1 /*
2 * mathtest.c - test rig for mathlib
3 *
4 * Copyright (c) 1998-2023, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
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 #ifndef PL
200 /* sincosf wrappers for easier testing. */
sincosf_sinf(float x)201 static float sincosf_sinf(float x) { float s,c; sincosf(x, &s, &c); return s; }
sincosf_cosf(float x)202 static float sincosf_cosf(float x) { float s,c; sincosf(x, &s, &c); return c; }
203 #endif
204
205 test_func tfuncs[] = {
206 /* trigonometric */
207 TFUNC(at_d,rt_d, acos, 4*ULPUNIT),
208 TFUNC(at_d,rt_d, asin, 4*ULPUNIT),
209 TFUNC(at_d,rt_d, atan, 4*ULPUNIT),
210 TFUNC(at_d2,rt_d, atan2, 4*ULPUNIT),
211
212 TFUNC(at_d,rt_d, tan, 2*ULPUNIT),
213 TFUNC(at_d,rt_d, sin, 2*ULPUNIT),
214 TFUNC(at_d,rt_d, cos, 2*ULPUNIT),
215
216 TFUNC(at_s,rt_s, acosf, 4*ULPUNIT),
217 TFUNC(at_s,rt_s, asinf, 4*ULPUNIT),
218 TFUNC(at_s,rt_s, atanf, 4*ULPUNIT),
219 TFUNC(at_s2,rt_s, atan2f, 4*ULPUNIT),
220 TFUNCARM(at_s,rt_s, tanf, 4*ULPUNIT),
221 TFUNCARM(at_s,rt_s, sinf, 3*ULPUNIT/4),
222 TFUNCARM(at_s,rt_s, cosf, 3*ULPUNIT/4),
223 #ifndef PL
224 TFUNCARM(at_s,rt_s, sincosf_sinf, 3*ULPUNIT/4),
225 TFUNCARM(at_s,rt_s, sincosf_cosf, 3*ULPUNIT/4),
226 #endif
227 /* hyperbolic */
228 TFUNC(at_d, rt_d, atanh, 4*ULPUNIT),
229 TFUNC(at_d, rt_d, asinh, 4*ULPUNIT),
230 TFUNC(at_d, rt_d, acosh, 4*ULPUNIT),
231 TFUNC(at_d,rt_d, tanh, 4*ULPUNIT),
232 TFUNC(at_d,rt_d, sinh, 4*ULPUNIT),
233 TFUNC(at_d,rt_d, cosh, 4*ULPUNIT),
234
235 TFUNC(at_s, rt_s, atanhf, 4*ULPUNIT),
236 TFUNC(at_s, rt_s, asinhf, 4*ULPUNIT),
237 TFUNC(at_s, rt_s, acoshf, 4*ULPUNIT),
238 TFUNC(at_s,rt_s, tanhf, 4*ULPUNIT),
239 TFUNC(at_s,rt_s, sinhf, 4*ULPUNIT),
240 TFUNC(at_s,rt_s, coshf, 4*ULPUNIT),
241
242 /* exponential and logarithmic */
243 TFUNC(at_d,rt_d, log, 3*ULPUNIT/4),
244 TFUNC(at_d,rt_d, log10, 3*ULPUNIT),
245 TFUNC(at_d,rt_d, log2, 3*ULPUNIT/4),
246 TFUNC(at_d,rt_d, log1p, 2*ULPUNIT),
247 TFUNC(at_d,rt_d, exp, 3*ULPUNIT/4),
248 TFUNC(at_d,rt_d, exp2, 3*ULPUNIT/4),
249 TFUNC(at_d,rt_d, expm1, ULPUNIT),
250 TFUNCARM(at_s,rt_s, logf, ULPUNIT),
251 TFUNC(at_s,rt_s, log10f, 3*ULPUNIT),
252 TFUNCARM(at_s,rt_s, log2f, ULPUNIT),
253 TFUNC(at_s,rt_s, log1pf, 2*ULPUNIT),
254 TFUNCARM(at_s,rt_s, expf, 3*ULPUNIT/4),
255 TFUNCARM(at_s,rt_s, exp2f, 3*ULPUNIT/4),
256 TFUNC(at_s,rt_s, expm1f, ULPUNIT),
257 TFUNC(at_d,rt_d, exp10, ULPUNIT),
258
259 /* power */
260 TFUNC(at_d2,rt_d, pow, 3*ULPUNIT/4),
261 TFUNC(at_d,rt_d, sqrt, ULPUNIT/2),
262 TFUNC(at_d,rt_d, cbrt, 2*ULPUNIT),
263 TFUNC(at_d2, rt_d, hypot, 4*ULPUNIT),
264
265 TFUNCARM(at_s2,rt_s, powf, ULPUNIT),
266 TFUNC(at_s,rt_s, sqrtf, ULPUNIT/2),
267 TFUNC(at_s,rt_s, cbrtf, 2*ULPUNIT),
268 TFUNC(at_s2, rt_s, hypotf, 4*ULPUNIT),
269
270 /* error function */
271 TFUNC(at_d,rt_d, erf, 16*ULPUNIT),
272 TFUNC(at_s,rt_s, erff, 16*ULPUNIT),
273 TFUNC(at_d,rt_d, erfc, 16*ULPUNIT),
274 TFUNC(at_s,rt_s, erfcf, 16*ULPUNIT),
275
276 /* gamma functions */
277 TFUNC(at_d,rt_d, tgamma, 16*ULPUNIT),
278 TFUNC(at_s,rt_s, tgammaf, 16*ULPUNIT),
279 TFUNC(at_d,rt_d, lgamma, 16*ULPUNIT | ABSLOWERBOUND),
280 TFUNC(at_s,rt_s, lgammaf, 16*ULPUNIT | ABSLOWERBOUND),
281
282 TFUNC(at_d,rt_d, ceil, 0),
283 TFUNC(at_s,rt_s, ceilf, 0),
284 TFUNC(at_d2,rt_d, copysign, 0),
285 TFUNC(at_s2,rt_s, copysignf, 0),
286 TFUNC(at_d,rt_d, floor, 0),
287 TFUNC(at_s,rt_s, floorf, 0),
288 TFUNC(at_d2,rt_d, fmax, 0),
289 TFUNC(at_s2,rt_s, fmaxf, 0),
290 TFUNC(at_d2,rt_d, fmin, 0),
291 TFUNC(at_s2,rt_s, fminf, 0),
292 TFUNC(at_d2,rt_d, fmod, 0),
293 TFUNC(at_s2,rt_s, fmodf, 0),
294 MFUNC(at_d, rt_i, fpclassify, 0),
295 MFUNC(at_s, rt_i, fpclassifyf, 0),
296 TFUNC(at_dip,rt_d, frexp, 0),
297 TFUNC(at_sip,rt_s, frexpf, 0),
298 MFUNC(at_d, rt_i, isfinite, 0),
299 MFUNC(at_s, rt_i, isfinitef, 0),
300 MFUNC(at_d, rt_i, isgreater, 0),
301 MFUNC(at_d, rt_i, isgreaterequal, 0),
302 MFUNC(at_s, rt_i, isgreaterequalf, 0),
303 MFUNC(at_s, rt_i, isgreaterf, 0),
304 MFUNC(at_d, rt_i, isinf, 0),
305 MFUNC(at_s, rt_i, isinff, 0),
306 MFUNC(at_d, rt_i, isless, 0),
307 MFUNC(at_d, rt_i, islessequal, 0),
308 MFUNC(at_s, rt_i, islessequalf, 0),
309 MFUNC(at_s, rt_i, islessf, 0),
310 MFUNC(at_d, rt_i, islessgreater, 0),
311 MFUNC(at_s, rt_i, islessgreaterf, 0),
312 MFUNC(at_d, rt_i, isnan, 0),
313 MFUNC(at_s, rt_i, isnanf, 0),
314 MFUNC(at_d, rt_i, isnormal, 0),
315 MFUNC(at_s, rt_i, isnormalf, 0),
316 MFUNC(at_d, rt_i, isunordered, 0),
317 MFUNC(at_s, rt_i, isunorderedf, 0),
318 TFUNC(at_di,rt_d, ldexp, 0),
319 TFUNC(at_si,rt_s, ldexpf, 0),
320 TFUNC(at_ddp,rt_d2, modf, 0),
321 TFUNC(at_ssp,rt_s2, modff, 0),
322 #ifndef BIGRANGERED
323 MFUNC(at_d, rt_d, rred, 2*ULPUNIT),
324 #else
325 MFUNC(at_d, rt_d, m_rred, ULPUNIT),
326 #endif
327 MFUNC(at_d, rt_i, signbit, 0),
328 MFUNC(at_s, rt_i, signbitf, 0),
329 };
330
331 /*
332 * keywords are: func size op1 op2 result res2 errno op1r op1i op2r op2i resultr resulti
