[thirdparty/glibc.git] / math / atest-sincos.c

/* Copyright (C) 1997-2013 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;
   mp_limb_t chk, round;

   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) \
       /* d = (n ? -1 : 1) * (s1 + (s2>>sh)) * x / (1>>N); */		      \
      do { 								      \
	 if (s2 != NULL) {						      \
	    if (sh > 0) {						      \
	       assert (sh < mpbpl);					      \
	       mpn_lshift (tmp, s1, SZ, sh);				      \
	       chk = (n ? mpn_sub_n : mpn_add_n)(tmp,tmp,s2+FRAC/mpbpl,SZ);   \
	    } else							      \
	       chk = (n ? mpn_sub_n : mpn_add_n)(tmp,s1,s2+FRAC/mpbpl,SZ);    \
	    /* assert(chk == 0); */					      \
	    mpn_mul_n(d,tmp,x,SZ);					      \
	 } else 							      \
	    mpn_mul_n(d,s1,x,SZ);					      \
	 /* assert(d[SZ*2-1] == 0); */					      \
	 assert(N+sh < mpbpl);						      \
	 if (N+sh > 0) mpn_rshift(d,d,2*SZ,N+sh);			      \
      } while(0)
#define summ(d,ss,s,n) \
      /* d = ss +/- (s[0]+2*s[1]+2*s[2]+s[3])/6; */			      \
      do { 								      \
	 chk = mpn_add_n(tmp,s[1]+FRAC/mpbpl,s[2]+FRAC/mpbpl,SZ);	      \
	 mpn_lshift(tmp,tmp,SZ,1);					      \
	 chk |= mpn_add_n(tmp,tmp,s[0]+FRAC/mpbpl,SZ);			      \
	 chk |= mpn_add_n(tmp,tmp,s[3]+FRAC/mpbpl,SZ);			      \
	 round = mpn_divmod_1(tmp,tmp,SZ,6);				      \
	 /* chk |= mpn_add_1(tmp,tmp,SZ, (round > 3) ); */		      \
         chk |= (n ? mpn_sub_n : mpn_add_n)(d,ss,tmp,SZ);		      \
	 /* assert(chk == 0); */					      \
      } 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;
}
Commit	Line	Data
568035b7	1	/* Copyright (C) 1997-2013 Free Software Foundation, Inc.
9a0a462c UD	2	This file is part of the GNU C Library.
	3	Contributed by Geoffrey Keating <Geoff.Keating@anu.edu.au>, 1997.
	4
	5	The GNU C Library is free software; you can redistribute it and/or
41bdb6e2 AJ	6	modify it under the terms of the GNU Lesser General Public
	7	License as published by the Free Software Foundation; either
	8	version 2.1 of the License, or (at your option) any later version.
9a0a462c UD	9
	10	The GNU C Library is distributed in the hope that it will be useful,
	11	but WITHOUT ANY WARRANTY; without even the implied warranty of
	12	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
41bdb6e2	13	Lesser General Public License for more details.
9a0a462c	14
41bdb6e2	15	You should have received a copy of the GNU Lesser General Public
59ba27a6 PE	16	License along with the GNU C Library; if not, see
59ba27a6 PE	17	<http://www.gnu.org/licenses/>. */
9a0a462c UD	18
	19	#include <stdio.h>
	20	#include <math.h>
48896b9d	21	#include <gmp.h>
9a0a462c UD	22	#include <string.h>
	23	#include <limits.h>
	24	#include <assert.h>
	25
	26	#define PRINT_ERRORS 0
	27
	28	#define N 0
	29	#define N2 20
	30	#define FRAC (32 * 4)
	31
	32	#define mpbpl (CHAR_BIT * sizeof (mp_limb_t))
