1 /*
2 * mathtest.c - test rig for mathlib
3 *
4 * Copyright (c) 1998-2018, 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 EXTERN_C int __ieee754_rem_pio2(double, double *);
44
45 int dmsd, dlsd;
46 int quiet = 0;
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 if(math_errhandling&MATH_ERRNO) {
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 break;
892 case k_errno:
893 ret.err = find(q, errnos, sizeof(errnos));
894 if (ret.err < 0)
895 goto balderdash;
896 break;
897 case k_errno_in:
898 ret.in_err = find(q, errnos, sizeof(errnos));
899 if (ret.err < 0)
900 goto balderdash;
901 ret.in_err_limit = ret.in_err + 1;
902 break;
903 case k_wrongresult:
904 case k_wrongstatus:
905 case k_wrongres2:
906 case k_wrongerrno:
907 /* quietly ignore these keys */
908 break;
909 default:
910 goto balderdash;
911 }
912 p = strtok(NULL, " \t");
913 }
914 ret.valid = 1;
915 return ret;
916
917 /* come here from almost any error */
918 balderdash:
919 ret.valid = 0;
920 return ret;
921 }
922
923 typedef enum {
924 test_comment, /* deliberately not a test */
925 test_invalid, /* accidentally not a test */
926 test_decline, /* was a test, and wasn't run */
927 test_fail, /* was a test, and failed */
928 test_pass /* was a test, and passed */
929 } testresult;
930
931 char failtext[512];
932
933 typedef union {
934 unsigned i[2];
935 double f;
936 double da[2];
937 } dbl;
938
939 typedef union {
940 unsigned i;
941 float f;
942 float da[2];
943 } sgl;
944
945 /* helper function for runtest */
print_error(int rettype,unsigned * result,char * text,char ** failp)946 void print_error(int rettype, unsigned *result, char* text, char** failp) {
947 special_op *sop;
948 char *str;
949
950 if(result) {
951 *failp += sprintf(*failp," %s=",text);
952 sop = find_special_op_from_op(result[0],result[1],is_double_rettype(rettype));
953 if(sop) {
954 *failp += sprintf(*failp,"%s",sop->name);
955 } else {
956 if(is_double_rettype(rettype)) {
957 str="%08x.%08x";
958 } else {
959 str="%08x";
960 }
961 *failp += sprintf(*failp,str,result[0],result[1]);
962 }
963 }
964 }
965
966
print_ulps_helper(const char * name,long long ulps,char ** failp)967 void print_ulps_helper(const char *name, long long ulps, char** failp) {
968 if(ulps == LLONG_MAX) {
969 *failp += sprintf(*failp, " %s=HUGE", name);
970 } else {
971 *failp += sprintf(*failp, " %s=%.3f", name, (double)ulps / ULPUNIT);
972 }
973 }
974
975 /* for complex args make ulpsr or ulpsri = 0 to not print */
print_ulps(int rettype,long long ulpsr,long long ulpsi,char ** failp)976 void print_ulps(int rettype, long long ulpsr, long long ulpsi, char** failp) {
977 if(is_complex_rettype(rettype)) {
978 if (ulpsr) print_ulps_helper("ulpsr",ulpsr,failp);
979 if (ulpsi) print_ulps_helper("ulpsi",ulpsi,failp);
980 } else {
981 if (ulpsr) print_ulps_helper("ulps",ulpsr,failp);
982 }
983 }
984
runtest(testdetail t)985 int runtest(testdetail t) {
986 int err, status;
987
988 dbl d_arg1, d_arg2, d_res, d_res2;
989 sgl s_arg1, s_arg2, s_res, s_res2;
990
991 int deferred_decline = FALSE;
992 char *failp = failtext;
993
994 unsigned int intres=0;
995
996 int res2_adjust = 0;
997
998 if (t.comment)
999 return test_comment;
1000 if (!t.valid)
1001 return test_invalid;
1002
1003 /* Set IEEE status to mathlib-normal */
1004 feclearexcept(FE_ALL_EXCEPT);
1005
1006 /* Deal with operands */
1007 #define DO_DOP(arg,op) arg.i[dmsd] = t.op[0]; arg.i[dlsd] = t.op[1]
1008 DO_DOP(d_arg1,op1r);
1009 DO_DOP(d_arg2,op2r);
1010 s_arg1.i = t.op1r[0]; s_arg2.i = t.op2r[0];
1011
1012 /*
1013 * Detect NaNs, infinities and denormals on input, and set a
1014 * deferred decline flag if we're in FO mode.