333 * also we ignore: wrongresult wrongres2 wrongerrno
334 * op1 equivalent to op1r, same with op2 and result
335 */
336
337 typedef struct {
338 test_func *func;
339 unsigned op1r[2]; /* real part, also used for non-complex numbers */
340 unsigned op1i[2]; /* imaginary part */
341 unsigned op2r[2];
342 unsigned op2i[2];
343 unsigned resultr[3];
344 unsigned resulti[3];
345 enum {
346 rc_none, rc_zero, rc_infinity, rc_nan, rc_finite
347 } resultc; /* special complex results, rc_none means use resultr and resulti as normal */
348 unsigned res2[2];
349 unsigned status; /* IEEE status return, if any */
350 unsigned maybestatus; /* for optional status, or allowance for spurious */
351 int nresult; /* number of result words */
352 int in_err, in_err_limit;
353 int err;
354 int maybeerr;
355 int valid;
356 int comment;
357 int random;
358 } testdetail;
359
360 enum { /* keywords */
361 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,
362 k_random, k_res2, k_result, k_resultc, k_resulti, k_resultr, k_status,
363 k_wrongres2, k_wrongresult, k_wrongstatus, k_wrongerrno
364 };
365 char *keywords[] = {
366 "errno", "errno_in", "error", "func", "maybeerror", "maybestatus", "op1", "op1i", "op1r", "op2", "op2i", "op2r",
367 "random", "res2", "result", "resultc", "resulti", "resultr", "status",
368 "wrongres2", "wrongresult", "wrongstatus", "wrongerrno"
369 };
370
371 enum {
372 e_0, e_EDOM, e_ERANGE,
373
374 /*
375 * This enum makes sure that we have the right number of errnos in the
376 * errno[] array
377 */
378 e_number_of_errnos
379 };
380 char *errnos[] = {
381 "0", "EDOM", "ERANGE"
382 };
383
384 enum {
385 e_none, e_divbyzero, e_domain, e_overflow, e_underflow
386 };
387 char *errors[] = {
388 "0", "divbyzero", "domain", "overflow", "underflow"
389 };
390
391 static int verbose, fo, strict;
392
393 /* state toggled by random=on / random=off */
394 static int randomstate;
395
396 /* Canonify a double NaN: SNaNs all become 7FF00000.00000001 and QNaNs
397 * all become 7FF80000.00000001 */
canon_dNaN(unsigned a[2])398 void canon_dNaN(unsigned a[2]) {
399 if ((a[0] & 0x7FF00000) != 0x7FF00000)
400 return; /* not Inf or NaN */
401 if (!(a[0] & 0xFFFFF) && !a[1])
402 return; /* Inf */
403 a[0] &= 0x7FF80000; /* canonify top word */
404 a[1] = 0x00000001; /* canonify bottom word */
405 }
406
407 /* Canonify a single NaN: SNaNs all become 7F800001 and QNaNs
408 * all become 7FC00001. Returns classification of the NaN. */
canon_sNaN(unsigned a[1])409 void canon_sNaN(unsigned a[1]) {
410 if ((a[0] & 0x7F800000) != 0x7F800000)
411 return; /* not Inf or NaN */
412 if (!(a[0] & 0x7FFFFF))
413 return; /* Inf */
414 a[0] &= 0x7FC00000; /* canonify most bits */
415 a[0] |= 0x00000001; /* canonify bottom bit */
416 }
417
418 /*
419 * Detect difficult operands for FO mode.
420 */
is_dhard(unsigned a[2])421 int is_dhard(unsigned a[2])
422 {
423 if ((a[0] & 0x7FF00000) == 0x7FF00000)
424 return TRUE; /* inf or NaN */
425 if ((a[0] & 0x7FF00000) == 0 &&
426 ((a[0] & 0x7FFFFFFF) | a[1]) != 0)
427 return TRUE; /* denormal */
428 return FALSE;
429 }
is_shard(unsigned a[1])430 int is_shard(unsigned a[1])
431 {
432 if ((a[0] & 0x7F800000) == 0x7F800000)
433 return TRUE; /* inf or NaN */
434 if ((a[0] & 0x7F800000) == 0 &&
435 (a[0] & 0x7FFFFFFF) != 0)
436 return TRUE; /* denormal */
437 return FALSE;
438 }
439
440 /*
441 * Normalise all zeroes into +0, for FO mode.
442 */
dnormzero(unsigned a[2])443 void dnormzero(unsigned a[2])
444 {
445 if (a[0] == 0x80000000 && a[1] == 0)
446 a[0] = 0;
447 }
snormzero(unsigned a[1])448 void snormzero(unsigned a[1])
449 {
450 if (a[0] == 0x80000000)
451 a[0] = 0;
452 }
453
find(char * word,char ** array,int asize)454 static int find(char *word, char **array, int asize) {
455 int i, j;
456
457 asize /= sizeof(char *);
458
459 i = -1; j = asize; /* strictly between i and j */
460 while (j-i > 1) {
461 int k = (i+j) / 2;
462 int c = strcmp(word, array[k]);
463 if (c > 0)
464 i = k;
465 else if (c < 0)
466 j = k;
467 else /* found it! */
468 return k;
469 }
470 return -1; /* not found */
471 }
472
find_testfunc(char * word)473 static test_func* find_testfunc(char *word) {
474 int i, j, asize;
475
476 asize = sizeof(tfuncs)/sizeof(test_func);
477
478 i = -1; j = asize; /* strictly between i and j */
479 while (j-i > 1) {
480 int k = (i+j) / 2;
481 int c = strcmp(word, tfuncs[k].name);
482 if (c > 0)
483 i = k;
484 else if (c < 0)
485 j = k;
486 else /* found it! */
487 return tfuncs + k;
488 }
489 return NULL; /* not found */
490 }
491
calc_error(unsigned a[2],unsigned b[3],int shift,int rettype)492 static long long calc_error(unsigned a[2], unsigned b[3], int shift, int rettype) {
493 unsigned r0, r1, r2;
494 int sign, carry;
495 long long result;
496
497 /*
498 * If either number is infinite, require exact equality. If
499 * either number is NaN, require that both are NaN. If either
500 * of these requirements is broken, return INT_MAX.
