRACE
|
| + decDumpAr('*', acc, accunits); /* Show exact result */
|
| + #endif
|
| +
|
| + /* acc now contains the exact result of the multiplication, */
|
| + /* possibly with a leading zero unit; build the decNumber from */
|
| + /* it, noting if any residue */
|
| + res->bits=bits; /* set sign */
|
| + res->digits=decGetDigits(acc, accunits); /* count digits exactly */
|
| +
|
| + /* There can be a 31-bit wrap in calculating the exponent. */
|
| + /* This can only happen if both input exponents are negative and */
|
| + /* both their magnitudes are large. If there was a wrap, set a */
|
| + /* safe very negative exponent, from which decFinalize() will */
|
| + /* raise a hard underflow shortly. */
|
| + exponent=lhs->exponent+rhs->exponent; /* calculate exponent */
|
| + if (lhs->exponent<0 && rhs->exponent<0 && exponent>0)
|
| + exponent=-2*DECNUMMAXE; /* force underflow */
|
| + res->exponent=exponent; /* OK to overwrite now */
|
| +
|
| +
|
| + /* Set the coefficient. If any rounding, residue records */
|
| + decSetCoeff(res, set, acc, res->digits, &residue, status);
|
| + decFinish(res, set, &residue, status); /* final cleanup */
|
| + } while(0); /* end protected */
|
| +
|
| + if (allocacc!=NULL) free(allocacc); /* drop any storage used */
|
| + #if DECSUBSET
|
| + if (allocrhs!=NULL) free(allocrhs); /* .. */
|
| + if (alloclhs!=NULL) free(alloclhs); /* .. */
|
| + #endif
|
| + #if FASTMUL
|
| + if (allocrhi!=NULL) free(allocrhi); /* .. */
|
| + if (alloclhi!=NULL) free(alloclhi); /* .. */
|
| + #endif
|
| + return res;
|
| + } /* decMultiplyOp */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decExpOp -- effect exponentiation */
|
| +/* */
|
| +/* This computes C = exp(A) */
|
| +/* */
|
| +/* res is C, the result. C may be A */
|
| +/* rhs is A */
|
| +/* set is the context; note that rounding mode has no effect */
|
| +/* */
|
| +/* C must have space for set->digits digits. status is updated but */
|
| +/* not set. */
|
| +/* */
|
| +/* Restrictions: */
|
| +/* */
|
| +/* digits, emax, and -emin in the context must be less than */
|
| +/* 2*DEC_MAX_MATH (1999998), and the rhs must be within these */
|
| +/* bounds or a zero. This is an internal routine, so these */
|
| +/* restrictions are contractual and not enforced. */
|
| +/* */
|
| +/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */
|
| +/* almost always be correctly rounded, but may be up to 1 ulp in */
|
| +/* error in rare cases. */
|
| +/* */
|
| +/* Finite results will always be full precision and Inexact, except */
|
| +/* when A is a zero or -Infinity (giving 1 or 0 respectively). */
|
| +/* ------------------------------------------------------------------ */
|
| +/* This approach used here is similar to the algorithm described in */
|
| +/* */
|
| +/* Variable Precision Exponential Function, T. E. Hull and */
|
| +/* A. Abrham, ACM Transactions on Mathematical Software, Vol 12 #2, */
|
| +/* pp79-91, ACM, June 1986. */
|
| +/* */
|
| +/* with the main difference being that the iterations in the series */
|
| +/* evaluation are terminated dynamically (which does not require the */
|
| +/* extra variable-precision variables which are expensive in this */
|
| +/* context). */
|
| +/* */
|
| +/* The error analysis in Hull & Abrham's paper applies except for the */
|
| +/* round-off error accumulation during the series evaluation. This */
|
| +/* code does not precalculate the number of iterations and so cannot */
|
| +/* use Horner's scheme. Instead, the accumulation is done at double- */
|
| +/* precision, which ensures that the additions of the terms are exact */
|
| +/* and do not accumulate round-off (and any round-off errors in the */
|
| +/* terms themselves move 'to the right' faster than they can */
|
| +/* accumulate). This code also extends the calculation by allowing, */
|
| +/* in the spirit of other decNumber operators, the input to be more */
|
| +/* precise than the result (the precision used is based on the more */
|
| +/* precise of the input or requested result). */
|
| +/* */
|
| +/* Implementation notes: */
|
| +/* */
|
| +/* 1. This is separated out as decExpOp so it can be called from */
|
| +/* other Mathematical functions (notably Ln) with a wider range */
|
| +/* than normal. In particular, it can handle the slightly wider */
|
| +/* (double) range needed by Ln (which has to be able to calculate */
|
| +/* exp(-x) where x can be the tiniest number (Ntiny). */
|
| +/* */
|
| +/* 2. Normalizing x to be <=0.1 (instead of <=1) reduces loop */
|
| +/* iterations by appoximately a third with additional (although */
|
| +/* diminishing) returns as the range is reduced to even smaller */
|
| +/* fractions. However, h (the power of 10 used to correct the */
|
| +/* result at the end, see below) must be kept <=8 as otherwise */
|
| +/* the final result cannot be computed. Hence the leverage is a */
|
| +/* sliding value (8-h), where potentially the range is reduced */
|
| +/* more for smaller values. */
|
| +/* */
|
| +/* The leverage that can be applied in this way is severely */
|
| +/* limited by the cost of the raise-to-the power at the end, */
|
| +/* which dominates when the number of iterations is small (less */
|
| +/* than ten) or when rhs is short. As an example, the adjustment */
|
| +/* x**10,000,000 needs 31 multiplications, all but one full-width. */
|
| +/* */
|
| +/* 3. The restrictions (especially precision) could be raised with */
|
| +/* care, but the full decNumber range seems very hard within the */
|
| +/* 32-bit limits. */
|
| +/* */
|
| +/* 4. The working precisions for the static buffers are twice the */
|
| +/* obvious size to allow for calls from decNumberPower. */
|
| +/* ------------------------------------------------------------------ */
|
| +decNumber * decExpOp(decNumber *res, const decNumber *rhs,
|
| + decContext *set, uInt *status) {
|
| + uInt ignore=0; /* working status */
|
| + Int h; /* adjusted exponent for 0.xxxx */
|
| + Int p; /* working precision */
|
| + Int residue; /* rounding residue */
|
| + uInt needbytes; /* for space calculations */
|
| + const decNumber *x=rhs; /* (may point to safe copy later) */
|
| + decContext aset, tset, dset; /* working contexts */
|
| + Int comp; /* work */
|
| +
|
| + /* the argument is often copied to normalize it, so (unusually) it */
|
| + /* is treated like other buffers, using DECBUFFER, +1 in case */
|
| + /* DECBUFFER is 0 */
|
| + decNumber bufr[D2N(DECBUFFER*2+1)];
|
| + decNumber *allocrhs=NULL; /* non-NULL if rhs buffer allocated */
|
| +
|
| + /* the working precision will be no more than set->digits+8+1 */
|
| + /* so for on-stack buffers DECBUFFER+9 is used, +1 in case DECBUFFER */
|
| + /* is 0 (and twice that for the accumulator) */
|
| +
|
| + /* buffer for t, term (working precision plus) */
|
| + decNumber buft[D2N(DECBUFFER*2+9+1)];
|
| + decNumber *allocbuft=NULL; /* -> allocated buft, iff allocated */
|
| + decNumber *t=buft; /* term */
|
| + /* buffer for a, accumulator (working precision * 2), at least 9 */
|
| + decNumber bufa[D2N(DECBUFFER*4+18+1)];
|
| + decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */
|
| + decNumber *a=bufa; /* accumulator */
|
| + /* decNumber for the divisor term; this needs at most 9 digits */
|
| + /* and so can be fixed size [16 so can use standard context] */
|
| + decNumber bufd[D2N(16)];
|
| + decNumber *d=bufd; /* divisor */
|
| + decNumber numone; /* constant 1 */
|
| +
|
| + #if DECCHECK
|
| + Int iterations=0; /* for later sanity check */
|
| + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| + #endif
|
| +
|
| + do { /* protect allocated storage */
|
| + if (SPECIALARG) { /* handle infinities and NaNs */
|
| + if (decNumberIsInfinite(rhs)) { /* an infinity */
|
| + if (decNumberIsNegative(rhs)) /* -Infinity -> +0 */
|
| + uprv_decNumberZero(res);
|
| + else uprv_decNumberCopy(res, rhs); /* +Infinity -> self */
|
| + }
|
| + else decNaNs(res, rhs, NULL, set, status); /* a NaN */
|
| + break;}
|
| +
|
| + if (ISZERO(rhs)) { /* zeros -> exact 1 */
|
| + uprv_decNumberZero(res); /* make clean 1 */
|
| + *res->lsu=1; /* .. */
|
| + break;} /* [no status to set] */
|
| +
|
| + /* e**x when 0 < x < 0.66 is < 1+3x/2, hence can fast-path */
|
| + /* positive and negative tiny cases which will result in inexact */
|
| + /* 1. This also allows the later add-accumulate to always be */
|
| + /* exact (because its length will never be more than twice the */
|
| + /* working precision). */
|
| + /* The comparator (tiny) needs just one digit, so use the */
|
| + /* decNumber d for it (reused as the divisor, etc., below); its */
|
| + /* exponent is such that if x is positive it will have */
|
| + /* set->digits-1 zeros between the decimal point and the digit, */
|
| + /* which is 4, and if x is negative one more zero there as the */
|
| + /* more precise result will be of the form 0.9999999 rather than */
|
| + /* 1.0000001. Hence, tiny will be 0.0000004 if digits=7 and x>0 */
|
| + /* or 0.00000004 if digits=7 and x<0. If RHS not larger than */
|
| + /* this then the result will be 1.000000 */
|
| + uprv_decNumberZero(d); /* clean */
|
| + *d->lsu=4; /* set 4 .. */
|
| + d->exponent=-set->digits; /* * 10**(-d) */
|
| + if (decNumberIsNegative(rhs)) d->exponent--; /* negative case */
|
| + comp=decCompare(d, rhs, 1); /* signless compare */
|
| + if (comp==BADINT) {
|
| + *status|=DEC_Insufficient_storage;
|
| + break;}
|
| + if (comp>=0) { /* rhs < d */
|
| + Int shift=set->digits-1;
|
| + uprv_decNumberZero(res); /* set 1 */
|
| + *res->lsu=1; /* .. */
|
| + res->digits=decShiftToMost(res->lsu, 1, shift);
|
| + res->exponent=-shift; /* make 1.0000... */
|
| + *status|=DEC_Inexact | DEC_Rounded; /* .. inexactly */
|
| + break;} /* tiny */
|
| +
|
| + /* set up the context to be used for calculating a, as this is */
|
| + /* used on both paths below */
|
| + uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64);
|
| + /* accumulator bounds are as requested (could underflow) */
|
| + aset.emax=set->emax; /* usual bounds */
|
| + aset.emin=set->emin; /* .. */
|
| + aset.clamp=0; /* and no concrete format */
|
| +
|
| + /* calculate the adjusted (Hull & Abrham) exponent (where the */
|
| + /* decimal point is just to the left of the coefficient msd) */
|
| + h=rhs->exponent+rhs->digits;
|
| + /* if h>8 then 10**h cannot be calculated safely; however, when */
|
| + /* h=8 then exp(|rhs|) will be at least exp(1E+7) which is at */
|
| + /* least 6.59E+4342944, so (due to the restriction on Emax/Emin) */
|
| + /* overflow (or underflow to 0) is guaranteed -- so this case can */
|
| + /* be handled by simply forcing the appropriate excess */
|
| + if (h>8) { /* overflow/underflow */
|
| + /* set up here so Power call below will over or underflow to */
|
| + /* zero; set accumulator to either 2 or 0.02 */
|
| + /* [stack buffer for a is always big enough for this] */
|
| + uprv_decNumberZero(a);
|
| + *a->lsu=2; /* not 1 but < exp(1) */
|
| + if (decNumberIsNegative(rhs)) a->exponent=-2; /* make 0.02 */
|
| + h=8; /* clamp so 10**h computable */
|
| + p=9; /* set a working precision */
|
| + }
|
| + else { /* h<=8 */
|
| + Int maxlever=(rhs->digits>8?1:0);
|
| + /* [could/should increase this for precisions >40 or so, too] */
|
| +
|
| + /* if h is 8, cannot normalize to a lower upper limit because */
|
| + /* the final result will not be computable (see notes above), */
|
| + /* but leverage can be applied whenever h is less than 8. */
|
| + /* Apply as much as possible, up to a MAXLEVER digits, which */
|
| + /* sets the tradeoff against the cost of the later a**(10**h). */
|
| + /* As h is increased, the working precision below also */
|
| + /* increases to compensate for the "constant digits at the */
|
| + /* front" effect. */
|
| + Int lever=MINI(8-h, maxlever); /* leverage attainable */
|
| + Int use=-rhs->digits-lever; /* exponent to use for RHS */
|
| + h+=lever; /* apply leverage selected */
|
| + if (h<0) { /* clamp */
|
| + use+=h; /* [may end up subnormal] */
|
| + h=0;
|
| + }
|
| + /* Take a copy of RHS if it needs normalization (true whenever x>=1) */
|
| + if (rhs->exponent!=use) {
|
| + decNumber *newrhs=bufr; /* assume will fit on stack */
|
| + needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
|
| + if (needbytes>sizeof(bufr)) { /* need malloc space */
|
| + allocrhs=(decNumber *)malloc(needbytes);
|
| + if (allocrhs==NULL) { /* hopeless -- abandon */
|
| + *status|=DEC_Insufficient_storage;
|
| + break;}
|
| + newrhs=allocrhs; /* use the allocated space */
|
| + }
|
| + uprv_decNumberCopy(newrhs, rhs); /* copy to safe space */
|
| + newrhs->exponent=use; /* normalize; now <1 */
|
| + x=newrhs; /* ready for use */
|
| + /* decNumberShow(x); */
|
| + }
|
| +
|
| + /* Now use the usual power series to evaluate exp(x). The */
|
| + /* series starts as 1 + x + x^2/2 ... so prime ready for the */
|
| + /* third term by setting the term variable t=x, the accumulator */
|
| + /* a=1, and the divisor d=2. */
|
| +
|
| + /* First determine the working precision. From Hull & Abrham */
|
| + /* this is set->digits+h+2. However, if x is 'over-precise' we */
|
| + /* need to allow for all its digits to potentially participate */
|
| + /* (consider an x where all the excess digits are 9s) so in */
|
| + /* this case use x->digits+h+2 */
|
| + p=MAXI(x->digits, set->digits)+h+2; /* [h<=8] */
|
| +
|
| + /* a and t are variable precision, and depend on p, so space */
|
| + /* must be allocated for them if necessary */
|
| +
|
| + /* the accumulator needs to be able to hold 2p digits so that */
|
| + /* the additions on the second and subsequent iterations are */
|
| + /* sufficiently exact. */
|
| + needbytes=sizeof(decNumber)+(D2U(p*2)-1)*sizeof(Unit);
|
| + if (needbytes>sizeof(bufa)) { /* need malloc space */
|
| + allocbufa=(decNumber *)malloc(needbytes);
|
| + if (allocbufa==NULL) { /* hopeless -- abandon */
|
| + *status|=DEC_Insufficient_storage;
|
| + break;}
|
| + a=allocbufa; /* use the allocated space */
|
| + }
|
| + /* the term needs to be able to hold p digits (which is */
|
| + /* guaranteed to be larger than x->digits, so the initial copy */
|
| + /* is safe); it may also be used for the raise-to-power */
|
| + /* calculation below, which needs an extra two digits */
|
| + needbytes=sizeof(decNumber)+(D2U(p+2)-1)*sizeof(Unit);
|
| + if (needbytes>sizeof(buft)) { /* need malloc space */
|
| + allocbuft=(decNumber *)malloc(needbytes);
|
| + if (allocbuft==NULL) { /* hopeless -- abandon */
|
| + *status|=DEC_Insufficient_storage;
|
| + break;}
|
| + t=allocbuft; /* use the allocated space */
|
| + }
|
| +
|
| + uprv_decNumberCopy(t, x); /* term=x */
|
| + uprv_decNumberZero(a); *a->lsu=1; /* accumulator=1 */
|
| + uprv_decNumberZero(d); *d->lsu=2; /* divisor=2 */
|
| + uprv_decNumberZero(&numone); *numone.lsu=1; /* constant 1 for increment */
|
| +
|
| + /* set up the contexts for calculating a, t, and d */
|
| + uprv_decContextDefault(&tset, DEC_INIT_DECIMAL64);
|
| + dset=tset;
|
| + /* accumulator bounds are set above, set precision now */
|
| + aset.digits=p*2; /* double */
|
| + /* term bounds avoid any underflow or overflow */
|
| + tset.digits=p;
|
| + tset.emin=DEC_MIN_EMIN; /* [emax is plenty] */
|
| + /* [dset.digits=16, etc., are sufficient] */
|
| +
|
| + /* finally ready to roll */
|
| + for (;;) {
|
| + #if DECCHECK
|
| + iterations++;
|
| + #endif
|