1015 *
1016 * (We defer the decline rather than doing it immediately
1017 * because even in FO mode the operation is not permitted to
1018 * crash or tight-loop; so we _run_ the test, and then ignore
1019 * all the results.)
1020 */
1021 if (fo) {
1022 if (is_double_argtype(t.func->argtype) && is_dhard(t.op1r))
1023 deferred_decline = TRUE;
1024 if (t.func->argtype==at_d2 && is_dhard(t.op2r))
1025 deferred_decline = TRUE;
1026 if (is_single_argtype(t.func->argtype) && is_shard(t.op1r))
1027 deferred_decline = TRUE;
1028 if (t.func->argtype==at_s2 && is_shard(t.op2r))
1029 deferred_decline = TRUE;
1030 if (is_double_rettype(t.func->rettype) && is_dhard(t.resultr))
1031 deferred_decline = TRUE;
1032 if (t.func->rettype==rt_d2 && is_dhard(t.res2))
1033 deferred_decline = TRUE;
1034 if (is_single_argtype(t.func->rettype) && is_shard(t.resultr))
1035 deferred_decline = TRUE;
1036 if (t.func->rettype==rt_s2 && is_shard(t.res2))
1037 deferred_decline = TRUE;
1038 if (t.err == e_ERANGE)
1039 deferred_decline = TRUE;
1040 }
1041
1042 /*
1043 * Perform the operation
1044 */
1045
1046 errno = t.in_err == e_EDOM ? EDOM : t.in_err == e_ERANGE ? ERANGE : 0;
1047 if (t.err == e_0)
1048 t.err = t.in_err;
1049 if (t.maybeerr == e_0)
1050 t.maybeerr = t.in_err;
1051
1052 if(t.func->type == t_func) {
1053 switch(t.func->argtype) {
1054 case at_d: d_res.f = t.func->func.d_d_ptr(d_arg1.f); break;
1055 case at_s: s_res.f = t.func->func.s_s_ptr(s_arg1.f); break;
1056 case at_d2: d_res.f = t.func->func.d2_d_ptr(d_arg1.f, d_arg2.f); break;
1057 case at_s2: s_res.f = t.func->func.s2_s_ptr(s_arg1.f, s_arg2.f); break;
1058 case at_di: d_res.f = t.func->func.di_d_ptr(d_arg1.f, d_arg2.i[dmsd]); break;
1059 case at_si: s_res.f = t.func->func.si_s_ptr(s_arg1.f, s_arg2.i); break;
1060 case at_dip: d_res.f = t.func->func.dip_d_ptr(d_arg1.f, (int*)&intres); break;
1061 case at_sip: s_res.f = t.func->func.sip_s_ptr(s_arg1.f, (int*)&intres); break;
1062 case at_ddp: d_res.f = t.func->func.ddp_d_ptr(d_arg1.f, &d_res2.f); break;
1063 case at_ssp: s_res.f = t.func->func.ssp_s_ptr(s_arg1.f, &s_res2.f); break;
1064 default:
1065 printf("unhandled function: %s\n",t.func->name);
1066 return test_fail;
1067 }
1068 } else {
1069 /* 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); */
1070 switch(t.func->macro_name) {
1071 case m_isfinite: intres = isfinite(d_arg1.f); break;
1072 case m_isinf: intres = isinf(d_arg1.f); break;
1073 case m_isnan: intres = isnan(d_arg1.f); break;
1074 case m_isnormal: intres = isnormal(d_arg1.f); break;
1075 case m_signbit: intres = signbit(d_arg1.f); break;
1076 case m_fpclassify: intres = fpclassify(d_arg1.f); break;
1077 case m_isgreater: intres = isgreater(d_arg1.f, d_arg2.f); break;
1078 case m_isgreaterequal: intres = isgreaterequal(d_arg1.f, d_arg2.f); break;
