busybox/shell/math.c
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   1/*
   2 * arithmetic code ripped out of ash shell for code sharing
   3 *
   4 * Copyright (c) 1989, 1991, 1993, 1994
   5 *      The Regents of the University of California.  All rights reserved.
   6 *
   7 * Copyright (c) 1997-2005 Herbert Xu <herbert@gondor.apana.org.au>
   8 * was re-ported from NetBSD and debianized.
   9 *
  10 * This code is derived from software contributed to Berkeley by
  11 * Kenneth Almquist.
  12 *
  13 * Licensed under the GPL v2 or later, see the file LICENSE in this tarball.
  14 *
  15 * Original BSD copyright notice is retained at the end of this file.
  16 */
  17/*
  18 * rewrite arith.y to micro stack based cryptic algorithm by
  19 * Copyright (c) 2001 Aaron Lehmann <aaronl@vitelus.com>
  20 *
  21 * Modified by Paul Mundt <lethal@linux-sh.org> (c) 2004 to support
  22 * dynamic variables.
  23 *
  24 * Modified by Vladimir Oleynik <dzo@simtreas.ru> (c) 2001-2005 to be
  25 * used in busybox and size optimizations,
  26 * rewrote arith (see notes to this), added locale support,
  27 * rewrote dynamic variables.
  28 */
  29#include "libbb.h"
  30#include "math.h"
  31
  32#define a_e_h_t arith_eval_hooks_t
  33#define lookupvar (math_hooks->lookupvar)
  34#define setvar (math_hooks->setvar)
  35#define endofname (math_hooks->endofname)
  36
  37/* Copyright (c) 2001 Aaron Lehmann <aaronl@vitelus.com>
  38
  39   Permission is hereby granted, free of charge, to any person obtaining
  40   a copy of this software and associated documentation files (the
  41   "Software"), to deal in the Software without restriction, including
  42   without limitation the rights to use, copy, modify, merge, publish,
  43   distribute, sublicense, and/or sell copies of the Software, and to
  44   permit persons to whom the Software is furnished to do so, subject to
  45   the following conditions:
  46
  47   The above copyright notice and this permission notice shall be
  48   included in all copies or substantial portions of the Software.
  49
  50   THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
  51   EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
  52   MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
  53   IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
  54   CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
  55   TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
  56   SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
  57*/
  58
  59/* This is my infix parser/evaluator. It is optimized for size, intended
  60 * as a replacement for yacc-based parsers. However, it may well be faster
  61 * than a comparable parser written in yacc. The supported operators are
  62 * listed in #defines below. Parens, order of operations, and error handling
  63 * are supported. This code is thread safe. The exact expression format should
  64 * be that which POSIX specifies for shells. */
  65
  66/* The code uses a simple two-stack algorithm. See
  67 * http://www.onthenet.com.au/~grahamis/int2008/week02/lect02.html
  68 * for a detailed explanation of the infix-to-postfix algorithm on which
  69 * this is based (this code differs in that it applies operators immediately
  70 * to the stack instead of adding them to a queue to end up with an
  71 * expression). */
  72
  73/* To use the routine, call it with an expression string and error return
  74 * pointer */
  75
  76/*
  77 * Aug 24, 2001              Manuel Novoa III
  78 *
  79 * Reduced the generated code size by about 30% (i386) and fixed several bugs.
  80 *
  81 * 1) In arith_apply():
  82 *    a) Cached values of *numptr and &(numptr[-1]).
  83 *    b) Removed redundant test for zero denominator.
  84 *
  85 * 2) In arith():
  86 *    a) Eliminated redundant code for processing operator tokens by moving
  87 *       to a table-based implementation.  Also folded handling of parens
  88 *       into the table.
  89 *    b) Combined all 3 loops which called arith_apply to reduce generated
  90 *       code size at the cost of speed.
  91 *
  92 * 3) The following expressions were treated as valid by the original code:
  93 *       1()  ,    0!  ,    1 ( *3 )   .
  94 *    These bugs have been fixed by internally enclosing the expression in
  95 *    parens and then checking that all binary ops and right parens are
  96 *    preceded by a valid expression (NUM_TOKEN).