| + /* only the status from the accumulation is interesting */
|
| + /* [but it should remain unchanged after first add] */
|
| + decAddOp(a, a, t, &aset, 0, status); /* a=a+t */
|
| + decMultiplyOp(t, t, x, &tset, &ignore); /* t=t*x */
|
| + decDivideOp(t, t, d, &tset, DIVIDE, &ignore); /* t=t/d */
|
| + /* the iteration ends when the term cannot affect the result, */
|
| + /* if rounded to p digits, which is when its value is smaller */
|
| + /* than the accumulator by p+1 digits. There must also be */
|
| + /* full precision in a. */
|
| + if (((a->digits+a->exponent)>=(t->digits+t->exponent+p+1))
|
| + && (a->digits>=p)) break;
|
| + decAddOp(d, d, &numone, &dset, 0, &ignore); /* d=d+1 */
|
| + } /* iterate */
|
| +
|
| + #if DECCHECK
|
| + /* just a sanity check; comment out test to show always */
|
| + if (iterations>p+3)
|
| + printf("Exp iterations=%ld, status=%08lx, p=%ld, d=%ld\n",
|
| + (LI)iterations, (LI)*status, (LI)p, (LI)x->digits);
|
| + #endif
|
| + } /* h<=8 */
|
| +
|
| + /* apply postconditioning: a=a**(10**h) -- this is calculated */
|
| + /* at a slightly higher precision than Hull & Abrham suggest */
|
| + if (h>0) {
|
| + Int seenbit=0; /* set once a 1-bit is seen */
|
| + Int i; /* counter */
|
| + Int n=powers[h]; /* always positive */
|
| + aset.digits=p+2; /* sufficient precision */
|
| + /* avoid the overhead and many extra digits of decNumberPower */
|
| + /* as all that is needed is the short 'multipliers' loop; here */
|
| + /* accumulate the answer into t */
|
| + uprv_decNumberZero(t); *t->lsu=1; /* acc=1 */
|
| + for (i=1;;i++){ /* for each bit [top bit ignored] */
|
| + /* abandon if have had overflow or terminal underflow */
|
| + if (*status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */
|
| + if (*status&DEC_Overflow || ISZERO(t)) break;}
|
| + n=n<<1; /* move next bit to testable position */
|
| + if (n<0) { /* top bit is set */
|
| + seenbit=1; /* OK, have a significant bit */
|
| + decMultiplyOp(t, t, a, &aset, status); /* acc=acc*x */
|
| + }
|
| + if (i==31) break; /* that was the last bit */
|
| + if (!seenbit) continue; /* no need to square 1 */
|
| + decMultiplyOp(t, t, t, &aset, status); /* acc=acc*acc [square] */
|
| + } /*i*/ /* 32 bits */
|
| + /* decNumberShow(t); */
|
| + a=t; /* and carry on using t instead of a */
|
| + }
|
| +
|
| + /* Copy and round the result to res */
|
| + residue=1; /* indicate dirt to right .. */
|
| + if (ISZERO(a)) residue=0; /* .. unless underflowed to 0 */
|
| + aset.digits=set->digits; /* [use default rounding] */
|
| + decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */
|
| + decFinish(res, set, &residue, status); /* cleanup/set flags */
|
| + } while(0); /* end protected */
|
| +
|
| + if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */
|
| + if (allocbufa!=NULL) free(allocbufa); /* .. */
|
| + if (allocbuft!=NULL) free(allocbuft); /* .. */
|
| + /* [status is handled by caller] */
|
| + return res;
|
| + } /* decExpOp */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* Initial-estimate natural logarithm table */
|
| +/* */
|
| +/* LNnn -- 90-entry 16-bit table for values from .10 through .99. */
|
| +/* The result is a 4-digit encode of the coefficient (c=the */
|
| +/* top 14 bits encoding 0-9999) and a 2-digit encode of the */
|
| +/* exponent (e=the bottom 2 bits encoding 0-3) */
|
| +/* */
|
| +/* The resulting value is given by: */
|
| +/* */
|
| +/* v = -c * 10**(-e-3) */
|
| +/* */
|
| +/* where e and c are extracted from entry k = LNnn[x-10] */
|
| +/* where x is truncated (NB) into the range 10 through 99, */
|
| +/* and then c = k>>2 and e = k&3. */
|
| +/* ------------------------------------------------------------------ */
|
| +const uShort LNnn[90]={9016, 8652, 8316, 8008, 7724, 7456, 7208,
|
| + 6972, 6748, 6540, 6340, 6148, 5968, 5792, 5628, 5464, 5312,
|
| + 5164, 5020, 4884, 4748, 4620, 4496, 4376, 4256, 4144, 4032,
|
| + 39233, 38181, 37157, 36157, 35181, 34229, 33297, 32389, 31501, 30629,
|
| + 29777, 28945, 28129, 27329, 26545, 25777, 25021, 24281, 23553, 22837,
|
| + 22137, 21445, 20769, 20101, 19445, 18801, 18165, 17541, 16925, 16321,
|
| + 15721, 15133, 14553, 13985, 13421, 12865, 12317, 11777, 11241, 10717,
|
| + 10197, 9685, 9177, 8677, 8185, 7697, 7213, 6737, 6269, 5801,
|
| + 5341, 4889, 4437, 39930, 35534, 31186, 26886, 22630, 18418, 14254,
|
| + 10130, 6046, 20055};
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decLnOp -- effect natural logarithm */
|
| +/* */
|
| +/* This computes C = ln(A) */
|
| +/* */
|
| +/* res is C, the result. C may be A */
|
| +/* rhs is A */
|
| +/* set is the context; note that rounding mode has no effect */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* */
|
| +/* Notable cases: */
|
| +/* A<0 -> Invalid */
|
| +/* A=0 -> -Infinity (Exact) */
|
| +/* A=+Infinity -> +Infinity (Exact) */
|
| +/* A=1 exactly -> 0 (Exact) */
|
| +/* */
|
| +/* Restrictions (as for Exp): */
|
| +/* */
|
| +/* digits, emax, and -emin in the context must be less than */
|
| +/* DEC_MAX_MATH+11 (1000010), and the rhs must be within these */
|
| +/* bounds or a zero. This is an internal routine, so these */
|
| +/* restrictions are contractual and not enforced. */
|
| +/* */
|
| +/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */
|
| +/* almost always be correctly rounded, but may be up to 1 ulp in */
|
| +/* error in rare cases. */
|
| +/* ------------------------------------------------------------------ */
|
| +/* The result is calculated using Newton's method, with each */
|
| +/* iteration calculating a' = a + x * exp(-a) - 1. See, for example, */
|
| +/* Epperson 1989. */
|
| +/* */
|
| +/* The iteration ends when the adjustment x*exp(-a)-1 is tiny enough. */
|
| +/* This has to be calculated at the sum of the precision of x and the */
|
| +/* working precision. */
|
| +/* */
|
| +/* Implementation notes: */
|
| +/* */
|
| +/* 1. This is separated out as decLnOp so it can be called from */
|
| +/* other Mathematical functions (e.g., Log 10) with a wider range */
|
| +/* than normal. In particular, it can handle the slightly wider */
|
| +/* (+9+2) range needed by a power function. */
|
| +/* */
|
| +/* 2. The speed of this function is about 10x slower than exp, as */
|
| +/* it typically needs 4-6 iterations for short numbers, and the */
|
| +/* extra precision needed adds a squaring effect, twice. */
|
| +/* */
|
| +/* 3. Fastpaths are included for ln(10) and ln(2), up to length 40, */
|
| +/* as these are common requests. ln(10) is used by log10(x). */
|
| +/* */
|
| +/* 4. An iteration might be saved by widening the LNnn table, and */
|
| +/* would certainly save at least one if it were made ten times */
|
| +/* bigger, too (for truncated fractions 0.100 through 0.999). */
|
| +/* However, for most practical evaluations, at least four or five */
|
| +/* iterations will be neede -- so this would only speed up by */
|
| +/* 20-25% and that probably does not justify increasing the table */
|
| +/* size. */
|
| +/* */
|
| +/* 5. The static buffers are larger than might be expected to allow */
|
| +/* for calls from decNumberPower. */
|
| +/* ------------------------------------------------------------------ */
|
| +decNumber * decLnOp(decNumber *res, const decNumber *rhs,
|
| + decContext *set, uInt *status) {
|
| + uInt ignore=0; /* working status accumulator */
|
| + uInt needbytes; /* for space calculations */
|
| + Int residue; /* rounding residue */
|
| + Int r; /* rhs=f*10**r [see below] */
|
| + Int p; /* working precision */
|
| + Int pp; /* precision for iteration */
|
| + Int t; /* work */
|
| +
|
| + /* buffers for a (accumulator, typically precision+2) and b */
|
| + /* (adjustment calculator, same size) */
|
| + decNumber bufa[D2N(DECBUFFER+12)];
|
| + decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */
|
| + decNumber *a=bufa; /* accumulator/work */
|
| + decNumber bufb[D2N(DECBUFFER*2+2)];
|
| + decNumber *allocbufb=NULL; /* -> allocated bufa, iff allocated */
|
| + decNumber *b=bufb; /* adjustment/work */
|
| +
|
| + decNumber numone; /* constant 1 */
|
| + decNumber cmp; /* work */
|
| + decContext aset, bset; /* working contexts */
|
| +
|
| + #if DECCHECK
|
| + Int iterations=0; /* for later sanity check */
|
| + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
|
| + #endif
|
| +
|
| + do { /* protect allocated storage */
|
| + if (SPECIALARG) { /* handle infinities and NaNs */
|
| + if (decNumberIsInfinite(rhs)) { /* an infinity */
|
| + if (decNumberIsNegative(rhs)) /* -Infinity -> error */
|
| + *status|=DEC_Invalid_operation;
|
| + else uprv_decNumberCopy(res, rhs); /* +Infinity -> self */
|
| + }
|
| + else decNaNs(res, rhs, NULL, set, status); /* a NaN */
|
| + break;}
|
| +
|
| + if (ISZERO(rhs)) { /* +/- zeros -> -Infinity */
|
| + uprv_decNumberZero(res); /* make clean */
|
| + res->bits=DECINF|DECNEG; /* set - infinity */
|
| + break;} /* [no status to set] */
|
| +
|
| + /* Non-zero negatives are bad... */
|
| + if (decNumberIsNegative(rhs)) { /* -x -> error */
|
| + *status|=DEC_Invalid_operation;
|
| + break;}
|
| +
|
| + /* Here, rhs is positive, finite, and in range */
|
| +
|
| + /* lookaside fastpath code for ln(2) and ln(10) at common lengths */
|
| + if (rhs->exponent==0 && set->digits<=40) {
|
| + #if DECDPUN==1
|
| + if (rhs->lsu[0]==0 && rhs->lsu[1]==1 && rhs->digits==2) { /* ln(10) */
|
| + #else
|
| + if (rhs->lsu[0]==10 && rhs->digits==2) { /* ln(10) */
|
| + #endif
|
| + aset=*set; aset.round=DEC_ROUND_HALF_EVEN;
|
| + #define LN10 "2.302585092994045684017991454684364207601"
|
| + uprv_decNumberFromString(res, LN10, &aset);
|
| + *status|=(DEC_Inexact | DEC_Rounded); /* is inexact */
|
| + break;}
|
| + if (rhs->lsu[0]==2 && rhs->digits==1) { /* ln(2) */
|
| + aset=*set; aset.round=DEC_ROUND_HALF_EVEN;
|
| + #define LN2 "0.6931471805599453094172321214581765680755"
|
| + uprv_decNumberFromString(res, LN2, &aset);
|
| + *status|=(DEC_Inexact | DEC_Rounded);
|
| + break;}
|
| + } /* integer and short */
|
| +
|
| + /* Determine the working precision. This is normally the */
|
| + /* requested precision + 2, with a minimum of 9. However, if */
|
| + /* the rhs is 'over-precise' then allow for all its digits to */
|
| + /* potentially participate (consider an rhs where all the excess */
|
| + /* digits are 9s) so in this case use rhs->digits+2. */
|
| + p=MAXI(rhs->digits, MAXI(set->digits, 7))+2;
|
| +
|
| + /* Allocate space for the accumulator and the high-precision */
|
| + /* adjustment calculator, if necessary. The accumulator must */
|
| + /* be able to hold p digits, and the adjustment up to */
|
| + /* rhs->digits+p digits. They are also made big enough for 16 */
|
| + /* digits so that they can be used for calculating the initial */
|
| + /* estimate. */
|
| + needbytes=sizeof(decNumber)+(D2U(MAXI(p,16))-1)*sizeof(Unit);
|
| + if (needbytes>sizeof(bufa)) { /* need malloc space */
|
| + allocbufa=(decNumber *)malloc(needbytes);
|
| + if (allocbufa==NULL) { /* hopeless -- abandon */
|
| + *status|=DEC_Insufficient_storage;
|
| + break;}
|
| + a=allocbufa; /* use the allocated space */
|
| + }
|
| + pp=p+rhs->digits;
|
| + needbytes=sizeof(decNumber)+(D2U(MAXI(pp,16))-1)*sizeof(Unit);
|
| + if (needbytes>sizeof(bufb)) { /* need malloc space */
|
| + allocbufb=(decNumber *)malloc(needbytes);
|
| + if (allocbufb==NULL) { /* hopeless -- abandon */
|
| + *status|=DEC_Insufficient_storage;
|
| + break;}
|
| + b=allocbufb; /* use the allocated space */
|
| + }
|
| +
|
| + /* Prepare an initial estimate in acc. Calculate this by */
|
| + /* considering the coefficient of x to be a normalized fraction, */
|
| + /* f, with the decimal point at far left and multiplied by */
|
| + /* 10**r. Then, rhs=f*10**r and 0.1<=f<1, and */
|
| + /* ln(x) = ln(f) + ln(10)*r */
|
| + /* Get the initial estimate for ln(f) from a small lookup */
|
| + /* table (see above) indexed by the first two digits of f, */
|
| + /* truncated. */
|
| +
|
| + uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64); /* 16-digit extended */
|
| + r=rhs->exponent+rhs->digits; /* 'normalised' exponent */
|
| + uprv_decNumberFromInt32(a, r); /* a=r */
|
| + uprv_decNumberFromInt32(b, 2302585); /* b=ln(10) (2.302585) */
|
| + b->exponent=-6; /* .. */
|
| + decMultiplyOp(a, a, b, &aset, &ignore); /* a=a*b */
|
| + /* now get top two digits of rhs into b by simple truncate and */
|
| + /* force to integer */
|
| + residue=0; /* (no residue) */
|
| + aset.digits=2; aset.round=DEC_ROUND_DOWN;
|
| + decCopyFit(b, rhs, &aset, &residue, &ignore); /* copy & shorten */
|
| + b->exponent=0; /* make integer */
|
| + t=decGetInt(b); /* [cannot fail] */
|
| + if (t<10) t=X10(t); /* adjust single-digit b */
|
| + t=LNnn[t-10]; /* look up ln(b) */
|
| + uprv_decNumberFromInt32(b, t>>2); /* b=ln(b) coefficient */
|
| + b->exponent=-(t&3)-3; /* set exponent */
|
| + b->bits=DECNEG; /* ln(0.10)->ln(0.99) always -ve */
|
| + aset.digits=16; aset.round=DEC_ROUND_HALF_EVEN; /* restore */
|
| + decAddOp(a, a, b, &aset, 0, &ignore); /* acc=a+b */
|
| + /* the initial estimate is now in a, with up to 4 digits correct. */
|
| + /* When rhs is at or near Nmax the estimate will be low, so we */
|
| + /* will approach it from below, avoiding overflow when calling exp. */
|
| +
|
| + uprv_decNumberZero(&numone); *numone.lsu=1; /* constant 1 for adjustment */
|
| +
|
| + /* accumulator bounds are as requested (could underflow, but */
|
| + /* cannot overflow) */
|
| + aset.emax=set->emax;
|
| + aset.emin=set->emin;
|
| + aset.clamp=0; /* no concrete format */
|
| + /* set up a context to be used for the multiply and subtract */
|
| + bset=aset;
|
| + bset.emax=DEC_MAX_MATH*2; /* use double bounds for the */
|
| + bset.emin=-DEC_MAX_MATH*2; /* adjustment calculation */
|
| + /* [see decExpOp call below] */
|
| + /* for each iteration double the number of digits to calculate, */
|
| + /* up to a maximum of p */
|
| + pp=9; /* initial precision */
|
| + /* [initially 9 as then the sequence starts 7+2, 16+2, and */
|
| + /* 34+2, which is ideal for standard-sized numbers] */
|
| + aset.digits=pp; /* working context */
|
| + bset.digits=pp+rhs->digits; /* wider context */
|
| + for (;;) { /* iterate */
|
| + #if DECCHECK
|
| + iterations++;
|
| + if (iterations>24) break; /* consider 9 * 2**24 */
|
| + #endif
|
| + /* calculate the adjustment (exp(-a)*x-1) into b. This is a */
|
| + /* catastrophic subtraction but it really is the difference */
|
| + /* from 1 that is of interest. */
|
| + /* Use the internal entry point to Exp as it allows the double */
|
| + /* range for calculating exp(-a) when a is the tiniest subnormal. */
|
| + a->bits^=DECNEG; /* make -a */
|
| + decExpOp(b, a, &bset, &ignore); /* b=exp(-a) */
|
| + a->bits^=DECNEG; /* restore sign of a */
|
| + /* now multiply by rhs and subtract 1, at the wider precision */
|
| + decMultiplyOp(b, b, rhs, &bset, &ignore); /* b=b*rhs */
|
| + decAddOp(b, b, &numone, &bset, DECNEG, &ignore); /* b=b-1 */
|
| +
|
| + /* the iteration ends when the adjustment cannot affect the */
|
| + /* result by >=0.5 ulp (at the requested digits), which */
|
| + /* is when its value is smaller than the accumulator by */
|
| + /* set->digits+1 digits (or it is zero) -- this is a looser */
|
| + /* requirement than for Exp because all that happens to the */
|
| + /* accumulator after this is the final rounding (but note that */
|
