aboutsummaryrefslogtreecommitdiff
path: root/shell/math.c
blob: 9a46a937e41b96dc593e1e0ebdb46f1a6b7753ce (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
/*
 * arithmetic code ripped out of ash shell for code sharing
 *
 * Copyright (c) 1989, 1991, 1993, 1994
 *      The Regents of the University of California.  All rights reserved.
 *
 * Copyright (c) 1997-2005 Herbert Xu <herbert@gondor.apana.org.au>
 * was re-ported from NetBSD and debianized.
 *
 * This code is derived from software contributed to Berkeley by
 * Kenneth Almquist.
 *
 * Licensed under the GPL v2 or later, see the file LICENSE in this tarball.
 *
 * Original BSD copyright notice is retained at the end of this file.
 */
/*
 * rewrite arith.y to micro stack based cryptic algorithm by
 * Copyright (c) 2001 Aaron Lehmann <aaronl@vitelus.com>
 *
 * Modified by Paul Mundt <lethal@linux-sh.org> (c) 2004 to support
 * dynamic variables.
 *
 * Modified by Vladimir Oleynik <dzo@simtreas.ru> (c) 2001-2005 to be
 * used in busybox and size optimizations,
 * rewrote arith (see notes to this), added locale support,
 * rewrote dynamic variables.
 */

#include "busybox.h"
#include "math.h"

#define a_e_h_t arith_eval_hooks_t
#define lookupvar (math_hooks->lookupvar)
#define setvar (math_hooks->setvar)
#define endofname (math_hooks->endofname)

/* Copyright (c) 2001 Aaron Lehmann <aaronl@vitelus.com>

   Permission is hereby granted, free of charge, to any person obtaining
   a copy of this software and associated documentation files (the
   "Software"), to deal in the Software without restriction, including
   without limitation the rights to use, copy, modify, merge, publish,
   distribute, sublicense, and/or sell copies of the Software, and to
   permit persons to whom the Software is furnished to do so, subject to
   the following conditions:

   The above copyright notice and this permission notice shall be
   included in all copies or substantial portions of the Software.

   THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
   EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
   MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
   IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
   CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
   TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
   SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/

/* This is my infix parser/evaluator. It is optimized for size, intended
 * as a replacement for yacc-based parsers. However, it may well be faster
 * than a comparable parser written in yacc. The supported operators are
 * listed in #defines below. Parens, order of operations, and error handling
 * are supported. This code is thread safe. The exact expression format should
 * be that which POSIX specifies for shells. */

/* The code uses a simple two-stack algorithm. See
 * http://www.onthenet.com.au/~grahamis/int2008/week02/lect02.html
 * for a detailed explanation of the infix-to-postfix algorithm on which
 * this is based (this code differs in that it applies operators immediately
 * to the stack instead of adding them to a queue to end up with an
 * expression). */

/* To use the routine, call it with an expression string and error return
 * pointer */

/*
 * Aug 24, 2001              Manuel Novoa III
 *
 * Reduced the generated code size by about 30% (i386) and fixed several bugs.
 *
 * 1) In arith_apply():
 *    a) Cached values of *numptr and &(numptr[-1]).
 *    b) Removed redundant test for zero denominator.
 *
 * 2) In arith():
 *    a) Eliminated redundant code for processing operator tokens by moving
 *       to a table-based implementation.  Also folded handling of parens
 *       into the table.
 *    b) Combined all 3 loops which called arith_apply to reduce generated
 *       code size at the cost of speed.
 *
 * 3) The following expressions were treated as valid by the original code:
 *       1()  ,    0!  ,    1 ( *3 )   .
 *    These bugs have been fixed by internally enclosing the expression in
 *    parens and then checking that all binary ops and right parens are
 *    preceded by a valid expression (NUM_TOKEN).
 *
 * Note: It may be desirable to replace Aaron's test for whitespace with
 * ctype's isspace() if it is used by another busybox applet or if additional
 * whitespace chars should be considered.  Look below the "#include"s for a
 * precompiler test.
 */

