gcc/gmp/demos/expr/README - Issue 3050029: [gcc] GCC 4.5.0=>4.5.1

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Issue 3050029: [gcc] GCC 4.5.0=>4.5.1 (Closed) Base URL: ssh://git@gitrw.chromium.org:9222/nacl-toolchain.git

Patch Set: Created 10 years, 5 months ago

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Index: gcc/gmp/demos/expr/README

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-This file is part of the GNU MP Library.

-The GNU MP Library is free software; you can redistribute it and/or modify

-it under the terms of the GNU Lesser General Public License as published by

-the Free Software Foundation; either version 3 of the License, or (at your

-option) any later version.

-The GNU MP Library is distributed in the hope that it will be useful, but

-WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY

-or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public

-License for more details.

-You should have received a copy of the GNU Lesser General Public License

-along with the GNU MP Library. If not, see http://www.gnu.org/licenses/.

- GMP EXPRESSION EVALUATION

- -------------------------

-THIS CODE IS PRELIMINARY AND MAY BE SUBJECT TO INCOMPATIBLE CHANGES IN

-FUTURE VERSIONS OF GMP.

-The files in this directory implement a simple scheme of string based

-expression parsing and evaluation, supporting mpz, mpq and mpf.

-This will be slower than direct GMP library calls, but may be convenient in

-various circumstances, such as while prototyping, or for letting a user

-enter values in symbolic form. "2**5723-7" for example is a lot easier to

-enter or maintain than the equivalent written out in decimal.

-BUILDING

-Nothing in this directory is a normal part of libgmp, and nothing is built

-or installed, but various Makefile rules are available to compile

-everything.

-All the functions are available through a little library (there's no shared

-library since upward binary compatibility is not guaranteed).

- make libexpr.a

-In a program, prototypes are available using

- #include "expr.h"

-run-expr.c is a sample program doing evaluations from the command line.

- make run-expr

- ./run-expr '1+2*3'

-t-expr.c is self-test program, it prints nothing if successful.

- make t-expr

- ./t-expr

-The expr*.c sources don't depend on gmp-impl.h and can be compiled with just

-a standard installed GMP. This isn't true of t-expr though, since it uses

-some of the internal tests/libtests.la.

-SIMPLE USAGE

-int mpz_expr (mpz_t res, int base, const char *e, ...);

-int mpq_expr (mpq_t res, int base, const char *e, ...);

-int mpf_expr (mpf_t res, int base, const char *e, ...);

-These functions evaluate simple arithmetic expressions. For example,

- mpz_expr (result, 0, "123+456", NULL);

-Numbers are parsed by mpz_expr and mpq_expr the same as mpz_set_str with the

-given base. mpf_expr follows mpf_set_str, but supporting an "0x" prefix for

-hex when base==0.

- mpz_expr (result, 0, "0xAAAA * 0x5555", NULL);

-White space, as indicated by <ctype.h> isspace(), is ignored except for the

-purpose of separating tokens.

-Variables can be included in expressions by putting them in the varargs list

-after the string. "a", "b", "c" etc in the expression string designate

-those values. For example,

- mpq_t foo, bar;

- ...

- mpq_expr (q, 10, "2/3 + 1/a + b/2", foo, bar, NULL);

-Here "a" will be the value from foo and "b" from bar. Up to 26 variables

-can be included this way. The NULL must be present to indicate the end of

-the list.

-Variables can also be written "$a", "$b" etc. This is necessary when using

-bases greater than 10 since plain "a", "b" etc will otherwise be interpreted

-as numbers. For example,

- mpf_t quux;

- mpf_expr (f, 16, "F00F@-6 * $a", quux, NULL);

-All the standard C operators are available, with the usual precedences, plus

-"**" for exponentiation at the highest precedence (and right associative).

- Operators Precedence

- ** 220

- ~ ! - (unary) 210

- * / % 200

- + - 190

- << >> 180

- <= < >= > 170

- == != 160

- & 150

- ^ 140

- | 130

- && 120

- || 110

- ? : 100/101

-Currently only mpz_expr has the bitwise ~ % & ^ and | operators. The

-precedence numbers are of interest in the advanced usage described below.

