1 /*
2  * mathtest.c - test rig for mathlib
3  *
4  * Copyright (c) 1998-2022, 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 
258     /* power */
259     TFUNC(at_d2,rt_d, pow, 3*ULPUNIT/4),
260     TFUNC(at_d,rt_d, sqrt, ULPUNIT/2),
261     TFUNC(at_d,rt_d, cbrt, 2*ULPUNIT),
262     TFUNC(at_d2, rt_d, hypot, 4*ULPUNIT),
263 
264     TFUNCARM(at_s2,rt_s, powf, ULPUNIT),
265     TFUNC(at_s,rt_s, sqrtf, ULPUNIT/2),
266     TFUNC(at_s,rt_s, cbrtf, 2*ULPUNIT),
267     TFUNC(at_s2, rt_s, hypotf, 4*ULPUNIT),
268 
269     /* error function */
270     TFUNC(at_d,rt_d, erf, 16*ULPUNIT),
271     TFUNC(at_s,rt_s, erff, 16*ULPUNIT),
272     TFUNC(at_d,rt_d, erfc, 16*ULPUNIT),
273     TFUNC(at_s,rt_s, erfcf, 16*ULPUNIT),
274 
275     /* gamma functions */
276     TFUNC(at_d,rt_d, tgamma, 16*ULPUNIT),
277     TFUNC(at_s,rt_s, tgammaf, 16*ULPUNIT),
278     TFUNC(at_d,rt_d, lgamma, 16*ULPUNIT | ABSLOWERBOUND),
279     TFUNC(at_s,rt_s, lgammaf, 16*ULPUNIT | ABSLOWERBOUND),
280 
281     TFUNC(at_d,rt_d, ceil, 0),
282     TFUNC(at_s,rt_s, ceilf, 0),
283     TFUNC(at_d2,rt_d, copysign, 0),
284     TFUNC(at_s2,rt_s, copysignf, 0),
285     TFUNC(at_d,rt_d, floor, 0),
286     TFUNC(at_s,rt_s, floorf, 0),
287     TFUNC(at_d2,rt_d, fmax, 0),
288     TFUNC(at_s2,rt_s, fmaxf, 0),
289     TFUNC(at_d2,rt_d, fmin, 0),
290     TFUNC(at_s2,rt_s, fminf, 0),
291     TFUNC(at_d2,rt_d, fmod, 0),
292     TFUNC(at_s2,rt_s, fmodf, 0),
293     MFUNC(at_d, rt_i, fpclassify, 0),
294     MFUNC(at_s, rt_i, fpclassifyf, 0),
295     TFUNC(at_dip,rt_d, frexp, 0),
296     TFUNC(at_sip,rt_s, frexpf, 0),
297     MFUNC(at_d, rt_i, isfinite, 0),
298     MFUNC(at_s, rt_i, isfinitef, 0),
299     MFUNC(at_d, rt_i, isgreater, 0),
300     MFUNC(at_d, rt_i, isgreaterequal, 0),
301     MFUNC(at_s, rt_i, isgreaterequalf, 0),
302     MFUNC(at_s, rt_i, isgreaterf, 0),
303     MFUNC(at_d, rt_i, isinf, 0),
304     MFUNC(at_s, rt_i, isinff, 0),
305     MFUNC(at_d, rt_i, isless, 0),
306     MFUNC(at_d, rt_i, islessequal, 0),
307     MFUNC(at_s, rt_i, islessequalf, 0),
308     MFUNC(at_s, rt_i, islessf, 0),
309     MFUNC(at_d, rt_i, islessgreater, 0),
310     MFUNC(at_s, rt_i, islessgreaterf, 0),
311     MFUNC(at_d, rt_i, isnan, 0),
312     MFUNC(at_s, rt_i, isnanf, 0),
313     MFUNC(at_d, rt_i, isnormal, 0),
314     MFUNC(at_s, rt_i, isnormalf, 0),
315     MFUNC(at_d, rt_i, isunordered, 0),
316     MFUNC(at_s, rt_i, isunorderedf, 0),
317     TFUNC(at_di,rt_d, ldexp, 0),
318     TFUNC(at_si,rt_s, ldexpf, 0),
319     TFUNC(at_ddp,rt_d2, modf, 0),
320     TFUNC(at_ssp,rt_s2, modff, 0),
321 #ifndef BIGRANGERED
322     MFUNC(at_d, rt_d, rred, 2*ULPUNIT),
323 #else
324     MFUNC(at_d, rt_d, m_rred, ULPUNIT),
325 #endif
326     MFUNC(at_d, rt_i, signbit, 0),
327     MFUNC(at_s, rt_i, signbitf, 0),
328 };
329 
330 /*
331  * keywords are: func size op1 op2 result res2 errno op1r op1i op2r op2i resultr resulti
332  * also we ignore: wrongresult wrongres2 wrongerrno
333  * op1 equivalent to op1r, same with op2 and result
334  */
335 
336 typedef struct {
337     test_func *func;
338     unsigned op1r[2]; /* real part, also used for non-complex numbers */
339     unsigned op1i[2]; /* imaginary part */
340     unsigned op2r[2];
341     unsigned op2i[2];
342     unsigned resultr[3];
343     unsigned resulti[3];
344     enum {
345         rc_none, rc_zero, rc_infinity, rc_nan, rc_finite
346     } resultc; /* special complex results, rc_none means use resultr and resulti as normal */
347     unsigned res2[2];
348     unsigned status;                   /* IEEE status return, if any */
349     unsigned maybestatus;             /* for optional status, or allowance for spurious */
350     int nresult;                       /* number of result words */
351     int in_err, in_err_limit;
352     int err;
353     int maybeerr;
354     int valid;
355     int comment;
356     int random;
357 } testdetail;
358 
359 enum {                                 /* keywords */
360     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,
361     k_random, k_res2, k_result, k_resultc, k_resulti, k_resultr, k_status,
362     k_wrongres2, k_wrongresult, k_wrongstatus, k_wrongerrno
363 };
364 char *keywords[] = {
365     "errno", "errno_in", "error", "func", "maybeerror", "maybestatus", "op1", "op1i", "op1r", "op2", "op2i", "op2r",
366     "random", "res2", "result", "resultc", "resulti", "resultr", "status",
367     "wrongres2", "wrongresult", "wrongstatus", "wrongerrno"
368 };
369 
370 enum {
371     e_0, e_EDOM, e_ERANGE,
372 
373     /*
374      * This enum makes sure that we have the right number of errnos in the
375      * errno[] array
376      */
377     e_number_of_errnos
378 };
379 char *errnos[] = {
380     "0", "EDOM", "ERANGE"
381 };
382 
383 enum {
384     e_none, e_divbyzero, e_domain, e_overflow, e_underflow
385 };
386 char *errors[] = {
387     "0", "divbyzero", "domain", "overflow", "underflow"
388 };
389 
390 static int verbose, fo, strict;
391 
392 /* state toggled by random=on / random=off */
393 static int randomstate;
394 
395 /* Canonify a double NaN: SNaNs all become 7FF00000.00000001 and QNaNs
396  * all become 7FF80000.00000001 */
397 void canon_dNaN(unsigned a[2]) {
398     if ((a[0] & 0x7FF00000) != 0x7FF00000)
399         return;                        /* not Inf or NaN */
400     if (!(a[0] & 0xFFFFF) && !a[1])
401         return;                        /* Inf */
402     a[0] &= 0x7FF80000;                /* canonify top word */
403     a[1] = 0x00000001;                 /* canonify bottom word */
404 }
405 
406 /* Canonify a single NaN: SNaNs all become 7F800001 and QNaNs
407  * all become 7FC00001. Returns classification of the NaN. */
408 void canon_sNaN(unsigned a[1]) {
409     if ((a[0] & 0x7F800000) != 0x7F800000)
410         return;                        /* not Inf or NaN */
411     if (!(a[0] & 0x7FFFFF))
412         return;                        /* Inf */
413     a[0] &= 0x7FC00000;                /* canonify most bits */
414     a[0] |= 0x00000001;                /* canonify bottom bit */
415 }
416 
417 /*
418  * Detect difficult operands for FO mode.