/*
 * Aug 26, 2001              Manuel Novoa III
 *
 * Return 0 for null expressions.  Pointed out by Vladimir Oleynik.
 *
 * Merge in Aaron's comments previously posted to the busybox list,
 * modified slightly to take account of my changes to the code.
 *
 */

/*
 *  (C) 2003 Vladimir Oleynik <dzo@simtreas.ru>
 *
 * - allow access to variable,
 *   used recursive find value indirection (c=2*2; a="c"; $((a+=2)) produce 6)
 * - realize assign syntax (VAR=expr, +=, *= etc)
 * - realize exponentiation (** operator)
 * - realize comma separated - expr, expr
 * - realise ++expr --expr expr++ expr--
 * - realise expr ? expr : expr (but, second expr calculate always)
 * - allow hexadecimal and octal numbers
 * - was restored loses XOR operator
 * - remove one goto label, added three ;-)
 * - protect $((num num)) as true zero expr (Manuel`s error)
 * - always use special isspace(), see comment from bash ;-)
 */

#define arith_isspace(arithval) \
	(arithval == ' ' || arithval == '\n' || arithval == '\t')

typedef unsigned char operator;

/* An operator's token id is a bit of a bitfield. The lower 5 bits are the
 * precedence, and 3 high bits are an ID unique across operators of that
 * precedence. The ID portion is so that multiple operators can have the
 * same precedence, ensuring that the leftmost one is evaluated first.
 * Consider * and /. */

#define tok_decl(prec,id) (((id)<<5)|(prec))
#define PREC(op) ((op) & 0x1F)

#define TOK_LPAREN tok_decl(0,0)

#define TOK_COMMA tok_decl(1,0)

#define TOK_ASSIGN tok_decl(2,0)
#define TOK_AND_ASSIGN tok_decl(2,1)
#define TOK_OR_ASSIGN tok_decl(2,2)
#define TOK_XOR_ASSIGN tok_decl(2,3)
#define TOK_PLUS_ASSIGN tok_decl(2,4)
#define TOK_MINUS_ASSIGN tok_decl(2,5)
#define TOK_LSHIFT_ASSIGN tok_decl(2,6)
#define TOK_RSHIFT_ASSIGN tok_decl(2,7)

#define TOK_MUL_ASSIGN tok_decl(3,0)
#define TOK_DIV_ASSIGN tok_decl(3,1)
#define TOK_REM_ASSIGN tok_decl(3,2)

/* all assign is right associativity and precedence eq, but (7+3)<<5 > 256 */
#define convert_prec_is_assing(prec) do { if (prec == 3) prec = 2; } while (0)

/* conditional is right associativity too */
#define TOK_CONDITIONAL tok_decl(4,0)
#define TOK_CONDITIONAL_SEP tok_decl(4,1)

#define TOK_OR tok_decl(5,0)

#define TOK_AND tok_decl(6,0)

#define TOK_BOR tok_decl(7,0)

#define TOK_BXOR tok_decl(8,0)

#define TOK_BAND tok_decl(9,0)

#define TOK_EQ tok_decl(10,0)
#define TOK_NE tok_decl(10,1)

#define TOK_LT tok_decl(11,0)
#define TOK_GT tok_decl(11,1)
#define TOK_GE tok_decl(11,2)
#define TOK_LE tok_decl(11,3)

#define TOK_LSHIFT tok_decl(12,0)
#define TOK_RSHIFT tok_decl(12,1)

#define TOK_ADD tok_decl(13,0)
#define TOK_SUB tok_decl(13,1)

#define TOK_MUL tok_decl(14,0)
#define TOK_DIV tok_decl(14,1)
#define TOK_REM tok_decl(14,2)

/* exponent is right associativity */
#define TOK_EXPONENT tok_decl(15,1)

/* For now unary operators. */
#define UNARYPREC 16
#define TOK_BNOT tok_decl(UNARYPREC,0)
#define TOK_NOT tok_decl(UNARYPREC,1)

#define TOK_UMINUS tok_decl(UNARYPREC+1,0)
#define TOK_UPLUS tok_decl(UNARYPREC+1,1)