501 */
502 if (is_double_rettype(rettype)) {
503 if ((a[0] & 0x7FF00000) == 0x7FF00000 ||
504 (b[0] & 0x7FF00000) == 0x7FF00000) {
505 if (((a[0] & 0x800FFFFF) || a[1]) &&
506 ((b[0] & 0x800FFFFF) || b[1]) &&
507 (a[0] & 0x7FF00000) == 0x7FF00000 &&
508 (b[0] & 0x7FF00000) == 0x7FF00000)
509 return 0; /* both NaN - OK */
510 if (!((a[0] & 0xFFFFF) || a[1]) &&
511 !((b[0] & 0xFFFFF) || b[1]) &&
512 a[0] == b[0])
513 return 0; /* both same sign of Inf - OK */
514 return LLONG_MAX;
515 }
516 } else {
517 if ((a[0] & 0x7F800000) == 0x7F800000 ||
518 (b[0] & 0x7F800000) == 0x7F800000) {
519 if ((a[0] & 0x807FFFFF) &&
520 (b[0] & 0x807FFFFF) &&
521 (a[0] & 0x7F800000) == 0x7F800000 &&
522 (b[0] & 0x7F800000) == 0x7F800000)
523 return 0; /* both NaN - OK */
524 if (!(a[0] & 0x7FFFFF) &&
525 !(b[0] & 0x7FFFFF) &&
526 a[0] == b[0])
527 return 0; /* both same sign of Inf - OK */
528 return LLONG_MAX;
529 }
530 }
531
532 /*
533 * Both finite. Return INT_MAX if the signs differ.
534 */
535 if ((a[0] ^ b[0]) & 0x80000000)
536 return LLONG_MAX;
537
538 /*
539 * Now it's just straight multiple-word subtraction.
540 */
541 if (is_double_rettype(rettype)) {
542 r2 = -b[2]; carry = (r2 == 0);
543 r1 = a[1] + ~b[1] + carry; carry = (r1 < a[1] || (carry && r1 == a[1]));
544 r0 = a[0] + ~b[0] + carry;
545 } else {
546 r2 = -b[1]; carry = (r2 == 0);
547 r1 = a[0] + ~b[0] + carry; carry = (r1 < a[0] || (carry && r1 == a[0]));
548 r0 = ~0 + carry;
549 }
550
551 /*
552 * Forgive larger errors in specialised cases.
553 */
554 if (shift > 0) {
555 if (shift > 32*3)
556 return 0; /* all errors are forgiven! */
557 while (shift >= 32) {
558 r2 = r1;
559 r1 = r0;
560 r0 = -(r0 >> 31);
561 shift -= 32;
562 }
563
564 if (shift > 0) {
565 r2 = (r2 >> shift) | (r1 << (32-shift));
566 r1 = (r1 >> shift) | (r0 << (32-shift));
567 r0 = (r0 >> shift) | ((-(r0 >> 31)) << (32-shift));
568 }
569 }
570
571 if (r0 & 0x80000000) {
572 sign = 1;
573 r2 = ~r2; carry = (r2 == 0);
574 r1 = 0 + ~r1 + carry; carry = (carry && (r2 == 0));
575 r0 = 0 + ~r0 + carry;
576 } else {
577 sign = 0;
578 }
579
580 if (r0 >= (1LL<<(31-EXTRABITS)))
581 return LLONG_MAX; /* many ulps out */
582
583 result = (r2 >> (32-EXTRABITS)) & (ULPUNIT-1);
584 result |= r1 << EXTRABITS;
585 result |= (long long)r0 << (32+EXTRABITS);
586 if (sign)
587 result = -result;
588 return result;
589 }
590
591 /* special named operands */
592
593 typedef struct {
594 unsigned op1, op2;
595 char* name;
596 } special_op;
597
598 static special_op special_ops_double[] = {
599 {0x00000000,0x00000000,"0"},
600 {0x3FF00000,0x00000000,"1"},
601 {0x7FF00000,0x00000000,"inf"},
602 {0x7FF80000,0x00000001,"qnan"},
603 {0x7FF00000,0x00000001,"snan"},
604 {0x3ff921fb,0x54442d18,"pi2"},
605 {0x400921fb,0x54442d18,"pi"},
606 {0x3fe921fb,0x54442d18,"pi4"},
607 {0x4002d97c,0x7f3321d2,"3pi4"},
608 };
609
610 static special_op special_ops_float[] = {
611 {0x00000000,0,"0"},
612 {0x3f800000,0,"1"},
613 {0x7f800000,0,"inf"},
614 {0x7fc00000,0,"qnan"},
615 {0x7f800001,0,"snan"},
616 {0x3fc90fdb,0,"pi2"},
617 {0x40490fdb,0,"pi"},
618 {0x3f490fdb,0,"pi4"},
619 {0x4016cbe4,0,"3pi4"},
620 };
621
622 /*
623 This is what is returned by the below functions.
624 We need it to handle the sign of the number
625 */
626 static special_op tmp_op = {0,0,0};
627
find_special_op_from_op(unsigned op1,unsigned op2,int is_double)628 special_op* find_special_op_from_op(unsigned op1, unsigned op2, int is_double) {
629 int i;
630 special_op* sop;
631 if(is_double) {
632 sop = special_ops_double;
633 } else {
634 sop = special_ops_float;
635 }
636 for(i = 0; i < sizeof(special_ops_double)/sizeof(special_op); i++) {
637 if(sop->op1 == (op1&0x7fffffff) && sop->op2 == op2) {
638 if(tmp_op.name) free(tmp_op.name);
639 tmp_op.name = malloc(strlen(sop->name)+2);
640 if(op1>>31) {
641 sprintf(tmp_op.name,"-%s",sop->name);
642 } else {
643 strcpy(tmp_op.name,sop->name);
644 }
645 return &tmp_op;
646 }
647 sop++;
648 }
649 return NULL;
650 }
651
find_special_op_from_name(const char * name,int is_double)652 special_op* find_special_op_from_name(const char* name, int is_double) {
653 int i, neg=0;
654 special_op* sop;
655 if(is_double) {
656 sop = special_ops_double;
657 } else {
658 sop = special_ops_float;
659 }
660 if(*name=='-') {
661 neg=1;
662 name++;
663 } else if(*name=='+') {
664 name++;
665 }
666 for(i = 0; i < sizeof(special_ops_double)/sizeof(special_op); i++) {
667 if(0 == strcmp(name,sop->name)) {
668 tmp_op.op1 = sop->op1;
669 if(neg) {
670 tmp_op.op1 |= 0x80000000;
671 }
672 tmp_op.op2 = sop->op2;
673 return &tmp_op;
674 }
675 sop++;
676 }
677 return NULL;
678 }
679
680 /*
681 helper function for the below
682 type=0 for single, 1 for double, 2 for no sop
683 */
do_op(char * q,unsigned * op,const char * name,int num,int sop_type)684 int do_op(char* q, unsigned* op, const char* name, int num, int sop_type) {
685 int i;
686 int n=num;
687 special_op* sop = NULL;
688 for(i = 0; i < num; i++) {
689 op[i] = 0;
690 }
691 if(sop_type<2) {
692 sop = find_special_op_from_name(q,sop_type);
693 }
694 if(sop != NULL) {
695 op[0] = sop->op1;
696 op[1] = sop->op2;
697 } else {
698 switch(num) {
699 case 1: n = sscanf(q, "%x", &op[0]); break;
700 case 2: n = sscanf(q, "%x.%x", &op[0], &op[1]); break;
701 case 3: n = sscanf(q, "%x.%x.%x", &op[0], &op[1], &op[2]); break;
702 default: return -1;
703 }
704 }
705 if (verbose) {
706 printf("%s=",name);
707 for (i = 0; (i < n); ++i) printf("%x.", op[i]);
708 printf(" (n=%d)\n", n);
709 }
710 return n;
711 }
712
parsetest(char * testbuf,testdetail oldtest)713 testdetail parsetest(char *testbuf, testdetail oldtest) {
714 char *p; /* Current part of line: Option name */
715 char *q; /* Current part of line: Option value */
716 testdetail ret; /* What we return */
717 int k; /* Function enum from k_* */
718 int n; /* Used as returns for scanfs */
719 int argtype=2, rettype=2; /* for do_op */
720
721 /* clear ret */
722 memset(&ret, 0, sizeof(ret));
723
724 if (verbose) printf("Parsing line: %s\n", testbuf);