| + /* there must also be full precision in a, or a=0). */
|
| +
|
| + if (decNumberIsZero(b) ||
|
| + (a->digits+a->exponent)>=(b->digits+b->exponent+set->digits+1)) {
|
| + if (a->digits==p) break;
|
| + if (decNumberIsZero(a)) {
|
| + decCompareOp(&cmp, rhs, &numone, &aset, COMPARE, &ignore); /* rhs=1 ? */
|
| + if (cmp.lsu[0]==0) a->exponent=0; /* yes, exact 0 */
|
| + else *status|=(DEC_Inexact | DEC_Rounded); /* no, inexact */
|
| + break;
|
| + }
|
| + /* force padding if adjustment has gone to 0 before full length */
|
| + if (decNumberIsZero(b)) b->exponent=a->exponent-p;
|
| + }
|
| +
|
| + /* not done yet ... */
|
| + decAddOp(a, a, b, &aset, 0, &ignore); /* a=a+b for next estimate */
|
| + if (pp==p) continue; /* precision is at maximum */
|
| + /* lengthen the next calculation */
|
| + pp=pp*2; /* double precision */
|
| + if (pp>p) pp=p; /* clamp to maximum */
|
| + aset.digits=pp; /* working context */
|
| + bset.digits=pp+rhs->digits; /* wider context */
|
| + } /* Newton's iteration */
|
| +
|
| + #if DECCHECK
|
| + /* just a sanity check; remove the test to show always */
|
| + if (iterations>24)
|
| + printf("Ln iterations=%ld, status=%08lx, p=%ld, d=%ld\n",
|
| + (LI)iterations, (LI)*status, (LI)p, (LI)rhs->digits);
|
| + #endif
|
| +
|
| + /* Copy and round the result to res */
|
| + residue=1; /* indicate dirt to right */
|
| + if (ISZERO(a)) residue=0; /* .. unless underflowed to 0 */
|
| + aset.digits=set->digits; /* [use default rounding] */
|
| + decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */
|
| + decFinish(res, set, &residue, status); /* cleanup/set flags */
|
| + } while(0); /* end protected */
|
| +
|
| + if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
|
| + if (allocbufb!=NULL) free(allocbufb); /* .. */
|
| + /* [status is handled by caller] */
|
| + return res;
|
| + } /* decLnOp */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decQuantizeOp -- force exponent to requested value */
|
| +/* */
|
| +/* This computes C = op(A, B), where op adjusts the coefficient */
|
| +/* of C (by rounding or shifting) such that the exponent (-scale) */
|
| +/* of C has the value B or matches the exponent of B. */
|
| +/* The numerical value of C will equal A, except for the effects of */
|
| +/* any rounding that occurred. */
|
| +/* */
|
| +/* res is C, the result. C may be A or B */
|
| +/* lhs is A, the number to adjust */
|
| +/* rhs is B, the requested exponent */
|
| +/* set is the context */
|
| +/* quant is 1 for quantize or 0 for rescale */
|
| +/* status is the status accumulator (this can be called without */
|
| +/* risk of control loss) */
|
| +/* */
|
| +/* C must have space for set->digits digits. */
|
| +/* */
|
| +/* Unless there is an error or the result is infinite, the exponent */
|
| +/* after the operation is guaranteed to be that requested. */
|
| +/* ------------------------------------------------------------------ */
|
| +static decNumber * decQuantizeOp(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set,
|
| + Flag quant, uInt *status) {
|
| + #if DECSUBSET
|
| + decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */
|
| + decNumber *allocrhs=NULL; /* .., rhs */
|
| + #endif
|
| + const decNumber *inrhs=rhs; /* save original rhs */
|
| + Int reqdigits=set->digits; /* requested DIGITS */
|
| + Int reqexp; /* requested exponent [-scale] */
|
| + Int residue=0; /* rounding residue */
|
| + Int etiny=set->emin-(reqdigits-1);
|
| +
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| + #endif
|
| +
|
| + do { /* protect allocated storage */
|
| + #if DECSUBSET
|
| + if (!set->extended) {
|
| + /* reduce operands and set lostDigits status, as needed */
|
| + if (lhs->digits>reqdigits) {
|
| + alloclhs=decRoundOperand(lhs, set, status);
|
| + if (alloclhs==NULL) break;
|
| + lhs=alloclhs;
|
| + }
|
| + if (rhs->digits>reqdigits) { /* [this only checks lostDigits] */
|
| + allocrhs=decRoundOperand(rhs, set, status);
|
| + if (allocrhs==NULL) break;
|
| + rhs=allocrhs;
|
| + }
|
| + }
|
| + #endif
|
| + /* [following code does not require input rounding] */
|
| +
|
| + /* Handle special values */
|
| + if (SPECIALARGS) {
|
| + /* NaNs get usual processing */
|
| + if (SPECIALARGS & (DECSNAN | DECNAN))
|
| + decNaNs(res, lhs, rhs, set, status);
|
| + /* one infinity but not both is bad */
|
| + else if ((lhs->bits ^ rhs->bits) & DECINF)
|
| + *status|=DEC_Invalid_operation;
|
| + /* both infinity: return lhs */
|
| + else uprv_decNumberCopy(res, lhs); /* [nop if in place] */
|
| + break;
|
| + }
|
| +
|
| + /* set requested exponent */
|
| + if (quant) reqexp=inrhs->exponent; /* quantize -- match exponents */
|
| + else { /* rescale -- use value of rhs */
|
| + /* Original rhs must be an integer that fits and is in range, */
|
| + /* which could be from -1999999997 to +999999999, thanks to */
|
| + /* subnormals */
|
| + reqexp=decGetInt(inrhs); /* [cannot fail] */
|
| + }
|
| +
|
| + #if DECSUBSET
|
| + if (!set->extended) etiny=set->emin; /* no subnormals */
|
| + #endif
|
| +
|
| + if (reqexp==BADINT /* bad (rescale only) or .. */
|
| + || reqexp==BIGODD || reqexp==BIGEVEN /* very big (ditto) or .. */
|
| + || (reqexp<etiny) /* < lowest */
|
| + || (reqexp>set->emax)) { /* > emax */
|
| + *status|=DEC_Invalid_operation;
|
| + break;}
|
| +
|
| + /* the RHS has been processed, so it can be overwritten now if necessary */
|
| + if (ISZERO(lhs)) { /* zero coefficient unchanged */
|
| + uprv_decNumberCopy(res, lhs); /* [nop if in place] */
|
| + res->exponent=reqexp; /* .. just set exponent */
|
| + #if DECSUBSET
|
| + if (!set->extended) res->bits=0; /* subset specification; no -0 */
|
| + #endif
|
| + }
|
| + else { /* non-zero lhs */
|
| + Int adjust=reqexp-lhs->exponent; /* digit adjustment needed */
|
| + /* if adjusted coefficient will definitely not fit, give up now */
|
| + if ((lhs->digits-adjust)>reqdigits) {
|
| + *status|=DEC_Invalid_operation;
|
| + break;
|
| + }
|
| +
|
| + if (adjust>0) { /* increasing exponent */
|
| + /* this will decrease the length of the coefficient by adjust */
|
| + /* digits, and must round as it does so */
|
| + decContext workset; /* work */
|
| + workset=*set; /* clone rounding, etc. */
|
| + workset.digits=lhs->digits-adjust; /* set requested length */
|
| + /* [note that the latter can be <1, here] */
|
| + decCopyFit(res, lhs, &workset, &residue, status); /* fit to result */
|
| + decApplyRound(res, &workset, residue, status); /* .. and round */
|
| + residue=0; /* [used] */
|
| + /* If just rounded a 999s case, exponent will be off by one; */
|
| + /* adjust back (after checking space), if so. */
|
| + if (res->exponent>reqexp) {
|
| + /* re-check needed, e.g., for quantize(0.9999, 0.001) under */
|
| + /* set->digits==3 */
|
| + if (res->digits==reqdigits) { /* cannot shift by 1 */
|
| + *status&=~(DEC_Inexact | DEC_Rounded); /* [clean these] */
|
| + *status|=DEC_Invalid_operation;
|
| + break;
|
| + }
|
| + res->digits=decShiftToMost(res->lsu, res->digits, 1); /* shift */
|
| + res->exponent--; /* (re)adjust the exponent. */
|
| + }
|
| + #if DECSUBSET
|
| + if (ISZERO(res) && !set->extended) res->bits=0; /* subset; no -0 */
|
| + #endif
|
| + } /* increase */
|
| + else /* adjust<=0 */ { /* decreasing or = exponent */
|
| + /* this will increase the length of the coefficient by -adjust */
|
| + /* digits, by adding zero or more trailing zeros; this is */
|
| + /* already checked for fit, above */
|
| + uprv_decNumberCopy(res, lhs); /* [it will fit] */
|
| + /* if padding needed (adjust<0), add it now... */
|
| + if (adjust<0) {
|
| + res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
|
| + res->exponent+=adjust; /* adjust the exponent */
|
| + }
|
| + } /* decrease */
|
| + } /* non-zero */
|
| +
|
| + /* Check for overflow [do not use Finalize in this case, as an */
|
| + /* overflow here is a "don't fit" situation] */
|
| + if (res->exponent>set->emax-res->digits+1) { /* too big */
|
| + *status|=DEC_Invalid_operation;
|
| + break;
|
| + }
|
| + else {
|
| + decFinalize(res, set, &residue, status); /* set subnormal flags */
|
| + *status&=~DEC_Underflow; /* suppress Underflow [as per 754] */
|
| + }
|
| + } while(0); /* end protected */
|
| +
|
| + #if DECSUBSET
|
| + if (allocrhs!=NULL) free(allocrhs); /* drop any storage used */
|
| + if (alloclhs!=NULL) free(alloclhs); /* .. */
|
| + #endif
|
| + return res;
|
| + } /* decQuantizeOp */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decCompareOp -- compare, min, or max two Numbers */
|
| +/* */
|
| +/* This computes C = A ? B and carries out one of four operations: */
|
| +/* COMPARE -- returns the signum (as a number) giving the */
|
| +/* result of a comparison unless one or both */
|
| +/* operands is a NaN (in which case a NaN results) */
|
| +/* COMPSIG -- as COMPARE except that a quiet NaN raises */
|
| +/* Invalid operation. */
|
| +/* COMPMAX -- returns the larger of the operands, using the */
|
| +/* 754 maxnum operation */
|
| +/* COMPMAXMAG -- ditto, comparing absolute values */
|
| +/* COMPMIN -- the 754 minnum operation */
|
| +/* COMPMINMAG -- ditto, comparing absolute values */
|
| +/* COMTOTAL -- returns the signum (as a number) giving the */
|
| +/* result of a comparison using 754 total ordering */
|
| +/* */
|
| +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
|
| +/* lhs is A */
|
| +/* rhs is B */
|
| +/* set is the context */
|
| +/* op is the operation flag */
|
| +/* status is the usual accumulator */
|
| +/* */
|
| +/* C must have space for one digit for COMPARE or set->digits for */
|
| +/* COMPMAX, COMPMIN, COMPMAXMAG, or COMPMINMAG. */
|
| +/* ------------------------------------------------------------------ */
|
| +/* The emphasis here is on speed for common cases, and avoiding */
|
| +/* coefficient comparison if possible. */
|
| +/* ------------------------------------------------------------------ */
|
| +static decNumber * decCompareOp(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set,
|
| + Flag op, uInt *status) {
|
| + #if DECSUBSET
|
| + decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */
|
| + decNumber *allocrhs=NULL; /* .., rhs */
|
| + #endif
|
| + Int result=0; /* default result value */
|
| + uByte merged; /* work */
|
| +
|
| + #if DECCHECK
|
| + if (decCheckOperands(res, lhs, rhs, set)) return res;
|
| + #endif
|
| +
|
| + do { /* protect allocated storage */
|
| + #if DECSUBSET
|
| + if (!set->extended) {
|
| + /* reduce operands and set lostDigits status, as needed */
|
| + if (lhs->digits>set->digits) {
|
| + alloclhs=decRoundOperand(lhs, set, status);
|
| + if (alloclhs==NULL) {result=BADINT; break;}
|
| + lhs=alloclhs;
|
| + }
|
| + if (rhs->digits>set->digits) {
|
| + allocrhs=decRoundOperand(rhs, set, status);
|
| + if (allocrhs==NULL) {result=BADINT; break;}
|
| + rhs=allocrhs;
|
| + }
|
| + }
|
| + #endif
|
| + /* [following code does not require input rounding] */
|
| +
|
| + /* If total ordering then handle differing signs 'up front' */
|
| + if (op==COMPTOTAL) { /* total ordering */
|
| + if (decNumberIsNegative(lhs) & !decNumberIsNegative(rhs)) {
|
| + result=-1;
|
| + break;
|
| + }
|
| + if (!decNumberIsNegative(lhs) & decNumberIsNegative(rhs)) {
|
| + result=+1;
|
| + break;
|
| + }
|
| + }
|
| +
|
| + /* handle NaNs specially; let infinities drop through */
|
| + /* This assumes sNaN (even just one) leads to NaN. */
|
| + merged=(lhs->bits | rhs->bits) & (DECSNAN | DECNAN);
|
| + if (merged) { /* a NaN bit set */
|
| + if (op==COMPARE); /* result will be NaN */
|
| + else if (op==COMPSIG) /* treat qNaN as sNaN */
|
| + *status|=DEC_Invalid_operation | DEC_sNaN;
|
| + else if (op==COMPTOTAL) { /* total ordering, always finite */
|
| + /* signs are known to be the same; compute the ordering here */
|
| + /* as if the signs are both positive, then invert for negatives */
|
| + if (!decNumberIsNaN(lhs)) result=-1;
|
| + else if (!decNumberIsNaN(rhs)) result=+1;
|
| + /* here if both NaNs */
|
| + else if (decNumberIsSNaN(lhs) && decNumberIsQNaN(rhs)) result=-1;
|
| + else if (decNumberIsQNaN(lhs) && decNumberIsSNaN(rhs)) result=+1;
|
| + else { /* both NaN or both sNaN */
|
| + /* now it just depends on the payload */
|
| + result=decUnitCompare(lhs->lsu, D2U(lhs->digits),
|
| + rhs->lsu, D2U(rhs->digits), 0);
|
| + /* [Error not possible, as these are 'aligned'] */
|
| + } /* both same NaNs */
|
| + if (decNumberIsNegative(lhs)) result=-result;
|
| + break;
|
| + } /* total order */
|
| +
|
| + else if (merged & DECSNAN); /* sNaN -> qNaN */
|
| + else { /* here if MIN or MAX and one or two quiet NaNs */
|
| + /* min or max -- 754 rules ignore single NaN */
|
| + if (!decNumberIsNaN(lhs) || !decNumberIsNaN(rhs)) {
|
| + /* just one NaN; force choice to be the non-NaN operand */
|
| + op=COMPMAX;
|
| + if (lhs->bits & DECNAN) result=-1; /* pick rhs */
|
| + else result=+1; /* pick lhs */
|
| + break;
|
| + }
|
| + } /* max or min */
|
| + op=COMPNAN; /* use special path */
|
| + decNaNs(res, lhs, rhs, set, status); /* propagate NaN */
|
| + break;
|
| + }
|
| + /* have numbers */
|
| + if (op==COMPMAXMAG || op==COMPMINMAG) result=decCompare(lhs, rhs, 1);
|
| + else result=decCompare(lhs, rhs, 0); /* sign matters */
|
| + } while(0); /* end protected */
|
| +
|
| + if (result==BADINT) *status|=DEC_Insufficient_storage; /* rare */
|
| + else {
|
| + if (op==COMPARE || op==COMPSIG ||op==COMPTOTAL) { /* returning signum */
|
| + if (op==COMPTOTAL && result==0) {
|
| + /* operands are numerically equal or same NaN (and same sign, */
|
| + /* tested first); if identical, leave result 0 */
|
| + if (lhs->exponent!=rhs->exponent) {
|
| + if (lhs->exponent<rhs->exponent) result=-1;
|
| + else result=+1;
|
| + if (decNumberIsNegative(lhs)) result=-result;
|
| + } /* lexp!=rexp */
|
| + } /* total-order by exponent */
|
| + uprv_decNumberZero(res); /* [always a valid result] */
|
| + if (result!=0) { /* must be -1 or +1 */
|
| + *res->lsu=1;
|
| + if (result<0) res->bits=DECNEG;
|
| + }
|
| + }
|
| + else if (op==COMPNAN); /* special, drop through */
|
| + else { /* MAX or MIN, non-NaN result */
|
| + Int residue=0; /* rounding accumulator */
|
| + /* choose the operand for the result */
|
| + const decNumber *choice;
|
| + if (result==0) { /* operands are numerically equal */
|
| + /* choose according to sign then exponent (see 754) */
|
| + uByte slhs=(lhs->bits & DECNEG);
|
| + uByte srhs=(rhs->bits & DECNEG);
|
| + #if DECSUBSET
|
| + if (!set->extended) { /* subset: force left-hand */
|
| + op=COMPMAX;
|
| + result=+1;
|
| + }
|
| + else
|
| + #endif
|
| + if (slhs!=srhs) { /* signs differ */
|
| + if (slhs) result=-1; /* rhs is max */
|
| + else result=+1; /* lhs is max */
|
| + }
|
| + else if (slhs && srhs) { /* both negative */
|
| + if (lhs->exponent<rhs->exponent) result=+1;
|
| + else result=-1;
|
| + /* [if equal, use lhs, technically identical] */
|
| + }
|
| + else { /* both positive */
|
| + if (lhs->exponent>rhs->exponent) result=+1;
|
| + else result=-1;
|
| + /* [ditto] */
|
| + }
|
| + } /* numerically equal */
|
| + /* here result will be non-0; reverse if looking for MIN */
|
| + if (op==COMPMIN || op==COMPMINMAG) result=-result;
|
| + choice=(result>0 ? lhs : rhs); /* choose */
|
| + /* copy chosen to result, rounding if need be */
|
| + decCopyFit(res, choice, set, &residue, status);
|
| + decFinish(res, set, &residue, status);
|
| + }
|
| + }
|
| + #if DECSUBSET
|