#define PREC_PRE (UNARYPREC+2)

#define TOK_PRE_INC tok_decl(PREC_PRE, 0)
#define TOK_PRE_DEC tok_decl(PREC_PRE, 1)

#define PREC_POST (UNARYPREC+3)

#define TOK_POST_INC tok_decl(PREC_POST, 0)
#define TOK_POST_DEC tok_decl(PREC_POST, 1)

#define SPEC_PREC (UNARYPREC+4)

#define TOK_NUM tok_decl(SPEC_PREC, 0)
#define TOK_RPAREN tok_decl(SPEC_PREC, 1)

#define NUMPTR (*numstackptr)

static int
tok_have_assign(operator op)
{
	operator prec = PREC(op);

	convert_prec_is_assing(prec);
	return (prec == PREC(TOK_ASSIGN) ||
			prec == PREC_PRE || prec == PREC_POST);
}

static int
is_right_associativity(operator prec)
{
	return (prec == PREC(TOK_ASSIGN) || prec == PREC(TOK_EXPONENT)
	        || prec == PREC(TOK_CONDITIONAL));
}

typedef struct {
	arith_t val;
	arith_t contidional_second_val;
	char contidional_second_val_initialized;
	char *var;      /* if NULL then is regular number,
			   else is variable name */
} v_n_t;

typedef struct chk_var_recursive_looped_t {
	const char *var;
	struct chk_var_recursive_looped_t *next;
} chk_var_recursive_looped_t;

static chk_var_recursive_looped_t *prev_chk_var_recursive;

static int
arith_lookup_val(v_n_t *t, a_e_h_t *math_hooks)
{
	if (t->var) {
		const char * p = lookupvar(t->var);

		if (p) {
			int errcode;

			/* recursive try as expression */
			chk_var_recursive_looped_t *cur;
			chk_var_recursive_looped_t cur_save;

			for (cur = prev_chk_var_recursive; cur; cur = cur->next) {
				if (strcmp(cur->var, t->var) == 0) {
					/* expression recursion loop detected */
					return -5;
				}
			}
			/* save current lookuped var name */
			cur = prev_chk_var_recursive;
			cur_save.var = t->var;
			cur_save.next = cur;
			prev_chk_var_recursive = &cur_save;

			t->val = arith (p, &errcode, math_hooks);
			/* restore previous ptr after recursiving */
			prev_chk_var_recursive = cur;
			return errcode;
		}
		/* allow undefined var as 0 */
		t->val = 0;
	}
	return 0;
}

/* "applying" a token means performing it on the top elements on the integer
 * stack. For a unary operator it will only change the top element, but a
 * binary operator will pop two arguments and push a result */
static int
arith_apply(operator op, v_n_t *numstack, v_n_t **numstackptr, a_e_h_t *math_hooks)
{
	v_n_t *numptr_m1;
	arith_t numptr_val, rez;
	int ret_arith_lookup_val;

	/* There is no operator that can work without arguments */
	if (NUMPTR == numstack) goto err;
	numptr_m1 = NUMPTR - 1;

	/* check operand is var with noninteger value */
	ret_arith_lookup_val = arith_lookup_val(numptr_m1, math_hooks);
	if (ret_arith_lookup_val)
		return ret_arith_lookup_val;

	rez = numptr_m1->val;
	if (op == TOK_UMINUS)
		rez *= -1;
	else if (op == TOK_NOT)
		rez = !rez;
	else if (op == TOK_BNOT)
		rez = ~rez;
	else if (op == TOK_POST_INC || op == TOK_PRE_INC)
		rez++;
	else if (op == TOK_POST_DEC || op == TOK_PRE_DEC)
		rez--;
	else if (op != TOK_UPLUS) {
		/* Binary operators */

		/* check and binary operators need two arguments */
		if (numptr_m1 == numstack) goto err;

