summaryrefslogtreecommitdiff
path: root/math/atest-sincos.c
blob: 5ad59b224d2048771b39f4ca92e69ecea86aedad (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
/* Copyright (C) 1997-2014 Free Software Foundation, Inc.
   This file is part of the GNU C Library.
   Contributed by Geoffrey Keating <Geoff.Keating@anu.edu.au>, 1997.

   The GNU C Library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 2.1 of the License, or (at your option) any later version.

   The GNU C Library is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with the GNU C Library; if not, see
   <http://www.gnu.org/licenses/>.  */

#include <stdio.h>
#include <math.h>
#include <gmp.h>
#include <string.h>
#include <limits.h>
#include <assert.h>

#define PRINT_ERRORS 0

#define N 0
#define N2 20
#define FRAC (32 * 4)

#define mpbpl (CHAR_BIT * sizeof (mp_limb_t))
#define SZ (FRAC / mpbpl + 1)
typedef mp_limb_t mp1[SZ], mp2[SZ * 2];

/* These strings have exactly 100 hex digits in them.  */
static const char sin1[101] =
"d76aa47848677020c6e9e909c50f3c3289e511132f518b4def"
"b6ca5fd6c649bdfb0bd9ff1edcd4577655b5826a3d3b50c264";
static const char cos1[101] =
"8a51407da8345c91c2466d976871bd29a2373a894f96c3b7f2"
"300240b760e6fa96a94430a52d0e9e43f3450e3b8ff99bc934";
static const char hexdig[] = "0123456789abcdef";

static void
print_mpn_hex (const mp_limb_t *x, unsigned size)
{
   char value[size + 1];
   unsigned i;
   const unsigned final = (size * 4 > SZ * mpbpl) ? SZ * mpbpl / 4 : size;

   memset (value, '0', size);

   for (i = 0; i < final ; i++)
     value[size-1-i] = hexdig[x[i * 4 / mpbpl] >> (i * 4) % mpbpl & 0xf];

   value[size] = '\0';
   fputs (value, stdout);
}

static void
sincosx_mpn (mp1 si, mp1 co, mp1 xx, mp1 ix)
{
   int i;
   mp2 s[4], c[4];
   mp1 tmp, x;

   if (ix == NULL)
     {
       memset (si, 0, sizeof (mp1));
       memset (co, 0, sizeof (mp1));
       co[SZ-1] = 1;
       memcpy (x, xx, sizeof (mp1));
     }
   else
      mpn_sub_n (x, xx, ix, SZ);

   for (i = 0; i < 1 << N; i++)
     {
#define add_shift_mulh(d,x,s1,s2,sh,n) \
      do { 								      \
	 if (s2 != NULL) {						      \
	    if (sh > 0) {						      \
	       assert (sh < mpbpl);					      \
	       mpn_lshift (tmp, s1, SZ, sh);				      \
	       if (n)							      \
	         mpn_sub_n (tmp,tmp,s2+FRAC/mpbpl,SZ);			      \
	       else							      \
	         mpn_add_n (tmp,tmp,s2+FRAC/mpbpl,SZ);			      \
	    } else {							      \
	       if (n)							      \
	         mpn_sub_n (tmp,s1,s2+FRAC/mpbpl,SZ);			      \
	       else							      \
	         mpn_add_n (tmp,s1,s2+FRAC/mpbpl,SZ);			      \
	    }								      \
	    mpn_mul_n(d,tmp,x,SZ);					      \
	 } else 							      \
	    mpn_mul_n(d,s1,x,SZ);					      \
	 assert(N+sh < mpbpl);						      \
	 if (N+sh > 0) mpn_rshift(d,d,2*SZ,N+sh);			      \
      } while(0)
#define summ(d,ss,s,n) \
      do { 								      \
	 mpn_add_n(tmp,s[1]+FRAC/mpbpl,s[2]+FRAC/mpbpl,SZ);		      \
	 mpn_lshift(tmp,tmp,SZ,1);					      \
	 mpn_add_n(tmp,tmp,s[0]+FRAC/mpbpl,SZ);				      \
	 mpn_add_n(tmp,tmp,s[3]+FRAC/mpbpl,SZ);				      \
	 mpn_divmod_1(tmp,tmp,SZ,6);					      \
	 if (n)								      \
           mpn_sub_n (d,ss,tmp,SZ);					      \
	 else								      \
           mpn_add_n (d,ss,tmp,SZ);					      \
      } while (0)