419  */
420 int is_dhard(unsigned a[2])
421 {
422     if ((a[0] & 0x7FF00000) == 0x7FF00000)
423         return TRUE;                   /* inf or NaN */
424     if ((a[0] & 0x7FF00000) == 0 &&
425         ((a[0] & 0x7FFFFFFF) | a[1]) != 0)
426         return TRUE;                   /* denormal */
427     return FALSE;
428 }
429 int is_shard(unsigned a[1])
430 {
431     if ((a[0] & 0x7F800000) == 0x7F800000)
432         return TRUE;                   /* inf or NaN */
433     if ((a[0] & 0x7F800000) == 0 &&
434         (a[0] & 0x7FFFFFFF) != 0)
435         return TRUE;                   /* denormal */
436     return FALSE;
437 }
438 
439 /*
440  * Normalise all zeroes into +0, for FO mode.
441  */
442 void dnormzero(unsigned a[2])
443 {
444     if (a[0] == 0x80000000 && a[1] == 0)
445         a[0] = 0;
446 }
447 void snormzero(unsigned a[1])
448 {
449     if (a[0] == 0x80000000)
450         a[0] = 0;
451 }
452 
453 static int find(char *word, char **array, int asize) {
454     int i, j;
455 
456     asize /= sizeof(char *);
457 
458     i = -1; j = asize;                 /* strictly between i and j */
459     while (j-i > 1) {
460         int k = (i+j) / 2;
461         int c = strcmp(word, array[k]);
462         if (c > 0)
463             i = k;
464         else if (c < 0)
465             j = k;
466         else                           /* found it! */
467             return k;
468     }
469     return -1;                         /* not found */
470 }
471 
472 static test_func* find_testfunc(char *word) {
473     int i, j, asize;
474 
475     asize = sizeof(tfuncs)/sizeof(test_func);
476 
477     i = -1; j = asize;                 /* strictly between i and j */
478     while (j-i > 1) {
479         int k = (i+j) / 2;
480         int c = strcmp(word, tfuncs[k].name);
481         if (c > 0)
482             i = k;
483         else if (c < 0)
484             j = k;
485         else                           /* found it! */
486             return tfuncs + k;
487     }
488     return NULL;                         /* not found */
489 }
490 
491 static long long calc_error(unsigned a[2], unsigned b[3], int shift, int rettype) {
492     unsigned r0, r1, r2;
493     int sign, carry;
494     long long result;
495 
496     /*
497      * If either number is infinite, require exact equality. If
498      * either number is NaN, require that both are NaN. If either
499      * of these requirements is broken, return INT_MAX.
500      */
501     if (is_double_rettype(rettype)) {
502         if ((a[0] & 0x7FF00000) == 0x7FF00000 ||
503             (b[0] & 0x7FF00000) == 0x7FF00000) {
504             if (((a[0] & 0x800FFFFF) || a[1]) &&
505                 ((b[0] & 0x800FFFFF) || b[1]) &&
506                 (a[0] & 0x7FF00000) == 0x7FF00000 &&
507                 (b[0] & 0x7FF00000) == 0x7FF00000)
508                 return 0;              /* both NaN - OK */
509             if (!((a[0] & 0xFFFFF) || a[1]) &&
510                 !((b[0] & 0xFFFFF) || b[1]) &&
511                 a[0] == b[0])
512                 return 0;              /* both same sign of Inf - OK */
513             return LLONG_MAX;
514         }
515     } else {
516         if ((a[0] & 0x7F800000) == 0x7F800000 ||
517             (b[0] & 0x7F800000) == 0x7F800000) {
518             if ((a[0] & 0x807FFFFF) &&
519                 (b[0] & 0x807FFFFF) &&
520                 (a[0] & 0x7F800000) == 0x7F800000 &&
521                 (b[0] & 0x7F800000) == 0x7F800000)
522                 return 0;              /* both NaN - OK */
523             if (!(a[0] & 0x7FFFFF) &&
524                 !(b[0] & 0x7FFFFF) &&
525                 a[0] == b[0])
526                 return 0;              /* both same sign of Inf - OK */
527             return LLONG_MAX;
528         }
529     }
530 
531     /*
532      * Both finite. Return INT_MAX if the signs differ.
533      */
534     if ((a[0] ^ b[0]) & 0x80000000)
535         return LLONG_MAX;
536 
537     /*
538      * Now it's just straight multiple-word subtraction.
539      */
540     if (is_double_rettype(rettype)) {
541         r2 = -b[2]; carry = (r2 == 0);
542         r1 = a[1] + ~b[1] + carry; carry = (r1 < a[1] || (carry && r1 == a[1]));
543         r0 = a[0] + ~b[0] + carry;
544     } else {
545         r2 = -b[1]; carry = (r2 == 0);
546         r1 = a[0] + ~b[0] + carry; carry = (r1 < a[0] || (carry && r1 == a[0]));
547         r0 = ~0 + carry;
548     }
549 
550     /*
551      * Forgive larger errors in specialised cases.