1079 case m_isless: intres = isless(d_arg1.f, d_arg2.f); break;
1080 case m_islessequal: intres = islessequal(d_arg1.f, d_arg2.f); break;
1081 case m_islessgreater: intres = islessgreater(d_arg1.f, d_arg2.f); break;
1082 case m_isunordered: intres = isunordered(d_arg1.f, d_arg2.f); break;
1083
1084 case m_isfinitef: intres = isfinite(s_arg1.f); break;
1085 case m_isinff: intres = isinf(s_arg1.f); break;
1086 case m_isnanf: intres = isnan(s_arg1.f); break;
1087 case m_isnormalf: intres = isnormal(s_arg1.f); break;
1088 case m_signbitf: intres = signbit(s_arg1.f); break;
1089 case m_fpclassifyf: intres = fpclassify(s_arg1.f); break;
1090 case m_isgreaterf: intres = isgreater(s_arg1.f, s_arg2.f); break;
1091 case m_isgreaterequalf: intres = isgreaterequal(s_arg1.f, s_arg2.f); break;
1092 case m_islessf: intres = isless(s_arg1.f, s_arg2.f); break;
1093 case m_islessequalf: intres = islessequal(s_arg1.f, s_arg2.f); break;
1094 case m_islessgreaterf: intres = islessgreater(s_arg1.f, s_arg2.f); break;
1095 case m_isunorderedf: intres = isunordered(s_arg1.f, s_arg2.f); break;
1096
1097 case m_rred: intres = 3 & __ieee754_rem_pio2(d_arg1.f, d_res.da); break;
1098 default:
1099 printf("unhandled macro: %s\n",t.func->name);
1100 return test_fail;
1101 }
1102 }
1103
1104 /*
1105 * Decline the test if the deferred decline flag was set above.
1106 */
1107 if (deferred_decline)
1108 return test_decline;
1109
1110 /* printf("intres=%i\n",intres); */
1111
1112 /* Clear the fail text (indicating a pass unless we change it) */
1113 failp[0] = '\0';
1114
1115 /* Check the IEEE status bits (except INX, which we disregard).
1116 * We don't bother with this for complex numbers, because the
1117 * complex functions are hard to get exactly right and we don't
1118 * have to anyway (C99 annex G is only informative). */
1119 if (!(is_complex_argtype(t.func->argtype) || is_complex_rettype(t.func->rettype))) {
1120 status = fetestexcept(FE_INVALID|FE_DIVBYZERO|FE_OVERFLOW|FE_UNDERFLOW);
1121 if ((status|t.maybestatus) != (t.status|t.maybestatus)) {
1122 if (quiet) failtext[0]='x';
1123 else {
1124 failp += sprintf(failp,
1125 " wrongstatus=%s%s%s%s%s",
1126 (status & FE_INVALID ? "i" : ""),
1127 (status & FE_DIVBYZERO ? "z" : ""),
1128 (status & FE_OVERFLOW ? "o" : ""),
1129 (status & FE_UNDERFLOW ? "u" : ""),
1130 (status ? "" : "OK"));
1131 }
1132 }
1133 }
1134
1135 /* Check the result */
1136 {
1137 unsigned resultr[2], resulti[2];
1138 unsigned tresultr[3], tresulti[3], wres;
1139
1140 switch(t.func->rettype) {
1141 case rt_d:
1142 case rt_d2:
1143 tresultr[0] = t.resultr[0];
1144 tresultr[1] = t.resultr[1];
1145 resultr[0] = d_res.i[dmsd]; resultr[1] = d_res.i[dlsd];
1146 wres = 2;
1147 break;
1148 case rt_i:
1149 tresultr[0] = t.resultr[0];