725 while (*testbuf && isspace(*testbuf)) testbuf++;
726 if (testbuf[0] == ';' || testbuf[0] == '#' || testbuf[0] == '!' ||
727 testbuf[0] == '>' || testbuf[0] == '\0') {
728 ret.comment = 1;
729 if (verbose) printf("Line is a comment\n");
730 return ret;
731 }
732 ret.comment = 0;
733
734 if (*testbuf == '+') {
735 if (oldtest.valid) {
736 ret = oldtest; /* structure copy */
737 } else {
738 fprintf(stderr, "copy from invalid: ignored\n");
739 }
740 testbuf++;
741 }
742
743 ret.random = randomstate;
744
745 ret.in_err = 0;
746 ret.in_err_limit = e_number_of_errnos;
747
748 p = strtok(testbuf, " \t");
749 while (p != NULL) {
750 q = strchr(p, '=');
751 if (!q)
752 goto balderdash;
753 *q++ = '\0';
754 k = find(p, keywords, sizeof(keywords));
755 switch (k) {
756 case k_random:
757 randomstate = (!strcmp(q, "on"));
758 ret.comment = 1;
759 return ret; /* otherwise ignore this line */
760 case k_func:
761 if (verbose) printf("func=%s ", q);
762 //ret.func = find(q, funcs, sizeof(funcs));
763 ret.func = find_testfunc(q);
764 if (ret.func == NULL)
765 {
766 if (verbose) printf("(id=unknown)\n");
767 goto balderdash;
768 }
769 if(is_single_argtype(ret.func->argtype))
770 argtype = 0;
771 else if(is_double_argtype(ret.func->argtype))
772 argtype = 1;
773 if(is_single_rettype(ret.func->rettype))
774 rettype = 0;
775 else if(is_double_rettype(ret.func->rettype))
776 rettype = 1;
777 //ret.size = sizes[ret.func];
778 if (verbose) printf("(name=%s) (size=%d)\n", ret.func->name, ret.func->argtype);
779 break;
780 case k_op1:
781 case k_op1r:
782 n = do_op(q,ret.op1r,"op1r",2,argtype);
783 if (n < 1)
784 goto balderdash;
785 break;
786 case k_op1i:
787 n = do_op(q,ret.op1i,"op1i",2,argtype);
788 if (n < 1)
789 goto balderdash;
790 break;
791 case k_op2:
792 case k_op2r:
793 n = do_op(q,ret.op2r,"op2r",2,argtype);
794 if (n < 1)
795 goto balderdash;
796 break;
797 case k_op2i:
798 n = do_op(q,ret.op2i,"op2i",2,argtype);
799 if (n < 1)
800 goto balderdash;
801 break;
802 case k_resultc:
803 puts(q);
804 if(strncmp(q,"inf",3)==0) {
805 ret.resultc = rc_infinity;
806 } else if(strcmp(q,"zero")==0) {
807 ret.resultc = rc_zero;
808 } else if(strcmp(q,"nan")==0) {
809 ret.resultc = rc_nan;
810 } else if(strcmp(q,"finite")==0) {
811 ret.resultc = rc_finite;
812 } else {
813 goto balderdash;
814 }
815 break;
816 case k_result:
817 case k_resultr:
818 n = (do_op)(q,ret.resultr,"resultr",3,rettype);
819 if (n < 1)
820 goto balderdash;
821 ret.nresult = n; /* assume real and imaginary have same no. words */
822 break;
823 case k_resulti:
824 n = do_op(q,ret.resulti,"resulti",3,rettype);
825 if (n < 1)
826 goto balderdash;
827 break;
828 case k_res2:
829 n = do_op(q,ret.res2,"res2",2,rettype);
830 if (n < 1)
831 goto balderdash;
832 break;
833 case k_status:
834 while (*q) {
835 if (*q == 'i') ret.status |= FE_INVALID;
836 if (*q == 'z') ret.status |= FE_DIVBYZERO;
837 if (*q == 'o') ret.status |= FE_OVERFLOW;
838 if (*q == 'u') ret.status |= FE_UNDERFLOW;
839 q++;
840 }
841 break;
842 case k_maybeerror:
843 n = find(q, errors, sizeof(errors));
844 if (n < 0)
845 goto balderdash;
846 if(math_errhandling&MATH_ERREXCEPT) {
847 switch(n) {
848 case e_domain: ret.maybestatus |= FE_INVALID; break;
849 case e_divbyzero: ret.maybestatus |= FE_DIVBYZERO; break;
850 case e_overflow: ret.maybestatus |= FE_OVERFLOW; break;
851 case e_underflow: ret.maybestatus |= FE_UNDERFLOW; break;
852 }
853 }
854 {
855 switch(n) {
856 case e_domain:
857 ret.maybeerr = e_EDOM; break;
858 case e_divbyzero:
859 case e_overflow:
860 case e_underflow:
861 ret.maybeerr = e_ERANGE; break;
862 }
863 }
864 case k_maybestatus:
865 while (*q) {
866 if (*q == 'i') ret.maybestatus |= FE_INVALID;
867 if (*q == 'z') ret.maybestatus |= FE_DIVBYZERO;
868 if (*q == 'o') ret.maybestatus |= FE_OVERFLOW;
869 if (*q == 'u') ret.maybestatus |= FE_UNDERFLOW;
870 q++;
871 }
872 break;
873 case k_error:
874 n = find(q, errors, sizeof(errors));
875 if (n < 0)
876 goto balderdash;
877 if(math_errhandling&MATH_ERREXCEPT) {
878 switch(n) {
879 case e_domain: ret.status |= FE_INVALID; break;
880 case e_divbyzero: ret.status |= FE_DIVBYZERO; break;
881 case e_overflow: ret.status |= FE_OVERFLOW; break;
882 case e_underflow: ret.status |= FE_UNDERFLOW; break;
883 }
884 }
885 if(math_errhandling&MATH_ERRNO) {
886 switch(n) {
887 case e_domain:
888 ret.err = e_EDOM; break;
889 case e_divbyzero:
890 case e_overflow:
891 case e_underflow:
892 ret.err = e_ERANGE; break;
893 }
894 }
895 if(!(math_errhandling&MATH_ERRNO)) {
896 switch(n) {
897 case e_domain:
898 ret.maybeerr = e_EDOM; break;
899 case e_divbyzero:
900 case e_overflow:
901 case e_underflow:
902 ret.maybeerr = e_ERANGE; break;
903 }
904 }
905 break;
906 case k_errno:
907 ret.err = find(q, errnos, sizeof(errnos));
908 if (ret.err < 0)
909 goto balderdash;
910 break;
911 case k_errno_in:
912 ret.in_err = find(q, errnos, sizeof(errnos));
913 if (ret.err < 0)
914 goto balderdash;
915 ret.in_err_limit = ret.in_err + 1;
916 break;
917 case k_wrongresult:
918 case k_wrongstatus:
919 case k_wrongres2:
920 case k_wrongerrno:
921 /* quietly ignore these keys */
922 break;
923 default:
924 goto balderdash;
925 }
926 p = strtok(NULL, " \t");
927 }
928 ret.valid = 1;
929 return ret;
930
931 /* come here from almost any error */
932 balderdash:
933 ret.valid = 0;
934 return ret;
935 }
936
937 typedef enum {
938 test_comment, /* deliberately not a test */
939 test_invalid, /* accidentally not a test */
940 test_decline, /* was a test, and wasn't run */
941 test_fail, /* was a test, and failed */
942 test_pass /* was a test, and passed */
943 } testresult;
944
945 char failtext[512];
946
947 typedef union {
948 unsigned i[2];
949 double f;
950 double da[2];
951 } dbl;
952
953 typedef union {
954 unsigned i;
955 float f;
956 float da[2];
957 } sgl;
958
959 /* helper function for runtest */
print_error(int rettype,unsigned * result,char * text,char ** failp)960 void print_error(int rettype, unsigned *result, char* text, char** failp) {
961 special_op *sop;
962 char *str;
963
964 if(result) {