  97 *
  98 * Note: It may be desirable to replace Aaron's test for whitespace with
  99 * ctype's isspace() if it is used by another busybox applet or if additional
 100 * whitespace chars should be considered.  Look below the "#include"s for a
 101 * precompiler test.
 102 */
 103
 104/*
 105 * Aug 26, 2001              Manuel Novoa III
 106 *
 107 * Return 0 for null expressions.  Pointed out by Vladimir Oleynik.
 108 *
 109 * Merge in Aaron's comments previously posted to the busybox list,
 110 * modified slightly to take account of my changes to the code.
 111 *
 112 */
 113
 114/*
 115 *  (C) 2003 Vladimir Oleynik <dzo@simtreas.ru>
 116 *
 117 * - allow access to variable,
 118 *   used recursive find value indirection (c=2*2; a="c"; $((a+=2)) produce 6)
 119 * - realize assign syntax (VAR=expr, +=, *= etc)
 120 * - realize exponentiation (** operator)
 121 * - realize comma separated - expr, expr
 122 * - realise ++expr --expr expr++ expr--
 123 * - realise expr ? expr : expr (but, second expr calculate always)
 124 * - allow hexadecimal and octal numbers
 125 * - was restored loses XOR operator
 126 * - remove one goto label, added three ;-)
 127 * - protect $((num num)) as true zero expr (Manuel`s error)
 128 * - always use special isspace(), see comment from bash ;-)
 129 */
 130
 131#define arith_isspace(arithval) \
 132        (arithval == ' ' || arithval == '\n' || arithval == '\t')
 133
 134typedef unsigned char operator;
 135
 136/* An operator's token id is a bit of a bitfield. The lower 5 bits are the
 137 * precedence, and 3 high bits are an ID unique across operators of that
 138 * precedence. The ID portion is so that multiple operators can have the
 139 * same precedence, ensuring that the leftmost one is evaluated first.
 140 * Consider * and /. */
 141
 142#define tok_decl(prec,id) (((id)<<5)|(prec))
 143#define PREC(op) ((op) & 0x1F)
 144
 145#define TOK_LPAREN tok_decl(0,0)
 146
 147#define TOK_COMMA tok_decl(1,0)
 148
 149#define TOK_ASSIGN tok_decl(2,0)
 150#define TOK_AND_ASSIGN tok_decl(2,1)
 151#define TOK_OR_ASSIGN tok_decl(2,2)
 152#define TOK_XOR_ASSIGN tok_decl(2,3)
 153#define TOK_PLUS_ASSIGN tok_decl(2,4)
 154#define TOK_MINUS_ASSIGN tok_decl(2,5)
 155#define TOK_LSHIFT_ASSIGN tok_decl(2,6)
 156#define TOK_RSHIFT_ASSIGN tok_decl(2,7)
 157
 158#define TOK_MUL_ASSIGN tok_decl(3,0)
 159#define TOK_DIV_ASSIGN tok_decl(3,1)
 160#define TOK_REM_ASSIGN tok_decl(3,2)
 161
 162/* all assign is right associativity and precedence eq, but (7+3)<<5 > 256 */
 163#define convert_prec_is_assing(prec) do { if (prec == 3) prec = 2; } while (0)
 164
 165/* conditional is right associativity too */
 166#define TOK_CONDITIONAL tok_decl(4,0)
 167#define TOK_CONDITIONAL_SEP tok_decl(4,1)
 168
 169#define TOK_OR tok_decl(5,0)
 170
 171#define TOK_AND tok_decl(6,0)
 172
 173#define TOK_BOR tok_decl(7,0)
 174
 175#define TOK_BXOR tok_decl(8,0)
 176
 177#define TOK_BAND tok_decl(9,0)
 178
 179#define TOK_EQ tok_decl(10,0)
 180#define TOK_NE tok_decl(10,1)
 181
 182#define TOK_LT tok_decl(11,0)
 183#define TOK_GT tok_decl(11,1)
 184#define TOK_GE tok_decl(11,2)
 185#define TOK_LE tok_decl(11,3)
 186
 187#define TOK_LSHIFT tok_decl(12,0)
 188#define TOK_RSHIFT tok_decl(12,1)
 189
 190#define TOK_ADD tok_decl(13,0)
 191#define TOK_SUB tok_decl(13,1)
 192
 193#define TOK_MUL tok_decl(14,0)
 194#define TOK_DIV tok_decl(14,1)
 195#define TOK_REM tok_decl(14,2)
 196
 197/* exponent is right associativity */
 198#define TOK_EXPONENT tok_decl(15,1)
 199
 200/* For now unary operators. */
 201#define UNARYPREC 16
 202#define TOK_BNOT tok_decl(UNARYPREC,0)
 203#define TOK_NOT tok_decl(UNARYPREC,1)
 204
 205#define TOK_UMINUS tok_decl(UNARYPREC+1,0)
 206#define TOK_UPLUS tok_decl(UNARYPREC+1,1)
 207
 208#define PREC_PRE (UNARYPREC+2)
 209
 210#define TOK_PRE_INC tok_decl(PREC_PRE, 0)
 211#define TOK_PRE_DEC tok_decl(PREC_PRE, 1)
 212
 213#define PREC_POST (UNARYPREC+3)