1150 resultr[0] = intres;
1151 wres = 1;
1152 break;
1153 case rt_s:
1154 case rt_s2:
1155 tresultr[0] = t.resultr[0];
1156 resultr[0] = s_res.i;
1157 wres = 1;
1158 break;
1159 default:
1160 puts("unhandled rettype in runtest");
1161 wres = 0;
1162 }
1163 if(t.resultc != rc_none) {
1164 int err = 0;
1165 switch(t.resultc) {
1166 case rc_zero:
1167 if(resultr[0] != 0 || resulti[0] != 0 ||
1168 (wres==2 && (resultr[1] != 0 || resulti[1] != 0))) {
1169 err = 1;
1170 }
1171 break;
1172 case rc_infinity:
1173 if(wres==1) {
1174 if(!((resultr[0]&0x7fffffff)==0x7f800000 ||
1175 (resulti[0]&0x7fffffff)==0x7f800000)) {
1176 err = 1;
1177 }
1178 } else {
1179 if(!(((resultr[0]&0x7fffffff)==0x7ff00000 && resultr[1]==0) ||
1180 ((resulti[0]&0x7fffffff)==0x7ff00000 && resulti[1]==0))) {
1181 err = 1;
1182 }
1183 }
1184 break;
1185 case rc_nan:
1186 if(wres==1) {
1187 if(!((resultr[0]&0x7fffffff)>0x7f800000 ||
1188 (resulti[0]&0x7fffffff)>0x7f800000)) {
1189 err = 1;
1190 }
1191 } else {
1192 canon_dNaN(resultr);
1193 canon_dNaN(resulti);
1194 if(!(((resultr[0]&0x7fffffff)>0x7ff00000 && resultr[1]==1) ||
1195 ((resulti[0]&0x7fffffff)>0x7ff00000 && resulti[1]==1))) {
1196 err = 1;
1197 }
1198 }
1199 break;
1200 case rc_finite:
1201 if(wres==1) {
1202 if(!((resultr[0]&0x7fffffff)<0x7f800000 ||
1203 (resulti[0]&0x7fffffff)<0x7f800000)) {
1204 err = 1;
1205 }
1206 } else {
1207 if(!((resultr[0]&0x7fffffff)<0x7ff00000 ||
1208 (resulti[0]&0x7fffffff)<0x7ff00000)) {
1209 err = 1;
1210 }
1211 }
1212 break;
1213 default:
1214 break;
1215 }
1216 if(err) {
1217 print_error(t.func->rettype,resultr,"wrongresultr",&failp);
1218 print_error(t.func->rettype,resulti,"wrongresulti",&failp);
1219 }
1220 } else if (t.nresult > wres) {
1221 /*
1222 * The test case data has provided the result to more
1223 * than double precision. Instead of testing exact
1224 * equality, we test against our maximum error
1225 * tolerance.
1226 */
1227 int rshift, ishift;
1228 long long ulpsr, ulpsi, ulptolerance;
1229
1230 tresultr[wres] = t.resultr[wres] << (32-EXTRABITS);
1231 tresulti[wres] = t.resulti[wres] << (32-EXTRABITS);
1232 if(strict) {
1233 ulptolerance = 4096; /* one ulp */
1234 } else {
1235 ulptolerance = t.func->tolerance;
1236 }
1237 rshift = ishift = 0;
1238 if (ulptolerance & ABSLOWERBOUND) {
1239 /*
1240 * Hack for the lgamma functions, which have an
1241 * error behaviour that can't conveniently be
1242 * characterised in pure ULPs. Really, we want to
1243 * say that the error in lgamma is "at most N ULPs,
1244 * or at most an absolute error of X, whichever is
1245 * larger", for appropriately chosen N,X. But since
1246 * these two functions are the only cases where it
1247 * arises, I haven't bothered to do it in a nice way
1248 * in the function table above.
