1 /*
2  * ULP error checking tool for math functions.
3  *
4  * Copyright (c) 2019-2020, Arm Limited.
5  * SPDX-License-Identifier: MIT
6  */
7 
8 #include <ctype.h>
9 #include <fenv.h>
10 #include <float.h>
11 #include <math.h>
12 #include <stdint.h>
13 #include <stdio.h>
14 #include <stdlib.h>
15 #include <string.h>
16 #include "mathlib.h"
17 
18 /* Don't depend on mpfr by default.  */
19 #ifndef USE_MPFR
20 # define USE_MPFR 0
21 #endif
22 #if USE_MPFR
23 # include <mpfr.h>
24 #endif
25 
26 #ifndef WANT_VMATH
27 /* Enable the build of vector math code.  */
28 # define WANT_VMATH 1
29 #endif
30 
31 static inline uint64_t
32 asuint64 (double f)
33 {
34   union
35   {
36     double f;
37     uint64_t i;
38   } u = {f};
39   return u.i;
40 }
41 
42 static inline double
43 asdouble (uint64_t i)
44 {
45   union
46   {
47     uint64_t i;
48     double f;
49   } u = {i};
50   return u.f;
51 }
52 
53 static inline uint32_t
54 asuint (float f)
55 {
56   union
57   {
58     float f;
59     uint32_t i;
60   } u = {f};
61   return u.i;
62 }
63 
64 static inline float
65 asfloat (uint32_t i)
66 {
67   union
68   {
69     uint32_t i;
70     float f;
71   } u = {i};
72   return u.f;
73 }
74 
75 static uint64_t seed = 0x0123456789abcdef;
76 static uint64_t
77 rand64 (void)
78 {
79   seed = 6364136223846793005ull * seed + 1;
80   return seed ^ (seed >> 32);
81 }
82 
83 /* Uniform random in [0,n].  */
84 static uint64_t
85 randn (uint64_t n)
86 {
87   uint64_t r, m;
88 
89   if (n == 0)
90     return 0;
91   n++;
92   if (n == 0)
93     return rand64 ();
94   for (;;)
95     {
96       r = rand64 ();
97       m = r % n;
98       if (r - m <= -n)
99 	return m;
100     }
101 }
102 
103 struct gen
104 {
105   uint64_t start;
106   uint64_t len;
107   uint64_t start2;
108   uint64_t len2;
109   uint64_t off;
110   uint64_t step;
111   uint64_t cnt;
112 };
113 
114 struct args_f1
115 {
116   float x;
117 };
118 
119 struct args_f2
120 {
121   float x;
122   float x2;
123 };
124 
125 struct args_d1
126 {
127   double x;
128 };
129 
130 struct args_d2
131 {
132   double x;
133   double x2;
134 };
135 
136 /* result = y + tail*2^ulpexp.  */
137 struct ret_f
138 {
139   float y;
140   double tail;
141   int ulpexp;
142   int ex;
143   int ex_may;
144 };
145 
146 struct ret_d
147 {
148   double y;
149   double tail;
150   int ulpexp;
151   int ex;
152   int ex_may;
153 };
154 
155 static inline uint64_t
156 next1 (struct gen *g)
157 {
158   /* For single argument use randomized incremental steps,
159      that produce dense sampling without collisions and allow
160      testing all inputs in a range.  */
161   uint64_t r = g->start + g->off;
162   g->off += g->step + randn (g->step / 2);
163   if (g->off > g->len)
164     g->off -= g->len; /* hack.  */
165   return r;
166 }
167 
168 static inline uint64_t
169 next2 (uint64_t *x2, struct gen *g)
170 {
171   /* For two arguments use uniform random sampling.  */
172   uint64_t r = g->start + randn (g->len);
173   *x2 = g->start2 + randn (g->len2);
174   return r;
175 }
176 