 214
 215#define TOK_POST_INC tok_decl(PREC_POST, 0)
 216#define TOK_POST_DEC tok_decl(PREC_POST, 1)
 217
 218#define SPEC_PREC (UNARYPREC+4)
 219
 220#define TOK_NUM tok_decl(SPEC_PREC, 0)
 221#define TOK_RPAREN tok_decl(SPEC_PREC, 1)
 222
 223#define NUMPTR (*numstackptr)
 224
 225static int
 226tok_have_assign(operator op)
 227{
 228        operator prec = PREC(op);
 229
 230        convert_prec_is_assing(prec);
 231        return (prec == PREC(TOK_ASSIGN) ||
 232                        prec == PREC_PRE || prec == PREC_POST);
 233}
 234
 235static int
 236is_right_associativity(operator prec)
 237{
 238        return (prec == PREC(TOK_ASSIGN) || prec == PREC(TOK_EXPONENT)
 239                || prec == PREC(TOK_CONDITIONAL));
 240}
 241
 242typedef struct {
 243        arith_t val;
 244        arith_t contidional_second_val;
 245        char contidional_second_val_initialized;
 246        char *var;      /* if NULL then is regular number,
 247                           else is variable name */
 248} v_n_t;
 249
 250typedef struct chk_var_recursive_looped_t {
 251        const char *var;
 252        struct chk_var_recursive_looped_t *next;
 253} chk_var_recursive_looped_t;
 254
 255static chk_var_recursive_looped_t *prev_chk_var_recursive;
 256
 257static int
 258arith_lookup_val(v_n_t *t, a_e_h_t *math_hooks)
 259{
 260        if (t->var) {
 261                const char * p = lookupvar(t->var);
 262
 263                if (p) {
 264                        int errcode;
 265
 266                        /* recursive try as expression */
 267                        chk_var_recursive_looped_t *cur;
 268                        chk_var_recursive_looped_t cur_save;
 269
 270                        for (cur = prev_chk_var_recursive; cur; cur = cur->next) {
 271                                if (strcmp(cur->var, t->var) == 0) {
 272                                        /* expression recursion loop detected */
 273                                        return -5;
 274                                }
 275                        }
 276                        /* save current lookuped var name */
 277                        cur = prev_chk_var_recursive;
 278                        cur_save.var = t->var;
 279                        cur_save.next = cur;
 280                        prev_chk_var_recursive = &cur_save;
 281
 282                        t->val = arith (p, &errcode, math_hooks);
 283                        /* restore previous ptr after recursiving */
 284                        prev_chk_var_recursive = cur;
 285                        return errcode;
 286                }
 287                /* allow undefined var as 0 */
 288                t->val = 0;
 289        }
 290        return 0;
 291}
 292
 293/* "applying" a token means performing it on the top elements on the integer
 294 * stack. For a unary operator it will only change the top element, but a
 295 * binary operator will pop two arguments and push a result */
 296static int
 297arith_apply(operator op, v_n_t *numstack, v_n_t **numstackptr, a_e_h_t *math_hooks)
 298{
 299        v_n_t *numptr_m1;
 300        arith_t numptr_val, rez;
 301        int ret_arith_lookup_val;
 302
 303        /* There is no operator that can work without arguments */
 304        if (NUMPTR == numstack) goto err;
 305        numptr_m1 = NUMPTR - 1;
 306
 307        /* check operand is var with noninteger value */
 308        ret_arith_lookup_val = arith_lookup_val(numptr_m1, math_hooks);
 309        if (ret_arith_lookup_val)
 310                return ret_arith_lookup_val;
 311
 312        rez = numptr_m1->val;
 313        if (op == TOK_UMINUS)
 314                rez *= -1;
 315        else if (op == TOK_NOT)
 316                rez = !rez;
 317        else if (op == TOK_BNOT)
 318                rez = ~rez;
 319        else if (op == TOK_POST_INC || op == TOK_PRE_INC)
 320                rez++;
