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| 1 /* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2f.c */ |
| 2 /* |
| 3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
| 4 * Debugged and optimized by Bruce D. Evans. |
| 5 */ |
| 6 /* |
| 7 * ==================================================== |
| 8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| 9 * |
| 10 * Developed at SunPro, a Sun Microsystems, Inc. business. |
| 11 * Permission to use, copy, modify, and distribute this |
| 12 * software is freely granted, provided that this notice |
| 13 * is preserved. |
| 14 * ==================================================== |
| 15 */ |
| 16 /* __rem_pio2f(x,y) |
| 17 * |
| 18 * return the remainder of x rem pi/2 in *y |
| 19 * use double precision for everything except passing x |
| 20 * use __rem_pio2_large() for large x |
| 21 */ |
| 22 |
| 23 #include "libm.h" |
| 24 |
| 25 #if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1 |
| 26 #define EPS DBL_EPSILON |
| 27 #elif FLT_EVAL_METHOD==2 |
| 28 #define EPS LDBL_EPSILON |
| 29 #endif |
| 30 |
| 31 /* |
| 32 * invpio2: 53 bits of 2/pi |
| 33 * pio2_1: first 25 bits of pi/2 |
| 34 * pio2_1t: pi/2 - pio2_1 |
| 35 */ |
| 36 static const double |
| 37 toint = 1.5/EPS, |
| 38 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ |
| 39 pio2_1 = 1.57079631090164184570e+00, /* 0x3FF921FB, 0x50000000 */ |
| 40 pio2_1t = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */ |
| 41 |
| 42 int __rem_pio2f(float x, double *y) |
| 43 { |
| 44 union {float f; uint32_t i;} u = {x}; |
| 45 double tx[1],ty[1]; |
| 46 double_t fn; |
| 47 uint32_t ix; |
| 48 int n, sign, e0; |
| 49 |
| 50 ix = u.i & 0x7fffffff; |
| 51 /* 25+53 bit pi is good enough for medium size */ |
| 52 if (ix < 0x4dc90fdb) { /* |x| ~< 2^28*(pi/2), medium size */ |
| 53 /* Use a specialized rint() to get fn. Assume round-to-nearest.
*/ |
| 54 fn = (double_t)x*invpio2 + toint - toint; |
| 55 n = (int32_t)fn; |
| 56 *y = x - fn*pio2_1 - fn*pio2_1t; |
| 57 return n; |
| 58 } |
| 59 if(ix>=0x7f800000) { /* x is inf or NaN */ |
| 60 *y = x-x; |
| 61 return 0; |
| 62 } |
| 63 /* scale x into [2^23, 2^24-1] */ |
| 64 sign = u.i>>31; |
| 65 e0 = (ix>>23) - (0x7f+23); /* e0 = ilogb(|x|)-23, positive */ |
| 66 u.i = ix - (e0<<23); |
| 67 tx[0] = u.f; |
| 68 n = __rem_pio2_large(tx,ty,e0,1,0); |
| 69 if (sign) { |
| 70 *y = -ty[0]; |
| 71 return -n; |
| 72 } |
| 73 *y = ty[0]; |
| 74 return n; |
| 75 } |
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