		/* ... and they pop one */
		--NUMPTR;
		numptr_val = rez;
		if (op == TOK_CONDITIONAL) {
			if (!numptr_m1->contidional_second_val_initialized) {
				/* protect $((expr1 ? expr2)) without ": expr" */
				goto err;
			}
			rez = numptr_m1->contidional_second_val;
		} else if (numptr_m1->contidional_second_val_initialized) {
			/* protect $((expr1 : expr2)) without "expr ? " */
			goto err;
		}
		numptr_m1 = NUMPTR - 1;
		if (op != TOK_ASSIGN) {
			/* check operand is var with noninteger value for not '=' */
			ret_arith_lookup_val = arith_lookup_val(numptr_m1, math_hooks);
			if (ret_arith_lookup_val)
				return ret_arith_lookup_val;
		}
		if (op == TOK_CONDITIONAL) {
			numptr_m1->contidional_second_val = rez;
		}
		rez = numptr_m1->val;
		if (op == TOK_BOR || op == TOK_OR_ASSIGN)
			rez |= numptr_val;
		else if (op == TOK_OR)
			rez = numptr_val || rez;
		else if (op == TOK_BAND || op == TOK_AND_ASSIGN)
			rez &= numptr_val;
		else if (op == TOK_BXOR || op == TOK_XOR_ASSIGN)
			rez ^= numptr_val;
		else if (op == TOK_AND)
			rez = rez && numptr_val;
		else if (op == TOK_EQ)
			rez = (rez == numptr_val);
		else if (op == TOK_NE)
			rez = (rez != numptr_val);
		else if (op == TOK_GE)
			rez = (rez >= numptr_val);
		else if (op == TOK_RSHIFT || op == TOK_RSHIFT_ASSIGN)
			rez >>= numptr_val;
		else if (op == TOK_LSHIFT || op == TOK_LSHIFT_ASSIGN)
			rez <<= numptr_val;
		else if (op == TOK_GT)
			rez = (rez > numptr_val);
		else if (op == TOK_LT)
			rez = (rez < numptr_val);
		else if (op == TOK_LE)
			rez = (rez <= numptr_val);
		else if (op == TOK_MUL || op == TOK_MUL_ASSIGN)
			rez *= numptr_val;
		else if (op == TOK_ADD || op == TOK_PLUS_ASSIGN)
			rez += numptr_val;
		else if (op == TOK_SUB || op == TOK_MINUS_ASSIGN)
			rez -= numptr_val;
		else if (op == TOK_ASSIGN || op == TOK_COMMA)
			rez = numptr_val;
		else if (op == TOK_CONDITIONAL_SEP) {
			if (numptr_m1 == numstack) {
				/* protect $((expr : expr)) without "expr ? " */
				goto err;
			}
			numptr_m1->contidional_second_val_initialized = op;
			numptr_m1->contidional_second_val = numptr_val;
		} else if (op == TOK_CONDITIONAL) {
			rez = rez ?
				numptr_val : numptr_m1->contidional_second_val;
		} else if (op == TOK_EXPONENT) {
			if (numptr_val < 0)
				return -3;      /* exponent less than 0 */
			else {
				arith_t c = 1;

				if (numptr_val)
					while (numptr_val--)
						c *= rez;
				rez = c;
			}
		} else if (numptr_val==0)          /* zero divisor check */
			return -2;
		else if (op == TOK_DIV || op == TOK_DIV_ASSIGN)
			rez /= numptr_val;
		else if (op == TOK_REM || op == TOK_REM_ASSIGN)
			rez %= numptr_val;
	}
	if (tok_have_assign(op)) {
		char buf[sizeof(arith_t_type)*3 + 2];

		if (numptr_m1->var == NULL) {
			/* Hmm, 1=2 ? */
			goto err;
		}
		/* save to shell variable */
		snprintf(buf, sizeof(buf), arith_t_fmt, (arith_t_type) rez);
		setvar(numptr_m1->var, buf, 0);
		/* after saving, make previous value for v++ or v-- */
		if (op == TOK_POST_INC)
			rez--;
		else if (op == TOK_POST_DEC)
			rez++;
	}
	numptr_m1->val = rez;
	/* protect geting var value, is number now */
	numptr_m1->var = NULL;
	return 0;
 err:
	return -1;
}