 321        else if (op == TOK_POST_DEC || op == TOK_PRE_DEC)
 322                rez--;
 323        else if (op != TOK_UPLUS) {
 324                /* Binary operators */
 325
 326                /* check and binary operators need two arguments */
 327                if (numptr_m1 == numstack) goto err;
 328
 329                /* ... and they pop one */
 330                --NUMPTR;
 331                numptr_val = rez;
 332                if (op == TOK_CONDITIONAL) {
 333                        if (!numptr_m1->contidional_second_val_initialized) {
 334                                /* protect $((expr1 ? expr2)) without ": expr" */
 335                                goto err;
 336                        }
 337                        rez = numptr_m1->contidional_second_val;
 338                } else if (numptr_m1->contidional_second_val_initialized) {
 339                        /* protect $((expr1 : expr2)) without "expr ? " */
 340                        goto err;
 341                }
 342                numptr_m1 = NUMPTR - 1;
 343                if (op != TOK_ASSIGN) {
 344                        /* check operand is var with noninteger value for not '=' */
 345                        ret_arith_lookup_val = arith_lookup_val(numptr_m1, math_hooks);
 346                        if (ret_arith_lookup_val)
 347                                return ret_arith_lookup_val;
 348                }
 349                if (op == TOK_CONDITIONAL) {
 350                        numptr_m1->contidional_second_val = rez;
 351                }
 352                rez = numptr_m1->val;
 353                if (op == TOK_BOR || op == TOK_OR_ASSIGN)
 354                        rez |= numptr_val;
 355                else if (op == TOK_OR)
 356                        rez = numptr_val || rez;
 357                else if (op == TOK_BAND || op == TOK_AND_ASSIGN)
 358                        rez &= numptr_val;
 359                else if (op == TOK_BXOR || op == TOK_XOR_ASSIGN)
 360                        rez ^= numptr_val;
 361                else if (op == TOK_AND)
 362                        rez = rez && numptr_val;
 363                else if (op == TOK_EQ)
 364                        rez = (rez == numptr_val);
 365                else if (op == TOK_NE)
 366                        rez = (rez != numptr_val);
 367                else if (op == TOK_GE)
 368                        rez = (rez >= numptr_val);
 369                else if (op == TOK_RSHIFT || op == TOK_RSHIFT_ASSIGN)
 370                        rez >>= numptr_val;
 371                else if (op == TOK_LSHIFT || op == TOK_LSHIFT_ASSIGN)
 372                        rez <<= numptr_val;
 373                else if (op == TOK_GT)
 374                        rez = (rez > numptr_val);
 375                else if (op == TOK_LT)
 376                        rez = (rez < numptr_val);
 377                else if (op == TOK_LE)
 378                        rez = (rez <= numptr_val);
 379                else if (op == TOK_MUL || op == TOK_MUL_ASSIGN)
 380                        rez *= numptr_val;
 381                else if (op == TOK_ADD || op == TOK_PLUS_ASSIGN)
 382                        rez += numptr_val;
 383                else if (op == TOK_SUB || op == TOK_MINUS_ASSIGN)
 384                        rez -= numptr_val;
 385                else if (op == TOK_ASSIGN || op == TOK_COMMA)
 386                        rez = numptr_val;
 387                else if (op == TOK_CONDITIONAL_SEP) {
 388                        if (numptr_m1 == numstack) {
 389                                /* protect $((expr : expr)) without "expr ? " */
 390                                goto err;
 391                        }
 392                        numptr_m1->contidional_second_val_initialized = op;
 393                        numptr_m1->contidional_second_val = numptr_val;
 394                } else if (op == TOK_CONDITIONAL) {
 395                        rez = rez ?