| + if (allocrhs!=NULL) free(allocrhs); /* free any storage used */
|
| + if (alloclhs!=NULL) free(alloclhs); /* .. */
|
| + #endif
|
| + return res;
|
| + } /* decCompareOp */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decCompare -- compare two decNumbers by numerical value */
|
| +/* */
|
| +/* This routine compares A ? B without altering them. */
|
| +/* */
|
| +/* Arg1 is A, a decNumber which is not a NaN */
|
| +/* Arg2 is B, a decNumber which is not a NaN */
|
| +/* Arg3 is 1 for a sign-independent compare, 0 otherwise */
|
| +/* */
|
| +/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */
|
| +/* (the only possible failure is an allocation error) */
|
| +/* ------------------------------------------------------------------ */
|
| +static Int decCompare(const decNumber *lhs, const decNumber *rhs,
|
| + Flag abs_c) {
|
| + Int result; /* result value */
|
| + Int sigr; /* rhs signum */
|
| + Int compare; /* work */
|
| +
|
| + result=1; /* assume signum(lhs) */
|
| + if (ISZERO(lhs)) result=0;
|
| + if (abs_c) {
|
| + if (ISZERO(rhs)) return result; /* LHS wins or both 0 */
|
| + /* RHS is non-zero */
|
| + if (result==0) return -1; /* LHS is 0; RHS wins */
|
| + /* [here, both non-zero, result=1] */
|
| + }
|
| + else { /* signs matter */
|
| + if (result && decNumberIsNegative(lhs)) result=-1;
|
| + sigr=1; /* compute signum(rhs) */
|
| + if (ISZERO(rhs)) sigr=0;
|
| + else if (decNumberIsNegative(rhs)) sigr=-1;
|
| + if (result > sigr) return +1; /* L > R, return 1 */
|
| + if (result < sigr) return -1; /* L < R, return -1 */
|
| + if (result==0) return 0; /* both 0 */
|
| + }
|
| +
|
| + /* signums are the same; both are non-zero */
|
| + if ((lhs->bits | rhs->bits) & DECINF) { /* one or more infinities */
|
| + if (decNumberIsInfinite(rhs)) {
|
| + if (decNumberIsInfinite(lhs)) result=0;/* both infinite */
|
| + else result=-result; /* only rhs infinite */
|
| + }
|
| + return result;
|
| + }
|
| + /* must compare the coefficients, allowing for exponents */
|
| + if (lhs->exponent>rhs->exponent) { /* LHS exponent larger */
|
| + /* swap sides, and sign */
|
| + const decNumber *temp=lhs;
|
| + lhs=rhs;
|
| + rhs=temp;
|
| + result=-result;
|
| + }
|
| + compare=decUnitCompare(lhs->lsu, D2U(lhs->digits),
|
| + rhs->lsu, D2U(rhs->digits),
|
| + rhs->exponent-lhs->exponent);
|
| + if (compare!=BADINT) compare*=result; /* comparison succeeded */
|
| + return compare;
|
| + } /* decCompare */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decUnitCompare -- compare two >=0 integers in Unit arrays */
|
| +/* */
|
| +/* This routine compares A ? B*10**E where A and B are unit arrays */
|
| +/* A is a plain integer */
|
| +/* B has an exponent of E (which must be non-negative) */
|
| +/* */
|
| +/* Arg1 is A first Unit (lsu) */
|
| +/* Arg2 is A length in Units */
|
| +/* Arg3 is B first Unit (lsu) */
|
| +/* Arg4 is B length in Units */
|
| +/* Arg5 is E (0 if the units are aligned) */
|
| +/* */
|
| +/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */
|
| +/* (the only possible failure is an allocation error, which can */
|
| +/* only occur if E!=0) */
|
| +/* ------------------------------------------------------------------ */
|
| +static Int decUnitCompare(const Unit *a, Int alength,
|
| + const Unit *b, Int blength, Int exp) {
|
| + Unit *acc; /* accumulator for result */
|
| + Unit accbuff[SD2U(DECBUFFER*2+1)]; /* local buffer */
|
| + Unit *allocacc=NULL; /* -> allocated acc buffer, iff allocated */
|
| + Int accunits, need; /* units in use or needed for acc */
|
| + const Unit *l, *r, *u; /* work */
|
| + Int expunits, exprem, result; /* .. */
|
| +
|
| + if (exp==0) { /* aligned; fastpath */
|
| + if (alength>blength) return 1;
|
| + if (alength<blength) return -1;
|
| + /* same number of units in both -- need unit-by-unit compare */
|
| + l=a+alength-1;
|
| + r=b+alength-1;
|
| + for (;l>=a; l--, r--) {
|
| + if (*l>*r) return 1;
|
| + if (*l<*r) return -1;
|
| + }
|
| + return 0; /* all units match */
|
| + } /* aligned */
|
| +
|
| + /* Unaligned. If one is >1 unit longer than the other, padded */
|
| + /* approximately, then can return easily */
|
| + if (alength>blength+(Int)D2U(exp)) return 1;
|
| + if (alength+1<blength+(Int)D2U(exp)) return -1;
|
| +
|
| + /* Need to do a real subtract. For this, a result buffer is needed */
|
| + /* even though only the sign is of interest. Its length needs */
|
| + /* to be the larger of alength and padded blength, +2 */
|
| + need=blength+D2U(exp); /* maximum real length of B */
|
| + if (need<alength) need=alength;
|
| + need+=2;
|
| + acc=accbuff; /* assume use local buffer */
|
| + if (need*sizeof(Unit)>sizeof(accbuff)) {
|
| + allocacc=(Unit *)malloc(need*sizeof(Unit));
|
| + if (allocacc==NULL) return BADINT; /* hopeless -- abandon */
|
| + acc=allocacc;
|
| + }
|
| + /* Calculate units and remainder from exponent. */
|
| + expunits=exp/DECDPUN;
|
| + exprem=exp%DECDPUN;
|
| + /* subtract [A+B*(-m)] */
|
| + accunits=decUnitAddSub(a, alength, b, blength, expunits, acc,
|
| + -(Int)powers[exprem]);
|
| + /* [UnitAddSub result may have leading zeros, even on zero] */
|
| + if (accunits<0) result=-1; /* negative result */
|
| + else { /* non-negative result */
|
| + /* check units of the result before freeing any storage */
|
| + for (u=acc; u<acc+accunits-1 && *u==0;) u++;
|
| + result=(*u==0 ? 0 : +1);
|
| + }
|
| + /* clean up and return the result */
|
| + if (allocacc!=NULL) free(allocacc); /* drop any storage used */
|
| + return result;
|
| + } /* decUnitCompare */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decUnitAddSub -- add or subtract two >=0 integers in Unit arrays */
|
| +/* */
|
| +/* This routine performs the calculation: */
|
| +/* */
|
| +/* C=A+(B*M) */
|
| +/* */
|
| +/* Where M is in the range -DECDPUNMAX through +DECDPUNMAX. */
|
| +/* */
|
| +/* A may be shorter or longer than B. */
|
| +/* */
|
| +/* Leading zeros are not removed after a calculation. The result is */
|
| +/* either the same length as the longer of A and B (adding any */
|
| +/* shift), or one Unit longer than that (if a Unit carry occurred). */
|
| +/* */
|
| +/* A and B content are not altered unless C is also A or B. */
|
| +/* C may be the same array as A or B, but only if no zero padding is */
|
| +/* requested (that is, C may be B only if bshift==0). */
|
| +/* C is filled from the lsu; only those units necessary to complete */
|
| +/* the calculation are referenced. */
|
| +/* */
|
| +/* Arg1 is A first Unit (lsu) */
|
| +/* Arg2 is A length in Units */
|
| +/* Arg3 is B first Unit (lsu) */
|
| +/* Arg4 is B length in Units */
|
| +/* Arg5 is B shift in Units (>=0; pads with 0 units if positive) */
|
| +/* Arg6 is C first Unit (lsu) */
|
| +/* Arg7 is M, the multiplier */
|
| +/* */
|
| +/* returns the count of Units written to C, which will be non-zero */
|
| +/* and negated if the result is negative. That is, the sign of the */
|
| +/* returned Int is the sign of the result (positive for zero) and */
|
| +/* the absolute value of the Int is the count of Units. */
|
| +/* */
|
| +/* It is the caller's responsibility to make sure that C size is */
|
| +/* safe, allowing space if necessary for a one-Unit carry. */
|
| +/* */
|
| +/* This routine is severely performance-critical; *any* change here */
|
| +/* must be measured (timed) to assure no performance degradation. */
|
| +/* In particular, trickery here tends to be counter-productive, as */
|
| +/* increased complexity of code hurts register optimizations on */
|
| +/* register-poor architectures. Avoiding divisions is nearly */
|
| +/* always a Good Idea, however. */
|
| +/* */
|
| +/* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark */
|
| +/* (IBM Warwick, UK) for some of the ideas used in this routine. */
|
| +/* ------------------------------------------------------------------ */
|
| +static Int decUnitAddSub(const Unit *a, Int alength,
|
| + const Unit *b, Int blength, Int bshift,
|
| + Unit *c, Int m) {
|
| + const Unit *alsu=a; /* A lsu [need to remember it] */
|
| + Unit *clsu=c; /* C ditto */
|
| + Unit *minC; /* low water mark for C */
|
| + Unit *maxC; /* high water mark for C */
|
| + eInt carry=0; /* carry integer (could be Long) */
|
| + Int add; /* work */
|
| + #if DECDPUN<=4 /* myriadal, millenary, etc. */
|
| + Int est; /* estimated quotient */
|
| + #endif
|
| +
|
| + #if DECTRACE
|
| + if (alength<1 || blength<1)
|
| + printf("decUnitAddSub: alen blen m %ld %ld [%ld]\n", alength, blength, m);
|
| + #endif
|
| +
|
| + maxC=c+alength; /* A is usually the longer */
|
| + minC=c+blength; /* .. and B the shorter */
|
| + if (bshift!=0) { /* B is shifted; low As copy across */
|
| + minC+=bshift;
|
| + /* if in place [common], skip copy unless there's a gap [rare] */
|
| + if (a==c && bshift<=alength) {
|
| + c+=bshift;
|
| + a+=bshift;
|
| + }
|
| + else for (; c<clsu+bshift; a++, c++) { /* copy needed */
|
| + if (a<alsu+alength) *c=*a;
|
| + else *c=0;
|
| + }
|
| + }
|
| + if (minC>maxC) { /* swap */
|
| + Unit *hold=minC;
|
| + minC=maxC;
|
| + maxC=hold;
|
| + }
|
| +
|
| + /* For speed, do the addition as two loops; the first where both A */
|
| + /* and B contribute, and the second (if necessary) where only one or */
|
| + /* other of the numbers contribute. */
|
| + /* Carry handling is the same (i.e., duplicated) in each case. */
|
| + for (; c<minC; c++) {
|
| + carry+=*a;
|
| + a++;
|
| + carry+=((eInt)*b)*m; /* [special-casing m=1/-1 */
|
| + b++; /* here is not a win] */
|
| + /* here carry is new Unit of digits; it could be +ve or -ve */
|
| + if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */
|
| + *c=(Unit)carry;
|
| + carry=0;
|
| + continue;
|
| + }
|
| + #if DECDPUN==4 /* use divide-by-multiply */
|
| + if (carry>=0) {
|
| + est=(((ueInt)carry>>11)*53687)>>18;
|
| + *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
|
| + carry=est; /* likely quotient [89%] */
|
| + if (*c<DECDPUNMAX+1) continue; /* estimate was correct */
|
| + carry++;
|
| + *c-=DECDPUNMAX+1;
|
| + continue;
|
| + }
|
| + /* negative case */
|
| + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
|
| + est=(((ueInt)carry>>11)*53687)>>18;
|
| + *c=(Unit)(carry-est*(DECDPUNMAX+1));
|
| + carry=est-(DECDPUNMAX+1); /* correctly negative */
|
| + if (*c<DECDPUNMAX+1) continue; /* was OK */
|
| + carry++;
|
| + *c-=DECDPUNMAX+1;
|
| + #elif DECDPUN==3
|
| + if (carry>=0) {
|
| + est=(((ueInt)carry>>3)*16777)>>21;
|
| + *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
|
| + carry=est; /* likely quotient [99%] */
|
| + if (*c<DECDPUNMAX+1) continue; /* estimate was correct */
|
| + carry++;
|
| + *c-=DECDPUNMAX+1;
|
| + continue;
|
| + }
|
| + /* negative case */
|
| + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
|
| + est=(((ueInt)carry>>3)*16777)>>21;
|
| + *c=(Unit)(carry-est*(DECDPUNMAX+1));
|
| + carry=est-(DECDPUNMAX+1); /* correctly negative */
|
| + if (*c<DECDPUNMAX+1) continue; /* was OK */
|
| + carry++;
|
| + *c-=DECDPUNMAX+1;
|
| + #elif DECDPUN<=2
|
| + /* Can use QUOT10 as carry <= 4 digits */
|
| + if (carry>=0) {
|
| + est=QUOT10(carry, DECDPUN);
|
| + *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
|
| + carry=est; /* quotient */
|
| + continue;
|
| + }
|
| + /* negative case */
|
| + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
|
| + est=QUOT10(carry, DECDPUN);
|
| + *c=(Unit)(carry-est*(DECDPUNMAX+1));
|
| + carry=est-(DECDPUNMAX+1); /* correctly negative */
|
| + #else
|
| + /* remainder operator is undefined if negative, so must test */
|
| + if ((ueInt)carry<(DECDPUNMAX+1)*2) { /* fastpath carry +1 */
|
| + *c=(Unit)(carry-(DECDPUNMAX+1)); /* [helps additions] */
|
| + carry=1;
|
| + continue;
|
| + }
|
| + if (carry>=0) {
|
| + *c=(Unit)(carry%(DECDPUNMAX+1));
|
| + carry=carry/(DECDPUNMAX+1);
|
| + continue;
|
| + }
|
| + /* negative case */
|
| + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
|
| + *c=(Unit)(carry%(DECDPUNMAX+1));
|
| + carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);
|
| + #endif
|
| + } /* c */
|
| +
|
| + /* now may have one or other to complete */
|
| + /* [pretest to avoid loop setup/shutdown] */
|
| + if (c<maxC) for (; c<maxC; c++) {
|
| + if (a<alsu+alength) { /* still in A */
|
| + carry+=*a;
|
| + a++;
|
| + }
|
| + else { /* inside B */
|
| + carry+=((eInt)*b)*m;
|
| + b++;
|
| + }
|
| + /* here carry is new Unit of digits; it could be +ve or -ve and */
|
| + /* magnitude up to DECDPUNMAX squared */
|
| + if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */
|
| + *c=(Unit)carry;
|
| + carry=0;
|
| + continue;
|
| + }
|
| + /* result for this unit is negative or >DECDPUNMAX */
|
| + #if DECDPUN==4 /* use divide-by-multiply */
|
| + if (carry>=0) {
|
| + est=(((ueInt)carry>>11)*53687)>>18;
|
| + *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
|
| + carry=est; /* likely quotient [79.7%] */
|
| + if (*c<DECDPUNMAX+1) continue; /* estimate was correct */
|
| + carry++;
|
| + *c-=DECDPUNMAX+1;
|
| + continue;
|
| + }
|
| + /* negative case */
|
| + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
|
| + est=(((ueInt)carry>>11)*53687)>>18;
|
| + *c=(Unit)(carry-est*(DECDPUNMAX+1));
|
| + carry=est-(DECDPUNMAX+1); /* correctly negative */
|
| + if (*c<DECDPUNMAX+1) continue; /* was OK */
|
| + carry++;
|
| + *c-=DECDPUNMAX+1;
|
| + #elif DECDPUN==3
|
| + if (carry>=0) {
|
| + est=(((ueInt)carry>>3)*16777)>>21;
|
| + *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
|
| + carry=est; /* likely quotient [99%] */
|
| + if (*c<DECDPUNMAX+1) continue; /* estimate was correct */
|
| + carry++;
|
| + *c-=DECDPUNMAX+1;
|
| + continue;
|
| + }
|
| + /* negative case */
|
| + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
|
| + est=(((ueInt)carry>>3)*16777)>>21;
|
| + *c=(Unit)(carry-est*(DECDPUNMAX+1));
|
| + carry=est-(DECDPUNMAX+1); /* correctly negative */
|
| + if (*c<DECDPUNMAX+1) continue; /* was OK */
|
| + carry++;
|
| + *c-=DECDPUNMAX+1;
|
| + #elif DECDPUN<=2
|
| + if (carry>=0) {
|
| + est=QUOT10(carry, DECDPUN);
|
| + *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
|
| + carry=est; /* quotient */
|
| + continue;
|
| + }
|
| + /* negative case */
|
| + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
|
| + est=QUOT10(carry, DECDPUN);
|
| + *c=(Unit)(carry-est*(DECDPUNMAX+1));
|
| + carry=est-(DECDPUNMAX+1); /* correctly negative */
|
| + #else
|
| + if ((ueInt)carry<(DECDPUNMAX+1)*2){ /* fastpath carry 1 */
|
| + *c=(Unit)(carry-(DECDPUNMAX+1));
|
| + carry=1;
|
| + continue;
|
| + }
|
| + /* remainder operator is undefined if negative, so must test */
|
| + if (carry>=0) {
|
| + *c=(Unit)(carry%(DECDPUNMAX+1));
|
| + carry=carry/(DECDPUNMAX+1);
|
| + continue;
|
| + }
|
| + /* negative case */
|
| + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
|
| + *c=(Unit)(carry%(DECDPUNMAX+1));
|
| + carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);
|
| + #endif
|
| + } /* c */
|
| +
|
| + /* OK, all A and B processed; might still have carry or borrow */
|
| + /* return number of Units in the result, negated if a borrow */
|
| + if (carry==0) return c-clsu; /* no carry, so no more to do */
|
| + if (carry>0) { /* positive carry */
|
| + *c=(Unit)carry; /* place as new unit */
|
| + c++; /* .. */
|
| + return c-clsu;
|
| + }
|
| + /* -ve carry: it's a borrow; complement needed */
|
| + add=1; /* temporary carry... */
|
| + for (c=clsu; c<maxC; c++) {