1249 *
1250 * (The difficult cases arise with negative input
1251 * values such that |gamma(x)| is very near to 1; in
1252 * this situation implementations tend to separately
1253 * compute lgamma(|x|) and the log of the correction
1254 * term from the Euler reflection formula, and
1255 * subtract - which catastrophically loses
1256 * significance.)
1257 *
1258 * As far as I can tell, nobody cares about this:
1259 * GNU libm doesn't get those cases right either,
1260 * and OpenCL explicitly doesn't state a ULP error
1261 * limit for lgamma. So my guess is that this is
1262 * simply considered acceptable error behaviour for
1263 * this particular function, and hence I feel free
1264 * to allow for it here.
1265 */
1266 ulptolerance &= ~ABSLOWERBOUND;
1267 if (t.op1r[0] & 0x80000000) {
1268 if (t.func->rettype == rt_d)
1269 rshift = 0x400 - ((tresultr[0] >> 20) & 0x7ff);
1270 else if (t.func->rettype == rt_s)
1271 rshift = 0x80 - ((tresultr[0] >> 23) & 0xff);
1272 if (rshift < 0)
1273 rshift = 0;
1274 }
1275 }
1276 if (ulptolerance & PLUSMINUSPIO2) {
1277 ulptolerance &= ~PLUSMINUSPIO2;
1278 /*
1279 * Hack for range reduction, which can reduce
1280 * borderline cases in the wrong direction, i.e.
1281 * return a value just outside one end of the interval
1282 * [-pi/4,+pi/4] when it could have returned a value
1283 * just inside the other end by subtracting an
1284 * adjacent multiple of pi/2.
1285 *
1286 * We tolerate this, up to a point, because the
1287 * trigonometric functions making use of the output of
1288 * rred can cope and because making the range reducer
1289 * do the exactly right thing in every case would be
1290 * more expensive.
1291 */
1292 if (wres == 1) {
1293 /* Upper bound of overshoot derived in rredf.h */
1294 if ((resultr[0]&0x7FFFFFFF) <= 0x3f494b02 &&
1295 (resultr[0]&0x7FFFFFFF) > 0x3f490fda &&
1296 (resultr[0]&0x80000000) != (tresultr[0]&0x80000000)) {
1297 unsigned long long val;
1298 val = tresultr[0];
1299 val = (val << 32) | tresultr[1];
1300 /*
1301 * Compute the alternative permitted result by
1302 * subtracting from the sum of the extended
1303 * single-precision bit patterns of +pi/4 and
1304 * -pi/4. This is a horrible hack which only
1305 * works because we can be confident that
1306 * numbers in this range all have the same
1307 * exponent!
1308 */
1309 val = 0xfe921fb54442d184ULL - val;
1310 tresultr[0] = val >> 32;
1311 tresultr[1] = (val >> (32-EXTRABITS)) << (32-EXTRABITS);
1312 /*
1313 * Also, expect a correspondingly different
1314 * value of res2 as a result of this change.
1315 * The adjustment depends on whether we just
1316 * flipped the result from + to - or vice
1317 * versa.
1318 */
1319 if (resultr[0] & 0x80000000) {
1320 res2_adjust = +1;
1321 } else {
1322 res2_adjust = -1;
1323 }
1324 }
1325 }
1326 }
1327 ulpsr = calc_error(resultr, tresultr, rshift, t.func->rettype);
1328 if(is_complex_rettype(t.func->rettype)) {
1329 ulpsi = calc_error(resulti, tresulti, ishift, t.func->rettype);
1330 } else {
1331 ulpsi = 0;
1332 }
1333 unsigned *rr = (ulpsr > ulptolerance || ulpsr < -ulptolerance) ? resultr : NULL;
1334 unsigned *ri = (ulpsi > ulptolerance || ulpsi < -ulptolerance) ? resulti : NULL;
1335 /* printf("tolerance=%i, ulpsr=%i, ulpsi=%i, rr=%p, ri=%p\n",ulptolerance,ulpsr,ulpsi,rr,ri); */
1336 if (rr || ri) {
1337 if (quiet) failtext[0]='x';
1338 else {
1339 print_error(t.func->rettype,rr,"wrongresultr",&failp);
1340 print_error(t.func->rettype,ri,"wrongresulti",&failp);
1341 print_ulps(t.func->rettype,rr ? ulpsr : 0, ri ? ulpsi : 0,&failp);
1342 }
1343 }
1344 } else {
1345 if(is_complex_rettype(t.func->rettype))
1346 /*
1347 * Complex functions are not fully supported,
1348 * this is unreachable, but prevents warnings.