 396                                numptr_val : numptr_m1->contidional_second_val;
 397                } else if (op == TOK_EXPONENT) {
 398                        if (numptr_val < 0)
 399                                return -3;      /* exponent less than 0 */
 400                        else {
 401                                arith_t c = 1;
 402
 403                                if (numptr_val)
 404                                        while (numptr_val--)
 405                                                c *= rez;
 406                                rez = c;
 407                        }
 408                } else if (numptr_val==0)          /* zero divisor check */
 409                        return -2;
 410                else if (op == TOK_DIV || op == TOK_DIV_ASSIGN)
 411                        rez /= numptr_val;
 412                else if (op == TOK_REM || op == TOK_REM_ASSIGN)
 413                        rez %= numptr_val;
 414        }
 415        if (tok_have_assign(op)) {
 416                char buf[sizeof(arith_t)*3 + 2];
 417
 418                if (numptr_m1->var == NULL) {
 419                        /* Hmm, 1=2 ? */
 420                        goto err;
 421                }
 422                /* save to shell variable */
 423                sprintf(buf, arith_t_fmt, rez);
 424                setvar(numptr_m1->var, buf, 0);
 425                /* after saving, make previous value for v++ or v-- */
 426                if (op == TOK_POST_INC)
 427                        rez--;
 428                else if (op == TOK_POST_DEC)
 429                        rez++;
 430        }
 431        numptr_m1->val = rez;
 432        /* protect geting var value, is number now */
 433        numptr_m1->var = NULL;
 434        return 0;
 435 err:
 436        return -1;
 437}
 438
 439/* longest must be first */
 440static const char op_tokens[] ALIGN1 = {
 441        '<','<','=',0, TOK_LSHIFT_ASSIGN,
 442        '>','>','=',0, TOK_RSHIFT_ASSIGN,
 443        '<','<',    0, TOK_LSHIFT,
 444        '>','>',    0, TOK_RSHIFT,
 445        '|','|',    0, TOK_OR,
 446        '&','&',    0, TOK_AND,
 447        '!','=',    0, TOK_NE,
 448        '<','=',    0, TOK_LE,
 449        '>','=',    0, TOK_GE,
 450        '=','=',    0, TOK_EQ,
 451        '|','=',    0, TOK_OR_ASSIGN,
 452        '&','=',    0, TOK_AND_ASSIGN,
 453        '*','=',    0, TOK_MUL_ASSIGN,
 454        '/','=',    0, TOK_DIV_ASSIGN,
 455        '%','=',    0, TOK_REM_ASSIGN,
 456        '+','=',    0, TOK_PLUS_ASSIGN,
 457        '-','=',    0, TOK_MINUS_ASSIGN,
 458        '-','-',    0, TOK_POST_DEC,
 459        '^','=',    0, TOK_XOR_ASSIGN,
 460        '+','+',    0, TOK_POST_INC,
 461        '*','*',    0, TOK_EXPONENT,
 462        '!',        0, TOK_NOT,
 463        '<',        0, TOK_LT,
 464        '>',        0, TOK_GT,
 465        '=',        0, TOK_ASSIGN,
 466        '|',        0, TOK_BOR,
 467        '&',        0, TOK_BAND,
 468        '*',        0, TOK_MUL,
 469        '/',        0, TOK_DIV,
 470        '%',        0, TOK_REM,
 471        '+',        0, TOK_ADD,
 472        '-',        0, TOK_SUB,
 473        '^',        0, TOK_BXOR,
 474        /* uniq */
 475        '~',        0, TOK_BNOT,
 476        ',',        0, TOK_COMMA,
 477        '?',        0, TOK_CONDITIONAL,
 478        ':',        0, TOK_CONDITIONAL_SEP,
 479        ')',        0, TOK_RPAREN,
 480        '(',        0, TOK_LPAREN,
 481        0
 482};
 483/* ptr to ")" */
 484#define endexpression (&op_tokens[sizeof(op_tokens)-7])
 485
 486arith_t
 487arith(const char *expr, int *perrcode, a_e_h_t *math_hooks)
 488{
 489        char arithval; /* Current character under analysis */
 490        operator lasttok, op;
 491        operator prec;
 492        operator *stack, *stackptr;
 493        const char *p = endexpression;
 494        int errcode;
 495        v_n_t *numstack, *numstackptr;
 496        unsigned datasizes = strlen(expr) + 2;
 497
 498        /* Stack of integers */
 499        /* The proof that there can be no more than strlen(startbuf)/2+1 integers
 500         * in any given correct or incorrect expression is left as an exercise to
 501         * the reader. */
 502        numstackptr = numstack = alloca((datasizes / 2) * sizeof(numstack[0]));
 503        /* Stack of operator tokens */