177 static struct args_f1
178 next_f1 (void *g)
179 {
180   return (struct args_f1){asfloat (next1 (g))};
181 }
182 
183 static struct args_f2
184 next_f2 (void *g)
185 {
186   uint64_t x2;
187   uint64_t x = next2 (&x2, g);
188   return (struct args_f2){asfloat (x), asfloat (x2)};
189 }
190 
191 static struct args_d1
192 next_d1 (void *g)
193 {
194   return (struct args_d1){asdouble (next1 (g))};
195 }
196 
197 static struct args_d2
198 next_d2 (void *g)
199 {
200   uint64_t x2;
201   uint64_t x = next2 (&x2, g);
202   return (struct args_d2){asdouble (x), asdouble (x2)};
203 }
204 
205 struct conf
206 {
207   int r;
208   int rc;
209   int quiet;
210   int mpfr;
211   int fenv;
212   unsigned long long n;
213   double softlim;
214   double errlim;
215 };
216 
217 /* Wrappers for sincos.  */
218 static float sincosf_sinf(float x) {(void)cosf(x); return sinf(x);}
219 static float sincosf_cosf(float x) {(void)sinf(x); return cosf(x);}
220 static double sincos_sin(double x) {(void)cos(x); return sin(x);}
221 static double sincos_cos(double x) {(void)sin(x); return cos(x);}
222 #if USE_MPFR
223 static int sincos_mpfr_sin(mpfr_t y, const mpfr_t x, mpfr_rnd_t r) { mpfr_cos(y,x,r); return mpfr_sin(y,x,r); }
224 static int sincos_mpfr_cos(mpfr_t y, const mpfr_t x, mpfr_rnd_t r) { mpfr_sin(y,x,r); return mpfr_cos(y,x,r); }
225 #endif
226 
227 /* A bit of a hack: call vector functions twice with the same
228    input in lane 0 but a different value in other lanes: once
229    with an in-range value and then with a special case value.  */
230 static int secondcall;
231 
232 /* Wrappers for vector functions.  */
233 #if __aarch64__ && WANT_VMATH
234 typedef __f32x4_t v_float;
235 typedef __f64x2_t v_double;
236 static const float fv[2] = {1.0f, -INFINITY};
237 static const double dv[2] = {1.0, -INFINITY};
238 static inline v_float argf(float x) { return (v_float){x,x,x,fv[secondcall]}; }
239 static inline v_double argd(double x) { return (v_double){x,dv[secondcall]}; }
240 
241 static float v_sinf(float x) { return __v_sinf(argf(x))[0]; }
242 static float v_cosf(float x) { return __v_cosf(argf(x))[0]; }
243 static float v_expf_1u(float x) { return __v_expf_1u(argf(x))[0]; }
244 static float v_expf(float x) { return __v_expf(argf(x))[0]; }
245 static float v_exp2f_1u(float x) { return __v_exp2f_1u(argf(x))[0]; }
246 static float v_exp2f(float x) { return __v_exp2f(argf(x))[0]; }
247 static float v_logf(float x) { return __v_logf(argf(x))[0]; }
248 static float v_powf(float x, float y) { return __v_powf(argf(x),argf(y))[0]; }
249 static double v_sin(double x) { return __v_sin(argd(x))[0]; }
250 static double v_cos(double x) { return __v_cos(argd(x))[0]; }
251 static double v_exp(double x) { return __v_exp(argd(x))[0]; }
252 static double v_log(double x) { return __v_log(argd(x))[0]; }
253 static double v_pow(double x, double y) { return __v_pow(argd(x),argd(y))[0]; }
254 #ifdef __vpcs
255 static float vn_sinf(float x) { return __vn_sinf(argf(x))[0]; }
256 static float vn_cosf(float x) { return __vn_cosf(argf(x))[0]; }