|
| + add=DECDPUNMAX+add-*c;
|
| + if (add<=DECDPUNMAX) {
|
| + *c=(Unit)add;
|
| + add=0;
|
| + }
|
| + else {
|
| + *c=0;
|
| + add=1;
|
| + }
|
| + }
|
| + /* add an extra unit iff it would be non-zero */
|
| + #if DECTRACE
|
| + printf("UAS borrow: add %ld, carry %ld\n", add, carry);
|
| + #endif
|
| + if ((add-carry-1)!=0) {
|
| + *c=(Unit)(add-carry-1);
|
| + c++; /* interesting, include it */
|
| + }
|
| + return clsu-c; /* -ve result indicates borrowed */
|
| + } /* decUnitAddSub */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decTrim -- trim trailing zeros or normalize */
|
| +/* */
|
| +/* dn is the number to trim or normalize */
|
| +/* set is the context to use to check for clamp */
|
| +/* all is 1 to remove all trailing zeros, 0 for just fraction ones */
|
| +/* noclamp is 1 to unconditional (unclamped) trim */
|
| +/* dropped returns the number of discarded trailing zeros */
|
| +/* returns dn */
|
| +/* */
|
| +/* If clamp is set in the context then the number of zeros trimmed */
|
| +/* may be limited if the exponent is high. */
|
| +/* All fields are updated as required. This is a utility operation, */
|
| +/* so special values are unchanged and no error is possible. */
|
| +/* ------------------------------------------------------------------ */
|
| +static decNumber * decTrim(decNumber *dn, decContext *set, Flag all,
|
| + Flag noclamp, Int *dropped) {
|
| + Int d, exp; /* work */
|
| + uInt cut; /* .. */
|
| + Unit *up; /* -> current Unit */
|
| +
|
| + #if DECCHECK
|
| + if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn;
|
| + #endif
|
| +
|
| + *dropped=0; /* assume no zeros dropped */
|
| + if ((dn->bits & DECSPECIAL) /* fast exit if special .. */
|
| + || (*dn->lsu & 0x01)) return dn; /* .. or odd */
|
| + if (ISZERO(dn)) { /* .. or 0 */
|
| + dn->exponent=0; /* (sign is preserved) */
|
| + return dn;
|
| + }
|
| +
|
| + /* have a finite number which is even */
|
| + exp=dn->exponent;
|
| + cut=1; /* digit (1-DECDPUN) in Unit */
|
| + up=dn->lsu; /* -> current Unit */
|
| + for (d=0; d<dn->digits-1; d++) { /* [don't strip the final digit] */
|
| + /* slice by powers */
|
| + #if DECDPUN<=4
|
| + uInt quot=QUOT10(*up, cut);
|
| + if ((*up-quot*powers[cut])!=0) break; /* found non-0 digit */
|
| + #else
|
| + if (*up%powers[cut]!=0) break; /* found non-0 digit */
|
| + #endif
|
| + /* have a trailing 0 */
|
| + if (!all) { /* trimming */
|
| + /* [if exp>0 then all trailing 0s are significant for trim] */
|
| + if (exp<=0) { /* if digit might be significant */
|
| + if (exp==0) break; /* then quit */
|
| + exp++; /* next digit might be significant */
|
| + }
|
| + }
|
| + cut++; /* next power */
|
| + if (cut>DECDPUN) { /* need new Unit */
|
| + up++;
|
| + cut=1;
|
| + }
|
| + } /* d */
|
| + if (d==0) return dn; /* none to drop */
|
| +
|
| + /* may need to limit drop if clamping */
|
| + if (set->clamp && !noclamp) {
|
| + Int maxd=set->emax-set->digits+1-dn->exponent;
|
| + if (maxd<=0) return dn; /* nothing possible */
|
| + if (d>maxd) d=maxd;
|
| + }
|
| +
|
| + /* effect the drop */
|
| + decShiftToLeast(dn->lsu, D2U(dn->digits), d);
|
| + dn->exponent+=d; /* maintain numerical value */
|
| + dn->digits-=d; /* new length */
|
| + *dropped=d; /* report the count */
|
| + return dn;
|
| + } /* decTrim */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decReverse -- reverse a Unit array in place */
|
| +/* */
|
| +/* ulo is the start of the array */
|
| +/* uhi is the end of the array (highest Unit to include) */
|
| +/* */
|
| +/* The units ulo through uhi are reversed in place (if the number */
|
| +/* of units is odd, the middle one is untouched). Note that the */
|
| +/* digit(s) in each unit are unaffected. */
|
| +/* ------------------------------------------------------------------ */
|
| +static void decReverse(Unit *ulo, Unit *uhi) {
|
| + Unit temp;
|
| + for (; ulo<uhi; ulo++, uhi--) {
|
| + temp=*ulo;
|
| + *ulo=*uhi;
|
| + *uhi=temp;
|
| + }
|
| + return;
|
| + } /* decReverse */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decShiftToMost -- shift digits in array towards most significant */
|
| +/* */
|
| +/* uar is the array */
|
| +/* digits is the count of digits in use in the array */
|
| +/* shift is the number of zeros to pad with (least significant); */
|
| +/* it must be zero or positive */
|
| +/* */
|
| +/* returns the new length of the integer in the array, in digits */
|
| +/* */
|
| +/* No overflow is permitted (that is, the uar array must be known to */
|
| +/* be large enough to hold the result, after shifting). */
|
| +/* ------------------------------------------------------------------ */
|
| +static Int decShiftToMost(Unit *uar, Int digits, Int shift) {
|
| + Unit *target, *source, *first; /* work */
|
| + Int cut; /* odd 0's to add */
|
| + uInt next; /* work */
|
| +
|
| + if (shift==0) return digits; /* [fastpath] nothing to do */
|
| + if ((digits+shift)<=DECDPUN) { /* [fastpath] single-unit case */
|
| + *uar=(Unit)(*uar*powers[shift]);
|
| + return digits+shift;
|
| + }
|
| +
|
| + next=0; /* all paths */
|
| + source=uar+D2U(digits)-1; /* where msu comes from */
|
| + target=source+D2U(shift); /* where upper part of first cut goes */
|
| + cut=DECDPUN-MSUDIGITS(shift); /* where to slice */
|
| + if (cut==0) { /* unit-boundary case */
|
| + for (; source>=uar; source--, target--) *target=*source;
|
| + }
|
| + else {
|
| + first=uar+D2U(digits+shift)-1; /* where msu of source will end up */
|
| + for (; source>=uar; source--, target--) {
|
| + /* split the source Unit and accumulate remainder for next */
|
| + #if DECDPUN<=4
|
| + uInt quot=QUOT10(*source, cut);
|
| + uInt rem=*source-quot*powers[cut];
|
| + next+=quot;
|
| + #else
|
| + uInt rem=*source%powers[cut];
|
| + next+=*source/powers[cut];
|
| + #endif
|
| + if (target<=first) *target=(Unit)next; /* write to target iff valid */
|
| + next=rem*powers[DECDPUN-cut]; /* save remainder for next Unit */
|
| + }
|
| + } /* shift-move */
|
| +
|
| + /* propagate any partial unit to one below and clear the rest */
|
| + for (; target>=uar; target--) {
|
| + *target=(Unit)next;
|
| + next=0;
|
| + }
|
| + return digits+shift;
|
| + } /* decShiftToMost */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decShiftToLeast -- shift digits in array towards least significant */
|
| +/* */
|
| +/* uar is the array */
|
| +/* units is length of the array, in units */
|
| +/* shift is the number of digits to remove from the lsu end; it */
|
| +/* must be zero or positive and <= than units*DECDPUN. */
|
| +/* */
|
| +/* returns the new length of the integer in the array, in units */
|
| +/* */
|
| +/* Removed digits are discarded (lost). Units not required to hold */
|
| +/* the final result are unchanged. */
|
| +/* ------------------------------------------------------------------ */
|
| +static Int decShiftToLeast(Unit *uar, Int units, Int shift) {
|
| + Unit *target, *up; /* work */
|
| + Int cut, count; /* work */
|
| + Int quot, rem; /* for division */
|
| +
|
| + if (shift==0) return units; /* [fastpath] nothing to do */
|
| + if (shift==units*DECDPUN) { /* [fastpath] little to do */
|
| + *uar=0; /* all digits cleared gives zero */
|
| + return 1; /* leaves just the one */
|
| + }
|
| +
|
| + target=uar; /* both paths */
|
| + cut=MSUDIGITS(shift);
|
| + if (cut==DECDPUN) { /* unit-boundary case; easy */
|
| + up=uar+D2U(shift);
|
| + for (; up<uar+units; target++, up++) *target=*up;
|
| + return target-uar;
|
| + }
|
| +
|
| + /* messier */
|
| + up=uar+D2U(shift-cut); /* source; correct to whole Units */
|
| + count=units*DECDPUN-shift; /* the maximum new length */
|
| + #if DECDPUN<=4
|
| + quot=QUOT10(*up, cut);
|
| + #else
|
| + quot=*up/powers[cut];
|
| + #endif
|
| + for (; ; target++) {
|
| + *target=(Unit)quot;
|
| + count-=(DECDPUN-cut);
|
| + if (count<=0) break;
|
| + up++;
|
| + quot=*up;
|
| + #if DECDPUN<=4
|
| + quot=QUOT10(quot, cut);
|
| + rem=*up-quot*powers[cut];
|
| + #else
|
| + rem=quot%powers[cut];
|
| + quot=quot/powers[cut];
|
| + #endif
|
| + *target=(Unit)(*target+rem*powers[DECDPUN-cut]);
|
| + count-=cut;
|
| + if (count<=0) break;
|
| + }
|
| + return target-uar+1;
|
| + } /* decShiftToLeast */
|
| +
|
| +#if DECSUBSET
|
| +/* ------------------------------------------------------------------ */
|
| +/* decRoundOperand -- round an operand [used for subset only] */
|
| +/* */
|
| +/* dn is the number to round (dn->digits is > set->digits) */
|
| +/* set is the relevant context */
|
| +/* status is the status accumulator */
|
| +/* */
|
| +/* returns an allocated decNumber with the rounded result. */
|
| +/* */
|
| +/* lostDigits and other status may be set by this. */
|
| +/* */
|
| +/* Since the input is an operand, it must not be modified. */
|
| +/* Instead, return an allocated decNumber, rounded as required. */
|
| +/* It is the caller's responsibility to free the allocated storage. */
|
| +/* */
|
| +/* If no storage is available then the result cannot be used, so NULL */
|
| +/* is returned. */
|
| +/* ------------------------------------------------------------------ */
|
| +static decNumber *decRoundOperand(const decNumber *dn, decContext *set,
|
| + uInt *status) {
|
| + decNumber *res; /* result structure */
|
| + uInt newstatus=0; /* status from round */
|
| + Int residue=0; /* rounding accumulator */
|
| +
|
| + /* Allocate storage for the returned decNumber, big enough for the */
|
| + /* length specified by the context */
|
| + res=(decNumber *)malloc(sizeof(decNumber)
|
| + +(D2U(set->digits)-1)*sizeof(Unit));
|
| + if (res==NULL) {
|
| + *status|=DEC_Insufficient_storage;
|
| + return NULL;
|
| + }
|
| + decCopyFit(res, dn, set, &residue, &newstatus);
|
| + decApplyRound(res, set, residue, &newstatus);
|
| +
|
| + /* If that set Inexact then "lost digits" is raised... */
|
| + if (newstatus & DEC_Inexact) newstatus|=DEC_Lost_digits;
|
| + *status|=newstatus;
|
| + return res;
|
| + } /* decRoundOperand */
|
| +#endif
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decCopyFit -- copy a number, truncating the coefficient if needed */
|
| +/* */
|
| +/* dest is the target decNumber */
|
| +/* src is the source decNumber */
|
| +/* set is the context [used for length (digits) and rounding mode] */
|
| +/* residue is the residue accumulator */
|
| +/* status contains the current status to be updated */
|
| +/* */
|
| +/* (dest==src is allowed and will be a no-op if fits) */
|
| +/* All fields are updated as required. */
|
| +/* ------------------------------------------------------------------ */
|
| +static void decCopyFit(decNumber *dest, const decNumber *src,
|
| + decContext *set, Int *residue, uInt *status) {
|
| + dest->bits=src->bits;
|
| + dest->exponent=src->exponent;
|
| + decSetCoeff(dest, set, src->lsu, src->digits, residue, status);
|
| + } /* decCopyFit */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decSetCoeff -- set the coefficient of a number */
|
| +/* */
|
| +/* dn is the number whose coefficient array is to be set. */
|
| +/* It must have space for set->digits digits */
|
| +/* set is the context [for size] */
|
| +/* lsu -> lsu of the source coefficient [may be dn->lsu] */
|
| +/* len is digits in the source coefficient [may be dn->digits] */
|
| +/* residue is the residue accumulator. This has values as in */
|
| +/* decApplyRound, and will be unchanged unless the */
|
| +/* target size is less than len. In this case, the */
|
| +/* coefficient is truncated and the residue is updated to */
|
| +/* reflect the previous residue and the dropped digits. */
|
| +/* status is the status accumulator, as usual */
|
| +/* */
|
| +/* The coefficient may already be in the number, or it can be an */
|
| +/* external intermediate array. If it is in the number, lsu must == */
|
| +/* dn->lsu and len must == dn->digits. */
|
| +/* */
|
| +/* Note that the coefficient length (len) may be < set->digits, and */
|
| +/* in this case this merely copies the coefficient (or is a no-op */
|
| +/* if dn->lsu==lsu). */
|
| +/* */
|
| +/* Note also that (only internally, from decQuantizeOp and */
|
| +/* decSetSubnormal) the value of set->digits may be less than one, */
|
| +/* indicating a round to left. This routine handles that case */
|
| +/* correctly; caller ensures space. */
|
| +/* */
|
| +/* dn->digits, dn->lsu (and as required), and dn->exponent are */
|
| +/* updated as necessary. dn->bits (sign) is unchanged. */
|
| +/* */
|
| +/* DEC_Rounded status is set if any digits are discarded. */
|
| +/* DEC_Inexact status is set if any non-zero digits are discarded, or */
|
| +/* incoming residue was non-0 (implies rounded) */
|
| +/* ------------------------------------------------------------------ */
|
| +/* mapping array: maps 0-9 to canonical residues, so that a residue */
|
| +/* can be adjusted in the range [-1, +1] and achieve correct rounding */
|
| +/* 0 1 2 3 4 5 6 7 8 9 */
|
| +static const uByte resmap[10]={0, 3, 3, 3, 3, 5, 7, 7, 7, 7};
|
| +static void decSetCoeff(decNumber *dn, decContext *set, const Unit *lsu,
|
| + Int len, Int *residue, uInt *status) {
|
| + Int discard; /* number of digits to discard */
|
| + uInt cut; /* cut point in Unit */
|
| + const Unit *up; /* work */
|
| + Unit *target; /* .. */
|
| + Int count; /* .. */
|
| + #if DECDPUN<=4
|
| + uInt temp; /* .. */
|
| + #endif
|
| +
|
| + discard=len-set->digits; /* digits to discard */
|
| + if (discard<=0) { /* no digits are being discarded */
|
| + if (dn->lsu!=lsu) { /* copy needed */
|
| + /* copy the coefficient array to the result number; no shift needed */
|
| + count=len; /* avoids D2U */
|
| + up=lsu;
|
| + for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)
|
| + *target=*up;
|
| + dn->digits=len; /* set the new length */
|
| + }
|
| + /* dn->exponent and residue are unchanged, record any inexactitude */
|
| + if (*residue!=0) *status|=(DEC_Inexact | DEC_Rounded);
|
| + return;
|
| + }
|
| +
|
| + /* some digits must be discarded ... */
|
| + dn->exponent+=discard; /* maintain numerical value */
|
| + *status|=DEC_Rounded; /* accumulate Rounded status */
|
| + if (*residue>1) *residue=1; /* previous residue now to right, so reduce */
|
| +
|
| + if (discard>len) { /* everything, +1, is being discarded */
|
| + /* guard digit is 0 */
|
| + /* residue is all the number [NB could be all 0s] */
|
| + if (*residue<=0) { /* not already positive */
|
| + count=len; /* avoids D2U */
|
| + for (up=lsu; count>0; up++, count-=DECDPUN) if (*up!=0) { /* found non-0 */
|
| + *residue=1;
|
| + break; /* no need to check any others */
|
| + }
|
| + }
|
| + if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */
|
| + *dn->lsu=0; /* coefficient will now be 0 */
|
| + dn->digits=1; /* .. */
|
| + return;
|
| + } /* total discard */
|
| +
|
| + /* partial discard [most common case] */
|
| + /* here, at least the first (most significant) discarded digit exists */
|
| +
|
| + /* spin up the number, noting residue during the spin, until get to */
|
| + /* the Unit with the first discarded digit. When reach it, extract */
|
| + /* it and remember its position */
|
| + count=0;
|
| + for (up=lsu;; up++) {
|
| + count+=DECDPUN;
|
| + if (count>=discard) break; /* full ones all checked */
|
| + if (*up!=0) *residue=1;
|
| + } /* up */
|
| +
|
| + /* here up -> Unit with first discarded digit */
|
| + cut=discard-(count-DECDPUN)-1;
|