 504        stackptr = stack = alloca(datasizes * sizeof(stack[0]));
 505
 506        *stackptr++ = lasttok = TOK_LPAREN;     /* start off with a left paren */
 507        *perrcode = errcode = 0;
 508
 509        while (1) {
 510                arithval = *expr;
 511                if (arithval == 0) {
 512                        if (p == endexpression) {
 513                                /* Null expression. */
 514                                return 0;
 515                        }
 516
 517                        /* This is only reached after all tokens have been extracted from the
 518                         * input stream. If there are still tokens on the operator stack, they
 519                         * are to be applied in order. At the end, there should be a final
 520                         * result on the integer stack */
 521
 522                        if (expr != endexpression + 1) {
 523                                /* If we haven't done so already, */
 524                                /* append a closing right paren */
 525                                expr = endexpression;
 526                                /* and let the loop process it. */
 527                                continue;
 528                        }
 529                        /* At this point, we're done with the expression. */
 530                        if (numstackptr != numstack+1) {
 531                                /* ... but if there isn't, it's bad */
 532 err:
 533                                *perrcode = -1;
 534                                return *perrcode;
 535                        }
 536                        if (numstack->var) {
 537                                /* expression is $((var)) only, lookup now */
 538                                errcode = arith_lookup_val(numstack, math_hooks);
 539                        }
 540 ret:
 541                        *perrcode = errcode;
 542                        return numstack->val;
 543                }
 544
 545                /* Continue processing the expression. */
 546                if (arith_isspace(arithval)) {
 547                        /* Skip whitespace */
 548                        goto prologue;
 549                }
 550                p = endofname(expr);
 551                if (p != expr) {
 552                        size_t var_name_size = (p-expr) + 1;  /* trailing zero */
 553
 554                        numstackptr->var = alloca(var_name_size);
 555                        safe_strncpy(numstackptr->var, expr, var_name_size);
 556                        expr = p;
 557 num:
 558                        numstackptr->contidional_second_val_initialized = 0;
 559                        numstackptr++;
 560                        lasttok = TOK_NUM;
 561                        continue;
 562                }
 563                if (isdigit(arithval)) {
 564                        numstackptr->var = NULL;
 565                        numstackptr->val = strto_arith_t(expr, (char **) &expr, 0);
 566                        goto num;
 567                }
 568                for (p = op_tokens; ; p++) {
 569                        const char *o;
 570
 571                        if (*p == 0) {
 572                                /* strange operator not found */
 573                                goto err;
 574                        }
 575                        for (o = expr; *p && *o == *p; p++)
 576                                o++;
 577                        if (!*p) {
 578                                /* found */
 579                                expr = o - 1;
 580                                break;
 581                        }
 582                        /* skip tail uncompared token */
 583                        while (*p)
 584                                p++;
 585                        /* skip zero delim */
 586                        p++;
 587                }
 588                op = p[1];
 589
 590                /* post grammar: a++ reduce to num */
 591                if (lasttok == TOK_POST_INC || lasttok == TOK_POST_DEC)
 592                        lasttok = TOK_NUM;
 593
 594                /* Plus and minus are binary (not unary) _only_ if the last
 595                 * token was as number, or a right paren (which pretends to be
 596                 * a number, since it evaluates to one). Think about it.