257 static float vn_expf_1u(float x) { return __vn_expf_1u(argf(x))[0]; }
258 static float vn_expf(float x) { return __vn_expf(argf(x))[0]; }
259 static float vn_exp2f_1u(float x) { return __vn_exp2f_1u(argf(x))[0]; }
260 static float vn_exp2f(float x) { return __vn_exp2f(argf(x))[0]; }
261 static float vn_logf(float x) { return __vn_logf(argf(x))[0]; }
262 static float vn_powf(float x, float y) { return __vn_powf(argf(x),argf(y))[0]; }
263 static double vn_sin(double x) { return __vn_sin(argd(x))[0]; }
264 static double vn_cos(double x) { return __vn_cos(argd(x))[0]; }
265 static double vn_exp(double x) { return __vn_exp(argd(x))[0]; }
266 static double vn_log(double x) { return __vn_log(argd(x))[0]; }
267 static double vn_pow(double x, double y) { return __vn_pow(argd(x),argd(y))[0]; }
268 static float Z_sinf(float x) { return _ZGVnN4v_sinf(argf(x))[0]; }
269 static float Z_cosf(float x) { return _ZGVnN4v_cosf(argf(x))[0]; }
270 static float Z_expf(float x) { return _ZGVnN4v_expf(argf(x))[0]; }
271 static float Z_exp2f(float x) { return _ZGVnN4v_exp2f(argf(x))[0]; }
272 static float Z_logf(float x) { return _ZGVnN4v_logf(argf(x))[0]; }
273 static float Z_powf(float x, float y) { return _ZGVnN4vv_powf(argf(x),argf(y))[0]; }
274 static double Z_sin(double x) { return _ZGVnN2v_sin(argd(x))[0]; }
275 static double Z_cos(double x) { return _ZGVnN2v_cos(argd(x))[0]; }
276 static double Z_exp(double x) { return _ZGVnN2v_exp(argd(x))[0]; }
277 static double Z_log(double x) { return _ZGVnN2v_log(argd(x))[0]; }
278 static double Z_pow(double x, double y) { return _ZGVnN2vv_pow(argd(x),argd(y))[0]; }
279 #endif
280 #endif
281 
282 struct fun
283 {
284   const char *name;
285   int arity;
286   int singleprec;
287   int twice;
288   union
289   {
290     float (*f1) (float);
291     float (*f2) (float, float);
292     double (*d1) (double);
293     double (*d2) (double, double);
294   } fun;
295   union
296   {
297     double (*f1) (double);
298     double (*f2) (double, double);
299     long double (*d1) (long double);
300     long double (*d2) (long double, long double);
301   } fun_long;
302 #if USE_MPFR
303   union
304   {
305     int (*f1) (mpfr_t, const mpfr_t, mpfr_rnd_t);
306     int (*f2) (mpfr_t, const mpfr_t, const mpfr_t, mpfr_rnd_t);
307     int (*d1) (mpfr_t, const mpfr_t, mpfr_rnd_t);
308     int (*d2) (mpfr_t, const mpfr_t, const mpfr_t, mpfr_rnd_t);
309   } fun_mpfr;
310 #endif
311 };
312 
313 static const struct fun fun[] = {
314 #if USE_MPFR
315 # define F(x, x_wrap, x_long, x_mpfr, a, s, t, twice) \
316   {#x, a, s, twice, {.t = x_wrap}, {.t = x_long}, {.t = x_mpfr}},
317 #else
318 # define F(x, x_wrap, x_long, x_mpfr, a, s, t, twice) \
319   {#x, a, s, twice, {.t = x_wrap}, {.t = x_long}},
320 #endif
321 #define F1(x) F (x##f, x##f, x, mpfr_##x, 1, 1, f1, 0)
322 #define F2(x) F (x##f, x##f, x, mpfr_##x, 2, 1, f2, 0)
323 #define D1(x) F (x, x, x##l, mpfr_##x, 1, 0, d1, 0)
324 #define D2(x) F (x, x, x##l, mpfr_##x, 2, 0, d2, 0)
325  F1 (sin)
326  F1 (cos)
