%{ /* A simple integer desk calculator using yacc and gmp. Copyright 2000, 2001 Free Software Foundation, Inc. This file is part of the GNU MP Library. This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program 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 General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ /* This is a simple program, meant only to show one way to use GMP for this sort of thing. There's few features, and error checking is minimal. Standard input is read, there's no command line options. Examples: 2+3*4 expressions are evaluated x=5^6 variables a to z can be set and used Operators: + - * arithmetic / % division and remainder (rounding towards negative infinity) ^ exponentiation ! factorial << >> left and right shifts <= >= > \ comparisons, giving 1 if true, 0 if false == != < / && || logical and/or, giving 1 if true, 0 if false Functions: abs(n) absolute value bin(n,m) binomial coefficient fib(n) fibonacci number gcd(a,b,..) greatest common divisor kron(a,b) kronecker symbol lcm(a,b,..) least common multiple nextprime(n) next prime after n powm(b,e,m) modulo powering, b^e%m root(n,r) r-th root sqrt(n) square root Other: hex \ set hex or decimal for input and output decimal / ("0x" can be used for hex too) quit exit program (EOF works too) ; statements are separated with a ; or newline \ continue expressions with \ before newline # xxx comments are # though to newline Hex numbers must be entered in upper case, to distinguish them from the variables a to f (like in bc). Expressions are evaluated as they're read. If user defined functions were wanted it'd be necessary to build a parse tree like pexpr.c does, or a list of operations for a stack based evaluator. That would also make it possible to detect and optimize evaluations "mod m" like pexpr.c does. A stack is used for intermediate values in the expression evaluation, separate from the yacc parser stack. This is simple, makes error recovery easy, minimizes the junk around mpz calls in the rules, and saves initializing or clearing "mpz_t"s during a calculation. A disadvantage though is that variables must be copied to the stack to be worked on. A more sophisticated calculator or language system might be able to avoid that when executing a compiled or semi-compiled form. Avoiding repeated initializing and clearing of "mpz_t"s is important. In this program the time spent parsing is obviously much greater than any possible saving from this, but a proper calculator or language should take some trouble over it. Don't be surprised if an init/clear takes 3 or more times as long as a 10 limb addition, depending on the system (see the mpz_init_realloc_clear example in tune/README). */ #include #include #include "gmp.h" #define numberof(x) (sizeof (x) / sizeof ((x)[0])) int ibase = 0; int obase = 10; /* The stack is a fixed size, which means there's a limit on the nesting allowed in expressions. A more sophisticated program could let it grow dynamically. */ mpz_t stack[100]; mpz_ptr sp = stack[0]; #define CHECK_OVERFLOW() \ if (sp >= stack[numberof(stack)]) \ { \ fprintf (stderr, \ "Value stack overflow, too much nesting in expression\n"); \ YYERROR; \ } #define CHECK_EMPTY() \ if (sp != stack[0]) \ { \ fprintf (stderr, "Oops, expected the value stack to be empty\n"); \ sp = stack[0]; \ } mpz_t variable[26]; #define CHECK_VARIABLE(var) \ if ((var) < 0 || (var) >= numberof (variable)) \ { \ fprintf (stderr, "Oops, bad variable somehow: %d\n", var); \ YYERROR; \ } #define CHECK_UI(name,z) \ if (! mpz_fits_ulong_p (z)) \ { \ fprintf (stderr, \ "Operand must fit in an \"unsigned long\" for %s\n", name); \ YYERROR; \ } %} %union { char *str; int var; } %token EOS BAD %token HEX DECIMAL QUIT %token ABS BIN FIB GCD KRON LCM NEXTPRIME POWM ROOT SQRT %token NUMBER %token VARIABLE /* operators, increasing precedence */ %left LOR %left LAND %nonassoc '<' '>' EQ NE LE GE %left LSHIFT RSHIFT %left '+' '-' %left '*' '/' '%' %nonassoc UMINUS %right '^' %nonassoc '!' %% top: statement | statements statement statements: statement EOS | statements statement EOS | error EOS ={ sp = stack[0]; yyerrok; } statement: /* empty */ | e ={ mpz_out_str (stdout, obase, sp); putchar ('\n'); sp--; CHECK_EMPTY (); } | VARIABLE '=' e ={ CHECK_VARIABLE ($1); mpz_swap (variable[$1], sp); sp--; CHECK_EMPTY (); } | HEX ={ ibase = 16; obase = -16; } | DECIMAL ={ ibase = 0; obase = 10; } | QUIT ={ exit (0); } /* "e" leaves it's value on the top of the mpz stack. A rule like "e '+' e" will have done a reduction for the first "e" first and the second "e" second, so the code receives the values in that order on the stack. */ e: '(' e ')' /* value on stack */ | e '+' e ={ sp--; mpz_add (sp, sp, sp+1); } | e '-' e ={ sp--; mpz_sub (sp, sp, sp+1); } | e '*' e ={ sp--; mpz_mul (sp, sp, sp+1); } | e '/' e ={ sp--; mpz_fdiv_q (sp, sp, sp+1); } | e '%' e ={ sp--; mpz_fdiv_r (sp, sp, sp+1); } | e '^' e ={ CHECK_UI ("exponentiation", sp); sp--; mpz_pow_ui (sp, sp, mpz_get_ui (sp+1)); } | e LSHIFT e ={ CHECK_UI ("lshift", sp); sp--; mpz_mul_2exp (sp, sp, mpz_get_ui (sp+1)); } | e RSHIFT e ={ CHECK_UI ("rshift", sp); sp--; mpz_fdiv_q_2exp (sp, sp, mpz_get_ui (sp+1)); } | e '!' ={ CHECK_UI ("factorial", sp); mpz_fac_ui (sp, mpz_get_ui (sp)); } | '-' e %prec UMINUS ={ mpz_neg (sp, sp); } | e '<' e ={ sp--; mpz_set_ui (sp, mpz_cmp (sp, sp+1) < 0); } | e LE e ={ sp--; mpz_set_ui (sp, mpz_cmp (sp, sp+1) <= 0); } | e EQ e ={ sp--; mpz_set_ui (sp, mpz_cmp (sp, sp+1) == 0); } | e NE e ={ sp--; mpz_set_ui (sp, mpz_cmp (sp, sp+1) != 0); } | e GE e ={ sp--; mpz_set_ui (sp, mpz_cmp (sp, sp+1) >= 0); } | e '>' e ={ sp--; mpz_set_ui (sp, mpz_cmp (sp, sp+1) > 0); } | e LAND e ={ sp--; mpz_set_ui (sp, mpz_sgn (sp) && mpz_sgn (sp+1)); } | e LOR e ={ sp--; mpz_set_ui (sp, mpz_sgn (sp) || mpz_sgn (sp+1)); } | ABS '(' e ')' ={ mpz_abs (sp, sp); } | BIN '(' e ',' e ')' ={ sp--; CHECK_UI ("binomial", sp+1); mpz_bin_ui (sp, sp, mpz_get_ui (sp+1)); } | FIB '(' e ')' ={ CHECK_UI ("fibonacci", sp); mpz_fib_ui (sp, mpz_get_ui (sp)); } | GCD '(' gcdlist ')' /* value on stack */ | KRON '(' e ',' e ')' ={ sp--; mpz_set_si (sp, mpz_kronecker (sp, sp+1)); } | LCM '(' lcmlist ')' /* value on stack */ | NEXTPRIME '(' e ')' ={ mpz_nextprime (sp, sp); } | POWM '(' e ',' e ',' e ')' ={ sp -= 2; mpz_powm (sp, sp, sp+1, sp+2); } | ROOT '(' e ',' e ')' ={ sp--; CHECK_UI ("nth-root", sp+1); mpz_root (sp, sp, mpz_get_ui (sp+1)); } | SQRT '(' e ')' ={ mpz_sqrt (sp, sp); } | VARIABLE ={ sp++; CHECK_OVERFLOW (); CHECK_VARIABLE ($1); mpz_set (sp, variable[$1]); } | NUMBER ={ sp++; CHECK_OVERFLOW (); if (mpz_set_str (sp, $1, ibase) != 0) { fprintf (stderr, "Invalid number: %s\n", $1); YYERROR; } } gcdlist: e /* value on stack */ | gcdlist ',' e ={ sp--; mpz_gcd (sp, sp, sp+1); } lcmlist: e /* value on stack */ | lcmlist ',' e ={ sp--; mpz_lcm (sp, sp, sp+1); } %% yyerror (char *s) { fprintf (stderr, "%s\n", s); } int main (void) { int i; for (i = 0; i < numberof (variable); i++) mpz_init (variable[i]); for (i = 0; i < numberof (stack); i++) mpz_init (stack[i]); return yyparse (); }