552      */
553     if (shift > 0) {
554         if (shift > 32*3)
555             return 0;                  /* all errors are forgiven! */
556         while (shift >= 32) {
557             r2 = r1;
558             r1 = r0;
559             r0 = -(r0 >> 31);
560             shift -= 32;
561         }
562 
563         if (shift > 0) {
564             r2 = (r2 >> shift) | (r1 << (32-shift));
565             r1 = (r1 >> shift) | (r0 << (32-shift));
566             r0 = (r0 >> shift) | ((-(r0 >> 31)) << (32-shift));
567         }
568     }
569 
570     if (r0 & 0x80000000) {
571         sign = 1;
572         r2 = ~r2; carry = (r2 == 0);
573         r1 = 0 + ~r1 + carry; carry = (carry && (r2 == 0));
574         r0 = 0 + ~r0 + carry;
575     } else {
576         sign = 0;
577     }
578 
579     if (r0 >= (1LL<<(31-EXTRABITS)))
580         return LLONG_MAX;                /* many ulps out */
581 
582     result = (r2 >> (32-EXTRABITS)) & (ULPUNIT-1);
583     result |= r1 << EXTRABITS;
584     result |= (long long)r0 << (32+EXTRABITS);
585     if (sign)
586         result = -result;
587     return result;
588 }
589 
590 /* special named operands */
591 
592 typedef struct {
593     unsigned op1, op2;
594     char* name;
595 } special_op;
596 
597 static special_op special_ops_double[] = {
598     {0x00000000,0x00000000,"0"},
599     {0x3FF00000,0x00000000,"1"},
600     {0x7FF00000,0x00000000,"inf"},
601     {0x7FF80000,0x00000001,"qnan"},
602     {0x7FF00000,0x00000001,"snan"},
603     {0x3ff921fb,0x54442d18,"pi2"},
604     {0x400921fb,0x54442d18,"pi"},
605     {0x3fe921fb,0x54442d18,"pi4"},
606     {0x4002d97c,0x7f3321d2,"3pi4"},
607 };
608 
609 static special_op special_ops_float[] = {
610     {0x00000000,0,"0"},
611     {0x3f800000,0,"1"},
612     {0x7f800000,0,"inf"},
613     {0x7fc00000,0,"qnan"},
614     {0x7f800001,0,"snan"},
615     {0x3fc90fdb,0,"pi2"},
616     {0x40490fdb,0,"pi"},
617     {0x3f490fdb,0,"pi4"},
618     {0x4016cbe4,0,"3pi4"},
619 };
620 
621 /*
622    This is what is returned by the below functions.
623    We need it to handle the sign of the number
624 */
625 static special_op tmp_op = {0,0,0};
626 
627 special_op* find_special_op_from_op(unsigned op1, unsigned op2, int is_double) {
628     int i;
629     special_op* sop;
630     if(is_double) {
631         sop = special_ops_double;
632     } else {
633         sop = special_ops_float;
634     }
635     for(i = 0; i < sizeof(special_ops_double)/sizeof(special_op); i++) {
636         if(sop->op1 == (op1&0x7fffffff) && sop->op2 == op2) {
637             if(tmp_op.name) free(tmp_op.name);
638             tmp_op.name = malloc(strlen(sop->name)+2);
639             if(op1>>31) {
640                 sprintf(tmp_op.name,"-%s",sop->name);
641             } else {
642                 strcpy(tmp_op.name,sop->name);
643             }
644             return &tmp_op;
645         }
646         sop++;
647     }
648     return NULL;
649 }
650 
651 special_op* find_special_op_from_name(const char* name, int is_double) {
652     int i, neg=0;
653     special_op* sop;
654     if(is_double) {
655         sop = special_ops_double;
656     } else {
657         sop = special_ops_float;
658     }
659     if(*name=='-') {
660         neg=1;
661         name++;
662     } else if(*name=='+') {
663         name++;
664     }
665     for(i = 0; i < sizeof(special_ops_double)/sizeof(special_op); i++) {
666         if(0 == strcmp(name,sop->name)) {
667             tmp_op.op1 = sop->op1;
668             if(neg) {
669                 tmp_op.op1 |= 0x80000000;
670             }
671             tmp_op.op2 = sop->op2;
672             return &tmp_op;
673         }
674         sop++;
675     }
676     return NULL;
677 }
678 
679 /*
680    helper function for the below
681    type=0 for single, 1 for double, 2 for no sop
682 */
683 int do_op(char* q, unsigned* op, const char* name, int num, int sop_type) {
684     int i;
685     int n=num;
686     special_op* sop = NULL;
687     for(i = 0; i < num; i++) {
688         op[i] = 0;
689     }
690     if(sop_type<2) {
691         sop = find_special_op_from_name(q,sop_type);
692     }
693     if(sop != NULL) {
694         op[0] = sop->op1;
695         op[1] = sop->op2;
696     } else {
697         switch(num) {
698         case 1: n = sscanf(q, "%x", &op[0]); break;
699         case 2: n = sscanf(q, "%x.%x", &op[0], &op[1]); break;
700         case 3: n = sscanf(q, "%x.%x.%x", &op[0], &op[1], &op[2]); break;
701         default: return -1;
702         }
703     }
704     if (verbose) {
705         printf("%s=",name);
706         for (i = 0; (i < n); ++i) printf("%x.", op[i]);
707         printf(" (n=%d)\n", n);
708     }
709     return n;
710 }
711 
712 testdetail parsetest(char *testbuf, testdetail oldtest) {
713     char *p; /* Current part of line: Option name */
714     char *q; /* Current part of line: Option value */
715     testdetail ret; /* What we return */
716     int k; /* Function enum from k_* */
717     int n; /* Used as returns for scanfs */
718     int argtype=2, rettype=2; /* for do_op */
719 
720     /* clear ret */
721     memset(&ret, 0, sizeof(ret));
722 
723     if (verbose) printf("Parsing line: %s\n", testbuf);
724     while (*testbuf && isspace(*testbuf)) testbuf++;
725     if (testbuf[0] == ';' || testbuf[0] == '#' || testbuf[0] == '!' ||
726         testbuf[0] == '>' || testbuf[0] == '\0') {
727         ret.comment = 1;
728         if (verbose) printf("Line is a comment\n");
729         return ret;
730     }
731     ret.comment = 0;
732 
733     if (*testbuf == '+') {
734         if (oldtest.valid) {
735             ret = oldtest;             /* structure copy */
736         } else {
737             fprintf(stderr, "copy from invalid: ignored\n");
738         }
739         testbuf++;
740     }
741 
742     ret.random = randomstate;
743 
744     ret.in_err = 0;
745     ret.in_err_limit = e_number_of_errnos;
746 
747     p = strtok(testbuf, " \t");
748     while (p != NULL) {
749         q = strchr(p, '=');
750         if (!q)
751             goto balderdash;
752         *q++ = '\0';
753         k = find(p, keywords, sizeof(keywords));
754         switch (k) {
755         case k_random:
756             randomstate = (!strcmp(q, "on"));
757             ret.comment = 1;
758             return ret;                /* otherwise ignore this line */
759         case k_func:
760             if (verbose) printf("func=%s ", q);
761             //ret.func = find(q, funcs, sizeof(funcs));
762             ret.func = find_testfunc(q);
763             if (ret.func == NULL)
764                 {
765                     if (verbose) printf("(id=unknown)\n");
766                     goto balderdash;
767                 }
768             if(is_single_argtype(ret.func->argtype))
769                 argtype = 0;
770             else if(is_double_argtype(ret.func->argtype))
771                 argtype = 1;
772             if(is_single_rettype(ret.func->rettype))
773                 rettype = 0;
774             else if(is_double_rettype(ret.func->rettype))
775                 rettype = 1;
776             //ret.size = sizes[ret.func];
777             if (verbose) printf("(name=%s) (size=%d)\n", ret.func->name, ret.func->argtype);
778             break;
779         case k_op1:
780         case k_op1r:
781             n = do_op(q,ret.op1r,"op1r",2,argtype);
782             if (n < 1)
783                 goto balderdash;
784             break;
785         case k_op1i:
786             n = do_op(q,ret.op1i,"op1i",2,argtype);
787             if (n < 1)
788                 goto balderdash;
789             break;
790         case k_op2:
791         case k_op2r:
792             n = do_op(q,ret.op2r,"op2r",2,argtype);
793             if (n < 1)
794                 goto balderdash;
795             break;
796         case k_op2i:
797             n = do_op(q,ret.op2i,"op2i",2,argtype);
798             if (n < 1)
799                 goto balderdash;
800             break;