327  F (sincosf_sinf, sincosf_sinf, sincos_sin, sincos_mpfr_sin, 1, 1, f1, 0)
328  F (sincosf_cosf, sincosf_cosf, sincos_cos, sincos_mpfr_cos, 1, 1, f1, 0)
329  F1 (exp)
330  F1 (exp2)
331  F1 (log)
332  F1 (log2)
333  F2 (pow)
334  F1 (erf)
335  D1 (exp)
336  D1 (exp2)
337  D1 (log)
338  D1 (log2)
339  D2 (pow)
340  D1 (erf)
341 #if WANT_VMATH
342  F (__s_sinf, __s_sinf, sin, mpfr_sin, 1, 1, f1, 0)
343  F (__s_cosf, __s_cosf, cos, mpfr_cos, 1, 1, f1, 0)
344  F (__s_expf_1u, __s_expf_1u, exp, mpfr_exp, 1, 1, f1, 0)
345  F (__s_expf, __s_expf, exp, mpfr_exp, 1, 1, f1, 0)
346  F (__s_exp2f_1u, __s_exp2f_1u, exp2, mpfr_exp2, 1, 1, f1, 0)
347  F (__s_exp2f, __s_exp2f, exp2, mpfr_exp2, 1, 1, f1, 0)
348  F (__s_powf, __s_powf, pow, mpfr_pow, 2, 1, f2, 0)
349  F (__s_logf, __s_logf, log, mpfr_log, 1, 1, f1, 0)
350  F (__s_sin, __s_sin, sinl, mpfr_sin, 1, 0, d1, 0)
351  F (__s_cos, __s_cos, cosl, mpfr_cos, 1, 0, d1, 0)
352  F (__s_exp, __s_exp, expl, mpfr_exp, 1, 0, d1, 0)
353  F (__s_log, __s_log, logl, mpfr_log, 1, 0, d1, 0)
354  F (__s_pow, __s_pow, powl, mpfr_pow, 2, 0, d2, 0)
355 #if __aarch64__
356  F (__v_sinf, v_sinf, sin, mpfr_sin, 1, 1, f1, 1)
357  F (__v_cosf, v_cosf, cos, mpfr_cos, 1, 1, f1, 1)
358  F (__v_expf_1u, v_expf_1u, exp, mpfr_exp, 1, 1, f1, 1)
359  F (__v_expf, v_expf, exp, mpfr_exp, 1, 1, f1, 1)
360  F (__v_exp2f_1u, v_exp2f_1u, exp2, mpfr_exp2, 1, 1, f1, 1)
361  F (__v_exp2f, v_exp2f, exp2, mpfr_exp2, 1, 1, f1, 1)
362  F (__v_logf, v_logf, log, mpfr_log, 1, 1, f1, 1)
363  F (__v_powf, v_powf, pow, mpfr_pow, 2, 1, f2, 1)
364  F (__v_sin, v_sin, sinl, mpfr_sin, 1, 0, d1, 1)
365  F (__v_cos, v_cos, cosl, mpfr_cos, 1, 0, d1, 1)
366  F (__v_exp, v_exp, expl, mpfr_exp, 1, 0, d1, 1)
367  F (__v_log, v_log, logl, mpfr_log, 1, 0, d1, 1)
368  F (__v_pow, v_pow, powl, mpfr_pow, 2, 0, d2, 1)
369 #ifdef __vpcs
370  F (__vn_sinf, vn_sinf, sin, mpfr_sin, 1, 1, f1, 1)
371  F (__vn_cosf, vn_cosf, cos, mpfr_cos, 1, 1, f1, 1)
372  F (__vn_expf_1u, vn_expf_1u, exp, mpfr_exp, 1, 1, f1, 1)
373  F (__vn_expf, vn_expf, exp, mpfr_exp, 1, 1, f1, 1)
374  F (__vn_exp2f_1u, vn_exp2f_1u, exp2, mpfr_exp2, 1, 1, f1, 1)
375  F (__vn_exp2f, vn_exp2f, exp2, mpfr_exp2, 1, 1, f1, 1)
376  F (__vn_logf, vn_logf, log, mpfr_log, 1, 1, f1, 1)
377  F (__vn_powf, vn_powf, pow, mpfr_pow, 2, 1, f2, 1)
378  F (__vn_sin, vn_sin, sinl, mpfr_sin, 1, 0, d1, 1)
379  F (__vn_cos, vn_cos, cosl, mpfr_cos, 1, 0, d1, 1)
380  F (__vn_exp, vn_exp, expl, mpfr_exp, 1, 0, d1, 1)
381  F (__vn_log, vn_log, logl, mpfr_log, 1, 0, d1, 1)
382  F (__vn_pow, vn_pow, powl, mpfr_pow, 2, 0, d2, 1)
383  F (_ZGVnN4v_sinf, Z_sinf, sin, mpfr_sin, 1, 1, f1, 1)
384  F (_ZGVnN4v_cosf, Z_cosf, cos, mpfr_cos, 1, 1, f1, 1)
385  F (_ZGVnN4v_expf, Z_expf, exp, mpfr_exp, 1, 1, f1, 1)
386  F (_ZGVnN4v_exp2f, Z_exp2f, exp2, mpfr_exp2, 1, 1, f1, 1)
387  F (_ZGVnN4v_logf, Z_logf, log, mpfr_log, 1, 1, f1, 1)
388  F (_ZGVnN4vv_powf, Z_powf, pow, mpfr_pow, 2, 1, f2, 1)
389  F (_ZGVnN2v_sin, Z_sin, sinl, mpfr_sin, 1, 0, d1, 1)
390  F (_ZGVnN2v_cos, Z_cos, cosl, mpfr_cos, 1, 0, d1, 1)