965 *failp += sprintf(*failp," %s=",text);
966 sop = find_special_op_from_op(result[0],result[1],is_double_rettype(rettype));
967 if(sop) {
968 *failp += sprintf(*failp,"%s",sop->name);
969 } else {
970 if(is_double_rettype(rettype)) {
971 str="%08x.%08x";
972 } else {
973 str="%08x";
974 }
975 *failp += sprintf(*failp,str,result[0],result[1]);
976 }
977 }
978 }
979
980
print_ulps_helper(const char * name,long long ulps,char ** failp)981 void print_ulps_helper(const char *name, long long ulps, char** failp) {
982 if(ulps == LLONG_MAX) {
983 *failp += sprintf(*failp, " %s=HUGE", name);
984 } else {
985 *failp += sprintf(*failp, " %s=%.3f", name, (double)ulps / ULPUNIT);
986 }
987 }
988
989 /* for complex args make ulpsr or ulpsri = 0 to not print */
print_ulps(int rettype,long long ulpsr,long long ulpsi,char ** failp)990 void print_ulps(int rettype, long long ulpsr, long long ulpsi, char** failp) {
991 if(is_complex_rettype(rettype)) {
992 if (ulpsr) print_ulps_helper("ulpsr",ulpsr,failp);
993 if (ulpsi) print_ulps_helper("ulpsi",ulpsi,failp);
994 } else {
995 if (ulpsr) print_ulps_helper("ulps",ulpsr,failp);
996 }
997 }
998
runtest(testdetail t)999 int runtest(testdetail t) {
1000 int err, status;
1001
1002 dbl d_arg1, d_arg2, d_res, d_res2;
1003 sgl s_arg1, s_arg2, s_res, s_res2;
1004
1005 int deferred_decline = FALSE;
1006 char *failp = failtext;
1007
1008 unsigned int intres=0;
1009
1010 int res2_adjust = 0;
1011
1012 if (t.comment)
1013 return test_comment;
1014 if (!t.valid)
1015 return test_invalid;
1016
1017 /* Set IEEE status to mathlib-normal */
1018 feclearexcept(FE_ALL_EXCEPT);
1019
1020 /* Deal with operands */
1021 #define DO_DOP(arg,op) arg.i[dmsd] = t.op[0]; arg.i[dlsd] = t.op[1]
1022 DO_DOP(d_arg1,op1r);
1023 DO_DOP(d_arg2,op2r);
1024 s_arg1.i = t.op1r[0]; s_arg2.i = t.op2r[0];
1025 s_res.i = 0;
1026
1027 /*
1028 * Detect NaNs, infinities and denormals on input, and set a
1029 * deferred decline flag if we're in FO mode.
1030 *
1031 * (We defer the decline rather than doing it immediately
1032 * because even in FO mode the operation is not permitted to
1033 * crash or tight-loop; so we _run_ the test, and then ignore
1034 * all the results.)
1035 */
1036 if (fo) {
1037 if (is_double_argtype(t.func->argtype) && is_dhard(t.op1r))
1038 deferred_decline = TRUE;
1039 if (t.func->argtype==at_d2 && is_dhard(t.op2r))
1040 deferred_decline = TRUE;
1041 if (is_single_argtype(t.func->argtype) && is_shard(t.op1r))
1042 deferred_decline = TRUE;
1043 if (t.func->argtype==at_s2 && is_shard(t.op2r))
1044 deferred_decline = TRUE;
1045 if (is_double_rettype(t.func->rettype) && is_dhard(t.resultr))
1046 deferred_decline = TRUE;
1047 if (t.func->rettype==rt_d2 && is_dhard(t.res2))
1048 deferred_decline = TRUE;
1049 if (is_single_argtype(t.func->rettype) && is_shard(t.resultr))
1050 deferred_decline = TRUE;
1051 if (t.func->rettype==rt_s2 && is_shard(t.res2))
1052 deferred_decline = TRUE;
1053 if (t.err == e_ERANGE)
1054 deferred_decline = TRUE;
1055 }
1056
1057 /*
1058 * Perform the operation
1059 */
1060
1061 errno = t.in_err == e_EDOM ? EDOM : t.in_err == e_ERANGE ? ERANGE : 0;
1062 if (t.err == e_0)
1063 t.err = t.in_err;
1064 if (t.maybeerr == e_0)
1065 t.maybeerr = t.in_err;
1066
1067 if(t.func->type == t_func) {
1068 switch(t.func->argtype) {
1069 case at_d: d_res.f = t.func->func.d_d_ptr(d_arg1.f); break;
1070 case at_s: s_res.f = t.func->func.s_s_ptr(s_arg1.f); break;
1071 case at_d2: d_res.f = t.func->func.d2_d_ptr(d_arg1.f, d_arg2.f); break;
1072 case at_s2: s_res.f = t.func->func.s2_s_ptr(s_arg1.f, s_arg2.f); break;
1073 case at_di: d_res.f = t.func->func.di_d_ptr(d_arg1.f, d_arg2.i[dmsd]); break;
1074 case at_si: s_res.f = t.func->func.si_s_ptr(s_arg1.f, s_arg2.i); break;
1075 case at_dip: d_res.f = t.func->func.dip_d_ptr(d_arg1.f, (int*)&intres); break;
1076 case at_sip: s_res.f = t.func->func.sip_s_ptr(s_arg1.f, (int*)&intres); break;
1077 case at_ddp: d_res.f = t.func->func.ddp_d_ptr(d_arg1.f, &d_res2.f); break;
1078 case at_ssp: s_res.f = t.func->func.ssp_s_ptr(s_arg1.f, &s_res2.f); break;
1079 default:
1080 printf("unhandled function: %s\n",t.func->name);
1081 return test_fail;
1082 }
1083 } else {
1084 /* 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); */
1085 switch(t.func->macro_name) {
1086 case m_isfinite: intres = isfinite(d_arg1.f); break;
1087 case m_isinf: intres = isinf(d_arg1.f); break;
1088 case m_isnan: intres = isnan(d_arg1.f); break;
1089 case m_isnormal: intres = isnormal(d_arg1.f); break;
1090 case m_signbit: intres = signbit(d_arg1.f); break;
1091 case m_fpclassify: intres = fpclassify(d_arg1.f); break;
1092 case m_isgreater: intres = isgreater(d_arg1.f, d_arg2.f); break;
1093 case m_isgreaterequal: intres = isgreaterequal(d_arg1.f, d_arg2.f); break;
1094 case m_isless: intres = isless(d_arg1.f, d_arg2.f); break;
1095 case m_islessequal: intres = islessequal(d_arg1.f, d_arg2.f); break;
1096 case m_islessgreater: intres = islessgreater(d_arg1.f, d_arg2.f); break;
1097 case m_isunordered: intres = isunordered(d_arg1.f, d_arg2.f); break;
1098
1099 case m_isfinitef: intres = isfinite(s_arg1.f); break;
1100 case m_isinff: intres = isinf(s_arg1.f); break;
1101 case m_isnanf: intres = isnan(s_arg1.f); break;
1102 case m_isnormalf: intres = isnormal(s_arg1.f); break;
1103 case m_signbitf: intres = signbit(s_arg1.f); break;
1104 case m_fpclassifyf: intres = fpclassify(s_arg1.f); break;
1105 case m_isgreaterf: intres = isgreater(s_arg1.f, s_arg2.f); break;
1106 case m_isgreaterequalf: intres = isgreaterequal(s_arg1.f, s_arg2.f); break;
1107 case m_islessf: intres = isless(s_arg1.f, s_arg2.f); break;
1108 case m_islessequalf: intres = islessequal(s_arg1.f, s_arg2.f); break;
1109 case m_islessgreaterf: intres = islessgreater(s_arg1.f, s_arg2.f); break;
1110 case m_isunorderedf: intres = isunordered(s_arg1.f, s_arg2.f); break;
1111
1112 default:
1113 printf("unhandled macro: %s\n",t.func->name);
1114 return test_fail;
1115 }
1116 }
1117
1118 /*
1119 * Decline the test if the deferred decline flag was set above.
