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