391  F (_ZGVnN2v_exp, Z_exp, expl, mpfr_exp, 1, 0, d1, 1)
392  F (_ZGVnN2v_log, Z_log, logl, mpfr_log, 1, 0, d1, 1)
393  F (_ZGVnN2vv_pow, Z_pow, powl, mpfr_pow, 2, 0, d2, 1)
394 #endif
395 #endif
396 #endif
397 #undef F
398 #undef F1
399 #undef F2
400 #undef D1
401 #undef D2
402  {0}};
403 
404 /* Boilerplate for generic calls.  */
405 
406 static inline int
407 ulpscale_f (float x)
408 {
409   int e = asuint (x) >> 23 & 0xff;
410   if (!e)
411     e++;
412   return e - 0x7f - 23;
413 }
414 static inline int
415 ulpscale_d (double x)
416 {
417   int e = asuint64 (x) >> 52 & 0x7ff;
418   if (!e)
419     e++;
420   return e - 0x3ff - 52;
421 }
422 static inline float
423 call_f1 (const struct fun *f, struct args_f1 a)
424 {
425   return f->fun.f1 (a.x);
426 }
427 static inline float
428 call_f2 (const struct fun *f, struct args_f2 a)
429 {
430   return f->fun.f2 (a.x, a.x2);
431 }
432 
433 static inline double
434 call_d1 (const struct fun *f, struct args_d1 a)
435 {
436   return f->fun.d1 (a.x);
437 }
438 static inline double
439 call_d2 (const struct fun *f, struct args_d2 a)
440 {
441   return f->fun.d2 (a.x, a.x2);
442 }
443 static inline double
444 call_long_f1 (const struct fun *f, struct args_f1 a)
445 {
446   return f->fun_long.f1 (a.x);
447 }
448 static inline double
449 call_long_f2 (const struct fun *f, struct args_f2 a)
450 {
451   return f->fun_long.f2 (a.x, a.x2);
452 }
453 static inline long double
454 call_long_d1 (const struct fun *f, struct args_d1 a)
455 {
456   return f->fun_long.d1 (a.x);
457 }
458 static inline long double
459 call_long_d2 (const struct fun *f, struct args_d2 a)
460 {
461   return f->fun_long.d2 (a.x, a.x2);
462 }
463 static inline void
464 printcall_f1 (const struct fun *f, struct args_f1 a)
465 {
466   printf ("%s(%a)", f->name, a.x);
467 }
468 static inline void
469 printcall_f2 (const struct fun *f, struct args_f2 a)
470 {
471   printf ("%s(%a, %a)", f->name, a.x, a.x2);
472 }
473 static inline void
474 printcall_d1 (const struct fun *f, struct args_d1 a)
475 {
476   printf ("%s(%a)", f->name, a.x);
477 }
478 static inline void
479 printcall_d2 (const struct fun *f, struct args_d2 a)
480 {
481   printf ("%s(%a, %a)", f->name, a.x, a.x2);
482 }
483 static inline void
484 printgen_f1 (const struct fun *f, struct gen *gen)
485 {
486   printf ("%s in [%a;%a]", f->name, asfloat (gen->start),
487 	  asfloat (gen->start + gen->len));
488 }
489 static inline void
490 printgen_f2 (const struct fun *f, struct gen *gen)
491 {
492   printf ("%s in [%a;%a] x [%a;%a]", f->name, asfloat (gen->start),
493 	  asfloat (gen->start + gen->len), asfloat (gen->start2),
494 	  asfloat (gen->start2 + gen->len2));
495 }
496 static inline void
497 printgen_d1 (const struct fun *f, struct gen *gen)
498 {
499   printf ("%s in [%a;%a]", f->name, asdouble (gen->start),
500 	  asdouble (gen->start + gen->len));
501 }
502 static inline void
503 printgen_d2 (const struct fun *f, struct gen *gen)
504 {
505   printf ("%s in [%a;%a] x [%a;%a]", f->name, asdouble (gen->start),
