1 /*
2 * mathtest.c - test rig for mathlib
3 *
4 * Copyright (c) 1998-2019, Arm Limited.
5 * SPDX-License-Identifier: MIT
6 */
7
8 #include <assert.h>
9 #include <stdio.h>
10 #include <stdlib.h>
11 #include <string.h>
12 #include <setjmp.h>
13 #include <ctype.h>
14 #include <math.h>
15 #include <errno.h>
16 #include <limits.h>
17 #include <fenv.h>
18 #include "mathlib.h"
19
20 #ifndef math_errhandling
21 # define math_errhandling 0
22 #endif
23
24 #ifdef __cplusplus
25 #define EXTERN_C extern "C"
26 #else
27 #define EXTERN_C extern
28 #endif
29
30 #ifndef TRUE
31 #define TRUE 1
32 #endif
33 #ifndef FALSE
34 #define FALSE 0
35 #endif
36
37 #ifdef IMPORT_SYMBOL
38 #define STR2(x) #x
39 #define STR(x) STR2(x)
40 _Pragma(STR(import IMPORT_SYMBOL))
41 #endif
42
43 int dmsd, dlsd;
44 int quiet = 0;
45 int doround = 0;
46 unsigned statusmask = FE_ALL_EXCEPT;
47
48 #define EXTRABITS (12)
49 #define ULPUNIT (1<<EXTRABITS)
50
51 typedef int (*test) (void);
52
53 /*
54 struct to hold info about a function (which could actually be a macro)
55 */
56 typedef struct {
57 enum {
58 t_func, t_macro
59 } type;
60 enum {
61 at_d, at_s, /* double or single precision float */
62 at_d2, at_s2, /* same, but taking two args */
63 at_di, at_si, /* double/single and an int */
64 at_dip, at_sip, /* double/single and an int ptr */
65 at_ddp, at_ssp, /* d/s and a d/s ptr */
66 at_dc, at_sc, /* double or single precision complex */
67 at_dc2, at_sc2 /* same, but taking two args */
68 } argtype;
69 enum {
70 rt_d, rt_s, rt_i, /* double, single, int */
71 rt_dc, rt_sc, /* double, single precision complex */
72 rt_d2, rt_s2 /* also use res2 */
73 } rettype;
74 union {
75 void* ptr;
76 double (*d_d_ptr)(double);
77 float (*s_s_ptr)(float);
78 int (*d_i_ptr)(double);
79 int (*s_i_ptr)(float);
80 double (*d2_d_ptr)(double, double);
81 float (*s2_s_ptr)(float, float);
82 double (*di_d_ptr)(double,int);
83 float (*si_s_ptr)(float,int);
84 double (*dip_d_ptr)(double,int*);
85 float (*sip_s_ptr)(float,int*);
86 double (*ddp_d_ptr)(double,double*);
87 float (*ssp_s_ptr)(float,float*);
88 } func;
89 enum {
90 m_none,
91 m_isfinite, m_isfinitef,
92 m_isgreater, m_isgreaterequal,
93 m_isgreaterequalf, m_isgreaterf,
94 m_isinf, m_isinff,
95 m_isless, m_islessequal,
96 m_islessequalf, m_islessf,
97 m_islessgreater, m_islessgreaterf,
98 m_isnan, m_isnanf,
99 m_isnormal, m_isnormalf,
100 m_isunordered, m_isunorderedf,
101 m_fpclassify, m_fpclassifyf,
102 m_signbit, m_signbitf,
103 /* not actually a macro, but makes things easier */
104 m_rred, m_rredf,
105 m_cadd, m_csub, m_cmul, m_cdiv,
106 m_caddf, m_csubf, m_cmulf, m_cdivf
107 } macro_name; /* only used if a macro/something that can't be done using func */
108 long long tolerance;
109 const char* name;
110 } test_func;
111
112 /* used in qsort */
compare_tfuncs(const void * a,const void * b)113 int compare_tfuncs(const void* a, const void* b) {
114 return strcmp(((test_func*)a)->name, ((test_func*)b)->name);
115 }
116
is_double_argtype(int argtype)117 int is_double_argtype(int argtype) {
118 switch(argtype) {
119 case at_d:
120 case at_d2:
121 case at_dc:
122 case at_dc2:
123 return 1;
124 default:
125 return 0;
126 }
127 }
128
is_single_argtype(int argtype)129 int is_single_argtype(int argtype) {
130 switch(argtype) {
131 case at_s:
132 case at_s2:
133 case at_sc:
134 case at_sc2:
135 return 1;
136 default:
137 return 0;
138 }
139 }
140
is_double_rettype(int rettype)141 int is_double_rettype(int rettype) {
142 switch(rettype) {
143 case rt_d:
144 case rt_dc:
145 case rt_d2:
146 return 1;
147 default:
148 return 0;
149 }
150 }
151
is_single_rettype(int rettype)152 int is_single_rettype(int rettype) {
153 switch(rettype) {
154 case rt_s:
155 case rt_sc:
156 case rt_s2:
157 return 1;
158 default:
159 return 0;
160 }
161 }
162
is_complex_argtype(int argtype)163 int is_complex_argtype(int argtype) {
164 switch(argtype) {
165 case at_dc:
166 case at_sc:
167 case at_dc2:
168 case at_sc2:
169 return 1;
170 default:
171 return 0;
172 }
173 }
174
is_complex_rettype(int rettype)175 int is_complex_rettype(int rettype) {
176 switch(rettype) {
177 case rt_dc:
178 case rt_sc:
179 return 1;
180 default:
181 return 0;
182 }
183 }
184
185 /*
186 * Special-case flags indicating that some functions' error
187 * tolerance handling is more complicated than a fixed relative
188 * error bound.
189 */
190 #define ABSLOWERBOUND 0x4000000000000000LL
191 #define PLUSMINUSPIO2 0x1000000000000000LL
192
193 #define ARM_PREFIX(x) x
194
195 #define TFUNC(arg,ret,name,tolerance) { t_func, arg, ret, (void*)&name, m_none, tolerance, #name }
196 #define TFUNCARM(arg,ret,name,tolerance) { t_func, arg, ret, (void*)& ARM_PREFIX(name), m_none, tolerance, #name }
197 #define MFUNC(arg,ret,name,tolerance) { t_macro, arg, ret, NULL, m_##name, tolerance, #name }
198
199 /* sincosf wrappers for easier testing. */
sincosf_sinf(float x)200 static float sincosf_sinf(float x) { float s,c; sincosf(x, &s, &c); return s; }
sincosf_cosf(float x)201 static float sincosf_cosf(float x) { float s,c; sincosf(x, &s, &c); return c; }
202
203 test_func tfuncs[] = {
204 /* trigonometric */
205 TFUNC(at_d,rt_d, acos, 4*ULPUNIT),
206 TFUNC(at_d,rt_d, asin, 4*ULPUNIT),
207 TFUNC(at_d,rt_d, atan, 4*ULPUNIT),
208 TFUNC(at_d2,rt_d, atan2, 4*ULPUNIT),
209
210 TFUNC(at_d,rt_d, tan, 2*ULPUNIT),
211 TFUNC(at_d,rt_d, sin, 2*ULPUNIT),
212 TFUNC(at_d,rt_d, cos, 2*ULPUNIT),
213
214 TFUNC(at_s,rt_s, acosf, 4*ULPUNIT),
215 TFUNC(at_s,rt_s, asinf, 4*ULPUNIT),
216 TFUNC(at_s,rt_s, atanf, 4*ULPUNIT),
217 TFUNC(at_s2,rt_s, atan2f, 4*ULPUNIT),
218 TFUNCARM(at_s,rt_s, tanf, 4*ULPUNIT),
219 TFUNCARM(at_s,rt_s, sinf, 3*ULPUNIT/4),
220 TFUNCARM(at_s,rt_s, cosf, 3*ULPUNIT/4),
221 TFUNCARM(at_s,rt_s, sincosf_sinf, 3*ULPUNIT/4),
222 TFUNCARM(at_s,rt_s, sincosf_cosf, 3*ULPUNIT/4),
223
224 /* hyperbolic */
225 TFUNC(at_d, rt_d, atanh, 4*ULPUNIT),
226 TFUNC(at_d, rt_d, asinh, 4*ULPUNIT),
227 TFUNC(at_d, rt_d, acosh, 4*ULPUNIT),
228 TFUNC(at_d,rt_d, tanh, 4*ULPUNIT),
229 TFUNC(at_d,rt_d, sinh, 4*ULPUNIT),
230 TFUNC(at_d,rt_d, cosh, 4*ULPUNIT),
231
232 TFUNC(at_s, rt_s, atanhf, 4*ULPUNIT),
233 TFUNC(at_s, rt_s, asinhf, 4*ULPUNIT),