1349 */
1350 abort();
1351 /*
1352 * The test case data has provided the result in
1353 * exactly the output precision. Therefore we must
1354 * complain about _any_ violation.
1355 */
1356 switch(t.func->rettype) {
1357 case rt_dc:
1358 canon_dNaN(tresulti);
1359 canon_dNaN(resulti);
1360 if (fo) {
1361 dnormzero(tresulti);
1362 dnormzero(resulti);
1363 }
1364 /* deliberate fall-through */
1365 case rt_d:
1366 canon_dNaN(tresultr);
1367 canon_dNaN(resultr);
1368 if (fo) {
1369 dnormzero(tresultr);
1370 dnormzero(resultr);
1371 }
1372 break;
1373 case rt_sc:
1374 canon_sNaN(tresulti);
1375 canon_sNaN(resulti);
1376 if (fo) {
1377 snormzero(tresulti);
1378 snormzero(resulti);
1379 }
1380 /* deliberate fall-through */
1381 case rt_s:
1382 canon_sNaN(tresultr);
1383 canon_sNaN(resultr);
1384 if (fo) {
1385 snormzero(tresultr);
1386 snormzero(resultr);
1387 }
1388 break;
1389 default:
1390 break;
1391 }
1392 if(is_complex_rettype(t.func->rettype)) {
1393 unsigned *rr, *ri;
1394 if(resultr[0] != tresultr[0] ||
1395 (wres > 1 && resultr[1] != tresultr[1])) {
1396 rr = resultr;
1397 } else {
1398 rr = NULL;
1399 }
1400 if(resulti[0] != tresulti[0] ||
1401 (wres > 1 && resulti[1] != tresulti[1])) {
1402 ri = resulti;
1403 } else {
1404 ri = NULL;
1405 }
1406 if(rr || ri) {
1407 if (quiet) failtext[0]='x';
1408 print_error(t.func->rettype,rr,"wrongresultr",&failp);
1409 print_error(t.func->rettype,ri,"wrongresulti",&failp);
1410 }
1411 } else if (resultr[0] != tresultr[0] ||
1412 (wres > 1 && resultr[1] != tresultr[1])) {
1413 if (quiet) failtext[0]='x';
1414 print_error(t.func->rettype,resultr,"wrongresult",&failp);
1415 }
1416 }
1417 /*
1418 * Now test res2, for those functions (frexp, modf, rred)
1419 * which use it.