-Various functions are available too. For example,

- mpz_expr (res, 10, "gcd(123,456,789) * abs(a)", var, NULL);

-The following is the full set of functions,

- mpz_expr

- abs bin clrbit cmp cmpabs congruent_p divisible_p even_p fib fac

- gcd hamdist invert jacobi kronecker lcm lucnum max min nextprime

- odd_p perfect_power_p perfect_square_p popcount powm

- probab_prime_p root scan0 scan1 setbit sgn sqrt

- mpq_expr

- abs, cmp, den, max, min, num, sgn

- mpf_expr

- abs, ceil, cmp, eq, floor, integer_p, max, min, reldiff, sgn,

- sqrt, trunc

-All these are the same as the GMP library functions, except that min and max

-don't exist in the library. Note also that min, max, gcd and lcm take any

-number of arguments, not just two.

-mpf_expr does all calculations to the precision of the destination variable.

-Expression parsing can succeed or fail. The return value indicates this,

-and will be one of the following

- MPEXPR_RESULT_OK

- MPEXPR_RESULT_BAD_VARIABLE

- MPEXPR_RESULT_BAD_TABLE

- MPEXPR_RESULT_PARSE_ERROR

- MPEXPR_RESULT_NOT_UI

-BAD_VARIABLE is when a variable is referenced that hasn't been provided.

-For example if "c" is used when only two parameters have been passed.

-BAD_TABLE is applicable to the advanced usage described below.

-PARSE_ERROR is a general syntax error, returned for any mal-formed input

-string.

-NOT_UI is returned when an attempt is made to use an operand that's bigger

-than an "unsigned long" with a function that's restricted to that range.

-For example "fib" is mpz_fib_ui and only accepts an "unsigned long".

-ADVANCED USAGE

-int mpz_expr_a (const struct mpexpr_operator_t *table,

- mpz_ptr res, int base, const char *e, size_t elen,

- mpz_srcptr var[26])

-int mpq_expr_a (const struct mpexpr_operator_t *table,

- mpq_ptr res, int base, const char *e, size_t elen,

- mpq_srcptr var[26])

-int mpf_expr_a (const struct mpexpr_operator_t *table,

- mpf_ptr res, int base, unsigned long prec,

- const char *e, size_t elen,

- mpf_srcptr var[26])

-These functions are an advanced interface to expression parsing.

-The string is taken as pointer and length. This makes it possible to parse

-an expression in the middle of somewhere without copying and null

-terminating it.

-Variables are an array of 26 pointers to the appropriate operands, or NULL

-for variables that are not available. Any combination of variables can be

-given, for example just "x" and "y" (var[23] and var[24]) could be set.

-Operators and functions are specified with a table. This makes it possible

-to provide additional operators or functions, or to completely change the

-syntax. The standard tables used by the simple functions above are

-available as

- const struct mpexpr_operator_t * const mpz_expr_standard_table;

- const struct mpexpr_operator_t * const mpq_expr_standard_table;

- const struct mpexpr_operator_t * const mpf_expr_standard_table;

-struct mpexpr_operator_t is the following

- struct mpexpr_operator_t {

- const char *name;

- mpexpr_fun_t fun;

- int type;

- int precedence;

- };

- typedef void (*mpexpr_fun_t) (void);

-As an example, the standard mpz_expr table entry for multiplication is as

-follows. See the source code for the full set of standard entries.

- { "*", (mpexpr_fun_t) mpz_mul, MPEXPR_TYPE_BINARY, 200 },

-"name" is the string to parse, "fun" is the function to call for it, "type"

-indicates what parameters the function takes (among other things), and

-"precedence" sets its operator precedence.