506 	  asdouble (gen->start + gen->len), asdouble (gen->start2),
507 	  asdouble (gen->start2 + gen->len2));
508 }
509 
510 #define reduce_f1(a, f, op) (f (a.x))
511 #define reduce_f2(a, f, op) (f (a.x) op f (a.x2))
512 #define reduce_d1(a, f, op) (f (a.x))
513 #define reduce_d2(a, f, op) (f (a.x) op f (a.x2))
514 
515 #ifndef IEEE_754_2008_SNAN
516 # define IEEE_754_2008_SNAN 1
517 #endif
518 static inline int
519 issignaling_f (float x)
520 {
521   uint32_t ix = asuint (x);
522   if (!IEEE_754_2008_SNAN)
523     return (ix & 0x7fc00000) == 0x7fc00000;
524   return 2 * (ix ^ 0x00400000) > 2u * 0x7fc00000;
525 }
526 static inline int
527 issignaling_d (double x)
528 {
529   uint64_t ix = asuint64 (x);
530   if (!IEEE_754_2008_SNAN)
531     return (ix & 0x7ff8000000000000) == 0x7ff8000000000000;
532   return 2 * (ix ^ 0x0008000000000000) > 2 * 0x7ff8000000000000ULL;
533 }
534 
535 #if USE_MPFR
536 static mpfr_rnd_t
537 rmap (int r)
538 {
539   switch (r)
540     {
541     case FE_TONEAREST:
542       return MPFR_RNDN;
543     case FE_TOWARDZERO:
544       return MPFR_RNDZ;
545     case FE_UPWARD:
546       return MPFR_RNDU;
547     case FE_DOWNWARD:
548       return MPFR_RNDD;
549     }
550   return -1;
551 }
552 
553 #define prec_mpfr_f 50
554 #define prec_mpfr_d 80
555 #define prec_f 24
556 #define prec_d 53
557 #define emin_f -148
558 #define emin_d -1073
559 #define emax_f 128
560 #define emax_d 1024
561 static inline int
562 call_mpfr_f1 (mpfr_t y, const struct fun *f, struct args_f1 a, mpfr_rnd_t r)
563 {
564   MPFR_DECL_INIT (x, prec_f);
565   mpfr_set_flt (x, a.x, MPFR_RNDN);
566   return f->fun_mpfr.f1 (y, x, r);
567 }
568 static inline int
569 call_mpfr_f2 (mpfr_t y, const struct fun *f, struct args_f2 a, mpfr_rnd_t r)
570 {
571   MPFR_DECL_INIT (x, prec_f);
572   MPFR_DECL_INIT (x2, prec_f);
573   mpfr_set_flt (x, a.x, MPFR_RNDN);
574   mpfr_set_flt (x2, a.x2, MPFR_RNDN);
575   return f->fun_mpfr.f2 (y, x, x2, r);
576 }
577 static inline int
578 call_mpfr_d1 (mpfr_t y, const struct fun *f, struct args_d1 a, mpfr_rnd_t r)
579 {
580   MPFR_DECL_INIT (x, prec_d);
581   mpfr_set_d (x, a.x, MPFR_RNDN);
582   return f->fun_mpfr.d1 (y, x, r);
583 }
584 static inline int
585 call_mpfr_d2 (mpfr_t y, const struct fun *f, struct args_d2 a, mpfr_rnd_t r)
586 {
587   MPFR_DECL_INIT (x, prec_d);
588   MPFR_DECL_INIT (x2, prec_d);
589   mpfr_set_d (x, a.x, MPFR_RNDN);
590   mpfr_set_d (x2, a.x2, MPFR_RNDN);
591   return f->fun_mpfr.d2 (y, x, x2, r);
592 }
593 #endif
594 
595 #define float_f float
596 #define double_f double
597 #define copysign_f copysignf
598 #define nextafter_f nextafterf
599 #define fabs_f fabsf
600 #define asuint_f asuint
601 #define asfloat_f asfloat
602 #define scalbn_f scalbnf
603 #define lscalbn_f scalbn
604 #define halfinf_f 0x1p127f
605 #define min_normal_f 0x1p-126f
606 
607 #define float_d double
608 #define double_d long double
609 #define copysign_d copysign
610 #define nextafter_d nextafter
611 #define fabs_d fabs
612 #define asuint_d asuint64
613 #define asfloat_d asdouble