801         case k_resultc:
802             puts(q);
803             if(strncmp(q,"inf",3)==0) {
804                 ret.resultc = rc_infinity;
805             } else if(strcmp(q,"zero")==0) {
806                 ret.resultc = rc_zero;
807             } else if(strcmp(q,"nan")==0) {
808                 ret.resultc = rc_nan;
809             } else if(strcmp(q,"finite")==0) {
810                 ret.resultc = rc_finite;
811             } else {
812                 goto balderdash;
813             }
814             break;
815         case k_result:
816         case k_resultr:
817             n = (do_op)(q,ret.resultr,"resultr",3,rettype);
818             if (n < 1)
819                 goto balderdash;
820             ret.nresult = n; /* assume real and imaginary have same no. words */
821             break;
822         case k_resulti:
823             n = do_op(q,ret.resulti,"resulti",3,rettype);
824             if (n < 1)
825                 goto balderdash;
826             break;
827         case k_res2:
828             n = do_op(q,ret.res2,"res2",2,rettype);
829             if (n < 1)
830                 goto balderdash;
831             break;
832         case k_status:
833             while (*q) {
834                 if (*q == 'i') ret.status |= FE_INVALID;
835                 if (*q == 'z') ret.status |= FE_DIVBYZERO;
836                 if (*q == 'o') ret.status |= FE_OVERFLOW;
837                 if (*q == 'u') ret.status |= FE_UNDERFLOW;
838                 q++;
839             }
840             break;
841         case k_maybeerror:
842             n = find(q, errors, sizeof(errors));
843             if (n < 0)
844                 goto balderdash;
845             if(math_errhandling&MATH_ERREXCEPT) {
846                 switch(n) {
847                 case e_domain: ret.maybestatus |= FE_INVALID; break;
848                 case e_divbyzero: ret.maybestatus |= FE_DIVBYZERO; break;
849                 case e_overflow: ret.maybestatus |= FE_OVERFLOW; break;
850                 case e_underflow: ret.maybestatus |= FE_UNDERFLOW; break;
851                 }
852             }
853             {
854                 switch(n) {
855                 case e_domain:
856                     ret.maybeerr = e_EDOM; break;
857                 case e_divbyzero:
858                 case e_overflow:
859                 case e_underflow:
860                     ret.maybeerr = e_ERANGE; break;
861                 }
862             }
863         case k_maybestatus:
864             while (*q) {
865                 if (*q == 'i') ret.maybestatus |= FE_INVALID;
866                 if (*q == 'z') ret.maybestatus |= FE_DIVBYZERO;
867                 if (*q == 'o') ret.maybestatus |= FE_OVERFLOW;
868                 if (*q == 'u') ret.maybestatus |= FE_UNDERFLOW;
869                 q++;
870             }
871             break;
872         case k_error:
873             n = find(q, errors, sizeof(errors));
874             if (n < 0)
875                 goto balderdash;
876             if(math_errhandling&MATH_ERREXCEPT) {
877                 switch(n) {
878                 case e_domain: ret.status |= FE_INVALID; break;
879                 case e_divbyzero: ret.status |= FE_DIVBYZERO; break;
880                 case e_overflow: ret.status |= FE_OVERFLOW; break;
881                 case e_underflow: ret.status |= FE_UNDERFLOW; break;
882                 }
883             }
884             if(math_errhandling&MATH_ERRNO) {
885                 switch(n) {
886                 case e_domain:
887                     ret.err = e_EDOM; break;
888                 case e_divbyzero:
889                 case e_overflow:
890                 case e_underflow:
891                     ret.err = e_ERANGE; break;
892                 }
893             }
894             if(!(math_errhandling&MATH_ERRNO)) {
895                 switch(n) {
896                 case e_domain:
897                     ret.maybeerr = e_EDOM; break;
898                 case e_divbyzero:
899                 case e_overflow:
900                 case e_underflow:
901                     ret.maybeerr = e_ERANGE; break;
902                 }
903             }
904             break;
905         case k_errno:
906             ret.err = find(q, errnos, sizeof(errnos));
907             if (ret.err < 0)
908                 goto balderdash;
909             break;
910         case k_errno_in:
911             ret.in_err = find(q, errnos, sizeof(errnos));
912             if (ret.err < 0)
913                 goto balderdash;
914             ret.in_err_limit = ret.in_err + 1;
915             break;
916         case k_wrongresult:
917         case k_wrongstatus:
918         case k_wrongres2:
919         case k_wrongerrno:
920             /* quietly ignore these keys */
921             break;
922         default:
923             goto balderdash;
924         }
925         p = strtok(NULL, " \t");
926     }
927     ret.valid = 1;
928     return ret;
929 
930     /* come here from almost any error */
931  balderdash:
932     ret.valid = 0;
933     return ret;
934 }
935 
936 typedef enum {
937     test_comment,                      /* deliberately not a test */
938     test_invalid,                      /* accidentally not a test */
939     test_decline,                      /* was a test, and wasn't run */
940     test_fail,                         /* was a test, and failed */
941     test_pass                          /* was a test, and passed */
942 } testresult;
943 
944 char failtext[512];
945 
946 typedef union {
947     unsigned i[2];
948     double f;
949     double da[2];
950 } dbl;
951 
952 typedef union {
953     unsigned i;
954     float f;
955     float da[2];
956 } sgl;
957 
958 /* helper function for runtest */
959 void print_error(int rettype, unsigned *result, char* text, char** failp) {
960     special_op *sop;
961     char *str;
962 
963     if(result) {
964         *failp += sprintf(*failp," %s=",text);
965         sop = find_special_op_from_op(result[0],result[1],is_double_rettype(rettype));
966         if(sop) {
967             *failp += sprintf(*failp,"%s",sop->name);
968         } else {
969             if(is_double_rettype(rettype)) {
970                 str="%08x.%08x";
971             } else {
972                 str="%08x";
973             }
974             *failp += sprintf(*failp,str,result[0],result[1]);
975         }
976     }
977 }
978 
979 
980 void print_ulps_helper(const char *name, long long ulps, char** failp) {
981     if(ulps == LLONG_MAX) {
982         *failp += sprintf(*failp, " %s=HUGE", name);
983     } else {
984         *failp += sprintf(*failp, " %s=%.3f", name, (double)ulps / ULPUNIT);
985     }
986 }
987 
988 /* for complex args make ulpsr or ulpsri = 0 to not print */
989 void print_ulps(int rettype, long long ulpsr, long long ulpsi, char** failp) {
990     if(is_complex_rettype(rettype)) {
991         if (ulpsr) print_ulps_helper("ulpsr",ulpsr,failp);
992         if (ulpsi) print_ulps_helper("ulpsi",ulpsi,failp);
993     } else {
994         if (ulpsr) print_ulps_helper("ulps",ulpsr,failp);
995     }
996 }
997 
998 int runtest(testdetail t) {
999     int err, status;
1000 
1001     dbl d_arg1, d_arg2, d_res, d_res2;
1002     sgl s_arg1, s_arg2, s_res, s_res2;
1003 
1004     int deferred_decline = FALSE;
1005     char *failp = failtext;
1006 
1007     unsigned int intres=0;
1008 
1009     int res2_adjust = 0;
1010 
1011     if (t.comment)
1012         return test_comment;
1013     if (!t.valid)
1014         return test_invalid;
1015 
1016     /* Set IEEE status to mathlib-normal */
1017     feclearexcept(FE_ALL_EXCEPT);
1018 
1019     /* Deal with operands */
1020 #define DO_DOP(arg,op) arg.i[dmsd] = t.op[0]; arg.i[dlsd] = t.op[1]
1021     DO_DOP(d_arg1,op1r);
1022     DO_DOP(d_arg2,op2r);
1023     s_arg1.i = t.op1r[0]; s_arg2.i = t.op2r[0];
1024 
1025     /*
1026      * Detect NaNs, infinities and denormals on input, and set a
1027      * deferred decline flag if we're in FO mode.