234 TFUNC(at_s, rt_s, acoshf, 4*ULPUNIT),
235 TFUNC(at_s,rt_s, tanhf, 4*ULPUNIT),
236 TFUNC(at_s,rt_s, sinhf, 4*ULPUNIT),
237 TFUNC(at_s,rt_s, coshf, 4*ULPUNIT),
238
239 /* exponential and logarithmic */
240 TFUNC(at_d,rt_d, log, 3*ULPUNIT/4),
241 TFUNC(at_d,rt_d, log10, 3*ULPUNIT),
242 TFUNC(at_d,rt_d, log2, 3*ULPUNIT/4),
243 TFUNC(at_d,rt_d, log1p, 2*ULPUNIT),
244 TFUNC(at_d,rt_d, exp, 3*ULPUNIT/4),
245 TFUNC(at_d,rt_d, exp2, 3*ULPUNIT/4),
246 TFUNC(at_d,rt_d, expm1, ULPUNIT),
247 TFUNCARM(at_s,rt_s, logf, ULPUNIT),
248 TFUNC(at_s,rt_s, log10f, 3*ULPUNIT),
249 TFUNCARM(at_s,rt_s, log2f, ULPUNIT),
250 TFUNC(at_s,rt_s, log1pf, 2*ULPUNIT),
251 TFUNCARM(at_s,rt_s, expf, 3*ULPUNIT/4),
252 TFUNCARM(at_s,rt_s, exp2f, 3*ULPUNIT/4),
253 TFUNC(at_s,rt_s, expm1f, ULPUNIT),
254
255 /* power */
256 TFUNC(at_d2,rt_d, pow, 3*ULPUNIT/4),
257 TFUNC(at_d,rt_d, sqrt, ULPUNIT/2),
258 TFUNC(at_d,rt_d, cbrt, 2*ULPUNIT),
259 TFUNC(at_d2, rt_d, hypot, 4*ULPUNIT),
260
261 TFUNCARM(at_s2,rt_s, powf, ULPUNIT),
262 TFUNC(at_s,rt_s, sqrtf, ULPUNIT/2),
263 TFUNC(at_s,rt_s, cbrtf, 2*ULPUNIT),
264 TFUNC(at_s2, rt_s, hypotf, 4*ULPUNIT),
265
266 /* error function */
267 TFUNC(at_d,rt_d, erf, 16*ULPUNIT),
268 TFUNC(at_s,rt_s, erff, 16*ULPUNIT),
269 TFUNC(at_d,rt_d, erfc, 16*ULPUNIT),
270 TFUNC(at_s,rt_s, erfcf, 16*ULPUNIT),
271
272 /* gamma functions */
273 TFUNC(at_d,rt_d, tgamma, 16*ULPUNIT),
274 TFUNC(at_s,rt_s, tgammaf, 16*ULPUNIT),
275 TFUNC(at_d,rt_d, lgamma, 16*ULPUNIT | ABSLOWERBOUND),
276 TFUNC(at_s,rt_s, lgammaf, 16*ULPUNIT | ABSLOWERBOUND),
277
278 TFUNC(at_d,rt_d, ceil, 0),
279 TFUNC(at_s,rt_s, ceilf, 0),
280 TFUNC(at_d2,rt_d, copysign, 0),
281 TFUNC(at_s2,rt_s, copysignf, 0),
282 TFUNC(at_d,rt_d, floor, 0),
283 TFUNC(at_s,rt_s, floorf, 0),
284 TFUNC(at_d2,rt_d, fmax, 0),
285 TFUNC(at_s2,rt_s, fmaxf, 0),
286 TFUNC(at_d2,rt_d, fmin, 0),
287 TFUNC(at_s2,rt_s, fminf, 0),
288 TFUNC(at_d2,rt_d, fmod, 0),
289 TFUNC(at_s2,rt_s, fmodf, 0),
290 MFUNC(at_d, rt_i, fpclassify, 0),
291 MFUNC(at_s, rt_i, fpclassifyf, 0),
292 TFUNC(at_dip,rt_d, frexp, 0),
293 TFUNC(at_sip,rt_s, frexpf, 0),
294 MFUNC(at_d, rt_i, isfinite, 0),
295 MFUNC(at_s, rt_i, isfinitef, 0),
296 MFUNC(at_d, rt_i, isgreater, 0),
297 MFUNC(at_d, rt_i, isgreaterequal, 0),
298 MFUNC(at_s, rt_i, isgreaterequalf, 0),
299 MFUNC(at_s, rt_i, isgreaterf, 0),
300 MFUNC(at_d, rt_i, isinf, 0),
301 MFUNC(at_s, rt_i, isinff, 0),
302 MFUNC(at_d, rt_i, isless, 0),
303 MFUNC(at_d, rt_i, islessequal, 0),
304 MFUNC(at_s, rt_i, islessequalf, 0),
305 MFUNC(at_s, rt_i, islessf, 0),
306 MFUNC(at_d, rt_i, islessgreater, 0),
307 MFUNC(at_s, rt_i, islessgreaterf, 0),
308 MFUNC(at_d, rt_i, isnan, 0),
309 MFUNC(at_s, rt_i, isnanf, 0),
310 MFUNC(at_d, rt_i, isnormal, 0),
311 MFUNC(at_s, rt_i, isnormalf, 0),
312 MFUNC(at_d, rt_i, isunordered, 0),
313 MFUNC(at_s, rt_i, isunorderedf, 0),
314 TFUNC(at_di,rt_d, ldexp, 0),
315 TFUNC(at_si,rt_s, ldexpf, 0),
316 TFUNC(at_ddp,rt_d2, modf, 0),
317 TFUNC(at_ssp,rt_s2, modff, 0),
318 #ifndef BIGRANGERED
319 MFUNC(at_d, rt_d, rred, 2*ULPUNIT),
320 #else
321 MFUNC(at_d, rt_d, m_rred, ULPUNIT),
322 #endif
323 MFUNC(at_d, rt_i, signbit, 0),
324 MFUNC(at_s, rt_i, signbitf, 0),
325 };
326
327 /*
328 * keywords are: func size op1 op2 result res2 errno op1r op1i op2r op2i resultr resulti
329 * also we ignore: wrongresult wrongres2 wrongerrno
330 * op1 equivalent to op1r, same with op2 and result
331 */
332
333 typedef struct {
334 test_func *func;
335 unsigned op1r[2]; /* real part, also used for non-complex numbers */
336 unsigned op1i[2]; /* imaginary part */
337 unsigned op2r[2];
338 unsigned op2i[2];
339 unsigned resultr[3];
340 unsigned resulti[3];
341 enum {
342 rc_none, rc_zero, rc_infinity, rc_nan, rc_finite
343 } resultc; /* special complex results, rc_none means use resultr and resulti as normal */
344 unsigned res2[2];
345 unsigned status; /* IEEE status return, if any */
346 unsigned maybestatus; /* for optional status, or allowance for spurious */
347 int nresult; /* number of result words */
348 int in_err, in_err_limit;
349 int err;
350 int maybeerr;
351 int valid;
352 int comment;
353 int random;
354 } testdetail;
355
356 enum { /* keywords */
357 k_errno, k_errno_in, k_error, k_func, k_maybeerror, k_maybestatus, k_op1, k_op1i, k_op1r, k_op2, k_op2i, k_op2r,
358 k_random, k_res2, k_result, k_resultc, k_resulti, k_resultr, k_status,
359 k_wrongres2, k_wrongresult, k_wrongstatus, k_wrongerrno
360 };
361 char *keywords[] = {
362 "errno", "errno_in", "error", "func", "maybeerror", "maybestatus", "op1", "op1i", "op1r", "op2", "op2i", "op2r",
363 "random", "res2", "result", "resultc", "resulti", "resultr", "status",
364 "wrongres2", "wrongresult", "wrongstatus", "wrongerrno"
365 };
366
367 enum {
368 e_0, e_EDOM, e_ERANGE,
369
370 /*
371 * This enum makes sure that we have the right number of errnos in the
372 * errno[] array
373 */
374 e_number_of_errnos
375 };
376 char *errnos[] = {
377 "0", "EDOM", "ERANGE"
378 };
379
380 enum {
381 e_none, e_divbyzero, e_domain, e_overflow, e_underflow
382 };
383 char *errors[] = {
384 "0", "divbyzero", "domain", "overflow", "underflow"
385 };
386
387 static int verbose, fo, strict;
388
389 /* state toggled by random=on / random=off */
390 static int randomstate;
391
392 /* Canonify a double NaN: SNaNs all become 7FF00000.00000001 and QNaNs
393 * all become 7FF80000.00000001 */
canon_dNaN(unsigned a[2])394 void canon_dNaN(unsigned a[2]) {
395 if ((a[0] & 0x7FF00000) != 0x7FF00000)
396 return; /* not Inf or NaN */
397 if (!(a[0] & 0xFFFFF) && !a[1])
398 return; /* Inf */
399 a[0] &= 0x7FF80000; /* canonify top word */
400 a[1] = 0x00000001; /* canonify bottom word */
401 }
402
403 /* Canonify a single NaN: SNaNs all become 7F800001 and QNaNs
404 * all become 7FC00001. Returns classification of the NaN. */
canon_sNaN(unsigned a[1])405 void canon_sNaN(unsigned a[1]) {
406 if ((a[0] & 0x7F800000) != 0x7F800000)
407 return; /* not Inf or NaN */
408 if (!(a[0] & 0x7FFFFF))
409 return; /* Inf */
410 a[0] &= 0x7FC00000; /* canonify most bits */
411 a[0] |= 0x00000001; /* canonify bottom bit */
412 }
413
414 /*
415 * Detect difficult operands for FO mode.