-A NULL for "name" indicates the end of the table, so for example an mpf

-table with nothing but addition could be

- struct mpexpr_operator_t table[] = {

- { "+", (mpexpr_fun_t) mpf_add, MPEXPR_TYPE_BINARY, 190 },

- { NULL }

- };

-A special type MPEXPR_TYPE_NEW_TABLE makes it possible to chain from one

-table to another. For example the following would add a "mod" operator to

-the standard mpz table,

- struct mpexpr_operator_t table[] = {

- { "mod", (mpexpr_fun_t) mpz_fdiv_r, MPEXPR_TYPE_BINARY, 125 },

- { (const char *) mpz_expr_standard_table, NULL, MPEXPR_TYPE_NEW_TABLE }

- };

-Notice the low precedence on "mod", so that for instance "45+26 mod 7"

-parses as "(45+26)mod7".

-Functions are designated by a precedence of 0. They always occur as

-"foo(expr)" and so have no need for a precedence level. mpq_abs in the

-standard mpq table is

- { "abs", (mpexpr_fun_t) mpq_abs, MPEXPR_TYPE_UNARY },

-Functions expecting no arguments as in "foo()" can be given with

-MPEXPR_TYPE_0ARY, or actual constants to be parsed as just "foo" are

-MPEXPR_TYPE_CONSTANT. For example if a "void mpf_const_pi(mpf_t f)"

-function existed (which it doesn't) it could be,

- { "pi", (mpexpr_fun_t) mpf_const_pi, MPEXPR_TYPE_CONSTANT },

-Parsing of operator names is done by seeking the table entry with the

-longest matching name. So for instance operators "<" and "<=" exist, and

-when presented with "x <= y" the parser matches "<=" because it's longer.

-Parsing of function names, on the other hand, is done by requiring a whole

-alphanumeric word to match. For example presented with "fib2zz(5)" the

-parser will attempt to find a function called "fib2zz". A function "fib"

-wouldn't be used because it doesn't match the whole word.

-The flag MPEXPR_TYPE_WHOLEWORD can be ORed into an operator type to override

-the default parsing style. Similarly MPEXPR_TYPE_OPERATOR into a function.

-Binary operators are left associative by default, meaning they're evaluated

-from left to right, so for example "1+2+3" is treated as "(1+2)+3".

-MPEXPR_TYPE_RIGHTASSOC can be ORed into the operator type to work from right

-to left as in "1+(2+3)". This is generally what's wanted for

-exponentiation, and for example the standard mpz table has

- { "**", (mpexpr_fun_t) mpz_pow_ui,

- MPEXPR_TYPE_BINARY_UI | MPEXPR_TYPE_RIGHTASSOC, 220 }

-Unary operators are postfix by default. For example a factorial to be used

-as "123!" might be

- { "!", (mpexpr_fun_t) mpz_fac_ui, MPEXPR_TYPE_UNARY_UI, 215 }

-MPEXPR_TYPE_PREFIX can be ORed into the type to get a prefix operator. For

-instance negation (unary minus) in the standard mpf table is

- { "-", (mpexpr_fun_t) mpf_neg,

- MPEXPR_TYPE_UNARY | MPEXPR_TYPE_PREFIX, 210 },

-The same operator can exist as a prefix unary and a binary, or as a prefix

-and postfix unary, simply by putting two entries in the table. While

-parsing the context determines which style is sought. But note that the

-same operator can't be both a postfix unary and a binary, since the parser

-doesn't try to look ahead to decide which ought to be used.

-When there's two entries for an operator, both prefix or both postfix (or

-binary), then the first in the table will be used. This makes it possible

-to override an entry in a standard table, for example to change the function

-it calls, or perhaps its precedence level. The following would change mpz

-division from tdiv to cdiv,

- struct mpexpr_operator_t table[] = {

- { "/", (mpexpr_fun_t) mpz_cdiv_q, MPEXPR_TYPE_BINARY, 200 },

- { "%", (mpexpr_fun_t) mpz_cdiv_r, MPEXPR_TYPE_BINARY, 200 },

- { (char *) mpz_expr_standard_table, NULL, MPEXPR_TYPE_NEW_TABLE }

- };

-The type field indicates what parameters the given function expects. The

-following styles of functions are supported. mpz_t is shown, but of course

-this is mpq_t for mpq_expr_a, mpf_t for mpf_expr_a, etc.