/* longest must be first */
static const char op_tokens[] ALIGN1 = {
	'<','<','=',0, TOK_LSHIFT_ASSIGN,
	'>','>','=',0, TOK_RSHIFT_ASSIGN,
	'<','<',    0, TOK_LSHIFT,
	'>','>',    0, TOK_RSHIFT,
	'|','|',    0, TOK_OR,
	'&','&',    0, TOK_AND,
	'!','=',    0, TOK_NE,
	'<','=',    0, TOK_LE,
	'>','=',    0, TOK_GE,
	'=','=',    0, TOK_EQ,
	'|','=',    0, TOK_OR_ASSIGN,
	'&','=',    0, TOK_AND_ASSIGN,
	'*','=',    0, TOK_MUL_ASSIGN,
	'/','=',    0, TOK_DIV_ASSIGN,
	'%','=',    0, TOK_REM_ASSIGN,
	'+','=',    0, TOK_PLUS_ASSIGN,
	'-','=',    0, TOK_MINUS_ASSIGN,
	'-','-',    0, TOK_POST_DEC,
	'^','=',    0, TOK_XOR_ASSIGN,
	'+','+',    0, TOK_POST_INC,
	'*','*',    0, TOK_EXPONENT,
	'!',        0, TOK_NOT,
	'<',        0, TOK_LT,
	'>',        0, TOK_GT,
	'=',        0, TOK_ASSIGN,
	'|',        0, TOK_BOR,
	'&',        0, TOK_BAND,
	'*',        0, TOK_MUL,
	'/',        0, TOK_DIV,
	'%',        0, TOK_REM,
	'+',        0, TOK_ADD,
	'-',        0, TOK_SUB,
	'^',        0, TOK_BXOR,
	/* uniq */
	'~',        0, TOK_BNOT,
	',',        0, TOK_COMMA,
	'?',        0, TOK_CONDITIONAL,
	':',        0, TOK_CONDITIONAL_SEP,
	')',        0, TOK_RPAREN,
	'(',        0, TOK_LPAREN,
	0
};
/* ptr to ")" */
#define endexpression (&op_tokens[sizeof(op_tokens)-7])

arith_t
arith(const char *expr, int *perrcode, a_e_h_t *math_hooks)
{
	char arithval; /* Current character under analysis */
	operator lasttok, op;
	operator prec;
	operator *stack, *stackptr;
	const char *p = endexpression;
	int errcode;
	v_n_t *numstack, *numstackptr;
	unsigned datasizes = strlen(expr) + 2;

	/* Stack of integers */
	/* The proof that there can be no more than strlen(startbuf)/2+1 integers
	 * in any given correct or incorrect expression is left as an exercise to
	 * the reader. */
	numstackptr = numstack = alloca((datasizes / 2) * sizeof(numstack[0]));
	/* Stack of operator tokens */
	stackptr = stack = alloca(datasizes * sizeof(stack[0]));

	*stackptr++ = lasttok = TOK_LPAREN;     /* start off with a left paren */
	*perrcode = errcode = 0;

	while (1) {
		arithval = *expr;
		if (arithval == 0) {
			if (p == endexpression) {
				/* Null expression. */
				return 0;
			}

			/* This is only reached after all tokens have been extracted from the
			 * input stream. If there are still tokens on the operator stack, they
			 * are to be applied in order. At the end, there should be a final
			 * result on the integer stack */

			if (expr != endexpression + 1) {
				/* If we haven't done so already, */
				/* append a closing right paren */
				expr = endexpression;
				/* and let the loop process it. */
				continue;
			}
			/* At this point, we're done with the expression. */
			if (numstackptr != numstack+1) {
				/* ... but if there isn't, it's bad */
 err:
				*perrcode = -1;
				return *perrcode;
			}
			if (numstack->var) {
				/* expression is $((var)) only, lookup now */
				errcode = arith_lookup_val(numstack, math_hooks);
			}
 ret:
			*perrcode = errcode;
			return numstack->val;
		}