1120 */
1121 if (deferred_decline)
1122 return test_decline;
1123
1124 /* printf("intres=%i\n",intres); */
1125
1126 /* Clear the fail text (indicating a pass unless we change it) */
1127 failp[0] = '\0';
1128
1129 /* Check the IEEE status bits (except INX, which we disregard).
1130 * We don't bother with this for complex numbers, because the
1131 * complex functions are hard to get exactly right and we don't
1132 * have to anyway (C99 annex G is only informative). */
1133 if (!(is_complex_argtype(t.func->argtype) || is_complex_rettype(t.func->rettype))) {
1134 status = fetestexcept(FE_INVALID|FE_DIVBYZERO|FE_OVERFLOW|FE_UNDERFLOW);
1135 if ((status|t.maybestatus|~statusmask) != (t.status|t.maybestatus|~statusmask)) {
1136 if (quiet) failtext[0]='x';
1137 else {
1138 failp += sprintf(failp,
1139 " wrongstatus=%s%s%s%s%s",
1140 (status & FE_INVALID ? "i" : ""),
1141 (status & FE_DIVBYZERO ? "z" : ""),
1142 (status & FE_OVERFLOW ? "o" : ""),
1143 (status & FE_UNDERFLOW ? "u" : ""),
1144 (status ? "" : "OK"));
1145 }
1146 }
1147 }
1148
1149 /* Check the result */
1150 {
1151 unsigned resultr[2], resulti[2];
1152 unsigned tresultr[3], tresulti[3], wres;
1153
1154 switch(t.func->rettype) {
1155 case rt_d:
1156 case rt_d2:
1157 tresultr[0] = t.resultr[0];
1158 tresultr[1] = t.resultr[1];
1159 resultr[0] = d_res.i[dmsd]; resultr[1] = d_res.i[dlsd];
1160 resulti[0] = resulti[1] = 0;
1161 wres = 2;
1162 break;
1163 case rt_i:
1164 tresultr[0] = t.resultr[0];
1165 resultr[0] = intres;
1166 resulti[0] = 0;
1167 wres = 1;
1168 break;
1169 case rt_s:
1170 case rt_s2:
1171 tresultr[0] = t.resultr[0];
1172 resultr[0] = s_res.i;
1173 resulti[0] = 0;
1174 wres = 1;
1175 break;
1176 default:
1177 puts("unhandled rettype in runtest");
1178 abort ();
1179 }
1180 if(t.resultc != rc_none) {
1181 int err = 0;
1182 switch(t.resultc) {
1183 case rc_zero:
1184 if(resultr[0] != 0 || resulti[0] != 0 ||
1185 (wres==2 && (resultr[1] != 0 || resulti[1] != 0))) {
1186 err = 1;
1187 }
1188 break;
1189 case rc_infinity:
1190 if(wres==1) {
1191 if(!((resultr[0]&0x7fffffff)==0x7f800000 ||
1192 (resulti[0]&0x7fffffff)==0x7f800000)) {
1193 err = 1;
1194 }
1195 } else {
1196 if(!(((resultr[0]&0x7fffffff)==0x7ff00000 && resultr[1]==0) ||
1197 ((resulti[0]&0x7fffffff)==0x7ff00000 && resulti[1]==0))) {
1198 err = 1;
1199 }
1200 }
1201 break;
1202 case rc_nan:
1203 if(wres==1) {
1204 if(!((resultr[0]&0x7fffffff)>0x7f800000 ||
1205 (resulti[0]&0x7fffffff)>0x7f800000)) {
1206 err = 1;
1207 }
1208 } else {
1209 canon_dNaN(resultr);
1210 canon_dNaN(resulti);
1211 if(!(((resultr[0]&0x7fffffff)>0x7ff00000 && resultr[1]==1) ||
1212 ((resulti[0]&0x7fffffff)>0x7ff00000 && resulti[1]==1))) {
1213 err = 1;
1214 }
1215 }
1216 break;
1217 case rc_finite:
1218 if(wres==1) {
1219 if(!((resultr[0]&0x7fffffff)<0x7f800000 ||
1220 (resulti[0]&0x7fffffff)<0x7f800000)) {
1221 err = 1;
1222 }
1223 } else {
1224 if(!((resultr[0]&0x7fffffff)<0x7ff00000 ||
1225 (resulti[0]&0x7fffffff)<0x7ff00000)) {
1226 err = 1;
1227 }
1228 }
1229 break;
1230 default:
1231 break;
1232 }
1233 if(err) {
1234 print_error(t.func->rettype,resultr,"wrongresultr",&failp);
1235 print_error(t.func->rettype,resulti,"wrongresulti",&failp);
1236 }
1237 } else if (t.nresult > wres) {
1238 /*
1239 * The test case data has provided the result to more
1240 * than double precision. Instead of testing exact
1241 * equality, we test against our maximum error
1242 * tolerance.
1243 */
1244 int rshift, ishift;
1245 long long ulpsr, ulpsi, ulptolerance;
1246
1247 tresultr[wres] = t.resultr[wres] << (32-EXTRABITS);
1248 tresulti[wres] = t.resulti[wres] << (32-EXTRABITS);
1249 if(strict) {
1250 ulptolerance = 4096; /* one ulp */
1251 } else {
1252 ulptolerance = t.func->tolerance;
1253 }
1254 rshift = ishift = 0;
1255 if (ulptolerance & ABSLOWERBOUND) {
1256 /*
1257 * Hack for the lgamma functions, which have an
1258 * error behaviour that can't conveniently be
1259 * characterised in pure ULPs. Really, we want to
1260 * say that the error in lgamma is "at most N ULPs,
1261 * or at most an absolute error of X, whichever is
1262 * larger", for appropriately chosen N,X. But since
1263 * these two functions are the only cases where it
1264 * arises, I haven't bothered to do it in a nice way
1265 * in the function table above.
1266 *
1267 * (The difficult cases arise with negative input
1268 * values such that |gamma(x)| is very near to 1; in
1269 * this situation implementations tend to separately
1270 * compute lgamma(|x|) and the log of the correction
1271 * term from the Euler reflection formula, and
1272 * subtract - which catastrophically loses
1273 * significance.)
1274 *
1275 * As far as I can tell, nobody cares about this:
1276 * GNU libm doesn't get those cases right either,
1277 * and OpenCL explicitly doesn't state a ULP error
1278 * limit for lgamma. So my guess is that this is
1279 * simply considered acceptable error behaviour for
1280 * this particular function, and hence I feel free
1281 * to allow for it here.