1420 */
1421 if (t.func->func.ptr == &frexp || t.func->func.ptr == &frexpf ||
1422 t.func->macro_name == m_rred || t.func->macro_name == m_rredf) {
1423 unsigned tres2 = t.res2[0];
1424 if (res2_adjust) {
1425 /* Fix for range reduction, propagated from further up */
1426 tres2 = (tres2 + res2_adjust) & 3;
1427 }
1428 if (tres2 != intres) {
1429 if (quiet) failtext[0]='x';
1430 else {
1431 failp += sprintf(failp,
1432 " wrongres2=%08x", intres);
1433 }
1434 }
1435 } else if (t.func->func.ptr == &modf || t.func->func.ptr == &modff) {
1436 tresultr[0] = t.res2[0];
1437 tresultr[1] = t.res2[1];
1438 if (is_double_rettype(t.func->rettype)) {
1439 canon_dNaN(tresultr);
1440 resultr[0] = d_res2.i[dmsd];
1441 resultr[1] = d_res2.i[dlsd];
1442 canon_dNaN(resultr);
1443 if (fo) {
1444 dnormzero(tresultr);
1445 dnormzero(resultr);
1446 }
1447 } else {
1448 canon_sNaN(tresultr);
1449 resultr[0] = s_res2.i;
1450 resultr[1] = s_res2.i;
1451 canon_sNaN(resultr);
1452 if (fo) {
1453 snormzero(tresultr);
1454 snormzero(resultr);
1455 }
1456 }
1457 if (resultr[0] != tresultr[0] ||
1458 (wres > 1 && resultr[1] != tresultr[1])) {
1459 if (quiet) failtext[0]='x';
1460 else {
1461 if (is_double_rettype(t.func->rettype))
1462 failp += sprintf(failp, " wrongres2=%08x.%08x",
1463 resultr[0], resultr[1]);
1464 else
1465 failp += sprintf(failp, " wrongres2=%08x",
1466 resultr[0]);
1467 }
1468 }
1469 }
1470 }
1471
1472 /* Check errno */
1473 err = (errno == EDOM ? e_EDOM : errno == ERANGE ? e_ERANGE : e_0);
1474 if (err != t.err && err != t.maybeerr) {
1475 if (quiet) failtext[0]='x';
1476 else {
1477 failp += sprintf(failp, " wrongerrno=%s expecterrno=%s ", errnos[err], errnos[t.err]);
1478 }
1479 }
1480
1481 return *failtext ? test_fail : test_pass;
1482 }
1483
1484 int passed, failed, declined;
1485
runtests(char * name,FILE * fp)1486 void runtests(char *name, FILE *fp) {
1487 char testbuf[512], linebuf[512];
1488 int lineno = 1;
1489 testdetail test;
1490
1491 test.valid = 0;
1492
1493 if (verbose) printf("runtests: %s\n", name);
1494 while (fgets(testbuf, sizeof(testbuf), fp)) {
1495 int res, print_errno;
1496 testbuf[strcspn(testbuf, "\r\n")] = '\0';
1497 strcpy(linebuf, testbuf);
1498 test = parsetest(testbuf, test);
1499 print_errno = 0;
1500 while (test.in_err < test.in_err_limit) {
1501 res = runtest(test);
1502 if (res == test_pass) {
1503 if (verbose)
1504 printf("%s:%d: pass\n", name, lineno);
1505 ++passed;
1506 } else if (res == test_decline) {
1507 if (verbose)
1508 printf("%s:%d: declined\n", name, lineno);
1509 ++declined;
1510 } else if (res == test_fail) {
1511 if (!quiet)
1512 printf("%s:%d: FAIL%s: %s%s%s%s\n", name, lineno,
1513 test.random ? " (random)" : "",
1514 linebuf,
1515 print_errno ? " errno_in=" : "",
1516 print_errno ? errnos[test.in_err] : "",
1517 failtext);
1518 ++failed;
1519 } else if (res == test_invalid) {
1520 printf("%s:%d: malformed: %s\n", name, lineno, linebuf);
1521 ++failed;
1522 }
1523 test.in_err++;
1524 print_errno = 1;
1525 lineno++;
1526 }
1527 }
1528 }
1529
main(int ac,char ** av)1530 int main(int ac, char **av) {
1531 char **files;
1532 int i, nfiles = 0;
1533 dbl d;
1534
1535 #ifdef MICROLIB
1536 /*
1537 * Invent argc and argv ourselves.
1538 */
1539 char *argv[256];
1540 char args[256];
1541 {
1542 int sargs[2];
1543 char *p;
1544
1545 ac = 0;
1546
1547 sargs[0]=(int)args;
1548 sargs[1]=(int)sizeof(args);
1549 if (!__semihost(0x15, sargs)) {
1550 args[sizeof(args)-1] = '\0'; /* just in case */
1551 p = args;
1552 while (1) {
1553 while (*p == ' ' || *p == '\t') p++;
1554 if (!*p) break;
1555 argv[ac++] = p;
1556 while (*p && *p != ' ' && *p != '\t') p++;
1557 if (*p) *p++ = '\0';
1558 }
1559 }
1560
1561 av = argv;
1562 }
1563 #endif
1564
1565 /* Sort tfuncs */
1566 qsort(tfuncs, sizeof(tfuncs)/sizeof(test_func), sizeof(test_func), &compare_tfuncs);
1567
1568 /*
1569 * Autodetect the `double' endianness.