1028      *
1029      * (We defer the decline rather than doing it immediately
1030      * because even in FO mode the operation is not permitted to
1031      * crash or tight-loop; so we _run_ the test, and then ignore
1032      * all the results.)
1033      */
1034     if (fo) {
1035         if (is_double_argtype(t.func->argtype) && is_dhard(t.op1r))
1036             deferred_decline = TRUE;
1037         if (t.func->argtype==at_d2 && is_dhard(t.op2r))
1038             deferred_decline = TRUE;
1039         if (is_single_argtype(t.func->argtype) && is_shard(t.op1r))
1040             deferred_decline = TRUE;
1041         if (t.func->argtype==at_s2 && is_shard(t.op2r))
1042             deferred_decline = TRUE;
1043         if (is_double_rettype(t.func->rettype) && is_dhard(t.resultr))
1044             deferred_decline = TRUE;
1045         if (t.func->rettype==rt_d2 && is_dhard(t.res2))
1046             deferred_decline = TRUE;
1047         if (is_single_argtype(t.func->rettype) && is_shard(t.resultr))
1048             deferred_decline = TRUE;
1049         if (t.func->rettype==rt_s2 && is_shard(t.res2))
1050             deferred_decline = TRUE;
1051         if (t.err == e_ERANGE)
1052             deferred_decline = TRUE;
1053     }
1054 
1055     /*
1056      * Perform the operation
1057      */
1058 
1059     errno = t.in_err == e_EDOM ? EDOM : t.in_err == e_ERANGE ? ERANGE : 0;
1060     if (t.err == e_0)
1061         t.err = t.in_err;
1062     if (t.maybeerr == e_0)
1063         t.maybeerr = t.in_err;
1064 
1065     if(t.func->type == t_func) {
1066         switch(t.func->argtype) {
1067         case at_d: d_res.f = t.func->func.d_d_ptr(d_arg1.f); break;
1068         case at_s: s_res.f = t.func->func.s_s_ptr(s_arg1.f); break;
1069         case at_d2: d_res.f = t.func->func.d2_d_ptr(d_arg1.f, d_arg2.f); break;
1070         case at_s2: s_res.f = t.func->func.s2_s_ptr(s_arg1.f, s_arg2.f); break;
1071         case at_di: d_res.f = t.func->func.di_d_ptr(d_arg1.f, d_arg2.i[dmsd]); break;
1072         case at_si: s_res.f = t.func->func.si_s_ptr(s_arg1.f, s_arg2.i); break;
1073         case at_dip: d_res.f = t.func->func.dip_d_ptr(d_arg1.f, (int*)&intres); break;
1074         case at_sip: s_res.f = t.func->func.sip_s_ptr(s_arg1.f, (int*)&intres); break;
1075         case at_ddp: d_res.f = t.func->func.ddp_d_ptr(d_arg1.f, &d_res2.f); break;
1076         case at_ssp: s_res.f = t.func->func.ssp_s_ptr(s_arg1.f, &s_res2.f); break;
1077         default:
1078             printf("unhandled function: %s\n",t.func->name);
1079             return test_fail;
1080         }
1081     } else {
1082         /* 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); */
1083         switch(t.func->macro_name) {
1084         case m_isfinite: intres = isfinite(d_arg1.f); break;
1085         case m_isinf: intres = isinf(d_arg1.f); break;
1086         case m_isnan: intres = isnan(d_arg1.f); break;
1087         case m_isnormal: intres = isnormal(d_arg1.f); break;
1088         case m_signbit: intres = signbit(d_arg1.f); break;
1089         case m_fpclassify: intres = fpclassify(d_arg1.f); break;
1090         case m_isgreater: intres = isgreater(d_arg1.f, d_arg2.f); break;
1091         case m_isgreaterequal: intres = isgreaterequal(d_arg1.f, d_arg2.f); break;
1092         case m_isless: intres = isless(d_arg1.f, d_arg2.f); break;
1093         case m_islessequal: intres = islessequal(d_arg1.f, d_arg2.f); break;
1094         case m_islessgreater: intres = islessgreater(d_arg1.f, d_arg2.f); break;
1095         case m_isunordered: intres = isunordered(d_arg1.f, d_arg2.f); break;
1096 
1097         case m_isfinitef: intres = isfinite(s_arg1.f); break;
1098         case m_isinff: intres = isinf(s_arg1.f); break;
1099         case m_isnanf: intres = isnan(s_arg1.f); break;
1100         case m_isnormalf: intres = isnormal(s_arg1.f); break;
1101         case m_signbitf: intres = signbit(s_arg1.f); break;
1102         case m_fpclassifyf: intres = fpclassify(s_arg1.f); break;
1103         case m_isgreaterf: intres = isgreater(s_arg1.f, s_arg2.f); break;
1104         case m_isgreaterequalf: intres = isgreaterequal(s_arg1.f, s_arg2.f); break;
1105         case m_islessf: intres = isless(s_arg1.f, s_arg2.f); break;
1106         case m_islessequalf: intres = islessequal(s_arg1.f, s_arg2.f); break;
1107         case m_islessgreaterf: intres = islessgreater(s_arg1.f, s_arg2.f); break;
1108         case m_isunorderedf: intres = isunordered(s_arg1.f, s_arg2.f); break;
1109 
1110         default:
1111             printf("unhandled macro: %s\n",t.func->name);
1112             return test_fail;
1113         }
1114     }
1115 
1116     /*
1117      * Decline the test if the deferred decline flag was set above.
1118      */
1119     if (deferred_decline)
1120         return test_decline;
1121 
1122     /* printf("intres=%i\n",intres); */
1123 
1124     /* Clear the fail text (indicating a pass unless we change it) */
1125     failp[0] = '\0';
1126 
1127     /* Check the IEEE status bits (except INX, which we disregard).