1282 */
1283 ulptolerance &= ~ABSLOWERBOUND;
1284 if (t.op1r[0] & 0x80000000) {
1285 if (t.func->rettype == rt_d)
1286 rshift = 0x400 - ((tresultr[0] >> 20) & 0x7ff);
1287 else if (t.func->rettype == rt_s)
1288 rshift = 0x80 - ((tresultr[0] >> 23) & 0xff);
1289 if (rshift < 0)
1290 rshift = 0;
1291 }
1292 }
1293 if (ulptolerance & PLUSMINUSPIO2) {
1294 ulptolerance &= ~PLUSMINUSPIO2;
1295 /*
1296 * Hack for range reduction, which can reduce
1297 * borderline cases in the wrong direction, i.e.
1298 * return a value just outside one end of the interval
1299 * [-pi/4,+pi/4] when it could have returned a value
1300 * just inside the other end by subtracting an
1301 * adjacent multiple of pi/2.
1302 *
1303 * We tolerate this, up to a point, because the
1304 * trigonometric functions making use of the output of
1305 * rred can cope and because making the range reducer
1306 * do the exactly right thing in every case would be
1307 * more expensive.
1308 */
1309 if (wres == 1) {
1310 /* Upper bound of overshoot derived in rredf.h */
1311 if ((resultr[0]&0x7FFFFFFF) <= 0x3f494b02 &&
1312 (resultr[0]&0x7FFFFFFF) > 0x3f490fda &&
1313 (resultr[0]&0x80000000) != (tresultr[0]&0x80000000)) {
1314 unsigned long long val;
1315 val = tresultr[0];
1316 val = (val << 32) | tresultr[1];
1317 /*
1318 * Compute the alternative permitted result by
1319 * subtracting from the sum of the extended
1320 * single-precision bit patterns of +pi/4 and
1321 * -pi/4. This is a horrible hack which only
1322 * works because we can be confident that
1323 * numbers in this range all have the same
1324 * exponent!
1325 */
1326 val = 0xfe921fb54442d184ULL - val;
1327 tresultr[0] = val >> 32;
1328 tresultr[1] = (val >> (32-EXTRABITS)) << (32-EXTRABITS);
1329 /*
1330 * Also, expect a correspondingly different
1331 * value of res2 as a result of this change.
1332 * The adjustment depends on whether we just
1333 * flipped the result from + to - or vice
1334 * versa.
1335 */
1336 if (resultr[0] & 0x80000000) {
1337 res2_adjust = +1;
1338 } else {
1339 res2_adjust = -1;
1340 }
1341 }
1342 }
1343 }
1344 ulpsr = calc_error(resultr, tresultr, rshift, t.func->rettype);
1345 if(is_complex_rettype(t.func->rettype)) {
1346 ulpsi = calc_error(resulti, tresulti, ishift, t.func->rettype);
1347 } else {
1348 ulpsi = 0;
1349 }
1350 unsigned *rr = (ulpsr > ulptolerance || ulpsr < -ulptolerance) ? resultr : NULL;
1351 unsigned *ri = (ulpsi > ulptolerance || ulpsi < -ulptolerance) ? resulti : NULL;
1352 /* printf("tolerance=%i, ulpsr=%i, ulpsi=%i, rr=%p, ri=%p\n",ulptolerance,ulpsr,ulpsi,rr,ri); */
1353 if (rr || ri) {
1354 if (quiet) failtext[0]='x';
1355 else {
1356 print_error(t.func->rettype,rr,"wrongresultr",&failp);
1357 print_error(t.func->rettype,ri,"wrongresulti",&failp);
1358 print_ulps(t.func->rettype,rr ? ulpsr : 0, ri ? ulpsi : 0,&failp);
1359 }
1360 }
1361 } else {
1362 if(is_complex_rettype(t.func->rettype))
1363 /*
1364 * Complex functions are not fully supported,
1365 * this is unreachable, but prevents warnings.
1366 */
1367 abort();
1368 /*
1369 * The test case data has provided the result in
1370 * exactly the output precision. Therefore we must
1371 * complain about _any_ violation.
1372 */
1373 switch(t.func->rettype) {
1374 case rt_dc:
1375 canon_dNaN(tresulti);
1376 canon_dNaN(resulti);
1377 if (fo) {
1378 dnormzero(tresulti);
1379 dnormzero(resulti);
1380 }
1381 /* deliberate fall-through */
1382 case rt_d:
1383 canon_dNaN(tresultr);
1384 canon_dNaN(resultr);
1385 if (fo) {
1386 dnormzero(tresultr);
1387 dnormzero(resultr);
1388 }
1389 break;
1390 case rt_sc:
1391 canon_sNaN(tresulti);
1392 canon_sNaN(resulti);
1393 if (fo) {
1394 snormzero(tresulti);
1395 snormzero(resulti);
1396 }
1397 /* deliberate fall-through */
1398 case rt_s:
1399 canon_sNaN(tresultr);
1400 canon_sNaN(resultr);
1401 if (fo) {
1402 snormzero(tresultr);
1403 snormzero(resultr);
1404 }
1405 break;
1406 default:
1407 break;
1408 }
1409 if(is_complex_rettype(t.func->rettype)) {
1410 unsigned *rr, *ri;
1411 if(resultr[0] != tresultr[0] ||
1412 (wres > 1 && resultr[1] != tresultr[1])) {
1413 rr = resultr;
1414 } else {
1415 rr = NULL;
1416 }
1417 if(resulti[0] != tresulti[0] ||
1418 (wres > 1 && resulti[1] != tresulti[1])) {
1419 ri = resulti;
1420 } else {
1421 ri = NULL;
1422 }
1423 if(rr || ri) {
1424 if (quiet) failtext[0]='x';
1425 print_error(t.func->rettype,rr,"wrongresultr",&failp);
1426 print_error(t.func->rettype,ri,"wrongresulti",&failp);
1427 }
1428 } else if (resultr[0] != tresultr[0] ||
1429 (wres > 1 && resultr[1] != tresultr[1])) {
1430 if (quiet) failtext[0]='x';
1431 print_error(t.func->rettype,resultr,"wrongresult",&failp);
1432 }
1433 }
1434 /*
1435 * Now test res2, for those functions (frexp, modf, rred)
1436 * which use it.