416 */
is_dhard(unsigned a[2])417 int is_dhard(unsigned a[2])
418 {
419 if ((a[0] & 0x7FF00000) == 0x7FF00000)
420 return TRUE; /* inf or NaN */
421 if ((a[0] & 0x7FF00000) == 0 &&
422 ((a[0] & 0x7FFFFFFF) | a[1]) != 0)
423 return TRUE; /* denormal */
424 return FALSE;
425 }
is_shard(unsigned a[1])426 int is_shard(unsigned a[1])
427 {
428 if ((a[0] & 0x7F800000) == 0x7F800000)
429 return TRUE; /* inf or NaN */
430 if ((a[0] & 0x7F800000) == 0 &&
431 (a[0] & 0x7FFFFFFF) != 0)
432 return TRUE; /* denormal */
433 return FALSE;
434 }
435
436 /*
437 * Normalise all zeroes into +0, for FO mode.
438 */
dnormzero(unsigned a[2])439 void dnormzero(unsigned a[2])
440 {
441 if (a[0] == 0x80000000 && a[1] == 0)
442 a[0] = 0;
443 }
snormzero(unsigned a[1])444 void snormzero(unsigned a[1])
445 {
446 if (a[0] == 0x80000000)
447 a[0] = 0;
448 }
449
find(char * word,char ** array,int asize)450 static int find(char *word, char **array, int asize) {
451 int i, j;
452
453 asize /= sizeof(char *);
454
455 i = -1; j = asize; /* strictly between i and j */
456 while (j-i > 1) {
457 int k = (i+j) / 2;
458 int c = strcmp(word, array[k]);
459 if (c > 0)
460 i = k;
461 else if (c < 0)
462 j = k;
463 else /* found it! */
464 return k;
465 }
466 return -1; /* not found */
467 }
468
find_testfunc(char * word)469 static test_func* find_testfunc(char *word) {
470 int i, j, asize;
471
472 asize = sizeof(tfuncs)/sizeof(test_func);
473
474 i = -1; j = asize; /* strictly between i and j */
475 while (j-i > 1) {
476 int k = (i+j) / 2;
477 int c = strcmp(word, tfuncs[k].name);
478 if (c > 0)
479 i = k;
480 else if (c < 0)
481 j = k;
482 else /* found it! */
483 return tfuncs + k;
484 }
485 return NULL; /* not found */
486 }
487
calc_error(unsigned a[2],unsigned b[3],int shift,int rettype)488 static long long calc_error(unsigned a[2], unsigned b[3], int shift, int rettype) {
489 unsigned r0, r1, r2;
490 int sign, carry;
491 long long result;
492
493 /*
494 * If either number is infinite, require exact equality. If
495 * either number is NaN, require that both are NaN. If either
496 * of these requirements is broken, return INT_MAX.
497 */
498 if (is_double_rettype(rettype)) {
499 if ((a[0] & 0x7FF00000) == 0x7FF00000 ||
500 (b[0] & 0x7FF00000) == 0x7FF00000) {
501 if (((a[0] & 0x800FFFFF) || a[1]) &&
502 ((b[0] & 0x800FFFFF) || b[1]) &&
503 (a[0] & 0x7FF00000) == 0x7FF00000 &&
504 (b[0] & 0x7FF00000) == 0x7FF00000)
505 return 0; /* both NaN - OK */
506 if (!((a[0] & 0xFFFFF) || a[1]) &&
507 !((b[0] & 0xFFFFF) || b[1]) &&
508 a[0] == b[0])
509 return 0; /* both same sign of Inf - OK */
510 return LLONG_MAX;
511 }
512 } else {
513 if ((a[0] & 0x7F800000) == 0x7F800000 ||
514 (b[0] & 0x7F800000) == 0x7F800000) {
515 if ((a[0] & 0x807FFFFF) &&
516 (b[0] & 0x807FFFFF) &&
517 (a[0] & 0x7F800000) == 0x7F800000 &&
518 (b[0] & 0x7F800000) == 0x7F800000)
519 return 0; /* both NaN - OK */
520 if (!(a[0] & 0x7FFFFF) &&
521 !(b[0] & 0x7FFFFF) &&
522 a[0] == b[0])
523 return 0; /* both same sign of Inf - OK */
524 return LLONG_MAX;
525 }
526 }
527
528 /*
529 * Both finite. Return INT_MAX if the signs differ.
530 */
531 if ((a[0] ^ b[0]) & 0x80000000)
532 return LLONG_MAX;
533
534 /*
535 * Now it's just straight multiple-word subtraction.
536 */
537 if (is_double_rettype(rettype)) {
538 r2 = -b[2]; carry = (r2 == 0);
539 r1 = a[1] + ~b[1] + carry; carry = (r1 < a[1] || (carry && r1 == a[1]));
540 r0 = a[0] + ~b[0] + carry;
541 } else {
542 r2 = -b[1]; carry = (r2 == 0);
543 r1 = a[0] + ~b[0] + carry; carry = (r1 < a[0] || (carry && r1 == a[0]));
544 r0 = ~0 + carry;
545 }
546
547 /*
548 * Forgive larger errors in specialised cases.
549 */
550 if (shift > 0) {
551 if (shift > 32*3)
552 return 0; /* all errors are forgiven! */
553 while (shift >= 32) {
554 r2 = r1;
555 r1 = r0;
556 r0 = -(r0 >> 31);
557 shift -= 32;
558 }
559
560 if (shift > 0) {
561 r2 = (r2 >> shift) | (r1 << (32-shift));
562 r1 = (r1 >> shift) | (r0 << (32-shift));
563 r0 = (r0 >> shift) | ((-(r0 >> 31)) << (32-shift));
564 }
565 }
566
567 if (r0 & 0x80000000) {
568 sign = 1;
569 r2 = ~r2; carry = (r2 == 0);
570 r1 = 0 + ~r1 + carry; carry = (carry && (r2 == 0));
571 r0 = 0 + ~r0 + carry;
572 } else {
573 sign = 0;
574 }
575
576 if (r0 >= (1LL<<(31-EXTRABITS)))
577 return LLONG_MAX; /* many ulps out */
578
579 result = (r2 >> (32-EXTRABITS)) & (ULPUNIT-1);
580 result |= r1 << EXTRABITS;
581 result |= (long long)r0 << (32+EXTRABITS);
582 if (sign)
583 result = -result;
584 return result;
585 }
586
587 /* special named operands */
588
589 typedef struct {
590 unsigned op1, op2;
591 char* name;
592 } special_op;
593
594 static special_op special_ops_double[] = {
595 {0x00000000,0x00000000,"0"},
596 {0x3FF00000,0x00000000,"1"},
597 {0x7FF00000,0x00000000,"inf"},
598 {0x7FF80000,0x00000001,"qnan"},
599 {0x7FF00000,0x00000001,"snan"},
600 {0x3ff921fb,0x54442d18,"pi2"},
601 {0x400921fb,0x54442d18,"pi"},
602 {0x3fe921fb,0x54442d18,"pi4"},
603 {0x4002d97c,0x7f3321d2,"3pi4"},
604 };
605
606 static special_op special_ops_float[] = {
607 {0x00000000,0,"0"},
608 {0x3f800000,0,"1"},
609 {0x7f800000,0,"inf"},
610 {0x7fc00000,0,"qnan"},
611 {0x7f800001,0,"snan"},
612 {0x3fc90fdb,0,"pi2"},
613 {0x40490fdb,0,"pi"},
614 {0x3f490fdb,0,"pi4"},
615 {0x4016cbe4,0,"3pi4"},
616 };