 597                 * It makes sense. */
 598                if (lasttok != TOK_NUM) {
 599                        switch (op) {
 600                        case TOK_ADD:
 601                                op = TOK_UPLUS;
 602                                break;
 603                        case TOK_SUB:
 604                                op = TOK_UMINUS;
 605                                break;
 606                        case TOK_POST_INC:
 607                                op = TOK_PRE_INC;
 608                                break;
 609                        case TOK_POST_DEC:
 610                                op = TOK_PRE_DEC;
 611                                break;
 612                        }
 613                }
 614                /* We don't want a unary operator to cause recursive descent on the
 615                 * stack, because there can be many in a row and it could cause an
 616                 * operator to be evaluated before its argument is pushed onto the
 617                 * integer stack. */
 618                /* But for binary operators, "apply" everything on the operator
 619                 * stack until we find an operator with a lesser priority than the
 620                 * one we have just extracted. */
 621                /* Left paren is given the lowest priority so it will never be
 622                 * "applied" in this way.
 623                 * if associativity is right and priority eq, applied also skip
 624                 */
 625                prec = PREC(op);
 626                if ((prec > 0 && prec < UNARYPREC) || prec == SPEC_PREC) {
 627                        /* not left paren or unary */
 628                        if (lasttok != TOK_NUM) {
 629                                /* binary op must be preceded by a num */
 630                                goto err;
 631                        }
 632                        while (stackptr != stack) {
 633                                if (op == TOK_RPAREN) {
 634                                        /* The algorithm employed here is simple: while we don't
 635                                         * hit an open paren nor the bottom of the stack, pop
 636                                         * tokens and apply them */
 637                                        if (stackptr[-1] == TOK_LPAREN) {
 638                                                --stackptr;
 639                                                /* Any operator directly after a */
 640                                                lasttok = TOK_NUM;
 641                                                /* close paren should consider itself binary */
 642                                                goto prologue;
 643                                        }
 644                                } else {
 645                                        operator prev_prec = PREC(stackptr[-1]);
 646
 647                                        convert_prec_is_assing(prec);
 648                                        convert_prec_is_assing(prev_prec);
 649                                        if (prev_prec < prec)
 650                                                break;
 651                                        /* check right assoc */
 652                                        if (prev_prec == prec && is_right_associativity(prec))
 653                                                break;
 654                                }
 655                                errcode = arith_apply(*--stackptr, numstack, &numstackptr, math_hooks);
 656                                if (errcode) goto ret;
 657                        }
 658                        if (op == TOK_RPAREN) {
 659                                goto err;
 660                        }
 661                }
 662
 663                /* Push this operator to the stack and remember it. */
 664                *stackptr++ = lasttok = op;
 665 prologue:
 666                ++expr;
 667        } /* while */
 668}
 669
 670/*
 671 * Copyright (c) 1989, 1991, 1993, 1994
 672 *      The Regents of the University of California.  All rights reserved.
 673 *
 674 * This code is derived from software contributed to Berkeley by
 675 * Kenneth Almquist.
 676 *
 677 * Redistribution and use in source and binary forms, with or without
 678 * modification, are permitted provided that the following conditions
 679 * are met:
 680 * 1. Redistributions of source code must retain the above copyright
 681 *    notice, this list of conditions and the following disclaimer.
 682 * 2. Redistributions in binary form must reproduce the above copyright
 683 *    notice, this list of conditions and the following disclaimer in the
 684 *    documentation and/or other materials provided with the distribution.
 685 * 3. Neither the name of the University nor the names of its contributors
 686 *    may be used to endorse or promote products derived from this software
 687 *    without specific prior written permission.
 688 *
 689 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
 690 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 691 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 692 * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
 693 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 694 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 695 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 696 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 697 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 698 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 699 * SUCH DAMAGE.
 700 */
 701