614 #define scalbn_d scalbn
615 #define lscalbn_d scalbnl
616 #define halfinf_d 0x1p1023
617 #define min_normal_d 0x1p-1022
618 
619 #define NEW_RT
620 #define RT(x) x##_f
621 #define T(x) x##_f1
622 #include "ulp.h"
623 #undef T
624 #define T(x) x##_f2
625 #include "ulp.h"
626 #undef T
627 #undef RT
628 
629 #define NEW_RT
630 #define RT(x) x##_d
631 #define T(x) x##_d1
632 #include "ulp.h"
633 #undef T
634 #define T(x) x##_d2
635 #include "ulp.h"
636 #undef T
637 #undef RT
638 
639 static void
640 usage (void)
641 {
642   puts ("./ulp [-q] [-m] [-f] [-r nudz] [-l soft-ulplimit] [-e ulplimit] func "
643 	"lo [hi [x lo2 hi2] [count]]");
644   puts ("Compares func against a higher precision implementation in [lo; hi].");
645   puts ("-q: quiet.");
646   puts ("-m: use mpfr even if faster method is available.");
647   puts ("-f: disable fenv testing (rounding modes and exceptions).");
648   puts ("Supported func:");
649   for (const struct fun *f = fun; f->name; f++)
650     printf ("\t%s\n", f->name);
651   exit (1);
652 }
653 
654 static int
655 cmp (const struct fun *f, struct gen *gen, const struct conf *conf)
656 {
657   int r = 1;
658   if (f->arity == 1 && f->singleprec)
659     r = cmp_f1 (f, gen, conf);
660   else if (f->arity == 2 && f->singleprec)
661     r = cmp_f2 (f, gen, conf);
662   else if (f->arity == 1 && !f->singleprec)
663     r = cmp_d1 (f, gen, conf);
664   else if (f->arity == 2 && !f->singleprec)
665     r = cmp_d2 (f, gen, conf);
666   else
667     usage ();
668   return r;
669 }
670 
671 static uint64_t
672 getnum (const char *s, int singleprec)
673 {
674   //	int i;
675   uint64_t sign = 0;
676   //	char buf[12];
677 
678   if (s[0] == '+')
679     s++;
680   else if (s[0] == '-')
681     {
682       sign = singleprec ? 1ULL << 31 : 1ULL << 63;
683       s++;
684     }
685   /* 0xXXXX is treated as bit representation, '-' flips the sign bit.  */
686   if (s[0] == '0' && tolower (s[1]) == 'x' && strchr (s, 'p') == 0)
687     return sign ^ strtoull (s, 0, 0);
688   //	/* SNaN, QNaN, NaN, Inf.  */
689   //	for (i=0; s[i] && i < sizeof buf; i++)
690   //		buf[i] = tolower(s[i]);
691   //	buf[i] = 0;
692   //	if (strcmp(buf, "snan") == 0)
693   //		return sign | (singleprec ? 0x7fa00000 : 0x7ff4000000000000);
694   //	if (strcmp(buf, "qnan") == 0 || strcmp(buf, "nan") == 0)
695   //		return sign | (singleprec ? 0x7fc00000 : 0x7ff8000000000000);
696   //	if (strcmp(buf, "inf") == 0 || strcmp(buf, "infinity") == 0)
697   //		return sign | (singleprec ? 0x7f800000 : 0x7ff0000000000000);
698   /* Otherwise assume it's a floating-point literal.  */
699   return sign
700 	 | (singleprec ? asuint (strtof (s, 0)) : asuint64 (strtod (s, 0)));
701 }
702 
703 static void
704 parsegen (struct gen *g, int argc, char *argv[], const struct fun *f)
705 {
706   int singleprec = f->singleprec;
707   int arity = f->arity;
708   uint64_t a, b, a2, b2, n;
709   if (argc < 1)
710     usage ();
711   b = a = getnum (argv[0], singleprec);
712   n = 0;
713   if (argc > 1 && strcmp (argv[1], "x") == 0)