| + if (cut==DECDPUN-1) { /* unit-boundary case (fast) */
|
| + Unit half=(Unit)powers[DECDPUN]>>1;
|
| + /* set residue directly */
|
| + if (*up>=half) {
|
| + if (*up>half) *residue=7;
|
| + else *residue+=5; /* add sticky bit */
|
| + }
|
| + else { /* <half */
|
| + if (*up!=0) *residue=3; /* [else is 0, leave as sticky bit] */
|
| + }
|
| + if (set->digits<=0) { /* special for Quantize/Subnormal :-( */
|
| + *dn->lsu=0; /* .. result is 0 */
|
| + dn->digits=1; /* .. */
|
| + }
|
| + else { /* shift to least */
|
| + count=set->digits; /* now digits to end up with */
|
| + dn->digits=count; /* set the new length */
|
| + up++; /* move to next */
|
| + /* on unit boundary, so shift-down copy loop is simple */
|
| + for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)
|
| + *target=*up;
|
| + }
|
| + } /* unit-boundary case */
|
| +
|
| + else { /* discard digit is in low digit(s), and not top digit */
|
| + uInt discard1; /* first discarded digit */
|
| + uInt quot, rem; /* for divisions */
|
| + if (cut==0) quot=*up; /* is at bottom of unit */
|
| + else /* cut>0 */ { /* it's not at bottom of unit */
|
| + #if DECDPUN<=4
|
| + quot=QUOT10(*up, cut);
|
| + rem=*up-quot*powers[cut];
|
| + #else
|
| + rem=*up%powers[cut];
|
| + quot=*up/powers[cut];
|
| + #endif
|
| + if (rem!=0) *residue=1;
|
| + }
|
| + /* discard digit is now at bottom of quot */
|
| + #if DECDPUN<=4
|
| + temp=(quot*6554)>>16; /* fast /10 */
|
| + /* Vowels algorithm here not a win (9 instructions) */
|
| + discard1=quot-X10(temp);
|
| + quot=temp;
|
| + #else
|
| + discard1=quot%10;
|
| + quot=quot/10;
|
| + #endif
|
| + /* here, discard1 is the guard digit, and residue is everything */
|
| + /* else [use mapping array to accumulate residue safely] */
|
| + *residue+=resmap[discard1];
|
| + cut++; /* update cut */
|
| + /* here: up -> Unit of the array with bottom digit */
|
| + /* cut is the division point for each Unit */
|
| + /* quot holds the uncut high-order digits for the current unit */
|
| + if (set->digits<=0) { /* special for Quantize/Subnormal :-( */
|
| + *dn->lsu=0; /* .. result is 0 */
|
| + dn->digits=1; /* .. */
|
| + }
|
| + else { /* shift to least needed */
|
| + count=set->digits; /* now digits to end up with */
|
| + dn->digits=count; /* set the new length */
|
| + /* shift-copy the coefficient array to the result number */
|
| + for (target=dn->lsu; ; target++) {
|
| + *target=(Unit)quot;
|
| + count-=(DECDPUN-cut);
|
| + if (count<=0) break;
|
| + up++;
|
| + quot=*up;
|
| + #if DECDPUN<=4
|
| + quot=QUOT10(quot, cut);
|
| + rem=*up-quot*powers[cut];
|
| + #else
|
| + rem=quot%powers[cut];
|
| + quot=quot/powers[cut];
|
| + #endif
|
| + *target=(Unit)(*target+rem*powers[DECDPUN-cut]);
|
| + count-=cut;
|
| + if (count<=0) break;
|
| + } /* shift-copy loop */
|
| + } /* shift to least */
|
| + } /* not unit boundary */
|
| +
|
| + if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */
|
| + return;
|
| + } /* decSetCoeff */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decApplyRound -- apply pending rounding to a number */
|
| +/* */
|
| +/* dn is the number, with space for set->digits digits */
|
| +/* set is the context [for size and rounding mode] */
|
| +/* residue indicates pending rounding, being any accumulated */
|
| +/* guard and sticky information. It may be: */
|
| +/* 6-9: rounding digit is >5 */
|
| +/* 5: rounding digit is exactly half-way */
|
| +/* 1-4: rounding digit is <5 and >0 */
|
| +/* 0: the coefficient is exact */
|
| +/* -1: as 1, but the hidden digits are subtractive, that */
|
| +/* is, of the opposite sign to dn. In this case the */
|
| +/* coefficient must be non-0. This case occurs when */
|
| +/* subtracting a small number (which can be reduced to */
|
| +/* a sticky bit); see decAddOp. */
|
| +/* status is the status accumulator, as usual */
|
| +/* */
|
| +/* This routine applies rounding while keeping the length of the */
|
| +/* coefficient constant. The exponent and status are unchanged */
|
| +/* except if: */
|
| +/* */
|
| +/* -- the coefficient was increased and is all nines (in which */
|
| +/* case Overflow could occur, and is handled directly here so */
|
| +/* the caller does not need to re-test for overflow) */
|
| +/* */
|
| +/* -- the coefficient was decreased and becomes all nines (in which */
|
| +/* case Underflow could occur, and is also handled directly). */
|
| +/* */
|
| +/* All fields in dn are updated as required. */
|
| +/* */
|
| +/* ------------------------------------------------------------------ */
|
| +static void decApplyRound(decNumber *dn, decContext *set, Int residue,
|
| + uInt *status) {
|
| + Int bump; /* 1 if coefficient needs to be incremented */
|
| + /* -1 if coefficient needs to be decremented */
|
| +
|
| + if (residue==0) return; /* nothing to apply */
|
| +
|
| + bump=0; /* assume a smooth ride */
|
| +
|
| + /* now decide whether, and how, to round, depending on mode */
|
| + switch (set->round) {
|
| + case DEC_ROUND_05UP: { /* round zero or five up (for reround) */
|
| + /* This is the same as DEC_ROUND_DOWN unless there is a */
|
| + /* positive residue and the lsd of dn is 0 or 5, in which case */
|
| + /* it is bumped; when residue is <0, the number is therefore */
|
| + /* bumped down unless the final digit was 1 or 6 (in which */
|
| + /* case it is bumped down and then up -- a no-op) */
|
| + Int lsd5=*dn->lsu%5; /* get lsd and quintate */
|
| + if (residue<0 && lsd5!=1) bump=-1;
|
| + else if (residue>0 && lsd5==0) bump=1;
|
| + /* [bump==1 could be applied directly; use common path for clarity] */
|
| + break;} /* r-05 */
|
| +
|
| + case DEC_ROUND_DOWN: {
|
| + /* no change, except if negative residue */
|
| + if (residue<0) bump=-1;
|
| + break;} /* r-d */
|
| +
|
| + case DEC_ROUND_HALF_DOWN: {
|
| + if (residue>5) bump=1;
|
| + break;} /* r-h-d */
|
| +
|
| + case DEC_ROUND_HALF_EVEN: {
|
| + if (residue>5) bump=1; /* >0.5 goes up */
|
| + else if (residue==5) { /* exactly 0.5000... */
|
| + /* 0.5 goes up iff [new] lsd is odd */
|
| + if (*dn->lsu & 0x01) bump=1;
|
| + }
|
| + break;} /* r-h-e */
|
| +
|
| + case DEC_ROUND_HALF_UP: {
|
| + if (residue>=5) bump=1;
|
| + break;} /* r-h-u */
|
| +
|
| + case DEC_ROUND_UP: {
|
| + if (residue>0) bump=1;
|
| + break;} /* r-u */
|
| +
|
| + case DEC_ROUND_CEILING: {
|
| + /* same as _UP for positive numbers, and as _DOWN for negatives */
|
| + /* [negative residue cannot occur on 0] */
|
| + if (decNumberIsNegative(dn)) {
|
| + if (residue<0) bump=-1;
|
| + }
|
| + else {
|
| + if (residue>0) bump=1;
|
| + }
|
| + break;} /* r-c */
|
| +
|
| + case DEC_ROUND_FLOOR: {
|
| + /* same as _UP for negative numbers, and as _DOWN for positive */
|
| + /* [negative residue cannot occur on 0] */
|
| + if (!decNumberIsNegative(dn)) {
|
| + if (residue<0) bump=-1;
|
| + }
|
| + else {
|
| + if (residue>0) bump=1;
|
| + }
|
| + break;} /* r-f */
|
| +
|
| + default: { /* e.g., DEC_ROUND_MAX */
|
| + *status|=DEC_Invalid_context;
|
| + #if DECTRACE || (DECCHECK && DECVERB)
|
| + printf("Unknown rounding mode: %d\n", set->round);
|
| + #endif
|
| + break;}
|
| + } /* switch */
|
| +
|
| + /* now bump the number, up or down, if need be */
|
| + if (bump==0) return; /* no action required */
|
| +
|
| + /* Simply use decUnitAddSub unless bumping up and the number is */
|
| + /* all nines. In this special case set to 100... explicitly */
|
| + /* and adjust the exponent by one (as otherwise could overflow */
|
| + /* the array) */
|
| + /* Similarly handle all-nines result if bumping down. */
|
| + if (bump>0) {
|
| + Unit *up; /* work */
|
| + uInt count=dn->digits; /* digits to be checked */
|
| + for (up=dn->lsu; ; up++) {
|
| + if (count<=DECDPUN) {
|
| + /* this is the last Unit (the msu) */
|
| + if (*up!=powers[count]-1) break; /* not still 9s */
|
| + /* here if it, too, is all nines */
|
| + *up=(Unit)powers[count-1]; /* here 999 -> 100 etc. */
|
| + for (up=up-1; up>=dn->lsu; up--) *up=0; /* others all to 0 */
|
| + dn->exponent++; /* and bump exponent */
|
| + /* [which, very rarely, could cause Overflow...] */
|
| + if ((dn->exponent+dn->digits)>set->emax+1) {
|
| + decSetOverflow(dn, set, status);
|
| + }
|
| + return; /* done */
|
| + }
|
| + /* a full unit to check, with more to come */
|
| + if (*up!=DECDPUNMAX) break; /* not still 9s */
|
| + count-=DECDPUN;
|
| + } /* up */
|
| + } /* bump>0 */
|
| + else { /* -1 */
|
| + /* here checking for a pre-bump of 1000... (leading 1, all */
|
| + /* other digits zero) */
|
| + Unit *up, *sup; /* work */
|
| + uInt count=dn->digits; /* digits to be checked */
|
| + for (up=dn->lsu; ; up++) {
|
| + if (count<=DECDPUN) {
|
| + /* this is the last Unit (the msu) */
|
| + if (*up!=powers[count-1]) break; /* not 100.. */
|
| + /* here if have the 1000... case */
|
| + sup=up; /* save msu pointer */
|
| + *up=(Unit)powers[count]-1; /* here 100 in msu -> 999 */
|
| + /* others all to all-nines, too */
|
| + for (up=up-1; up>=dn->lsu; up--) *up=(Unit)powers[DECDPUN]-1;
|
| + dn->exponent--; /* and bump exponent */
|
| +
|
| + /* iff the number was at the subnormal boundary (exponent=etiny) */
|
| + /* then the exponent is now out of range, so it will in fact get */
|
| + /* clamped to etiny and the final 9 dropped. */
|
| + /* printf(">> emin=%d exp=%d sdig=%d\n", set->emin, */
|
| + /* dn->exponent, set->digits); */
|
| + if (dn->exponent+1==set->emin-set->digits+1) {
|
| + if (count==1 && dn->digits==1) *sup=0; /* here 9 -> 0[.9] */
|
| + else {
|
| + *sup=(Unit)powers[count-1]-1; /* here 999.. in msu -> 99.. */
|
| + dn->digits--;
|
| + }
|
| + dn->exponent++;
|
| + *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
|
| + }
|
| + return; /* done */
|
| + }
|
| +
|
| + /* a full unit to check, with more to come */
|
| + if (*up!=0) break; /* not still 0s */
|
| + count-=DECDPUN;
|
| + } /* up */
|
| +
|
| + } /* bump<0 */
|
| +
|
| + /* Actual bump needed. Do it. */
|
| + decUnitAddSub(dn->lsu, D2U(dn->digits), uarrone, 1, 0, dn->lsu, bump);
|
| + } /* decApplyRound */
|
| +
|
| +#if DECSUBSET
|
| +/* ------------------------------------------------------------------ */
|
| +/* decFinish -- finish processing a number */
|
| +/* */
|
| +/* dn is the number */
|
| +/* set is the context */
|
| +/* residue is the rounding accumulator (as in decApplyRound) */
|
| +/* status is the accumulator */
|
| +/* */
|
| +/* This finishes off the current number by: */
|
| +/* 1. If not extended: */
|
| +/* a. Converting a zero result to clean '0' */
|
| +/* b. Reducing positive exponents to 0, if would fit in digits */
|
| +/* 2. Checking for overflow and subnormals (always) */
|
| +/* Note this is just Finalize when no subset arithmetic. */
|
| +/* All fields are updated as required. */
|
| +/* ------------------------------------------------------------------ */
|
| +static void decFinish(decNumber *dn, decContext *set, Int *residue,
|
| + uInt *status) {
|
| + if (!set->extended) {
|
| + if ISZERO(dn) { /* value is zero */
|
| + dn->exponent=0; /* clean exponent .. */
|
| + dn->bits=0; /* .. and sign */
|
| + return; /* no error possible */
|
| + }
|
| + if (dn->exponent>=0) { /* non-negative exponent */
|
| + /* >0; reduce to integer if possible */
|
| + if (set->digits >= (dn->exponent+dn->digits)) {
|
| + dn->digits=decShiftToMost(dn->lsu, dn->digits, dn->exponent);
|
| + dn->exponent=0;
|
| + }
|
| + }
|
| + } /* !extended */
|
| +
|
| + decFinalize(dn, set, residue, status);
|
| + } /* decFinish */
|
| +#endif
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decFinalize -- final check, clamp, and round of a number */
|
| +/* */
|
| +/* dn is the number */
|
| +/* set is the context */
|
| +/* residue is the rounding accumulator (as in decApplyRound) */
|
| +/* status is the status accumulator */
|
| +/* */
|
| +/* This finishes off the current number by checking for subnormal */
|
| +/* results, applying any pending rounding, checking for overflow, */
|
| +/* and applying any clamping. */
|
| +/* Underflow and overflow conditions are raised as appropriate. */
|
| +/* All fields are updated as required. */
|
| +/* ------------------------------------------------------------------ */
|
| +static void decFinalize(decNumber *dn, decContext *set, Int *residue,
|
| + uInt *status) {
|
| + Int shift; /* shift needed if clamping */
|
| + Int tinyexp=set->emin-dn->digits+1; /* precalculate subnormal boundary */
|
| +
|
| + /* Must be careful, here, when checking the exponent as the */
|
| + /* adjusted exponent could overflow 31 bits [because it may already */
|
| + /* be up to twice the expected]. */
|
| +
|
| + /* First test for subnormal. This must be done before any final */
|
| + /* round as the result could be rounded to Nmin or 0. */
|
| + if (dn->exponent<=tinyexp) { /* prefilter */
|
| + Int comp;
|
| + decNumber nmin;
|
| + /* A very nasty case here is dn == Nmin and residue<0 */
|
| + if (dn->exponent<tinyexp) {
|
| + /* Go handle subnormals; this will apply round if needed. */
|
| + decSetSubnormal(dn, set, residue, status);
|
| + return;
|
| + }
|
| + /* Equals case: only subnormal if dn=Nmin and negative residue */
|
| + uprv_decNumberZero(&nmin);
|
| + nmin.lsu[0]=1;
|
| + nmin.exponent=set->emin;
|
| + comp=decCompare(dn, &nmin, 1); /* (signless compare) */
|
| + if (comp==BADINT) { /* oops */
|
| + *status|=DEC_Insufficient_storage; /* abandon... */
|
| + return;
|
| + }
|
| + if (*residue<0 && comp==0) { /* neg residue and dn==Nmin */
|
| + decApplyRound(dn, set, *residue, status); /* might force down */
|
| + decSetSubnormal(dn, set, residue, status);
|
| + return;
|
| + }
|
| + }
|
| +
|
| + /* now apply any pending round (this could raise overflow). */
|
| + if (*residue!=0) decApplyRound(dn, set, *residue, status);
|
| +
|
| + /* Check for overflow [redundant in the 'rare' case] or clamp */
|
| + if (dn->exponent<=set->emax-set->digits+1) return; /* neither needed */
|
| +
|
| +
|
| + /* here when might have an overflow or clamp to do */
|
| + if (dn->exponent>set->emax-dn->digits+1) { /* too big */
|
| + decSetOverflow(dn, set, status);
|
| + return;
|
| + }
|
| + /* here when the result is normal but in clamp range */
|
| + if (!set->clamp) return;
|
| +
|
| + /* here when need to apply the IEEE exponent clamp (fold-down) */
|
| + shift=dn->exponent-(set->emax-set->digits+1);
|
| +
|
| + /* shift coefficient (if non-zero) */
|
| + if (!ISZERO(dn)) {
|
| + dn->digits=decShiftToMost(dn->lsu, dn->digits, shift);
|
| + }
|
| + dn->exponent-=shift; /* adjust the exponent to match */
|
| + *status|=DEC_Clamped; /* and record the dirty deed */
|
| + return;
|
| + } /* decFinalize */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decSetOverflow -- set number to proper overflow value */
|
| +/* */
|
| +/* dn is the number (used for sign [only] and result) */
|
| +/* set is the context [used for the rounding mode, etc.] */
|
| +/* status contains the current status to be updated */
|
| +/* */
|
| +/* This sets the sign of a number and sets its value to either */
|
| +/* Infinity or the maximum finite value, depending on the sign of */
|
| +/* dn and the rounding mode, following IEEE 754 rules. */
|
| +/* ------------------------------------------------------------------ */
|
| +static void decSetOverflow(decNumber *dn, decContext *set, uInt *status) {
|
| + Flag needmax=0; /* result is maximum finite value */
|