617
618 /*
619 This is what is returned by the below functions.
620 We need it to handle the sign of the number
621 */
622 static special_op tmp_op = {0,0,0};
623
find_special_op_from_op(unsigned op1,unsigned op2,int is_double)624 special_op* find_special_op_from_op(unsigned op1, unsigned op2, int is_double) {
625 int i;
626 special_op* sop;
627 if(is_double) {
628 sop = special_ops_double;
629 } else {
630 sop = special_ops_float;
631 }
632 for(i = 0; i < sizeof(special_ops_double)/sizeof(special_op); i++) {
633 if(sop->op1 == (op1&0x7fffffff) && sop->op2 == op2) {
634 if(tmp_op.name) free(tmp_op.name);
635 tmp_op.name = malloc(strlen(sop->name)+2);
636 if(op1>>31) {
637 sprintf(tmp_op.name,"-%s",sop->name);
638 } else {
639 strcpy(tmp_op.name,sop->name);
640 }
641 return &tmp_op;
642 }
643 sop++;
644 }
645 return NULL;
646 }
647
find_special_op_from_name(const char * name,int is_double)648 special_op* find_special_op_from_name(const char* name, int is_double) {
649 int i, neg=0;
650 special_op* sop;
651 if(is_double) {
652 sop = special_ops_double;
653 } else {
654 sop = special_ops_float;
655 }
656 if(*name=='-') {
657 neg=1;
658 name++;
659 } else if(*name=='+') {
660 name++;
661 }
662 for(i = 0; i < sizeof(special_ops_double)/sizeof(special_op); i++) {
663 if(0 == strcmp(name,sop->name)) {
664 tmp_op.op1 = sop->op1;
665 if(neg) {
666 tmp_op.op1 |= 0x80000000;
667 }
668 tmp_op.op2 = sop->op2;
669 return &tmp_op;
670 }
671 sop++;
672 }
673 return NULL;
674 }
675
676 /*
677 helper function for the below
678 type=0 for single, 1 for double, 2 for no sop
679 */
do_op(char * q,unsigned * op,const char * name,int num,int sop_type)680 int do_op(char* q, unsigned* op, const char* name, int num, int sop_type) {
681 int i;
682 int n=num;
683 special_op* sop = NULL;
684 for(i = 0; i < num; i++) {
685 op[i] = 0;
686 }
687 if(sop_type<2) {
688 sop = find_special_op_from_name(q,sop_type);
689 }
690 if(sop != NULL) {
691 op[0] = sop->op1;
692 op[1] = sop->op2;
693 } else {
694 switch(num) {
695 case 1: n = sscanf(q, "%x", &op[0]); break;
696 case 2: n = sscanf(q, "%x.%x", &op[0], &op[1]); break;
697 case 3: n = sscanf(q, "%x.%x.%x", &op[0], &op[1], &op[2]); break;
698 default: return -1;
699 }
700 }
701 if (verbose) {
702 printf("%s=",name);
703 for (i = 0; (i < n); ++i) printf("%x.", op[i]);
704 printf(" (n=%d)\n", n);
705 }
706 return n;
707 }
708
parsetest(char * testbuf,testdetail oldtest)709 testdetail parsetest(char *testbuf, testdetail oldtest) {
710 char *p; /* Current part of line: Option name */
711 char *q; /* Current part of line: Option value */
712 testdetail ret; /* What we return */
713 int k; /* Function enum from k_* */
714 int n; /* Used as returns for scanfs */
715 int argtype=2, rettype=2; /* for do_op */
716
717 /* clear ret */
718 memset(&ret, 0, sizeof(ret));
719
720 if (verbose) printf("Parsing line: %s\n", testbuf);
721 while (*testbuf && isspace(*testbuf)) testbuf++;
722 if (testbuf[0] == ';' || testbuf[0] == '#' || testbuf[0] == '!' ||
723 testbuf[0] == '>' || testbuf[0] == '\0') {
724 ret.comment = 1;
725 if (verbose) printf("Line is a comment\n");
726 return ret;
727 }
728 ret.comment = 0;
729
730 if (*testbuf == '+') {
731 if (oldtest.valid) {
732 ret = oldtest; /* structure copy */
733 } else {
734 fprintf(stderr, "copy from invalid: ignored\n");
735 }
736 testbuf++;
737 }
738
739 ret.random = randomstate;
740
741 ret.in_err = 0;
742 ret.in_err_limit = e_number_of_errnos;
743
744 p = strtok(testbuf, " \t");
745 while (p != NULL) {
746 q = strchr(p, '=');
747 if (!q)
748 goto balderdash;
749 *q++ = '\0';
750 k = find(p, keywords, sizeof(keywords));
751 switch (k) {
752 case k_random:
753 randomstate = (!strcmp(q, "on"));
754 ret.comment = 1;
755 return ret; /* otherwise ignore this line */
756 case k_func:
757 if (verbose) printf("func=%s ", q);
758 //ret.func = find(q, funcs, sizeof(funcs));
759 ret.func = find_testfunc(q);
760 if (ret.func == NULL)
761 {
762 if (verbose) printf("(id=unknown)\n");
763 goto balderdash;
764 }
765 if(is_single_argtype(ret.func->argtype))
766 argtype = 0;
767 else if(is_double_argtype(ret.func->argtype))
768 argtype = 1;
769 if(is_single_rettype(ret.func->rettype))
770 rettype = 0;
771 else if(is_double_rettype(ret.func->rettype))
772 rettype = 1;
773 //ret.size = sizes[ret.func];
774 if (verbose) printf("(name=%s) (size=%d)\n", ret.func->name, ret.func->argtype);
775 break;
776 case k_op1:
777 case k_op1r:
778 n = do_op(q,ret.op1r,"op1r",2,argtype);
779 if (n < 1)
780 goto balderdash;
781 break;
782 case k_op1i:
783 n = do_op(q,ret.op1i,"op1i",2,argtype);
784 if (n < 1)
785 goto balderdash;
786 break;
787 case k_op2:
788 case k_op2r:
789 n = do_op(q,ret.op2r,"op2r",2,argtype);
790 if (n < 1)
791 goto balderdash;
792 break;
793 case k_op2i:
794 n = do_op(q,ret.op2i,"op2i",2,argtype);
795 if (n < 1)
796 goto balderdash;
797 break;
798 case k_resultc:
799 puts(q);
800 if(strncmp(q,"inf",3)==0) {
801 ret.resultc = rc_infinity;
802 } else if(strcmp(q,"zero")==0) {
803 ret.resultc = rc_zero;
804 } else if(strcmp(q,"nan")==0) {
805 ret.resultc = rc_nan;
806 } else if(strcmp(q,"finite")==0) {
807 ret.resultc = rc_finite;
808 } else {
809 goto balderdash;
810 }
811 break;
812 case k_result:
813 case k_resultr:
814 n = (do_op)(q,ret.resultr,"resultr",3,rettype);
815 if (n < 1)
816 goto balderdash;
817 ret.nresult = n; /* assume real and imaginary have same no. words */
818 break;
819 case k_resulti:
820 n = do_op(q,ret.resulti,"resulti",3,rettype);
821 if (n < 1)
822 goto balderdash;
823 break;
824 case k_res2:
825 n = do_op(q,ret.res2,"res2",2,rettype);
826 if (n < 1)
827 goto balderdash;
828 break;
829 case k_status:
830 while (*q) {
831 if (*q == 'i') ret.status |= FE_INVALID;
832 if (*q == 'z') ret.status |= FE_DIVBYZERO;
833 if (*q == 'o') ret.status |= FE_OVERFLOW;
834 if (*q == 'u') ret.status |= FE_UNDERFLOW;
835 q++;
836 }
837 break;
838 case k_maybeerror:
839 n = find(q, errors, sizeof(errors));
840 if (n < 0)
841 goto balderdash;
842 if(math_errhandling&MATH_ERREXCEPT) {
843 switch(n) {
844 case e_domain: ret.maybestatus |= FE_INVALID; break;
845 case e_divbyzero: ret.maybestatus |= FE_DIVBYZERO; break;
846 case e_overflow: ret.maybestatus |= FE_OVERFLOW; break;
847 case e_underflow: ret.maybestatus |= FE_UNDERFLOW; break;
848 }
849 }
850 {
851 switch(n) {
852 case e_domain:
853 ret.maybeerr = e_EDOM; break;
854 case e_divbyzero:
855 case e_overflow:
856 case e_underflow:
857 ret.maybeerr = e_ERANGE; break;
858 }
859 }
860 case k_maybestatus:
861 while (*q) {
862 if (*q == 'i') ret.maybestatus |= FE_INVALID;
863 if (*q == 'z') ret.maybestatus |= FE_DIVBYZERO;
864 if (*q == 'o') ret.maybestatus |= FE_OVERFLOW;
865 if (*q == 'u') ret.maybestatus |= FE_UNDERFLOW;
866 q++;
867 }
868 break;
869 case k_error:
870 n = find(q, errors, sizeof(errors));
871 if (n < 0)
872 goto balderdash;
873 if(math_errhandling&MATH_ERREXCEPT) {
874 switch(n) {
875 case e_domain: ret.status |= FE_INVALID; break;
876 case e_divbyzero: ret.status |= FE_DIVBYZERO; break;
877 case e_overflow: ret.status |= FE_OVERFLOW; break;
878 case e_underflow: ret.status |= FE_UNDERFLOW; break;
879 }
880 }
881 if(math_errhandling&MATH_ERRNO) {
882 switch(n) {
883 case e_domain:
884 ret.err = e_EDOM; break;
885 case e_divbyzero:
886 case e_overflow:
887 case e_underflow:
888 ret.err = e_ERANGE; break;
889 }
890 }
891 if(!(math_errhandling&MATH_ERRNO)) {
892 switch(n) {
893 case e_domain:
894 ret.maybeerr = e_EDOM; break;
895 case e_divbyzero:
896 case e_overflow:
897 case e_underflow:
898 ret.maybeerr = e_ERANGE; break;
899 }
900 }
901 break;
902 case k_errno:
903 ret.err = find(q, errnos, sizeof(errnos));
904 if (ret.err < 0)
905 goto balderdash;
906 break;
907 case k_errno_in:
908 ret.in_err = find(q, errnos, sizeof(errnos));
909 if (ret.err < 0)
910 goto balderdash;
911 ret.in_err_limit = ret.in_err + 1;
912 break;
913 case k_wrongresult:
914 case k_wrongstatus:
915 case k_wrongres2:
916 case k_wrongerrno:
917 /* quietly ignore these keys */
918 break;
919 default:
920 goto balderdash;
921 }
922 p = strtok(NULL, " \t");
923 }
924 ret.valid = 1;
925 return ret;
926
927 /* come here from almost any error */
928 balderdash:
929 ret.valid = 0;
930 return ret;
931 }
932
933 typedef enum {
934 test_comment, /* deliberately not a test */
935 test_invalid, /* accidentally not a test */
936 test_decline, /* was a test, and wasn't run */
937 test_fail, /* was a test, and failed */
938 test_pass /* was a test, and passed */
939 } testresult;
940
941 char failtext[512];
942
943 typedef union {
944 unsigned i[2];
945 double f;
946 double da[2];
947 } dbl;
948
949 typedef union {
950 unsigned i;
951 float f;
952 float da[2];
953 } sgl;
954
955 /* helper function for runtest */
print_error(int rettype,unsigned * result,char * text,char ** failp)956 void print_error(int rettype, unsigned *result, char* text, char** failp) {
957 special_op *sop;
958 char *str;
959
960 if(result) {
961 *failp += sprintf(*failp," %s=",text);
962 sop = find_special_op_from_op(result[0],result[1],is_double_rettype(rettype));
963 if(sop) {
964 *failp += sprintf(*failp,"%s",sop->name);
965 } else {
966 if(is_double_rettype(rettype)) {
967 str="%08x.%08x";
968 } else {
969 str="%08x";
970 }
971 *failp += sprintf(*failp,str,result[0],result[1]);
972 }
973 }
974 }
975
976
print_ulps_helper(const char * name,long long ulps,char ** failp)977 void print_ulps_helper(const char *name, long long ulps, char** failp) {
978 if(ulps == LLONG_MAX) {
979 *failp += sprintf(*failp, " %s=HUGE", name);
980 } else {
981 *failp += sprintf(*failp, " %s=%.3f", name, (double)ulps / ULPUNIT);
982 }
983 }
984
985 /* for complex args make ulpsr or ulpsri = 0 to not print */
print_ulps(int rettype,long long ulpsr,long long ulpsi,char ** failp)986 void print_ulps(int rettype, long long ulpsr, long long ulpsi, char** failp) {
987 if(is_complex_rettype(rettype)) {
988 if (ulpsr) print_ulps_helper("ulpsr",ulpsr,failp);
989 if (ulpsi) print_ulps_helper("ulpsi",ulpsi,failp);
990 } else {
991 if (ulpsr) print_ulps_helper("ulps",ulpsr,failp);
992 }
993 }
994
runtest(testdetail t)995 int runtest(testdetail t) {
996 int err, status;
997
998 dbl d_arg1, d_arg2, d_res, d_res2;
999 sgl s_arg1, s_arg2, s_res, s_res2;
1000
1001 int deferred_decline = FALSE;
1002 char *failp = failtext;
1003
1004 unsigned int intres=0;
1005
1006 int res2_adjust = 0;
1007
1008 if (t.comment)
1009 return test_comment;
1010 if (!t.valid)
1011 return test_invalid;
1012
1013 /* Set IEEE status to mathlib-normal */
1014 feclearexcept(FE_ALL_EXCEPT);
1015
1016 /* Deal with operands */
1017 #define DO_DOP(arg,op) arg.i[dmsd] = t.op[0]; arg.i[dlsd] = t.op[1]
1018 DO_DOP(d_arg1,op1r);
1019 DO_DOP(d_arg2,op2r);
1020 s_arg1.i = t.op1r[0]; s_arg2.i = t.op2r[0];
1021
1022 /*
1023 * Detect NaNs, infinities and denormals on input, and set a
1024 * deferred decline flag if we're in FO mode.
1025 *
1026 * (We defer the decline rather than doing it immediately
1027 * because even in FO mode the operation is not permitted to
1028 * crash or tight-loop; so we _run_ the test, and then ignore
1029 * all the results.)