714     {
715       argc -= 2;
716       argv += 2;
717     }
718   else if (argc > 1)
719     {
720       b = getnum (argv[1], singleprec);
721       if (argc > 2 && strcmp (argv[2], "x") == 0)
722 	{
723 	  argc -= 3;
724 	  argv += 3;
725 	}
726     }
727   b2 = a2 = getnum (argv[0], singleprec);
728   if (argc > 1)
729     b2 = getnum (argv[1], singleprec);
730   if (argc > 2)
731     n = strtoull (argv[2], 0, 0);
732   if (argc > 3)
733     usage ();
734   //printf("ab %lx %lx ab2 %lx %lx n %lu\n", a, b, a2, b2, n);
735   if (arity == 1)
736     {
737       g->start = a;
738       g->len = b - a;
739       if (n - 1 > b - a)
740 	n = b - a + 1;
741       g->off = 0;
742       g->step = n ? (g->len + 1) / n : 1;
743       g->start2 = g->len2 = 0;
744       g->cnt = n;
745     }
746   else if (arity == 2)
747     {
748       g->start = a;
749       g->len = b - a;
750       g->off = g->step = 0;
751       g->start2 = a2;
752       g->len2 = b2 - a2;
753       g->cnt = n;
754     }
755   else
756     usage ();
757 }
758 
759 int
760 main (int argc, char *argv[])
761 {
762   const struct fun *f;
763   struct gen gen;
764   struct conf conf;
765   conf.rc = 'n';
766   conf.quiet = 0;
767   conf.mpfr = 0;
768   conf.fenv = 1;
769   conf.softlim = 0;
770   conf.errlim = INFINITY;
771   for (;;)
772     {
773       argc--;
774       argv++;
775       if (argc < 1)
776 	usage ();
777       if (argv[0][0] != '-')
778 	break;
779       switch (argv[0][1])
780 	{
781 	case 'e':
782 	  argc--;
783 	  argv++;
784 	  if (argc < 1)
785 	    usage ();
786 	  conf.errlim = strtod (argv[0], 0);
787 	  break;
788 	case 'f':
789 	  conf.fenv = 0;
790 	  break;
791 	case 'l':
792 	  argc--;
793 	  argv++;
794 	  if (argc < 1)
795 	    usage ();
796 	  conf.softlim = strtod (argv[0], 0);
797 	  break;
798 	case 'm':
799 	  conf.mpfr = 1;
800 	  break;
801 	case 'q':
802 	  conf.quiet = 1;
803 	  break;
804 	case 'r':
805 	  conf.rc = argv[0][2];
806 	  if (!conf.rc)
807 	    {
808 	      argc--;
809 	      argv++;
810 	      if (argc < 1)
811 		usage ();
812 	      conf.rc = argv[0][0];
813 	    }
814 	  break;
815 	default:
816 	  usage ();
817 	}
818     }
819   switch (conf.rc)
820     {
821     case 'n':
822       conf.r = FE_TONEAREST;
823       break;
824     case 'u':
825       conf.r = FE_UPWARD;
826       break;
827     case 'd':
828       conf.r = FE_DOWNWARD;
829       break;
830     case 'z':
831       conf.r = FE_TOWARDZERO;
832       break;
833     default:
834       usage ();
835     }
836   for (f = fun; f->name; f++)
837     if (strcmp (argv[0], f->name) == 0)
838       break;
839   if (!f->name)
840     usage ();
841   if (!f->singleprec && LDBL_MANT_DIG == DBL_MANT_DIG)
842     conf.mpfr = 1; /* Use mpfr if long double has no extra precision.  */
843   if (!USE_MPFR && conf.mpfr)
844     {
845       puts ("mpfr is not available.");
846       return 0;
847     }
848   argc--;
849   argv++;
850   parsegen (&gen, argc, argv, f);
851   conf.n = gen.cnt;
852   return cmp (f, &gen, &conf);
853 }
854