| + uByte sign=dn->bits&DECNEG; /* clean and save sign bit */
|
| +
|
| + if (ISZERO(dn)) { /* zero does not overflow magnitude */
|
| + Int emax=set->emax; /* limit value */
|
| + if (set->clamp) emax-=set->digits-1; /* lower if clamping */
|
| + if (dn->exponent>emax) { /* clamp required */
|
| + dn->exponent=emax;
|
| + *status|=DEC_Clamped;
|
| + }
|
| + return;
|
| + }
|
| +
|
| + uprv_decNumberZero(dn);
|
| + switch (set->round) {
|
| + case DEC_ROUND_DOWN: {
|
| + needmax=1; /* never Infinity */
|
| + break;} /* r-d */
|
| + case DEC_ROUND_05UP: {
|
| + needmax=1; /* never Infinity */
|
| + break;} /* r-05 */
|
| + case DEC_ROUND_CEILING: {
|
| + if (sign) needmax=1; /* Infinity if non-negative */
|
| + break;} /* r-c */
|
| + case DEC_ROUND_FLOOR: {
|
| + if (!sign) needmax=1; /* Infinity if negative */
|
| + break;} /* r-f */
|
| + default: break; /* Infinity in all other cases */
|
| + }
|
| + if (needmax) {
|
| + decSetMaxValue(dn, set);
|
| + dn->bits=sign; /* set sign */
|
| + }
|
| + else dn->bits=sign|DECINF; /* Value is +/-Infinity */
|
| + *status|=DEC_Overflow | DEC_Inexact | DEC_Rounded;
|
| + } /* decSetOverflow */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decSetMaxValue -- set number to +Nmax (maximum normal value) */
|
| +/* */
|
| +/* dn is the number to set */
|
| +/* set is the context [used for digits and emax] */
|
| +/* */
|
| +/* This sets the number to the maximum positive value. */
|
| +/* ------------------------------------------------------------------ */
|
| +static void decSetMaxValue(decNumber *dn, decContext *set) {
|
| + Unit *up; /* work */
|
| + Int count=set->digits; /* nines to add */
|
| + dn->digits=count;
|
| + /* fill in all nines to set maximum value */
|
| + for (up=dn->lsu; ; up++) {
|
| + if (count>DECDPUN) *up=DECDPUNMAX; /* unit full o'nines */
|
| + else { /* this is the msu */
|
| + *up=(Unit)(powers[count]-1);
|
| + break;
|
| + }
|
| + count-=DECDPUN; /* filled those digits */
|
| + } /* up */
|
| + dn->bits=0; /* + sign */
|
| + dn->exponent=set->emax-set->digits+1;
|
| + } /* decSetMaxValue */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decSetSubnormal -- process value whose exponent is <Emin */
|
| +/* */
|
| +/* dn is the number (used as input as well as output; it may have */
|
| +/* an allowed subnormal value, which may need to be rounded) */
|
| +/* set is the context [used for the rounding mode] */
|
| +/* residue is any pending residue */
|
| +/* status contains the current status to be updated */
|
| +/* */
|
| +/* If subset mode, set result to zero and set Underflow flags. */
|
| +/* */
|
| +/* Value may be zero with a low exponent; this does not set Subnormal */
|
| +/* but the exponent will be clamped to Etiny. */
|
| +/* */
|
| +/* Otherwise ensure exponent is not out of range, and round as */
|
| +/* necessary. Underflow is set if the result is Inexact. */
|
| +/* ------------------------------------------------------------------ */
|
| +static void decSetSubnormal(decNumber *dn, decContext *set, Int *residue,
|
| + uInt *status) {
|
| + decContext workset; /* work */
|
| + Int etiny, adjust; /* .. */
|
| +
|
| + #if DECSUBSET
|
| + /* simple set to zero and 'hard underflow' for subset */
|
| + if (!set->extended) {
|
| + uprv_decNumberZero(dn);
|
| + /* always full overflow */
|
| + *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
|
| + return;
|
| + }
|
| + #endif
|
| +
|
| + /* Full arithmetic -- allow subnormals, rounded to minimum exponent */
|
| + /* (Etiny) if needed */
|
| + etiny=set->emin-(set->digits-1); /* smallest allowed exponent */
|
| +
|
| + if ISZERO(dn) { /* value is zero */
|
| + /* residue can never be non-zero here */
|
| + #if DECCHECK
|
| + if (*residue!=0) {
|
| + printf("++ Subnormal 0 residue %ld\n", (LI)*residue);
|
| + *status|=DEC_Invalid_operation;
|
| + }
|
| + #endif
|
| + if (dn->exponent<etiny) { /* clamp required */
|
| + dn->exponent=etiny;
|
| + *status|=DEC_Clamped;
|
| + }
|
| + return;
|
| + }
|
| +
|
| + *status|=DEC_Subnormal; /* have a non-zero subnormal */
|
| + adjust=etiny-dn->exponent; /* calculate digits to remove */
|
| + if (adjust<=0) { /* not out of range; unrounded */
|
| + /* residue can never be non-zero here, except in the Nmin-residue */
|
| + /* case (which is a subnormal result), so can take fast-path here */
|
| + /* it may already be inexact (from setting the coefficient) */
|
| + if (*status&DEC_Inexact) *status|=DEC_Underflow;
|
| + return;
|
| + }
|
| +
|
| + /* adjust>0, so need to rescale the result so exponent becomes Etiny */
|
| + /* [this code is similar to that in rescale] */
|
| + workset=*set; /* clone rounding, etc. */
|
| + workset.digits=dn->digits-adjust; /* set requested length */
|
| + workset.emin-=adjust; /* and adjust emin to match */
|
| + /* [note that the latter can be <1, here, similar to Rescale case] */
|
| + decSetCoeff(dn, &workset, dn->lsu, dn->digits, residue, status);
|
| + decApplyRound(dn, &workset, *residue, status);
|
| +
|
| + /* Use 754 default rule: Underflow is set iff Inexact */
|
| + /* [independent of whether trapped] */
|
| + if (*status&DEC_Inexact) *status|=DEC_Underflow;
|
| +
|
| + /* if rounded up a 999s case, exponent will be off by one; adjust */
|
| + /* back if so [it will fit, because it was shortened earlier] */
|
| + if (dn->exponent>etiny) {
|
| + dn->digits=decShiftToMost(dn->lsu, dn->digits, 1);
|
| + dn->exponent--; /* (re)adjust the exponent. */
|
| + }
|
| +
|
| + /* if rounded to zero, it is by definition clamped... */
|
| + if (ISZERO(dn)) *status|=DEC_Clamped;
|
| + } /* decSetSubnormal */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decCheckMath - check entry conditions for a math function */
|
| +/* */
|
| +/* This checks the context and the operand */
|
| +/* */
|
| +/* rhs is the operand to check */
|
| +/* set is the context to check */
|
| +/* status is unchanged if both are good */
|
| +/* */
|
| +/* returns non-zero if status is changed, 0 otherwise */
|
| +/* */
|
| +/* Restrictions enforced: */
|
| +/* */
|
| +/* digits, emax, and -emin in the context must be less than */
|
| +/* DEC_MAX_MATH (999999), and A must be within these bounds if */
|
| +/* non-zero. Invalid_operation is set in the status if a */
|
| +/* restriction is violated. */
|
| +/* ------------------------------------------------------------------ */
|
| +static uInt decCheckMath(const decNumber *rhs, decContext *set,
|
| + uInt *status) {
|
| + uInt save=*status; /* record */
|
| + if (set->digits>DEC_MAX_MATH
|
| + || set->emax>DEC_MAX_MATH
|
| + || -set->emin>DEC_MAX_MATH) *status|=DEC_Invalid_context;
|
| + else if ((rhs->digits>DEC_MAX_MATH
|
| + || rhs->exponent+rhs->digits>DEC_MAX_MATH+1
|
| + || rhs->exponent+rhs->digits<2*(1-DEC_MAX_MATH))
|
| + && !ISZERO(rhs)) *status|=DEC_Invalid_operation;
|
| + return (*status!=save);
|
| + } /* decCheckMath */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decGetInt -- get integer from a number */
|
| +/* */
|
| +/* dn is the number [which will not be altered] */
|
| +/* */
|
| +/* returns one of: */
|
| +/* BADINT if there is a non-zero fraction */
|
| +/* the converted integer */
|
| +/* BIGEVEN if the integer is even and magnitude > 2*10**9 */
|
| +/* BIGODD if the integer is odd and magnitude > 2*10**9 */
|
| +/* */
|
| +/* This checks and gets a whole number from the input decNumber. */
|
| +/* The sign can be determined from dn by the caller when BIGEVEN or */
|
| +/* BIGODD is returned. */
|
| +/* ------------------------------------------------------------------ */
|
| +static Int decGetInt(const decNumber *dn) {
|
| + Int theInt; /* result accumulator */
|
| + const Unit *up; /* work */
|
| + Int got; /* digits (real or not) processed */
|
| + Int ilength=dn->digits+dn->exponent; /* integral length */
|
| + Flag neg=decNumberIsNegative(dn); /* 1 if -ve */
|
| +
|
| + /* The number must be an integer that fits in 10 digits */
|
| + /* Assert, here, that 10 is enough for any rescale Etiny */
|
| + #if DEC_MAX_EMAX > 999999999
|
| + #error GetInt may need updating [for Emax]
|
| + #endif
|
| + #if DEC_MIN_EMIN < -999999999
|
| + #error GetInt may need updating [for Emin]
|
| + #endif
|
| + if (ISZERO(dn)) return 0; /* zeros are OK, with any exponent */
|
| +
|
| + up=dn->lsu; /* ready for lsu */
|
| + theInt=0; /* ready to accumulate */
|
| + if (dn->exponent>=0) { /* relatively easy */
|
| + /* no fractional part [usual]; allow for positive exponent */
|
| + got=dn->exponent;
|
| + }
|
| + else { /* -ve exponent; some fractional part to check and discard */
|
| + Int count=-dn->exponent; /* digits to discard */
|
| + /* spin up whole units until reach the Unit with the unit digit */
|
| + for (; count>=DECDPUN; up++) {
|
| + if (*up!=0) return BADINT; /* non-zero Unit to discard */
|
| + count-=DECDPUN;
|
| + }
|
| + if (count==0) got=0; /* [a multiple of DECDPUN] */
|
| + else { /* [not multiple of DECDPUN] */
|
| + Int rem; /* work */
|
| + /* slice off fraction digits and check for non-zero */
|
| + #if DECDPUN<=4
|
| + theInt=QUOT10(*up, count);
|
| + rem=*up-theInt*powers[count];
|
| + #else
|
| + rem=*up%powers[count]; /* slice off discards */
|
| + theInt=*up/powers[count];
|
| + #endif
|
| + if (rem!=0) return BADINT; /* non-zero fraction */
|
| + /* it looks good */
|
| + got=DECDPUN-count; /* number of digits so far */
|
| + up++; /* ready for next */
|
| + }
|
| + }
|
| + /* now it's known there's no fractional part */
|
| +
|
| + /* tricky code now, to accumulate up to 9.3 digits */
|
| + if (got==0) {theInt=*up; got+=DECDPUN; up++;} /* ensure lsu is there */
|
| +
|
| + if (ilength<11) {
|
| + Int save=theInt;
|
| + /* collect any remaining unit(s) */
|
| + for (; got<ilength; up++) {
|
| + theInt+=*up*powers[got];
|
| + got+=DECDPUN;
|
| + }
|
| + if (ilength==10) { /* need to check for wrap */
|
| + if (theInt/(Int)powers[got-DECDPUN]!=(Int)*(up-1)) ilength=11;
|
| + /* [that test also disallows the BADINT result case] */
|
| + else if (neg && theInt>1999999997) ilength=11;
|
| + else if (!neg && theInt>999999999) ilength=11;
|
| + if (ilength==11) theInt=save; /* restore correct low bit */
|
| + }
|
| + }
|
| +
|
| + if (ilength>10) { /* too big */
|
| + if (theInt&1) return BIGODD; /* bottom bit 1 */
|
| + return BIGEVEN; /* bottom bit 0 */
|
| + }
|
| +
|
| + if (neg) theInt=-theInt; /* apply sign */
|
| + return theInt;
|
| + } /* decGetInt */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decDecap -- decapitate the coefficient of a number */
|
| +/* */
|
| +/* dn is the number to be decapitated */
|
| +/* drop is the number of digits to be removed from the left of dn; */
|
| +/* this must be <= dn->digits (if equal, the coefficient is */
|
| +/* set to 0) */
|
| +/* */
|
| +/* Returns dn; dn->digits will be <= the initial digits less drop */
|
| +/* (after removing drop digits there may be leading zero digits */
|
| +/* which will also be removed). Only dn->lsu and dn->digits change. */
|
| +/* ------------------------------------------------------------------ */
|
| +static decNumber *decDecap(decNumber *dn, Int drop) {
|
| + Unit *msu; /* -> target cut point */
|
| + Int cut; /* work */
|
| + if (drop>=dn->digits) { /* losing the whole thing */
|
| + #if DECCHECK
|
| + if (drop>dn->digits)
|
| + printf("decDecap called with drop>digits [%ld>%ld]\n",
|
| + (LI)drop, (LI)dn->digits);
|
| + #endif
|
| + dn->lsu[0]=0;
|
| + dn->digits=1;
|
| + return dn;
|
| + }
|
| + msu=dn->lsu+D2U(dn->digits-drop)-1; /* -> likely msu */
|
| + cut=MSUDIGITS(dn->digits-drop); /* digits to be in use in msu */
|
| + if (cut!=DECDPUN) *msu%=powers[cut]; /* clear left digits */
|
| + /* that may have left leading zero digits, so do a proper count... */
|
| + dn->digits=decGetDigits(dn->lsu, msu-dn->lsu+1);
|
| + return dn;
|
| + } /* decDecap */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decBiStr -- compare string with pairwise options */
|
| +/* */
|
| +/* targ is the string to compare */
|
| +/* str1 is one of the strings to compare against (length may be 0) */
|
| +/* str2 is the other; it must be the same length as str1 */
|
| +/* */
|
| +/* returns 1 if strings compare equal, (that is, it is the same */
|
| +/* length as str1 and str2, and each character of targ is in either */
|
| +/* str1 or str2 in the corresponding position), or 0 otherwise */
|
| +/* */
|
| +/* This is used for generic caseless compare, including the awkward */
|
| +/* case of the Turkish dotted and dotless Is. Use as (for example): */
|
| +/* if (decBiStr(test, "mike", "MIKE")) ... */
|
| +/* ------------------------------------------------------------------ */
|
| +static Flag decBiStr(const char *targ, const char *str1, const char *str2) {
|
| + for (;;targ++, str1++, str2++) {
|
| + if (*targ!=*str1 && *targ!=*str2) return 0;
|
| + /* *targ has a match in one (or both, if terminator) */
|
| + if (*targ=='\0') break;
|
| + } /* forever */
|
| + return 1;
|
| + } /* decBiStr */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNaNs -- handle NaN operand or operands */
|
| +/* */
|
| +/* res is the result number */
|
| +/* lhs is the first operand */
|
| +/* rhs is the second operand, or NULL if none */
|
| +/* context is used to limit payload length */
|
| +/* status contains the current status */
|
| +/* returns res in case convenient */
|
| +/* */
|
| +/* Called when one or both operands is a NaN, and propagates the */
|
| +/* appropriate result to res. When an sNaN is found, it is changed */
|
| +/* to a qNaN and Invalid operation is set. */
|
| +/* ------------------------------------------------------------------ */
|
| +static decNumber * decNaNs(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set,
|
| + uInt *status) {
|
| + /* This decision tree ends up with LHS being the source pointer, */
|
| + /* and status updated if need be */
|
| + if (lhs->bits & DECSNAN)
|
| + *status|=DEC_Invalid_operation | DEC_sNaN;
|
| + else if (rhs==NULL);
|
| + else if (rhs->bits & DECSNAN) {
|
| + lhs=rhs;
|
| + *status|=DEC_Invalid_operation | DEC_sNaN;
|
| + }
|
| + else if (lhs->bits & DECNAN);
|
| + else lhs=rhs;
|
| +
|
| + /* propagate the payload */
|
| + if (lhs->digits<=set->digits) uprv_decNumberCopy(res, lhs); /* easy */
|
| + else { /* too long */
|
| + const Unit *ul;
|
| + Unit *ur, *uresp1;
|
| + /* copy safe number of units, then decapitate */
|
| + res->bits=lhs->bits; /* need sign etc. */
|
| + uresp1=res->lsu+D2U(set->digits);
|
| + for (ur=res->lsu, ul=lhs->lsu; ur<uresp1; ur++, ul++) *ur=*ul;
|
| + res->digits=D2U(set->digits)*DECDPUN;
|
| + /* maybe still too long */
|
| + if (res->digits>set->digits) decDecap(res, res->digits-set->digits);
|
| + }
|
| +
|
| + res->bits&=~DECSNAN; /* convert any sNaN to NaN, while */
|
| + res->bits|=DECNAN; /* .. preserving sign */
|
| + res->exponent=0; /* clean exponent */
|
| + /* [coefficient was copied/decapitated] */
|
| + return res;
|
| + } /* decNaNs */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decStatus -- apply non-zero status */
|
| +/* */
|
| +/* dn is the number to set if error */
|
| +/* status contains the current status (not yet in context) */
|
| +/* set is the context */
|
| +/* */
|
| +/* If the status is an error status, the number is set to a NaN, */
|
| +/* unless the error was an overflow, divide-by-zero, or underflow, */
|
| +/* in which case the number will have already been set. */
|
| +/* */
|