1030 */
1031 if (fo) {
1032 if (is_double_argtype(t.func->argtype) && is_dhard(t.op1r))
1033 deferred_decline = TRUE;
1034 if (t.func->argtype==at_d2 && is_dhard(t.op2r))
1035 deferred_decline = TRUE;
1036 if (is_single_argtype(t.func->argtype) && is_shard(t.op1r))
1037 deferred_decline = TRUE;
1038 if (t.func->argtype==at_s2 && is_shard(t.op2r))
1039 deferred_decline = TRUE;
1040 if (is_double_rettype(t.func->rettype) && is_dhard(t.resultr))
1041 deferred_decline = TRUE;
1042 if (t.func->rettype==rt_d2 && is_dhard(t.res2))
1043 deferred_decline = TRUE;
1044 if (is_single_argtype(t.func->rettype) && is_shard(t.resultr))
1045 deferred_decline = TRUE;
1046 if (t.func->rettype==rt_s2 && is_shard(t.res2))
1047 deferred_decline = TRUE;
1048 if (t.err == e_ERANGE)
1049 deferred_decline = TRUE;
1050 }
1051
1052 /*
1053 * Perform the operation
1054 */
1055
1056 errno = t.in_err == e_EDOM ? EDOM : t.in_err == e_ERANGE ? ERANGE : 0;
1057 if (t.err == e_0)
1058 t.err = t.in_err;
1059 if (t.maybeerr == e_0)
1060 t.maybeerr = t.in_err;
1061
1062 if(t.func->type == t_func) {
1063 switch(t.func->argtype) {
1064 case at_d: d_res.f = t.func->func.d_d_ptr(d_arg1.f); break;
1065 case at_s: s_res.f = t.func->func.s_s_ptr(s_arg1.f); break;
1066 case at_d2: d_res.f = t.func->func.d2_d_ptr(d_arg1.f, d_arg2.f); break;
1067 case at_s2: s_res.f = t.func->func.s2_s_ptr(s_arg1.f, s_arg2.f); break;
1068 case at_di: d_res.f = t.func->func.di_d_ptr(d_arg1.f, d_arg2.i[dmsd]); break;
1069 case at_si: s_res.f = t.func->func.si_s_ptr(s_arg1.f, s_arg2.i); break;
1070 case at_dip: d_res.f = t.func->func.dip_d_ptr(d_arg1.f, (int*)&intres); break;
1071 case at_sip: s_res.f = t.func->func.sip_s_ptr(s_arg1.f, (int*)&intres); break;
1072 case at_ddp: d_res.f = t.func->func.ddp_d_ptr(d_arg1.f, &d_res2.f); break;
1073 case at_ssp: s_res.f = t.func->func.ssp_s_ptr(s_arg1.f, &s_res2.f); break;
1074 default:
1075 printf("unhandled function: %s\n",t.func->name);
1076 return test_fail;
1077 }
1078 } else {
1079 /* printf("macro: name=%s, num=%i, s1.i=0x%08x s1.f=%f\n",t.func->name, t.func->macro_name, s_arg1.i, (double)s_arg1.f); */
1080 switch(t.func->macro_name) {
1081 case m_isfinite: intres = isfinite(d_arg1.f); break;
1082 case m_isinf: intres = isinf(d_arg1.f); break;
1083 case m_isnan: intres = isnan(d_arg1.f); break;
1084 case m_isnormal: intres = isnormal(d_arg1.f); break;
1085 case m_signbit: intres = signbit(d_arg1.f); break;
1086 case m_fpclassify: intres = fpclassify(d_arg1.f); break;
1087 case m_isgreater: intres = isgreater(d_arg1.f, d_arg2.f); break;
1088 case m_isgreaterequal: intres = isgreaterequal(d_arg1.f, d_arg2.f); break;
1089 case m_isless: intres = isless(d_arg1.f, d_arg2.f); break;
1090 case m_islessequal: intres = islessequal(d_arg1.f, d_arg2.f); break;
1091 case m_islessgreater: intres = islessgreater(d_arg1.f, d_arg2.f); break;
1092 case m_isunordered: intres = isunordered(d_arg1.f, d_arg2.f); break;
1093
1094 case m_isfinitef: intres = isfinite(s_arg1.f); break;
1095 case m_isinff: intres = isinf(s_arg1.f); break;
1096 case m_isnanf: intres = isnan(s_arg1.f); break;
1097 case m_isnormalf: intres = isnormal(s_arg1.f); break;
1098 case m_signbitf: intres = signbit(s_arg1.f); break;
1099 case m_fpclassifyf: intres = fpclassify(s_arg1.f); break;
1100 case m_isgreaterf: intres = isgreater(s_arg1.f, s_arg2.f); break;
1101 case m_isgreaterequalf: intres = isgreaterequal(s_arg1.f, s_arg2.f); break;
1102 case m_islessf: intres = isless(s_arg1.f, s_arg2.f); break;
1103 case m_islessequalf: intres = islessequal(s_arg1.f, s_arg2.f); break;
1104 case m_islessgreaterf: intres = islessgreater(s_arg1.f, s_arg2.f); break;
1105 case m_isunorderedf: intres = isunordered(s_arg1.f, s_arg2.f); break;
1106
1107 default:
1108 printf("unhandled macro: %s\n",t.func->name);
1109 return test_fail;
1110 }
1111 }
1112
1113 /*
1114 * Decline the test if the deferred decline flag was set above.
1115 */
1116 if (deferred_decline)
1117 return test_decline;
1118
1119 /* printf("intres=%i\n",intres); */
1120
1121 /* Clear the fail text (indicating a pass unless we change it) */
1122 failp[0] = '\0';
1123
1124 /* Check the IEEE status bits (except INX, which we disregard).
1125 * We don't bother with this for complex numbers, because the
1126 * complex functions are hard to get exactly right and we don't
1127 * have to anyway (C99 annex G is only informative). */
1128 if (!(is_complex_argtype(t.func->argtype) || is_complex_rettype(t.func->rettype))) {
1129 status = fetestexcept(FE_INVALID|FE_DIVBYZERO|FE_OVERFLOW|FE_UNDERFLOW);
1130 if ((status|t.maybestatus|~statusmask) != (t.status|t.maybestatus|~statusmask)) {
1131 if (quiet) failtext[0]='x';
1132 else {
1133 failp += sprintf(failp,
1134 " wrongstatus=%s%s%s%s%s",
1135 (status & FE_INVALID ? "i" : ""),
1136 (status & FE_DIVBYZERO ? "z" : ""),
1137 (status & FE_OVERFLOW ? "o" : ""),
1138 (status & FE_UNDERFLOW ? "u" : ""),
1139 (status ? "" : "OK"));
1140 }
1141 }
1142 }
1143
1144 /* Check the result */
1145 {
1146 unsigned resultr[2], resulti[2];
1147 unsigned tresultr[3], tresulti[3], wres;
1148
1149 switch(t.func->rettype) {
1150 case rt_d:
1151 case rt_d2:
1152 tresultr[0] = t.resultr[0];
1153 tresultr[1] = t.resultr[1];
1154 resultr[0] = d_res.i[dmsd]; resultr[1] = d_res.i[dlsd];
1155 wres = 2;
1156 break;
1157 case rt_i:
1158 tresultr[0] = t.resultr[0];
1159 resultr[0] = intres;
1160 wres = 1;
1161 break;
1162 case rt_s:
1163 case rt_s2:
1164 tresultr[0] = t.resultr[0];
1165 resultr[0] = s_res.i;
1166 wres = 1;
1167 break;
1168 default:
1169 puts("unhandled rettype in runtest");
1170 wres = 0;
1171 }
1172 if(t.resultc != rc_none) {
1173 int err = 0;
1174 switch(t.resultc) {
1175 case rc_zero:
1176 if(resultr[0] != 0 || resulti[0] != 0 ||
1177 (wres==2 && (resultr[1] != 0 || resulti[1] != 0))) {
1178 err = 1;
1179 }
1180 break;
1181 case rc_infinity:
1182 if(wres==1) {
1183 if(!((resultr[0]&0x7fffffff)==0x7f800000 ||
1184 (resulti[0]&0x7fffffff)==0x7f800000)) {
1185 err = 1;
1186 }
1187 } else {
1188 if(!(((resultr[0]&0x7fffffff)==0x7ff00000 && resultr[1]==0) ||
1189 ((resulti[0]&0x7fffffff)==0x7ff00000 && resulti[1]==0))) {
1190 err = 1;
1191 }
1192 }
1193 break;
1194 case rc_nan:
1195 if(wres==1) {
1196 if(!((resultr[0]&0x7fffffff)>0x7f800000 ||
1197 (resulti[0]&0x7fffffff)>0x7f800000)) {
1198 err = 1;
1199 }
1200 } else {
1201 canon_dNaN(resultr);
1202 canon_dNaN(resulti);
1203 if(!(((resultr[0]&0x7fffffff)>0x7ff00000 && resultr[1]==1) ||
1204 ((resulti[0]&0x7fffffff)>0x7ff00000 && resulti[1]==1))) {
1205 err = 1;
1206 }
1207 }
1208 break;
1209 case rc_finite:
1210 if(wres==1) {
1211 if(!((resultr[0]&0x7fffffff)<0x7f800000 ||
1212 (resulti[0]&0x7fffffff)<0x7f800000)) {
1213 err = 1;
1214 }
1215 } else {
1216 if(!((resultr[0]&0x7fffffff)<0x7ff00000 ||
1217 (resulti[0]&0x7fffffff)<0x7ff00000)) {
1218 err = 1;
1219 }
1220 }
1221 break;
1222 default:
1223 break;
1224 }
1225 if(err) {
1226 print_error(t.func->rettype,resultr,"wrongresultr",&failp);
1227 print_error(t.func->rettype,resulti,"wrongresulti",&failp);
1228 }
1229 } else if (t.nresult > wres) {
1230 /*
1231 * The test case data has provided the result to more
1232 * than double precision. Instead of testing exact
1233 * equality, we test against our maximum error
1234 * tolerance.