1437 */
1438 if (t.func->func.ptr == &frexp || t.func->func.ptr == &frexpf ||
1439 t.func->macro_name == m_rred || t.func->macro_name == m_rredf) {
1440 unsigned tres2 = t.res2[0];
1441 if (res2_adjust) {
1442 /* Fix for range reduction, propagated from further up */
1443 tres2 = (tres2 + res2_adjust) & 3;
1444 }
1445 if (tres2 != intres) {
1446 if (quiet) failtext[0]='x';
1447 else {
1448 failp += sprintf(failp,
1449 " wrongres2=%08x", intres);
1450 }
1451 }
1452 } else if (t.func->func.ptr == &modf || t.func->func.ptr == &modff) {
1453 tresultr[0] = t.res2[0];
1454 tresultr[1] = t.res2[1];
1455 if (is_double_rettype(t.func->rettype)) {
1456 canon_dNaN(tresultr);
1457 resultr[0] = d_res2.i[dmsd];
1458 resultr[1] = d_res2.i[dlsd];
1459 canon_dNaN(resultr);
1460 if (fo) {
1461 dnormzero(tresultr);
1462 dnormzero(resultr);
1463 }
1464 } else {
1465 canon_sNaN(tresultr);
1466 resultr[0] = s_res2.i;
1467 resultr[1] = s_res2.i;
1468 canon_sNaN(resultr);
1469 if (fo) {
1470 snormzero(tresultr);
1471 snormzero(resultr);
1472 }
1473 }
1474 if (resultr[0] != tresultr[0] ||
1475 (wres > 1 && resultr[1] != tresultr[1])) {
1476 if (quiet) failtext[0]='x';
1477 else {
1478 if (is_double_rettype(t.func->rettype))
1479 failp += sprintf(failp, " wrongres2=%08x.%08x",
1480 resultr[0], resultr[1]);
1481 else
1482 failp += sprintf(failp, " wrongres2=%08x",
1483 resultr[0]);
1484 }
1485 }
1486 }
1487 }
1488
1489 /* Check errno */
1490 err = (errno == EDOM ? e_EDOM : errno == ERANGE ? e_ERANGE : e_0);
1491 if (err != t.err && err != t.maybeerr) {
1492 if (quiet) failtext[0]='x';
1493 else {
1494 failp += sprintf(failp, " wrongerrno=%s expecterrno=%s ", errnos[err], errnos[t.err]);
1495 }
1496 }
1497
1498 return *failtext ? test_fail : test_pass;
1499 }
1500
1501 int passed, failed, declined;
1502
runtests(char * name,FILE * fp)1503 void runtests(char *name, FILE *fp) {
1504 char testbuf[512], linebuf[512];
1505 int lineno = 1;
1506 testdetail test;
1507
1508 test.valid = 0;
1509
1510 if (verbose) printf("runtests: %s\n", name);
1511 while (fgets(testbuf, sizeof(testbuf), fp)) {
1512 int res, print_errno;
1513 testbuf[strcspn(testbuf, "\r\n")] = '\0';
1514 strcpy(linebuf, testbuf);
1515 test = parsetest(testbuf, test);
1516 print_errno = 0;
1517 while (test.in_err < test.in_err_limit) {
1518 res = runtest(test);
1519 if (res == test_pass) {
1520 if (verbose)
1521 printf("%s:%d: pass\n", name, lineno);
1522 ++passed;
1523 } else if (res == test_decline) {
1524 if (verbose)
1525 printf("%s:%d: declined\n", name, lineno);
1526 ++declined;
1527 } else if (res == test_fail) {
1528 if (!quiet)
1529 printf("%s:%d: FAIL%s: %s%s%s%s\n", name, lineno,
1530 test.random ? " (random)" : "",
1531 linebuf,
1532 print_errno ? " errno_in=" : "",
1533 print_errno ? errnos[test.in_err] : "",
1534 failtext);
1535 ++failed;
1536 } else if (res == test_invalid) {
1537 printf("%s:%d: malformed: %s\n", name, lineno, linebuf);
1538 ++failed;
1539 }
1540 test.in_err++;
1541 print_errno = 1;
1542 }
1543 lineno++;
1544 }
1545 }
1546
main(int ac,char ** av)1547 int main(int ac, char **av) {
1548 char **files;
1549 int i, nfiles = 0;
1550 dbl d;
1551
1552 #ifdef MICROLIB
1553 /*
1554 * Invent argc and argv ourselves.
1555 */
1556 char *argv[256];
1557 char args[256];
1558 {
1559 int sargs[2];
1560 char *p;
1561
1562 ac = 0;
1563
1564 sargs[0]=(int)args;
1565 sargs[1]=(int)sizeof(args);
1566 if (!__semihost(0x15, sargs)) {
1567 args[sizeof(args)-1] = '\0'; /* just in case */
1568 p = args;
1569 while (1) {
1570 while (*p == ' ' || *p == '\t') p++;
1571 if (!*p) break;
1572 argv[ac++] = p;
1573 while (*p && *p != ' ' && *p != '\t') p++;
1574 if (*p) *p++ = '\0';
1575 }
1576 }
1577
1578 av = argv;
1579 }
1580 #endif
1581
1582 /* Sort tfuncs */
1583 qsort(tfuncs, sizeof(tfuncs)/sizeof(test_func), sizeof(test_func), &compare_tfuncs);
1584
1585 /*
1586 * Autodetect the `double' endianness.
1587 */
1588 dmsd = 0;
1589 d.f = 1.0; /* 0x3ff00000 / 0x00000000 */
1590 if (d.i[dmsd] == 0) {
1591 dmsd = 1;
1592 }
1593 /*
1594 * Now dmsd denotes what the compiler thinks we're at. Let's
1595 * check that it agrees with what the runtime thinks.
1596 */
1597 d.i[0] = d.i[1] = 0x11111111;/* a random +ve number */
1598 d.f /= d.f; /* must now be one */
1599 if (d.i[dmsd] == 0) {
1600 fprintf(stderr, "YIKES! Compiler and runtime disagree on endianness"
1601 " of `double'. Bailing out\n");
1602 return 1;
1603 }
1604 dlsd = !dmsd;
1605
1606 /* default is terse */
1607 verbose = 0;
1608 fo = 0;
1609 strict = 0;
1610
1611 files = (char **)malloc((ac+1) * sizeof(char *));
1612 if (!files) {
1613 fprintf(stderr, "initial malloc failed!\n");
1614 return 1;
1615 }
1616 #ifdef NOCMDLINE
1617 files[nfiles++] = "testfile";
1618 #endif
1619
1620 while (--ac) {
1621 char *p = *++av;
1622 if (*p == '-') {
1623 static char *options[] = {
1624 "-fo",
1625 #if 0
1626 "-noinexact",
1627 "-noround",
1628 #endif
1629 "-nostatus",
1630 "-quiet",
1631 "-strict",
1632 "-v",
1633 "-verbose",
1634 };
1635 enum {
1636 op_fo,
1637 #if 0
1638 op_noinexact,
1639 op_noround,
1640 #endif
1641 op_nostatus,
1642 op_quiet,
1643 op_strict,
1644 op_v,
1645 op_verbose,
1646 };
1647 switch (find(p, options, sizeof(options))) {
1648 case op_quiet:
1649 quiet = 1;
1650 break;
1651 #if 0
1652 case op_noinexact:
1653 statusmask &= 0x0F; /* remove bit 4 */
1654 break;
1655 case op_noround:
1656 doround = 0;
1657 break;
1658 #endif
1659 case op_nostatus: /* no status word => noinx,noround */
1660 statusmask = 0;
1661 doround = 0;
1662 break;
1663 case op_v:
1664 case op_verbose:
1665 verbose = 1;
1666 break;
1667 case op_fo:
1668 fo = 1;
1669 break;
1670 case op_strict: /* tolerance is 1 ulp */
1671 strict = 1;
1672 break;
1673 default:
1674 fprintf(stderr, "unrecognised option: %s\n", p);
1675 break;
1676 }
1677 } else {
1678 files[nfiles++] = p;
1679 }
1680 }
1681
1682 passed = failed = declined = 0;
1683
1684 if (nfiles) {
1685 for (i = 0; i < nfiles; i++) {
1686 FILE *fp = fopen(files[i], "r");
1687 if (!fp) {
1688 fprintf(stderr, "Couldn't open %s\n", files[i]);
1689 } else
1690 runtests(files[i], fp);
1691 }
1692 } else
1693 runtests("(stdin)", stdin);
1694
1695 printf("Completed. Passed %d, failed %d (total %d",
1696 passed, failed, passed+failed);
1697 if (declined)
1698 printf(" plus %d declined", declined);
1699 printf(")\n");
1700 if (failed || passed == 0)
1701 return 1;
1702 printf("** TEST PASSED OK **\n");
1703 return 0;
1704 }
1705
undef_func()1706 void undef_func() {
1707 failed++;
1708 puts("ERROR: undefined function called");
1709 }
1710