1128      * We don't bother with this for complex numbers, because the
1129      * complex functions are hard to get exactly right and we don't
1130      * have to anyway (C99 annex G is only informative). */
1131     if (!(is_complex_argtype(t.func->argtype) || is_complex_rettype(t.func->rettype))) {
1132         status = fetestexcept(FE_INVALID|FE_DIVBYZERO|FE_OVERFLOW|FE_UNDERFLOW);
1133         if ((status|t.maybestatus|~statusmask) != (t.status|t.maybestatus|~statusmask)) {
1134             if (quiet) failtext[0]='x';
1135             else {
1136                 failp += sprintf(failp,
1137                                  " wrongstatus=%s%s%s%s%s",
1138                                  (status & FE_INVALID ? "i" : ""),
1139                                  (status & FE_DIVBYZERO ? "z" : ""),
1140                                  (status & FE_OVERFLOW ? "o" : ""),
1141                                  (status & FE_UNDERFLOW ? "u" : ""),
1142                                  (status ? "" : "OK"));
1143             }
1144         }
1145     }
1146 
1147     /* Check the result */
1148     {
1149         unsigned resultr[2], resulti[2];
1150         unsigned tresultr[3], tresulti[3], wres;
1151 
1152         switch(t.func->rettype) {
1153         case rt_d:
1154         case rt_d2:
1155             tresultr[0] = t.resultr[0];
1156             tresultr[1] = t.resultr[1];
1157             resultr[0] = d_res.i[dmsd]; resultr[1] = d_res.i[dlsd];
1158             wres = 2;
1159             break;
1160         case rt_i:
1161             tresultr[0] = t.resultr[0];
1162             resultr[0] = intres;
1163             wres = 1;
1164             break;
1165         case rt_s:
1166         case rt_s2:
1167             tresultr[0] = t.resultr[0];
1168             resultr[0] = s_res.i;
1169             wres = 1;
1170             break;
1171         default:
1172             puts("unhandled rettype in runtest");
1173             wres = 0;
1174         }
1175         if(t.resultc != rc_none) {
1176             int err = 0;
1177             switch(t.resultc) {
1178             case rc_zero:
1179                 if(resultr[0] != 0 || resulti[0] != 0 ||
1180                    (wres==2 && (resultr[1] != 0 || resulti[1] != 0))) {
1181                     err = 1;
1182                 }
1183                 break;
1184             case rc_infinity:
1185                 if(wres==1) {
1186                     if(!((resultr[0]&0x7fffffff)==0x7f800000 ||
1187                          (resulti[0]&0x7fffffff)==0x7f800000)) {
1188                         err = 1;
1189                     }
1190                 } else {
1191                   if(!(((resultr[0]&0x7fffffff)==0x7ff00000 && resultr[1]==0) ||
1192                        ((resulti[0]&0x7fffffff)==0x7ff00000 && resulti[1]==0))) {
1193                         err = 1;
1194                     }
1195                 }
1196                 break;
1197             case rc_nan:
1198                 if(wres==1) {
1199                     if(!((resultr[0]&0x7fffffff)>0x7f800000 ||
1200                          (resulti[0]&0x7fffffff)>0x7f800000)) {
1201                         err = 1;
1202                     }
1203                 } else {
1204                     canon_dNaN(resultr);
1205                     canon_dNaN(resulti);
1206                     if(!(((resultr[0]&0x7fffffff)>0x7ff00000 && resultr[1]==1) ||
1207                          ((resulti[0]&0x7fffffff)>0x7ff00000 && resulti[1]==1))) {
1208                         err = 1;
1209                     }
1210                 }
1211                 break;
1212             case rc_finite:
1213                 if(wres==1) {
1214                     if(!((resultr[0]&0x7fffffff)<0x7f800000 ||
1215                          (resulti[0]&0x7fffffff)<0x7f800000)) {
1216                         err = 1;
1217                     }
1218                 } else {
1219                     if(!((resultr[0]&0x7fffffff)<0x7ff00000 ||
1220                          (resulti[0]&0x7fffffff)<0x7ff00000)) {
1221                         err = 1;
1222                     }
1223                 }
1224                 break;
1225             default:
1226                 break;
1227             }
1228             if(err) {
1229                 print_error(t.func->rettype,resultr,"wrongresultr",&failp);
1230                 print_error(t.func->rettype,resulti,"wrongresulti",&failp);
1231             }
1232         } else if (t.nresult > wres) {
1233             /*
1234              * The test case data has provided the result to more
1235              * than double precision. Instead of testing exact
1236              * equality, we test against our maximum error
1237              * tolerance.
1238              */
1239             int rshift, ishift;
1240             long long ulpsr, ulpsi, ulptolerance;
1241 
1242             tresultr[wres] = t.resultr[wres] << (32-EXTRABITS);
1243             tresulti[wres] = t.resulti[wres] << (32-EXTRABITS);
1244             if(strict) {
1245                 ulptolerance = 4096; /* one ulp */
1246             } else {
1247                 ulptolerance = t.func->tolerance;
1248             }
1249             rshift = ishift = 0;
1250             if (ulptolerance & ABSLOWERBOUND) {
1251                 /*
1252                  * Hack for the lgamma functions, which have an
1253                  * error behaviour that can't conveniently be
1254                  * characterised in pure ULPs. Really, we want to
1255                  * say that the error in lgamma is "at most N ULPs,
1256                  * or at most an absolute error of X, whichever is
1257                  * larger", for appropriately chosen N,X. But since
1258                  * these two functions are the only cases where it
1259                  * arises, I haven't bothered to do it in a nice way
1260                  * in the function table above.
1261                  *
1262                  * (The difficult cases arise with negative input
1263                  * values such that |gamma(x)| is very near to 1; in
1264                  * this situation implementations tend to separately
1265                  * compute lgamma(|x|) and the log of the correction
1266                  * term from the Euler reflection formula, and
1267                  * subtract - which catastrophically loses
1268                  * significance.)
1269                  *
1270                  * As far as I can tell, nobody cares about this:
1271                  * GNU libm doesn't get those cases right either,
1272                  * and OpenCL explicitly doesn't state a ULP error
1273                  * limit for lgamma. So my guess is that this is
1274                  * simply considered acceptable error behaviour for
1275                  * this particular function, and hence I feel free
1276                  * to allow for it here.
1277                  */
1278                 ulptolerance &= ~ABSLOWERBOUND;
1279                 if (t.op1r[0] & 0x80000000) {
1280                     if (t.func->rettype == rt_d)
1281                         rshift = 0x400 - ((tresultr[0] >> 20) & 0x7ff);
1282                     else if (t.func->rettype == rt_s)
1283                         rshift = 0x80 - ((tresultr[0] >> 23) & 0xff);
1284                     if (rshift < 0)
1285                         rshift = 0;
1286                 }
1287             }
1288             if (ulptolerance & PLUSMINUSPIO2) {
1289                 ulptolerance &= ~PLUSMINUSPIO2;
1290                 /*
1291                  * Hack for range reduction, which can reduce
1292                  * borderline cases in the wrong direction, i.e.
1293                  * return a value just outside one end of the interval
1294                  * [-pi/4,+pi/4] when it could have returned a value
1295                  * just inside the other end by subtracting an
1296                  * adjacent multiple of pi/2.
1297                  *
1298                  * We tolerate this, up to a point, because the
1299                  * trigonometric functions making use of the output of
1300                  * rred can cope and because making the range reducer
1301                  * do the exactly right thing in every case would be
1302                  * more expensive.