1235 */
1236 int rshift, ishift;
1237 long long ulpsr, ulpsi, ulptolerance;
1238
1239 tresultr[wres] = t.resultr[wres] << (32-EXTRABITS);
1240 tresulti[wres] = t.resulti[wres] << (32-EXTRABITS);
1241 if(strict) {
1242 ulptolerance = 4096; /* one ulp */
1243 } else {
1244 ulptolerance = t.func->tolerance;
1245 }
1246 rshift = ishift = 0;
1247 if (ulptolerance & ABSLOWERBOUND) {
1248 /*
1249 * Hack for the lgamma functions, which have an
1250 * error behaviour that can't conveniently be
1251 * characterised in pure ULPs. Really, we want to
1252 * say that the error in lgamma is "at most N ULPs,
1253 * or at most an absolute error of X, whichever is
1254 * larger", for appropriately chosen N,X. But since
1255 * these two functions are the only cases where it
1256 * arises, I haven't bothered to do it in a nice way
1257 * in the function table above.
1258 *
1259 * (The difficult cases arise with negative input
1260 * values such that |gamma(x)| is very near to 1; in
1261 * this situation implementations tend to separately
1262 * compute lgamma(|x|) and the log of the correction
1263 * term from the Euler reflection formula, and
1264 * subtract - which catastrophically loses
1265 * significance.)
1266 *
1267 * As far as I can tell, nobody cares about this:
1268 * GNU libm doesn't get those cases right either,
1269 * and OpenCL explicitly doesn't state a ULP error
1270 * limit for lgamma. So my guess is that this is
1271 * simply considered acceptable error behaviour for
1272 * this particular function, and hence I feel free
1273 * to allow for it here.
1274 */
1275 ulptolerance &= ~ABSLOWERBOUND;
1276 if (t.op1r[0] & 0x80000000) {
1277 if (t.func->rettype == rt_d)
1278 rshift = 0x400 - ((tresultr[0] >> 20) & 0x7ff);
1279 else if (t.func->rettype == rt_s)
1280 rshift = 0x80 - ((tresultr[0] >> 23) & 0xff);
1281 if (rshift < 0)
1282 rshift = 0;
1283 }
1284 }
1285 if (ulptolerance & PLUSMINUSPIO2) {
1286 ulptolerance &= ~PLUSMINUSPIO2;
1287 /*
1288 * Hack for range reduction, which can reduce
1289 * borderline cases in the wrong direction, i.e.
1290 * return a value just outside one end of the interval
1291 * [-pi/4,+pi/4] when it could have returned a value
1292 * just inside the other end by subtracting an
1293 * adjacent multiple of pi/2.
1294 *
1295 * We tolerate this, up to a point, because the
1296 * trigonometric functions making use of the output of
1297 * rred can cope and because making the range reducer
1298 * do the exactly right thing in every case would be
1299 * more expensive.
1300 */
1301 if (wres == 1) {
1302 /* Upper bound of overshoot derived in rredf.h */
1303 if ((resultr[0]&0x7FFFFFFF) <= 0x3f494b02 &&
1304 (resultr[0]&0x7FFFFFFF) > 0x3f490fda &&
1305 (resultr[0]&0x80000000) != (tresultr[0]&0x80000000)) {
1306 unsigned long long val;
1307 val = tresultr[0];
1308 val = (val << 32) | tresultr[1];
1309 /*
1310 * Compute the alternative permitted result by
1311 * subtracting from the sum of the extended
1312 * single-precision bit patterns of +pi/4 and
1313 * -pi/4. This is a horrible hack which only
1314 * works because we can be confident that
1315 * numbers in this range all have the same
1316 * exponent!
1317 */
1318 val = 0xfe921fb54442d184ULL - val;
1319 tresultr[0] = val >> 32;
1320 tresultr[1] = (val >> (32-EXTRABITS)) << (32-EXTRABITS);
1321 /*
1322 * Also, expect a correspondingly different
1323 * value of res2 as a result of this change.
1324 * The adjustment depends on whether we just
1325 * flipped the result from + to - or vice
1326 * versa.
1327 */
1328 if (resultr[0] & 0x80000000) {
1329 res2_adjust = +1;
1330 } else {
1331 res2_adjust = -1;
1332 }
1333 }
1334 }
1335 }
1336 ulpsr = calc_error(resultr, tresultr, rshift, t.func->rettype);
1337 if(is_complex_rettype(t.func->rettype)) {
1338 ulpsi = calc_error(resulti, tresulti, ishift, t.func->rettype);
1339 } else {
1340 ulpsi = 0;
1341 }
1342 unsigned *rr = (ulpsr > ulptolerance || ulpsr < -ulptolerance) ? resultr : NULL;
1343 unsigned *ri = (ulpsi > ulptolerance || ulpsi < -ulptolerance) ? resulti : NULL;
1344 /* printf("tolerance=%i, ulpsr=%i, ulpsi=%i, rr=%p, ri=%p\n",ulptolerance,ulpsr,ulpsi,rr,ri); */
1345 if (rr || ri) {
1346 if (quiet) failtext[0]='x';
1347 else {
1348 print_error(t.func->rettype,rr,"wrongresultr",&failp);
1349 print_error(t.func->rettype,ri,"wrongresulti",&failp);
1350 print_ulps(t.func->rettype,rr ? ulpsr : 0, ri ? ulpsi : 0,&failp);
1351 }
1352 }
1353 } else {
1354 if(is_complex_rettype(t.func->rettype))
1355 /*
1356 * Complex functions are not fully supported,
1357 * this is unreachable, but prevents warnings.
1358 */
1359 abort();
1360 /*
1361 * The test case data has provided the result in
1362 * exactly the output precision. Therefore we must
1363 * complain about _any_ violation.
1364 */
1365 switch(t.func->rettype) {
1366 case rt_dc:
1367 canon_dNaN(tresulti);
1368 canon_dNaN(resulti);
1369 if (fo) {
1370 dnormzero(tresulti);
1371 dnormzero(resulti);
1372 }
1373 /* deliberate fall-through */
1374 case rt_d:
1375 canon_dNaN(tresultr);
1376 canon_dNaN(resultr);
1377 if (fo) {
1378 dnormzero(tresultr);
1379 dnormzero(resultr);
1380 }
1381 break;
1382 case rt_sc:
1383 canon_sNaN(tresulti);
1384 canon_sNaN(resulti);
1385 if (fo) {
1386 snormzero(tresulti);
1387 snormzero(resulti);
1388 }
1389 /* deliberate fall-through */
1390 case rt_s:
1391 canon_sNaN(tresultr);
1392 canon_sNaN(resultr);
1393 if (fo) {
1394 snormzero(tresultr);
1395 snormzero(resultr);
1396 }
1397 break;
1398 default:
1399 break;
1400 }
1401 if(is_complex_rettype(t.func->rettype)) {
1402 unsigned *rr, *ri;
1403 if(resultr[0] != tresultr[0] ||
1404 (wres > 1 && resultr[1] != tresultr[1])) {
1405 rr = resultr;
1406 } else {
1407 rr = NULL;
1408 }
1409 if(resulti[0] != tresulti[0] ||
1410 (wres > 1 && resulti[1] != tresulti[1])) {
1411 ri = resulti;
1412 } else {
1413 ri = NULL;
1414 }
1415 if(rr || ri) {
1416 if (quiet) failtext[0]='x';
1417 print_error(t.func->rettype,rr,"wrongresultr",&failp);
1418 print_error(t.func->rettype,ri,"wrongresulti",&failp);
1419 }
1420 } else if (resultr[0] != tresultr[0] ||
1421 (wres > 1 && resultr[1] != tresultr[1])) {
1422 if (quiet) failtext[0]='x';
1423 print_error(t.func->rettype,resultr,"wrongresult",&failp);
1424 }
1425 }
1426 /*
1427 * Now test res2, for those functions (frexp, modf, rred)
1428 * which use it.