| +/* The context status is then updated with the new status. Note that */
|
| +/* this may raise a signal, so control may never return from this */
|
| +/* routine (hence resources must be recovered before it is called). */
|
| +/* ------------------------------------------------------------------ */
|
| +static void decStatus(decNumber *dn, uInt status, decContext *set) {
|
| + if (status & DEC_NaNs) { /* error status -> NaN */
|
| + /* if cause was an sNaN, clear and propagate [NaN is already set up] */
|
| + if (status & DEC_sNaN) status&=~DEC_sNaN;
|
| + else {
|
| + uprv_decNumberZero(dn); /* other error: clean throughout */
|
| + dn->bits=DECNAN; /* and make a quiet NaN */
|
| + }
|
| + }
|
| + uprv_decContextSetStatus(set, status); /* [may not return] */
|
| + return;
|
| + } /* decStatus */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decGetDigits -- count digits in a Units array */
|
| +/* */
|
| +/* uar is the Unit array holding the number (this is often an */
|
| +/* accumulator of some sort) */
|
| +/* len is the length of the array in units [>=1] */
|
| +/* */
|
| +/* returns the number of (significant) digits in the array */
|
| +/* */
|
| +/* All leading zeros are excluded, except the last if the array has */
|
| +/* only zero Units. */
|
| +/* ------------------------------------------------------------------ */
|
| +/* This may be called twice during some operations. */
|
| +static Int decGetDigits(Unit *uar, Int len) {
|
| + Unit *up=uar+(len-1); /* -> msu */
|
| + Int digits=(len-1)*DECDPUN+1; /* possible digits excluding msu */
|
| + #if DECDPUN>4
|
| + uInt const *pow; /* work */
|
| + #endif
|
| + /* (at least 1 in final msu) */
|
| + #if DECCHECK
|
| + if (len<1) printf("decGetDigits called with len<1 [%ld]\n", (LI)len);
|
| + #endif
|
| +
|
| + for (; up>=uar; up--) {
|
| + if (*up==0) { /* unit is all 0s */
|
| + if (digits==1) break; /* a zero has one digit */
|
| + digits-=DECDPUN; /* adjust for 0 unit */
|
| + continue;}
|
| + /* found the first (most significant) non-zero Unit */
|
| + #if DECDPUN>1 /* not done yet */
|
| + if (*up<10) break; /* is 1-9 */
|
| + digits++;
|
| + #if DECDPUN>2 /* not done yet */
|
| + if (*up<100) break; /* is 10-99 */
|
| + digits++;
|
| + #if DECDPUN>3 /* not done yet */
|
| + if (*up<1000) break; /* is 100-999 */
|
| + digits++;
|
| + #if DECDPUN>4 /* count the rest ... */
|
| + for (pow=&powers[4]; *up>=*pow; pow++) digits++;
|
| + #endif
|
| + #endif
|
| + #endif
|
| + #endif
|
| + break;
|
| + } /* up */
|
| + return digits;
|
| + } /* decGetDigits */
|
| +
|
| +#if DECTRACE | DECCHECK
|
| +/* ------------------------------------------------------------------ */
|
| +/* decNumberShow -- display a number [debug aid] */
|
| +/* dn is the number to show */
|
| +/* */
|
| +/* Shows: sign, exponent, coefficient (msu first), digits */
|
| +/* or: sign, special-value */
|
| +/* ------------------------------------------------------------------ */
|
| +/* this is public so other modules can use it */
|
| +void uprv_decNumberShow(const decNumber *dn) {
|
| + const Unit *up; /* work */
|
| + uInt u, d; /* .. */
|
| + Int cut; /* .. */
|
| + char isign='+'; /* main sign */
|
| + if (dn==NULL) {
|
| + printf("NULL\n");
|
| + return;}
|
| + if (decNumberIsNegative(dn)) isign='-';
|
| + printf(" >> %c ", isign);
|
| + if (dn->bits&DECSPECIAL) { /* Is a special value */
|
| + if (decNumberIsInfinite(dn)) printf("Infinity");
|
| + else { /* a NaN */
|
| + if (dn->bits&DECSNAN) printf("sNaN"); /* signalling NaN */
|
| + else printf("NaN");
|
| + }
|
| + /* if coefficient and exponent are 0, no more to do */
|
| + if (dn->exponent==0 && dn->digits==1 && *dn->lsu==0) {
|
| + printf("\n");
|
| + return;}
|
| + /* drop through to report other information */
|
| + printf(" ");
|
| + }
|
| +
|
| + /* now carefully display the coefficient */
|
| + up=dn->lsu+D2U(dn->digits)-1; /* msu */
|
| + printf("%ld", (LI)*up);
|
| + for (up=up-1; up>=dn->lsu; up--) {
|
| + u=*up;
|
| + printf(":");
|
| + for (cut=DECDPUN-1; cut>=0; cut--) {
|
| + d=u/powers[cut];
|
| + u-=d*powers[cut];
|
| + printf("%ld", (LI)d);
|
| + } /* cut */
|
| + } /* up */
|
| + if (dn->exponent!=0) {
|
| + char esign='+';
|
| + if (dn->exponent<0) esign='-';
|
| + printf(" E%c%ld", esign, (LI)abs(dn->exponent));
|
| + }
|
| + printf(" [%ld]\n", (LI)dn->digits);
|
| + } /* decNumberShow */
|
| +#endif
|
| +
|
| +#if DECTRACE || DECCHECK
|
| +/* ------------------------------------------------------------------ */
|
| +/* decDumpAr -- display a unit array [debug/check aid] */
|
| +/* name is a single-character tag name */
|
| +/* ar is the array to display */
|
| +/* len is the length of the array in Units */
|
| +/* ------------------------------------------------------------------ */
|
| +static void decDumpAr(char name, const Unit *ar, Int len) {
|
| + Int i;
|
| + const char *spec;
|
| + #if DECDPUN==9
|
| + spec="%09d ";
|
| + #elif DECDPUN==8
|
| + spec="%08d ";
|
| + #elif DECDPUN==7
|
| + spec="%07d ";
|
| + #elif DECDPUN==6
|
| + spec="%06d ";
|
| + #elif DECDPUN==5
|
| + spec="%05d ";
|
| + #elif DECDPUN==4
|
| + spec="%04d ";
|
| + #elif DECDPUN==3
|
| + spec="%03d ";
|
| + #elif DECDPUN==2
|
| + spec="%02d ";
|
| + #else
|
| + spec="%d ";
|
| + #endif
|
| + printf(" :%c: ", name);
|
| + for (i=len-1; i>=0; i--) {
|
| + if (i==len-1) printf("%ld ", (LI)ar[i]);
|
| + else printf(spec, ar[i]);
|
| + }
|
| + printf("\n");
|
| + return;}
|
| +#endif
|
| +
|
| +#if DECCHECK
|
| +/* ------------------------------------------------------------------ */
|
| +/* decCheckOperands -- check operand(s) to a routine */
|
| +/* res is the result structure (not checked; it will be set to */
|
| +/* quiet NaN if error found (and it is not NULL)) */
|
| +/* lhs is the first operand (may be DECUNRESU) */
|
| +/* rhs is the second (may be DECUNUSED) */
|
| +/* set is the context (may be DECUNCONT) */
|
| +/* returns 0 if both operands, and the context are clean, or 1 */
|
| +/* otherwise (in which case the context will show an error, */
|
| +/* unless NULL). Note that res is not cleaned; caller should */
|
| +/* handle this so res=NULL case is safe. */
|
| +/* The caller is expected to abandon immediately if 1 is returned. */
|
| +/* ------------------------------------------------------------------ */
|
| +static Flag decCheckOperands(decNumber *res, const decNumber *lhs,
|
| + const decNumber *rhs, decContext *set) {
|
| + Flag bad=0;
|
| + if (set==NULL) { /* oops; hopeless */
|
| + #if DECTRACE || DECVERB
|
| + printf("Reference to context is NULL.\n");
|
| + #endif
|
| + bad=1;
|
| + return 1;}
|
| + else if (set!=DECUNCONT
|
| + && (set->digits<1 || set->round>=DEC_ROUND_MAX)) {
|
| + bad=1;
|
| + #if DECTRACE || DECVERB
|
| + printf("Bad context [digits=%ld round=%ld].\n",
|
| + (LI)set->digits, (LI)set->round);
|
| + #endif
|
| + }
|
| + else {
|
| + if (res==NULL) {
|
| + bad=1;
|
| + #if DECTRACE
|
| + /* this one not DECVERB as standard tests include NULL */
|
| + printf("Reference to result is NULL.\n");
|
| + #endif
|
| + }
|
| + if (!bad && lhs!=DECUNUSED) bad=(decCheckNumber(lhs));
|
| + if (!bad && rhs!=DECUNUSED) bad=(decCheckNumber(rhs));
|
| + }
|
| + if (bad) {
|
| + if (set!=DECUNCONT) uprv_decContextSetStatus(set, DEC_Invalid_operation);
|
| + if (res!=DECUNRESU && res!=NULL) {
|
| + uprv_decNumberZero(res);
|
| + res->bits=DECNAN; /* qNaN */
|
| + }
|
| + }
|
| + return bad;
|
| + } /* decCheckOperands */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decCheckNumber -- check a number */
|
| +/* dn is the number to check */
|
| +/* returns 0 if the number is clean, or 1 otherwise */
|
| +/* */
|
| +/* The number is considered valid if it could be a result from some */
|
| +/* operation in some valid context. */
|
| +/* ------------------------------------------------------------------ */
|
| +static Flag decCheckNumber(const decNumber *dn) {
|
| + const Unit *up; /* work */
|
| + uInt maxuint; /* .. */
|
| + Int ae, d, digits; /* .. */
|
| + Int emin, emax; /* .. */
|
| +
|
| + if (dn==NULL) { /* hopeless */
|
| + #if DECTRACE
|
| + /* this one not DECVERB as standard tests include NULL */
|
| + printf("Reference to decNumber is NULL.\n");
|
| + #endif
|
| + return 1;}
|
| +
|
| + /* check special values */
|
| + if (dn->bits & DECSPECIAL) {
|
| + if (dn->exponent!=0) {
|
| + #if DECTRACE || DECVERB
|
| + printf("Exponent %ld (not 0) for a special value [%02x].\n",
|
| + (LI)dn->exponent, dn->bits);
|
| + #endif
|
| + return 1;}
|
| +
|
| + /* 2003.09.08: NaNs may now have coefficients, so next tests Inf only */
|
| + if (decNumberIsInfinite(dn)) {
|
| + if (dn->digits!=1) {
|
| + #if DECTRACE || DECVERB
|
| + printf("Digits %ld (not 1) for an infinity.\n", (LI)dn->digits);
|
| + #endif
|
| + return 1;}
|
| + if (*dn->lsu!=0) {
|
| + #if DECTRACE || DECVERB
|
| + printf("LSU %ld (not 0) for an infinity.\n", (LI)*dn->lsu);
|
| + #endif
|
| + decDumpAr('I', dn->lsu, D2U(dn->digits));
|
| + return 1;}
|
| + } /* Inf */
|
| + /* 2002.12.26: negative NaNs can now appear through proposed IEEE */
|
| + /* concrete formats (decimal64, etc.). */
|
| + return 0;
|
| + }
|
| +
|
| + /* check the coefficient */
|
| + if (dn->digits<1 || dn->digits>DECNUMMAXP) {
|
| + #if DECTRACE || DECVERB
|
| + printf("Digits %ld in number.\n", (LI)dn->digits);
|
| + #endif
|
| + return 1;}
|
| +
|
| + d=dn->digits;
|
| +
|
| + for (up=dn->lsu; d>0; up++) {
|
| + if (d>DECDPUN) maxuint=DECDPUNMAX;
|
| + else { /* reached the msu */
|
| + maxuint=powers[d]-1;
|
| + if (dn->digits>1 && *up<powers[d-1]) {
|
| + #if DECTRACE || DECVERB
|
| + printf("Leading 0 in number.\n");
|
| + uprv_decNumberShow(dn);
|
| + #endif
|
| + return 1;}
|
| + }
|
| + if (*up>maxuint) {
|
| + #if DECTRACE || DECVERB
|
| + printf("Bad Unit [%08lx] in %ld-digit number at offset %ld [maxuint %ld].\n",
|
| + (LI)*up, (LI)dn->digits, (LI)(up-dn->lsu), (LI)maxuint);
|
| + #endif
|
| + return 1;}
|
| + d-=DECDPUN;
|
| + }
|
| +
|
| + /* check the exponent. Note that input operands can have exponents */
|
| + /* which are out of the set->emin/set->emax and set->digits range */
|
| + /* (just as they can have more digits than set->digits). */
|
| + ae=dn->exponent+dn->digits-1; /* adjusted exponent */
|
| + emax=DECNUMMAXE;
|
| + emin=DECNUMMINE;
|
| + digits=DECNUMMAXP;
|
| + if (ae<emin-(digits-1)) {
|
| + #if DECTRACE || DECVERB
|
| + printf("Adjusted exponent underflow [%ld].\n", (LI)ae);
|
| + uprv_decNumberShow(dn);
|
| + #endif
|
| + return 1;}
|
| + if (ae>+emax) {
|
| + #if DECTRACE || DECVERB
|
| + printf("Adjusted exponent overflow [%ld].\n", (LI)ae);
|
| + uprv_decNumberShow(dn);
|
| + #endif
|
| + return 1;}
|
| +
|
| + return 0; /* it's OK */
|
| + } /* decCheckNumber */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decCheckInexact -- check a normal finite inexact result has digits */
|
| +/* dn is the number to check */
|
| +/* set is the context (for status and precision) */
|
| +/* sets Invalid operation, etc., if some digits are missing */
|
| +/* [this check is not made for DECSUBSET compilation or when */
|
| +/* subnormal is not set] */
|
| +/* ------------------------------------------------------------------ */
|
| +static void decCheckInexact(const decNumber *dn, decContext *set) {
|
| + #if !DECSUBSET && DECEXTFLAG
|
| + if ((set->status & (DEC_Inexact|DEC_Subnormal))==DEC_Inexact
|
| + && (set->digits!=dn->digits) && !(dn->bits & DECSPECIAL)) {
|
| + #if DECTRACE || DECVERB
|
| + printf("Insufficient digits [%ld] on normal Inexact result.\n",
|
| + (LI)dn->digits);
|
| + uprv_decNumberShow(dn);
|
| + #endif
|
| + uprv_decContextSetStatus(set, DEC_Invalid_operation);
|
| + }
|
| + #else
|
| + /* next is a noop for quiet compiler */
|
| + if (dn!=NULL && dn->digits==0) set->status|=DEC_Invalid_operation;
|
| + #endif
|
| + return;
|
| + } /* decCheckInexact */
|
| +#endif
|
| +
|
| +#if DECALLOC
|
| +#undef malloc
|
| +#undef free
|
| +/* ------------------------------------------------------------------ */
|
| +/* decMalloc -- accountable allocation routine */
|
| +/* n is the number of bytes to allocate */
|
| +/* */
|
| +/* Semantics is the same as the stdlib malloc routine, but bytes */
|
| +/* allocated are accounted for globally, and corruption fences are */
|
| +/* added before and after the 'actual' storage. */
|
| +/* ------------------------------------------------------------------ */
|
| +/* This routine allocates storage with an extra twelve bytes; 8 are */
|
| +/* at the start and hold: */
|
| +/* 0-3 the original length requested */
|
| +/* 4-7 buffer corruption detection fence (DECFENCE, x4) */
|
| +/* The 4 bytes at the end also hold a corruption fence (DECFENCE, x4) */
|
| +/* ------------------------------------------------------------------ */
|
| +static void *decMalloc(size_t n) {
|
| + uInt size=n+12; /* true size */
|
| + void *alloc; /* -> allocated storage */
|
| + uByte *b, *b0; /* work */
|
| + uInt uiwork; /* for macros */
|
| +
|
| + alloc=malloc(size); /* -> allocated storage */
|
| + if (alloc==NULL) return NULL; /* out of strorage */
|
| + b0=(uByte *)alloc; /* as bytes */
|
| + decAllocBytes+=n; /* account for storage */
|
| + UBFROMUI(alloc, n); /* save n */
|
| + /* printf(" alloc ++ dAB: %ld (%ld)\n", (LI)decAllocBytes, (LI)n); */
|
| + for (b=b0+4; b<b0+8; b++) *b=DECFENCE;
|
| + for (b=b0+n+8; b<b0+n+12; b++) *b=DECFENCE;
|
| + return b0+8; /* -> play area */
|
| + } /* decMalloc */
|
| +
|
| +/* ------------------------------------------------------------------ */
|
| +/* decFree -- accountable free routine */
|
| +/* alloc is the storage to free */
|
| +/* */
|
| +/* Semantics is the same as the stdlib malloc routine, except that */
|
| +/* the global storage accounting is updated and the fences are */
|
| +/* checked to ensure that no routine has written 'out of bounds'. */
|
| +/* ------------------------------------------------------------------ */
|
| +/* This routine first checks that the fences have not been corrupted. */
|
| +/* It then frees the storage using the 'truw' storage address (that */
|
| +/* is, offset by 8). */
|
| +/* ------------------------------------------------------------------ */
|
| +static void decFree(void *alloc) {
|
| + uInt n; /* original length */
|
| + uByte *b, *b0; /* work */
|
| + uInt uiwork; /* for macros */
|
| +
|
| + if (alloc==NULL) return; /* allowed; it's a nop */
|
| + b0=(uByte *)alloc; /* as bytes */
|
| + b0-=8; /* -> true start of storage */
|
| + n=UBTOUI(b0); /* lift length */
|
| + for (b=b0+4; b<b0+8; b++) if (*b!=DECFENCE)
|
| + printf("=== Corrupt byte [%02x] at offset %d from %ld ===\n", *b,
|
| + b-b0-8, (LI)b0);
|
| + for (b=b0+n+8; b<b0+n+12; b++) if (*b!=DECFENCE)
|
| + printf("=== Corrupt byte [%02x] at offset +%d from %ld, n=%ld ===\n", *b,
|
| + b-b0-8, (LI)b0, (LI)n);
|
| + free(b0); /* drop the storage */
|
| + decAllocBytes-=n; /* account for storage */
|
| + /* printf(" free -- dAB: %d (%d)\n", decAllocBytes, -n); */
|
| + } /* decFree */
|
| +#define malloc(a) decMalloc(a)
|
| +#define free(a) decFree(a)
|
| +#endif
|
|
|
| Property changes on: icu46/source/i18n/decNumber.c
|
| ___________________________________________________________________
|
| Added: svn:eol-style
|
| + LF
|
|
|
|
|
Chromium Code Reviews
Issue 5516007:
Check in the pristine copy of ICU 4.6... (Closed)
Base URL: svn://chrome-svn/chrome/trunk/deps/third_party/