- MPEXPR_TYPE_CONSTANT void func (mpz_t result);

- MPEXPR_TYPE_0ARY void func (mpz_t result);

- MPEXPR_TYPE_I_0ARY int func (void);

- MPEXPR_TYPE_UNARY void func (mpz_t result, mpz_t op);

- MPEXPR_TYPE_UNARY_UI void func (mpz_t result, unsigned long op);

- MPEXPR_TYPE_I_UNARY int func (mpz_t op);

- MPEXPR_TYPE_I_UNARY_UI int func (unsigned long op);

- MPEXPR_TYPE_BINARY void func (mpz_t result, mpz_t op1, mpz_t op2);

- MPEXPR_TYPE_BINARY_UI void func (mpz_t result,

- mpz_t op1, unsigned long op2);

- MPEXPR_TYPE_I_BINARY int func (mpz_t op1, mpz_t op2);

- MPEXPR_TYPE_I_BINARY_UI int func (mpz_t op1, unsigned long op2);

- MPEXPR_TYPE_TERNARY void func (mpz_t result,

- mpz_t op1, mpz_t op2, mpz_t op3);

- MPEXPR_TYPE_TERNARY_UI void func (mpz_t result, mpz_t op1, mpz_t op2,

- unsigned long op3);

- MPEXPR_TYPE_I_TERNARY int func (mpz_t op1, mpz_t op2, mpz_t op3);

- MPEXPR_TYPE_I_TERNARY_UI int func (mpz_t op1, mpz_t op2,

- unsigned long op3);

-Notice the pattern of "UI" for the last parameter as an unsigned long, or

-"I" for the result as an "int" return value.

-It's important that the declared type for an operator or function matches

-the function pointer given. Any mismatch will have unpredictable results.

-For binary functions, a further type attribute is MPEXPR_TYPE_PAIRWISE which

-indicates that any number of arguments should be accepted, and evaluated by

-applying the given binary function to them pairwise. This is used by gcd,

-lcm, min and max. For example the standard mpz gcd is

- { "gcd", (mpexpr_fun_t) mpz_gcd,

- MPEXPR_TYPE_BINARY | MPEXPR_TYPE_PAIRWISE },

-Some special types exist for comparison operators (or functions).

-MPEXPR_TYPE_CMP_LT through MPEXPR_TYPE_CMP_GE expect an MPEXPR_TYPE_I_BINARY

-function, returning positive, negative or zero like mpz_cmp and similar.

-For example the standard mpf "!=" operator is

- { "!=", (mpexpr_fun_t) mpf_cmp, MPEXPR_TYPE_CMP_NE, 160 },

-But there's no obligation to use these types, for instance the standard mpq

-table just uses a plain MPEXPR_TYPE_I_BINARY and mpq_equal for "==".

-Further special types MPEXPR_TYPE_MIN and MPEXPR_TYPE_MAX exist to implement

-the min and max functions, and they take a function like mpf_cmp similarly.

-The standard mpf max function is

- { "max", (mpexpr_fun_t) mpf_cmp,

- MPEXPR_TYPE_MAX | MPEXPR_TYPE_PAIRWISE },

-These can be used as operators too, for instance the following would be the

->? operator which is a feature of GNU C++,

- { ">?", (mpexpr_fun_t) mpf_cmp, MPEXPR_TYPE_MAX, 175 },

-Other special types are used to define "(" ")" parentheses, "," function

-argument separator, "!" through "||" logical booleans, ternary "?" ":", and

-the "$" which introduces variables. See the sources for how they should be

-used.

-User definable operator tables will have various uses. For example,

- - a subset of the C operators, to be rid of infrequently used things

- - a more mathematical syntax like "." for multiply, "^" for powering,

- and "!" for factorial

- - a boolean evaluator with "^" for AND, "v" for OR

- - variables introduced with "%" instead of "$"

- - brackets as "[" and "]" instead of "(" and ")"

-The only fixed parts of the parsing are the treatment of numbers, whitespace

-and the two styles of operator/function name recognition.

