xref: /freebsd/contrib/arm-optimized-routines/math/test/mathtest.c (revision 5ca8e32633c4ffbbcd6762e5888b6a4ba0708c6c)
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 */
113 int compare_tfuncs(const void* a, const void* b) {
114     return strcmp(((test_func*)a)->name, ((test_func*)b)->name);
115 }
116 
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 
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 
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 
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 
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 
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.  */
201 static float sincosf_sinf(float x) { float s,c; sincosf(x, &s, &c); return s; }
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 */
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. */
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  */
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 }
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  */
443 void dnormzero(unsigned a[2])
444 {
445     if (a[0] == 0x80000000 && a[1] == 0)
446         a[0] = 0;
447 }
448 void snormzero(unsigned a[1])
449 {
450     if (a[0] == 0x80000000)
451         a[0] = 0;
452 }
453 
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 
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 
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 
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 
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 */
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 
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 */
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 
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 */
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 
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 
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 
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 
1706 void undef_func() {
1707     failed++;
1708     puts("ERROR: undefined function called");
1709 }
1710