1303                  */
1304                 if (wres == 1) {
1305                     /* Upper bound of overshoot derived in rredf.h */
1306                     if ((resultr[0]&0x7FFFFFFF) <= 0x3f494b02 &&
1307                         (resultr[0]&0x7FFFFFFF) > 0x3f490fda &&
1308                         (resultr[0]&0x80000000) != (tresultr[0]&0x80000000)) {
1309                         unsigned long long val;
1310                         val = tresultr[0];
1311                         val = (val << 32) | tresultr[1];
1312                         /*
1313                          * Compute the alternative permitted result by
1314                          * subtracting from the sum of the extended
1315                          * single-precision bit patterns of +pi/4 and
1316                          * -pi/4. This is a horrible hack which only
1317                          * works because we can be confident that
1318                          * numbers in this range all have the same
1319                          * exponent!
1320                          */
1321                         val = 0xfe921fb54442d184ULL - val;
1322                         tresultr[0] = val >> 32;
1323                         tresultr[1] = (val >> (32-EXTRABITS)) << (32-EXTRABITS);
1324                         /*
1325                          * Also, expect a correspondingly different
1326                          * value of res2 as a result of this change.
1327                          * The adjustment depends on whether we just
1328                          * flipped the result from + to - or vice
1329                          * versa.
1330                          */
1331                         if (resultr[0] & 0x80000000) {
1332                             res2_adjust = +1;
1333                         } else {
1334                             res2_adjust = -1;
1335                         }
1336                     }
1337                 }
1338             }
1339             ulpsr = calc_error(resultr, tresultr, rshift, t.func->rettype);
1340             if(is_complex_rettype(t.func->rettype)) {
1341                 ulpsi = calc_error(resulti, tresulti, ishift, t.func->rettype);
1342             } else {
1343                 ulpsi = 0;
1344             }
1345             unsigned *rr = (ulpsr > ulptolerance || ulpsr < -ulptolerance) ? resultr : NULL;
1346             unsigned *ri = (ulpsi > ulptolerance || ulpsi < -ulptolerance) ? resulti : NULL;
1347 /*             printf("tolerance=%i, ulpsr=%i, ulpsi=%i, rr=%p, ri=%p\n",ulptolerance,ulpsr,ulpsi,rr,ri); */
1348             if (rr || ri) {
1349                 if (quiet) failtext[0]='x';
1350                 else {
1351                     print_error(t.func->rettype,rr,"wrongresultr",&failp);
1352                     print_error(t.func->rettype,ri,"wrongresulti",&failp);
1353                     print_ulps(t.func->rettype,rr ? ulpsr : 0, ri ? ulpsi : 0,&failp);
1354                 }
1355             }
1356         } else {
1357             if(is_complex_rettype(t.func->rettype))
1358                 /*
1359                  * Complex functions are not fully supported,
1360                  * this is unreachable, but prevents warnings.
1361                  */
1362                 abort();
1363             /*
1364              * The test case data has provided the result in
1365              * exactly the output precision. Therefore we must
1366              * complain about _any_ violation.
1367              */
1368             switch(t.func->rettype) {
1369             case rt_dc:
1370                 canon_dNaN(tresulti);
1371                 canon_dNaN(resulti);
1372                 if (fo) {
1373                     dnormzero(tresulti);
1374                     dnormzero(resulti);
1375                 }
1376                 /* deliberate fall-through */
1377             case rt_d:
1378                 canon_dNaN(tresultr);
1379                 canon_dNaN(resultr);
1380                 if (fo) {
1381                     dnormzero(tresultr);
1382                     dnormzero(resultr);
1383                 }
1384                 break;
1385             case rt_sc:
1386                 canon_sNaN(tresulti);
1387                 canon_sNaN(resulti);
1388                 if (fo) {
1389                     snormzero(tresulti);
1390                     snormzero(resulti);
1391                 }
1392                 /* deliberate fall-through */
1393             case rt_s:
1394                 canon_sNaN(tresultr);
1395                 canon_sNaN(resultr);
1396                 if (fo) {
1397                     snormzero(tresultr);
1398                     snormzero(resultr);
1399                 }
1400                 break;
1401             default:
1402                 break;
1403             }
1404             if(is_complex_rettype(t.func->rettype)) {
1405                 unsigned *rr, *ri;
1406                 if(resultr[0] != tresultr[0] ||
1407                    (wres > 1 && resultr[1] != tresultr[1])) {
1408                     rr = resultr;
1409                 } else {
1410                     rr = NULL;
1411                 }
1412                 if(resulti[0] != tresulti[0] ||
1413                    (wres > 1 && resulti[1] != tresulti[1])) {
1414                     ri = resulti;
1415                 } else {
1416                     ri = NULL;
1417                 }
1418                 if(rr || ri) {
1419                     if (quiet) failtext[0]='x';
1420                     print_error(t.func->rettype,rr,"wrongresultr",&failp);
1421                     print_error(t.func->rettype,ri,"wrongresulti",&failp);
1422                 }
1423             } else if (resultr[0] != tresultr[0] ||
1424                        (wres > 1 && resultr[1] != tresultr[1])) {
1425                 if (quiet) failtext[0]='x';
1426                 print_error(t.func->rettype,resultr,"wrongresult",&failp);
1427             }
1428         }
1429         /*
1430          * Now test res2, for those functions (frexp, modf, rred)
1431          * which use it.