      add_shift_mulh (s[0], x, co, NULL, 0, 0); /* s0 = h * c; */
      add_shift_mulh (c[0], x, si, NULL, 0, 0); /* c0 = h * s; */
      add_shift_mulh (s[1], x, co, c[0], 1, 1); /* s1 = h * (c - c0/2); */
      add_shift_mulh (c[1], x, si, s[0], 1, 0); /* c1 = h * (s + s0/2); */
      add_shift_mulh (s[2], x, co, c[1], 1, 1); /* s2 = h * (c - c1/2); */
      add_shift_mulh (c[2], x, si, s[1], 1, 0); /* c2 = h * (s + s1/2); */
      add_shift_mulh (s[3], x, co, c[2], 0, 1); /* s3 = h * (c - c2); */
      add_shift_mulh (c[3], x, si, s[2], 0, 0); /* c3 = h * (s + s2); */
      summ (si, si, s, 0);        /* s = s + (s0+2*s1+2*s2+s3)/6; */
      summ (co, co, c, 1);        /* c = c - (c0+2*c1+2*c2+c3)/6; */
   }
#undef add_shift_mulh
#undef summ
}

static int
mpn_bitsize (const mp_limb_t *SRC_PTR, mp_size_t SIZE)
{
   int i, j;
   for (i = SIZE - 1; i > 0; i--)
     if (SRC_PTR[i] != 0)
       break;
   for (j = mpbpl - 1; j >= 0; j--)
     if ((SRC_PTR[i] & (mp_limb_t)1 << j) != 0)
       break;

   return i * mpbpl + j;
}

int
main (void)
{
  mp1 si, co, x, ox, xt, s2, c2, s3, c3;
  int i;
  int sin_errors = 0, cos_errors = 0;
  int sin_failures = 0, cos_failures = 0;
  mp1 sin_maxerror, cos_maxerror;
  int sin_maxerror_s = 0, cos_maxerror_s = 0;
  const double sf = pow (2, mpbpl);

  /* assert(mpbpl == mp_bits_per_limb);  */
  assert(FRAC / mpbpl * mpbpl == FRAC);

  memset (sin_maxerror, 0, sizeof (mp1));
  memset (cos_maxerror, 0, sizeof (mp1));
  memset (xt, 0, sizeof (mp1));
  xt[(FRAC - N2) / mpbpl] = (mp_limb_t)1 << (FRAC - N2) % mpbpl;

  for (i = 0; i < 1 << N2; i++)
    {
      int s2s, s3s, c2s, c3s, j;
      double ds2,dc2;

      mpn_mul_1 (x, xt, SZ, i);
      sincosx_mpn (si, co, x, i == 0 ? NULL : ox);
      memcpy (ox, x, sizeof (mp1));
      ds2 = sin (i / (double) (1 << N2));
      dc2 = cos (i / (double) (1 << N2));
      for (j = SZ-1; j >= 0; j--)
	{
	  s2[j] = (mp_limb_t) ds2;
	  ds2 = (ds2 - s2[j]) * sf;
	  c2[j] = (mp_limb_t) dc2;
	  dc2 = (dc2 - c2[j]) * sf;
	}
      if (mpn_cmp (si, s2, SZ) >= 0)
	mpn_sub_n (s3, si, s2, SZ);
      else
	mpn_sub_n (s3, s2, si, SZ);
      if (mpn_cmp (co, c2, SZ) >= 0)
	mpn_sub_n (c3, co, c2, SZ);
      else
	mpn_sub_n (c3, c2, co, SZ);