		/* Continue processing the expression. */
		if (arith_isspace(arithval)) {
			/* Skip whitespace */
			goto prologue;
		}
		p = endofname(expr);
		if (p != expr) {
			size_t var_name_size = (p-expr) + 1;  /* trailing zero */

			numstackptr->var = alloca(var_name_size);
			safe_strncpy(numstackptr->var, expr, var_name_size);
			expr = p;
 num:
			numstackptr->contidional_second_val_initialized = 0;
			numstackptr++;
			lasttok = TOK_NUM;
			continue;
		}
		if (isdigit(arithval)) {
			numstackptr->var = NULL;
			numstackptr->val = strto_arith_t(expr, (char **) &expr, 0);
			goto num;
		}
		for (p = op_tokens; ; p++) {
			const char *o;

			if (*p == 0) {
				/* strange operator not found */
				goto err;
			}
			for (o = expr; *p && *o == *p; p++)
				o++;
			if (!*p) {
				/* found */
				expr = o - 1;
				break;
			}
			/* skip tail uncompared token */
			while (*p)
				p++;
			/* skip zero delim */
			p++;
		}
		op = p[1];

		/* post grammar: a++ reduce to num */
		if (lasttok == TOK_POST_INC || lasttok == TOK_POST_DEC)
			lasttok = TOK_NUM;

		/* Plus and minus are binary (not unary) _only_ if the last
		 * token was as number, or a right paren (which pretends to be
		 * a number, since it evaluates to one). Think about it.
		 * It makes sense. */
		if (lasttok != TOK_NUM) {
			switch (op) {
			case TOK_ADD:
				op = TOK_UPLUS;
				break;
			case TOK_SUB:
				op = TOK_UMINUS;
				break;
			case TOK_POST_INC:
				op = TOK_PRE_INC;
				break;
			case TOK_POST_DEC:
				op = TOK_PRE_DEC;
				break;
			}
		}
		/* We don't want a unary operator to cause recursive descent on the
		 * stack, because there can be many in a row and it could cause an
		 * operator to be evaluated before its argument is pushed onto the
		 * integer stack. */
		/* But for binary operators, "apply" everything on the operator
		 * stack until we find an operator with a lesser priority than the
		 * one we have just extracted. */
		/* Left paren is given the lowest priority so it will never be
		 * "applied" in this way.
		 * if associativity is right and priority eq, applied also skip
		 */
		prec = PREC(op);
		if ((prec > 0 && prec < UNARYPREC) || prec == SPEC_PREC) {
			/* not left paren or unary */
			if (lasttok != TOK_NUM) {
				/* binary op must be preceded by a num */
				goto err;
			}
			while (stackptr != stack) {
				if (op == TOK_RPAREN) {
					/* The algorithm employed here is simple: while we don't
					 * hit an open paren nor the bottom of the stack, pop
					 * tokens and apply them */
					if (stackptr[-1] == TOK_LPAREN) {
						--stackptr;
						/* Any operator directly after a */
						lasttok = TOK_NUM;
						/* close paren should consider itself binary */
						goto prologue;
					}
				} else {
					operator prev_prec = PREC(stackptr[-1]);

					convert_prec_is_assing(prec);
					convert_prec_is_assing(prev_prec);
					if (prev_prec < prec)
						break;
					/* check right assoc */
					if (prev_prec == prec && is_right_associativity(prec))
						break;
				}
				errcode = arith_apply(*--stackptr, numstack, &numstackptr, math_hooks);
				if (errcode) goto ret;
			}
			if (op == TOK_RPAREN) {
				goto err;
			}
		}

		/* Push this operator to the stack and remember it. */
		*stackptr++ = lasttok = op;
 prologue:
		++expr;
	} /* while */
}

/*-
 * Copyright (c) 1989, 1991, 1993, 1994
 *      The Regents of the University of California.  All rights reserved.
 *
 * This code is derived from software contributed to Berkeley by
 * Kenneth Almquist.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. Neither the name of the University nor the names of its contributors
 *    may be used to endorse or promote products derived from this software
 *    without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 */