1570 */
1571 dmsd = 0;
1572 d.f = 1.0; /* 0x3ff00000 / 0x00000000 */
1573 if (d.i[dmsd] == 0) {
1574 dmsd = 1;
1575 }
1576 /*
1577 * Now dmsd denotes what the compiler thinks we're at. Let's
1578 * check that it agrees with what the runtime thinks.
1579 */
1580 d.i[0] = d.i[1] = 0x11111111;/* a random +ve number */
1581 d.f /= d.f; /* must now be one */
1582 if (d.i[dmsd] == 0) {
1583 fprintf(stderr, "YIKES! Compiler and runtime disagree on endianness"
1584 " of `double'. Bailing out\n");
1585 return 1;
1586 }
1587 dlsd = !dmsd;
1588
1589 /* default is terse */
1590 verbose = 0;
1591 fo = 0;
1592 strict = 0;
1593
1594 files = (char **)malloc((ac+1) * sizeof(char *));
1595 if (!files) {
1596 fprintf(stderr, "initial malloc failed!\n");
1597 return 1;
1598 }
1599 #ifdef NOCMDLINE
1600 files[nfiles++] = "testfile";
1601 #endif
1602
1603 while (--ac) {
1604 char *p = *++av;
1605 if (*p == '-') {
1606 static char *options[] = {
1607 "-fo",
1608 #if 0
1609 "-noinexact",
1610 "-noround",
1611 "-nostatus",
1612 #endif
1613 "-quiet",
1614 "-strict",
1615 "-v",
1616 "-verbose",
1617 };
1618 enum {
1619 op_fo,
1620 #if 0
1621 op_noinexact,
1622 op_noround,
1623 op_nostatus,
1624 #endif
1625 op_quiet,
1626 op_strict,
1627 op_v,
1628 op_verbose,
1629 };
1630 switch (find(p, options, sizeof(options))) {
1631 case op_quiet:
1632 quiet = 1;
1633 break;
1634 #if 0
1635 case op_noinexact:
1636 statusmask &= 0x0F; /* remove bit 4 */
1637 break;
1638 case op_noround:
1639 doround = 0;
1640 break;
1641 case op_nostatus: /* no status word => noinx,noround */
1642 statusmask = 0;
1643 doround = 0;
1644 break;
1645 #endif
1646 case op_v:
1647 case op_verbose:
1648 verbose = 1;
1649 break;
1650 case op_fo:
1651 fo = 1;
1652 break;
1653 case op_strict: /* tolerance is 1 ulp */
1654 strict = 1;
1655 break;
1656 default:
1657 fprintf(stderr, "unrecognised option: %s\n", p);
1658 break;
1659 }
1660 } else {
1661 files[nfiles++] = p;
1662 }
1663 }
1664
1665 passed = failed = declined = 0;
1666
1667 if (nfiles) {
1668 for (i = 0; i < nfiles; i++) {
1669 FILE *fp = fopen(files[i], "r");
1670 if (!fp) {
1671 fprintf(stderr, "Couldn't open %s\n", files[i]);
1672 } else
1673 runtests(files[i], fp);
1674 }
1675 } else
1676 runtests("(stdin)", stdin);
1677
1678 printf("Completed. Passed %d, failed %d (total %d",
1679 passed, failed, passed+failed);
1680 if (declined)
1681 printf(" plus %d declined", declined);
1682 printf(")\n");
1683 if (0 < passed && failed == 0)
1684 printf("** TEST PASSED OK **\n");
1685
1686 return 0;
1687 }
1688
undef_func()1689 void undef_func() {
1690 failed++;
1691 puts("ERROR: undefined function called");
1692 }
1693