-As a final example, the following would be a complete mpz table implementing

-some operators with a more mathematical syntax. Notice there's no need to

-preserve the standard precedence values, anything can be used so long as

-they're in the desired relation to each other. There's also no need to have

-entries in precedence order, but it's convenient to do so to show what comes

-where.

- static const struct mpexpr_operator_t table[] = {

- { "^", (mpexpr_fun_t) mpz_pow_ui,

- MPEXPR_TYPE_BINARY_UI | MPEXPR_TYPE_RIGHTASSOC, 9 },

- { "!", (mpexpr_fun_t) mpz_fac_ui, MPEXPR_TYPE_UNARY_UI, 8 },

- { "-", (mpexpr_fun_t) mpz_neg,

- MPEXPR_TYPE_UNARY | MPEXPR_TYPE_PREFIX, 7 },

- { "*", (mpexpr_fun_t) mpz_mul, MPEXPR_TYPE_BINARY, 6 },

- { "/", (mpexpr_fun_t) mpz_fdiv_q, MPEXPR_TYPE_BINARY, 6 },

- { "+", (mpexpr_fun_t) mpz_add, MPEXPR_TYPE_BINARY, 5 },

- { "-", (mpexpr_fun_t) mpz_sub, MPEXPR_TYPE_BINARY, 5 },

- { "mod", (mpexpr_fun_t) mpz_mod, MPEXPR_TYPE_BINARY, 6 },

- { ")", NULL, MPEXPR_TYPE_CLOSEPAREN, 4 },

- { "(", NULL, MPEXPR_TYPE_OPENPAREN, 3 },

- { ",", NULL, MPEXPR_TYPE_ARGSEP, 2 },

- { "$", NULL, MPEXPR_TYPE_VARIABLE, 1 },

- { NULL }

- };

-INTERNALS

-Operator precedence is implemented using a control and data stack, there's

-no C recursion. When an expression like 1+2*3 is read the "+" is held on

-the control stack and 1 on the data stack until "*" has been parsed and

-applied to 2 and 3. This happens any time a higher precedence operator

-follows a lower one, or when a right-associative operator like "**" is

-repeated.

-Parentheses are handled by making "(" a special prefix unary with a low

-precedence so a whole following expression is read. The special operator

-")" knows to discard the pending "(". Function arguments are handled

-similarly, with the function pretending to be a low precedence prefix unary

-operator, and with "," allowed within functions. The same special ")"

-operator recognises a pending function and will invoke it appropriately.

-The ternary "? :" operator is also handled using precedences. ":" is one

-level higher than "?", so when a valid a?b:c is parsed the ":" finds a "?"

-on the control stack. It's a parse error for ":" to find anything else.

-FUTURE

-The ternary "?:" operator evaluates the "false" side of its pair, which is

-wasteful, though it ought to be harmless. It'd be better if it could

-evaluate only the "true" side. Similarly for the logical booleans "&&" and

-"||" if they know their result already.

-Functions like MPEXPR_TYPE_BINARY could return a status indicating operand

-out of range or whatever, to get an error back through mpz_expr etc. That

-would want to be just an option, since plain mpz_add etc have no such

-return.

-Could have assignments like "a = b*c" modifying the input variables.

-Assignment could be an operator attribute, making it expect an lvalue.

-There would want to be a standard table without assignments available

-though, so user input could be safely parsed.

-The closing parethesis table entry could specify the type of open paren it

-expects, so that "(" and ")" could match and "[" and "]" match but not a

-mixture of the two. Currently "[" and "]" can be added, but there's no

-error on writing a mixed expression like "2*(3+4]". Maybe also there could

-be a way to say that functions can only be written with one or the other

-style of parens.

-----------------

-Local variables:

-mode: text

-fill-column: 76

-End:

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