1429 */
1430 if (t.func->func.ptr == &frexp || t.func->func.ptr == &frexpf ||
1431 t.func->macro_name == m_rred || t.func->macro_name == m_rredf) {
1432 unsigned tres2 = t.res2[0];
1433 if (res2_adjust) {
1434 /* Fix for range reduction, propagated from further up */
1435 tres2 = (tres2 + res2_adjust) & 3;
1436 }
1437 if (tres2 != intres) {
1438 if (quiet) failtext[0]='x';
1439 else {
1440 failp += sprintf(failp,
1441 " wrongres2=%08x", intres);
1442 }
1443 }
1444 } else if (t.func->func.ptr == &modf || t.func->func.ptr == &modff) {
1445 tresultr[0] = t.res2[0];
1446 tresultr[1] = t.res2[1];
1447 if (is_double_rettype(t.func->rettype)) {
1448 canon_dNaN(tresultr);
1449 resultr[0] = d_res2.i[dmsd];
1450 resultr[1] = d_res2.i[dlsd];
1451 canon_dNaN(resultr);
1452 if (fo) {
1453 dnormzero(tresultr);
1454 dnormzero(resultr);
1455 }
1456 } else {
1457 canon_sNaN(tresultr);
1458 resultr[0] = s_res2.i;
1459 resultr[1] = s_res2.i;
1460 canon_sNaN(resultr);
1461 if (fo) {
1462 snormzero(tresultr);
1463 snormzero(resultr);
1464 }
1465 }
1466 if (resultr[0] != tresultr[0] ||
1467 (wres > 1 && resultr[1] != tresultr[1])) {
1468 if (quiet) failtext[0]='x';
1469 else {
1470 if (is_double_rettype(t.func->rettype))
1471 failp += sprintf(failp, " wrongres2=%08x.%08x",
1472 resultr[0], resultr[1]);
1473 else
1474 failp += sprintf(failp, " wrongres2=%08x",
1475 resultr[0]);
1476 }
1477 }
1478 }
1479 }
1480
1481 /* Check errno */
1482 err = (errno == EDOM ? e_EDOM : errno == ERANGE ? e_ERANGE : e_0);
1483 if (err != t.err && err != t.maybeerr) {
1484 if (quiet) failtext[0]='x';
1485 else {
1486 failp += sprintf(failp, " wrongerrno=%s expecterrno=%s ", errnos[err], errnos[t.err]);
1487 }
1488 }
1489
1490 return *failtext ? test_fail : test_pass;
1491 }
1492
1493 int passed, failed, declined;
1494
runtests(char * name,FILE * fp)1495 void runtests(char *name, FILE *fp) {
1496 char testbuf[512], linebuf[512];
1497 int lineno = 1;
1498 testdetail test;
1499
1500 test.valid = 0;
1501
1502 if (verbose) printf("runtests: %s\n", name);
1503 while (fgets(testbuf, sizeof(testbuf), fp)) {
1504 int res, print_errno;
1505 testbuf[strcspn(testbuf, "\r\n")] = '\0';
1506 strcpy(linebuf, testbuf);
1507 test = parsetest(testbuf, test);
1508 print_errno = 0;
1509 while (test.in_err < test.in_err_limit) {
1510 res = runtest(test);
1511 if (res == test_pass) {
1512 if (verbose)
1513 printf("%s:%d: pass\n", name, lineno);
1514 ++passed;
1515 } else if (res == test_decline) {
1516 if (verbose)
1517 printf("%s:%d: declined\n", name, lineno);
1518 ++declined;
1519 } else if (res == test_fail) {
1520 if (!quiet)
1521 printf("%s:%d: FAIL%s: %s%s%s%s\n", name, lineno,
1522 test.random ? " (random)" : "",
1523 linebuf,
1524 print_errno ? " errno_in=" : "",
1525 print_errno ? errnos[test.in_err] : "",
1526 failtext);
1527 ++failed;
1528 } else if (res == test_invalid) {
1529 printf("%s:%d: malformed: %s\n", name, lineno, linebuf);
1530 ++failed;
1531 }
1532 test.in_err++;
1533 print_errno = 1;
1534 }
1535 lineno++;
1536 }
1537 }
1538
main(int ac,char ** av)1539 int main(int ac, char **av) {
1540 char **files;
1541 int i, nfiles = 0;
1542 dbl d;
1543
1544 #ifdef MICROLIB
1545 /*
1546 * Invent argc and argv ourselves.
1547 */
1548 char *argv[256];
1549 char args[256];
1550 {
1551 int sargs[2];
1552 char *p;
1553
1554 ac = 0;
1555
1556 sargs[0]=(int)args;
1557 sargs[1]=(int)sizeof(args);
1558 if (!__semihost(0x15, sargs)) {
1559 args[sizeof(args)-1] = '\0'; /* just in case */
1560 p = args;
1561 while (1) {
1562 while (*p == ' ' || *p == '\t') p++;
1563 if (!*p) break;
1564 argv[ac++] = p;
1565 while (*p && *p != ' ' && *p != '\t') p++;
1566 if (*p) *p++ = '\0';
1567 }
1568 }
1569
1570 av = argv;
1571 }
1572 #endif
1573
1574 /* Sort tfuncs */
1575 qsort(tfuncs, sizeof(tfuncs)/sizeof(test_func), sizeof(test_func), &compare_tfuncs);
1576
1577 /*
1578 * Autodetect the `double' endianness.
1579 */
1580 dmsd = 0;
1581 d.f = 1.0; /* 0x3ff00000 / 0x00000000 */
1582 if (d.i[dmsd] == 0) {
1583 dmsd = 1;
1584 }
1585 /*
1586 * Now dmsd denotes what the compiler thinks we're at. Let's
1587 * check that it agrees with what the runtime thinks.
1588 */
1589 d.i[0] = d.i[1] = 0x11111111;/* a random +ve number */
1590 d.f /= d.f; /* must now be one */
1591 if (d.i[dmsd] == 0) {
1592 fprintf(stderr, "YIKES! Compiler and runtime disagree on endianness"
1593 " of `double'. Bailing out\n");
1594 return 1;
1595 }
1596 dlsd = !dmsd;
1597
1598 /* default is terse */
1599 verbose = 0;
1600 fo = 0;
1601 strict = 0;
1602
1603 files = (char **)malloc((ac+1) * sizeof(char *));
1604 if (!files) {
1605 fprintf(stderr, "initial malloc failed!\n");
1606 return 1;
1607 }
1608 #ifdef NOCMDLINE
1609 files[nfiles++] = "testfile";
1610 #endif
1611
1612 while (--ac) {
1613 char *p = *++av;
1614 if (*p == '-') {
1615 static char *options[] = {
1616 "-fo",
1617 #if 0
1618 "-noinexact",
1619 "-noround",
1620 #endif
1621 "-nostatus",
1622 "-quiet",
1623 "-strict",
1624 "-v",
1625 "-verbose",
1626 };
1627 enum {
1628 op_fo,
1629 #if 0
1630 op_noinexact,
1631 op_noround,
1632 #endif
1633 op_nostatus,
1634 op_quiet,
1635 op_strict,
1636 op_v,
1637 op_verbose,
1638 };
1639 switch (find(p, options, sizeof(options))) {
1640 case op_quiet:
1641 quiet = 1;
1642 break;
1643 #if 0
1644 case op_noinexact:
1645 statusmask &= 0x0F; /* remove bit 4 */
1646 break;
1647 case op_noround:
1648 doround = 0;
1649 break;
1650 #endif
1651 case op_nostatus: /* no status word => noinx,noround */
1652 statusmask = 0;
1653 doround = 0;
1654 break;
1655 case op_v:
1656 case op_verbose:
1657 verbose = 1;
1658 break;
1659 case op_fo:
1660 fo = 1;
1661 break;
1662 case op_strict: /* tolerance is 1 ulp */
1663 strict = 1;
1664 break;
1665 default:
1666 fprintf(stderr, "unrecognised option: %s\n", p);
1667 break;
1668 }
1669 } else {
1670 files[nfiles++] = p;
1671 }
1672 }
1673
1674 passed = failed = declined = 0;
1675
1676 if (nfiles) {
1677 for (i = 0; i < nfiles; i++) {
1678 FILE *fp = fopen(files[i], "r");
1679 if (!fp) {
1680 fprintf(stderr, "Couldn't open %s\n", files[i]);
1681 } else
1682 runtests(files[i], fp);
1683 }
1684 } else
1685 runtests("(stdin)", stdin);
1686
1687 printf("Completed. Passed %d, failed %d (total %d",
1688 passed, failed, passed+failed);
1689 if (declined)
1690 printf(" plus %d declined", declined);
1691 printf(")\n");
1692 if (failed || passed == 0)
1693 return 1;
1694 printf("** TEST PASSED OK **\n");
1695 return 0;
1696 }
1697
undef_func()1698 void undef_func() {
1699 failed++;
1700 puts("ERROR: undefined function called");
1701 }
1702