1432          */
1433         if (t.func->func.ptr == &frexp || t.func->func.ptr == &frexpf ||
1434             t.func->macro_name == m_rred || t.func->macro_name == m_rredf) {
1435             unsigned tres2 = t.res2[0];
1436             if (res2_adjust) {
1437                 /* Fix for range reduction, propagated from further up */
1438                 tres2 = (tres2 + res2_adjust) & 3;
1439             }
1440             if (tres2 != intres) {
1441                 if (quiet) failtext[0]='x';
1442                 else {
1443                     failp += sprintf(failp,
1444                                      " wrongres2=%08x", intres);
1445                 }
1446             }
1447         } else if (t.func->func.ptr == &modf || t.func->func.ptr == &modff) {
1448             tresultr[0] = t.res2[0];
1449             tresultr[1] = t.res2[1];
1450             if (is_double_rettype(t.func->rettype)) {
1451                 canon_dNaN(tresultr);
1452                 resultr[0] = d_res2.i[dmsd];
1453                 resultr[1] = d_res2.i[dlsd];
1454                 canon_dNaN(resultr);
1455                 if (fo) {
1456                     dnormzero(tresultr);
1457                     dnormzero(resultr);
1458                 }
1459             } else {
1460                 canon_sNaN(tresultr);
1461                 resultr[0] = s_res2.i;
1462                 resultr[1] = s_res2.i;
1463                 canon_sNaN(resultr);
1464                 if (fo) {
1465                     snormzero(tresultr);
1466                     snormzero(resultr);
1467                 }
1468             }
1469             if (resultr[0] != tresultr[0] ||
1470                 (wres > 1 && resultr[1] != tresultr[1])) {
1471                 if (quiet) failtext[0]='x';
1472                 else {
1473                     if (is_double_rettype(t.func->rettype))
1474                         failp += sprintf(failp, " wrongres2=%08x.%08x",
1475                                          resultr[0], resultr[1]);
1476                     else
1477                         failp += sprintf(failp, " wrongres2=%08x",
1478                                          resultr[0]);
1479                 }
1480             }
1481         }
1482     }
1483 
1484     /* Check errno */
1485     err = (errno == EDOM ? e_EDOM : errno == ERANGE ? e_ERANGE : e_0);
1486     if (err != t.err && err != t.maybeerr) {
1487         if (quiet) failtext[0]='x';
1488         else {
1489             failp += sprintf(failp, " wrongerrno=%s expecterrno=%s ", errnos[err], errnos[t.err]);
1490         }
1491     }
1492 
1493     return *failtext ? test_fail : test_pass;
1494 }
1495 
1496 int passed, failed, declined;
1497 
1498 void runtests(char *name, FILE *fp) {
1499     char testbuf[512], linebuf[512];
1500     int lineno = 1;
1501     testdetail test;
1502 
1503     test.valid = 0;
1504 
1505     if (verbose) printf("runtests: %s\n", name);
1506     while (fgets(testbuf, sizeof(testbuf), fp)) {
1507         int res, print_errno;
1508         testbuf[strcspn(testbuf, "\r\n")] = '\0';
1509         strcpy(linebuf, testbuf);
1510         test = parsetest(testbuf, test);
1511         print_errno = 0;
1512         while (test.in_err < test.in_err_limit) {
1513             res = runtest(test);
1514             if (res == test_pass) {
1515                 if (verbose)
1516                     printf("%s:%d: pass\n", name, lineno);
1517                 ++passed;
1518             } else if (res == test_decline) {
1519                 if (verbose)
1520                     printf("%s:%d: declined\n", name, lineno);
1521                 ++declined;
1522             } else if (res == test_fail) {
1523                 if (!quiet)
1524                     printf("%s:%d: FAIL%s: %s%s%s%s\n", name, lineno,
1525                            test.random ? " (random)" : "",
1526                            linebuf,
1527                            print_errno ? " errno_in=" : "",
1528                            print_errno ? errnos[test.in_err] : "",
1529                            failtext);
1530                 ++failed;
1531             } else if (res == test_invalid) {
1532                 printf("%s:%d: malformed: %s\n", name, lineno, linebuf);
1533                 ++failed;
1534             }
1535             test.in_err++;
1536             print_errno = 1;
1537         }
1538         lineno++;
1539     }
1540 }
1541 
1542 int main(int ac, char **av) {
1543     char **files;
1544     int i, nfiles = 0;
1545     dbl d;
1546 
1547 #ifdef MICROLIB
1548     /*
1549      * Invent argc and argv ourselves.
1550      */
1551     char *argv[256];
1552     char args[256];
1553     {
1554         int sargs[2];
1555         char *p;
1556 
1557         ac = 0;
1558 
1559         sargs[0]=(int)args;
1560         sargs[1]=(int)sizeof(args);
1561         if (!__semihost(0x15, sargs)) {
1562             args[sizeof(args)-1] = '\0';   /* just in case */
1563             p = args;
1564             while (1) {
1565                 while (*p == ' ' || *p == '\t') p++;
1566                 if (!*p) break;
1567                 argv[ac++] = p;
1568                 while (*p && *p != ' ' && *p != '\t') p++;
1569                 if (*p) *p++ = '\0';
1570             }
1571         }
1572 
1573         av = argv;
1574     }
1575 #endif
1576 
1577     /* Sort tfuncs */
1578     qsort(tfuncs, sizeof(tfuncs)/sizeof(test_func), sizeof(test_func), &compare_tfuncs);
1579 
1580     /*
1581      * Autodetect the `double' endianness.
1582      */
1583     dmsd = 0;
1584     d.f = 1.0;                       /* 0x3ff00000 / 0x00000000 */
1585     if (d.i[dmsd] == 0) {
1586         dmsd = 1;
1587     }
1588     /*
1589      * Now dmsd denotes what the compiler thinks we're at. Let's
1590      * check that it agrees with what the runtime thinks.
1591      */
1592     d.i[0] = d.i[1] = 0x11111111;/* a random +ve number */
1593     d.f /= d.f;                    /* must now be one */
1594     if (d.i[dmsd] == 0) {
1595         fprintf(stderr, "YIKES! Compiler and runtime disagree on endianness"
1596                 " of `double'. Bailing out\n");
1597         return 1;
1598     }
1599     dlsd = !dmsd;
1600 
1601     /* default is terse */
1602     verbose = 0;
1603     fo = 0;
1604     strict = 0;
1605 
1606     files = (char **)malloc((ac+1) * sizeof(char *));
1607     if (!files) {
1608         fprintf(stderr, "initial malloc failed!\n");
1609         return 1;
1610     }
1611 #ifdef NOCMDLINE
1612     files[nfiles++] = "testfile";
1613 #endif
1614 
1615     while (--ac) {
1616         char *p = *++av;
1617         if (*p == '-') {
1618             static char *options[] = {
1619                 "-fo",
1620 #if 0
1621                 "-noinexact",
1622                 "-noround",
1623 #endif
1624                 "-nostatus",
1625                 "-quiet",
1626                 "-strict",
1627                 "-v",
1628                 "-verbose",
1629             };
1630             enum {
1631                 op_fo,
1632 #if 0
1633                 op_noinexact,
1634                 op_noround,
1635 #endif
1636                 op_nostatus,
1637                 op_quiet,
1638                 op_strict,
1639                 op_v,
1640                 op_verbose,
1641             };
1642             switch (find(p, options, sizeof(options))) {
1643             case op_quiet:
1644                 quiet = 1;
1645                 break;
1646 #if 0
1647             case op_noinexact:
1648                 statusmask &= 0x0F;    /* remove bit 4 */
1649                 break;
1650             case op_noround:
1651                 doround = 0;
1652                 break;
1653 #endif
1654             case op_nostatus:        /* no status word => noinx,noround */
1655                 statusmask = 0;
1656                 doround = 0;
1657                 break;
1658             case op_v:
1659             case op_verbose:
1660                 verbose = 1;
1661                 break;
1662             case op_fo:
1663                 fo = 1;
1664                 break;
1665             case op_strict: /* tolerance is 1 ulp */
1666                 strict = 1;
1667                 break;
1668             default:
1669                 fprintf(stderr, "unrecognised option: %s\n", p);
1670                 break;
1671             }
1672         } else {
1673             files[nfiles++] = p;
1674         }
1675     }
1676 
1677     passed = failed = declined = 0;
1678 
1679     if (nfiles) {
1680         for (i = 0; i < nfiles; i++) {
1681             FILE *fp = fopen(files[i], "r");
1682             if (!fp) {
1683                 fprintf(stderr, "Couldn't open %s\n", files[i]);
1684             } else
1685                 runtests(files[i], fp);
1686         }
1687     } else
1688         runtests("(stdin)", stdin);
1689 
1690     printf("Completed. Passed %d, failed %d (total %d",
1691            passed, failed, passed+failed);
1692     if (declined)
1693         printf(" plus %d declined", declined);
1694     printf(")\n");
1695     if (failed || passed == 0)
1696         return 1;
1697     printf("** TEST PASSED OK **\n");
1698     return 0;
1699 }
1700 
1701 void undef_func() {
1702     failed++;
1703     puts("ERROR: undefined function called");
1704 }
1705