      s2s = mpn_bitsize (s2, SZ);
      s3s = mpn_bitsize (s3, SZ);
      c2s = mpn_bitsize (c2, SZ);
      c3s = mpn_bitsize (c3, SZ);
      if ((s3s >= 0 && s2s - s3s < 54)
	  || (c3s >= 0 && c2s - c3s < 54)
	  || 0)
	{
#if PRINT_ERRORS
	  printf ("%06x ", i * (0x100000 / (1 << N2)));
	  print_mpn_hex(si, (FRAC / 4) + 1);
	  putchar (' ');
	  print_mpn_hex (co, (FRAC / 4) + 1);
	  putchar ('\n');
	  fputs ("       ", stdout);
	  print_mpn_hex (s2, (FRAC / 4) + 1);
	  putchar (' ');
	  print_mpn_hex (c2, (FRAC / 4) + 1);
	  putchar ('\n');
	  printf (" %c%c    ",
		  s3s >= 0 && s2s-s3s < 54 ? s2s - s3s == 53 ? 'e' : 'F' : 'P',
		  c3s >= 0 && c2s-c3s < 54 ? c2s - c3s == 53 ? 'e' : 'F' : 'P');
	  print_mpn_hex (s3, (FRAC / 4) + 1);
	  putchar (' ');
	  print_mpn_hex (c3, (FRAC / 4) + 1);
	  putchar ('\n');
#endif
	  sin_errors += s2s - s3s == 53;
	  cos_errors += c2s - c3s == 53;
	  sin_failures += s2s - s3s < 53;
	  cos_failures += c2s - c3s < 53;
	}
      if (s3s >= sin_maxerror_s
	  && mpn_cmp (s3, sin_maxerror, SZ) > 0)
	{
	  memcpy (sin_maxerror, s3, sizeof (mp1));
	  sin_maxerror_s = s3s;
	}
      if (c3s >= cos_maxerror_s
	  && mpn_cmp (c3, cos_maxerror, SZ) > 0)
	{
	  memcpy (cos_maxerror, c3, sizeof (mp1));
	  cos_maxerror_s = c3s;
	}
    }

   /* Check Range-Kutta against precomputed values of sin(1) and cos(1).  */
   memset (x, 0, sizeof (mp1));
   x[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
   sincosx_mpn (si, co, x, ox);

   memset (s2, 0, sizeof (mp1));
   memset (c2, 0, sizeof (mp1));
   for (i = 0; i < 100 && i < FRAC / 4; i++)
     {
       s2[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (hexdig, sin1[i])
						       - hexdig)
 					  << (FRAC - i * 4 - 4) % mpbpl);
       c2[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (hexdig, cos1[i])
						       - hexdig)
					  << (FRAC - i * 4 - 4) % mpbpl);
     }

   if (mpn_cmp (si, s2, SZ) >= 0)
     mpn_sub_n (s3, si, s2, SZ);
   else
     mpn_sub_n (s3, s2, si, SZ);
   if (mpn_cmp (co, c2, SZ) >= 0)
      mpn_sub_n (c3, co, c2, SZ);
   else
     mpn_sub_n (c3, c2, co, SZ);

   printf ("sin:\n");
   printf ("%d failures; %d errors; error rate %0.2f%%\n",
	   sin_failures, sin_errors, sin_errors * 100.0 / (double) (1 << N2));
   fputs ("maximum error:   ", stdout);
   print_mpn_hex (sin_maxerror, (FRAC / 4) + 1);
   fputs ("\nerror in sin(1): ", stdout);
   print_mpn_hex (s3, (FRAC / 4) + 1);

   fputs ("\n\ncos:\n", stdout);
   printf ("%d failures; %d errors; error rate %0.2f%%\n",
	   cos_failures, cos_errors, cos_errors * 100.0 / (double) (1 << N2));
   fputs ("maximum error:   ", stdout);
   print_mpn_hex (cos_maxerror, (FRAC / 4) + 1);
   fputs ("\nerror in cos(1): ", stdout);
   print_mpn_hex (c3, (FRAC / 4) + 1);
   putchar ('\n');

   return (sin_failures == 0 && cos_failures == 0) ? 0 : 1;
}