	33	#define SZ (FRAC / mpbpl + 1)
	34	typedef mp_limb_t mp1[SZ], mp2[SZ * 2];
	35
	36	/* These strings have exactly 100 hex digits in them. */
	37	static const char sin1[101] =
	38	"d76aa47848677020c6e9e909c50f3c3289e511132f518b4def"
	39	"b6ca5fd6c649bdfb0bd9ff1edcd4577655b5826a3d3b50c264";
	40	static const char cos1[101] =
	41	"8a51407da8345c91c2466d976871bd29a2373a894f96c3b7f2"
	42	"300240b760e6fa96a94430a52d0e9e43f3450e3b8ff99bc934";
	43	static const char hexdig[] = "0123456789abcdef";
	44
767b6275	45	static void
9a0a462c UD	46	print_mpn_hex (const mp_limb_t *x, unsigned size)
	47	{
	48	char value[size + 1];
	49	unsigned i;
	50	const unsigned final = (size * 4 > SZ * mpbpl) ? SZ * mpbpl / 4 : size;
	51
	52	memset (value, '0', size);
	53
	54	for (i = 0; i < final ; i++)
	55	value[size-1-i] = hexdig[x[i * 4 / mpbpl] >> (i * 4) % mpbpl & 0xf];
	56
	57	value[size] = '\0';
	58	fputs (value, stdout);
	59	}
	60
767b6275	61	static void
9a0a462c UD	62	sincosx_mpn (mp1 si, mp1 co, mp1 xx, mp1 ix)
	63	{
	64	int i;
	65	mp2 s[4], c[4];
	66	mp1 tmp, x;
	67	mp_limb_t chk, round;
	68
	69	if (ix == NULL)
	70	{
	71	memset (si, 0, sizeof (mp1));
	72	memset (co, 0, sizeof (mp1));
	73	co[SZ-1] = 1;
	74	memcpy (x, xx, sizeof (mp1));
	75	}
	76	else
	77	mpn_sub_n (x, xx, ix, SZ);
	78
	79	for (i = 0; i < 1 << N; i++)
	80	{
	81	#define add_shift_mulh(d,x,s1,s2,sh,n) \
	82	/* d = (n ? -1 : 1) * (s1 + (s2>>sh)) * x / (1>>N); */ \
	83	do { \
	84	if (s2 != NULL) { \
	85	if (sh > 0) { \
	86	assert (sh < mpbpl); \
	87	mpn_lshift (tmp, s1, SZ, sh); \
	88	chk = (n ? mpn_sub_n : mpn_add_n)(tmp,tmp,s2+FRAC/mpbpl,SZ); \
	89	} else \
	90	chk = (n ? mpn_sub_n : mpn_add_n)(tmp,s1,s2+FRAC/mpbpl,SZ); \
	91	/* assert(chk == 0); */ \
	92	mpn_mul_n(d,tmp,x,SZ); \
	93	} else \
	94	mpn_mul_n(d,s1,x,SZ); \
	95	/* assert(d[SZ2-1] == 0); / \
	96	assert(N+sh < mpbpl); \
	97	if (N+sh > 0) mpn_rshift(d,d,2*SZ,N+sh); \
	98	} while(0)
	99	#define summ(d,ss,s,n) \
	100	/* d = ss +/- (s[0]+2s[1]+2s[2]+s[3])/6; */ \
	101	do { \
	102	chk = mpn_add_n(tmp,s[1]+FRAC/mpbpl,s[2]+FRAC/mpbpl,SZ); \
	103	mpn_lshift(tmp,tmp,SZ,1); \
	104	chk \|= mpn_add_n(tmp,tmp,s[0]+FRAC/mpbpl,SZ); \
	105	chk \|= mpn_add_n(tmp,tmp,s[3]+FRAC/mpbpl,SZ); \
	106	round = mpn_divmod_1(tmp,tmp,SZ,6); \
	107	/* chk \|= mpn_add_1(tmp,tmp,SZ, (round > 3) ); */ \
	108	chk \|= (n ? mpn_sub_n : mpn_add_n)(d,ss,tmp,SZ); \
	109	/* assert(chk == 0); */ \
	110	} while (0)
	111
	112	add_shift_mulh (s[0], x, co, NULL, 0, 0); /* s0 = h * c; */
	113	add_shift_mulh (c[0], x, si, NULL, 0, 0); /* c0 = h * s; */
	114	add_shift_mulh (s[1], x, co, c[0], 1, 1); /* s1 = h * (c - c0/2); */
	115	add_shift_mulh (c[1], x, si, s[0], 1, 0); /* c1 = h * (s + s0/2); */
	116	add_shift_mulh (s[2], x, co, c[1], 1, 1); /* s2 = h * (c - c1/2); */
	117	add_shift_mulh (c[2], x, si, s[1], 1, 0); /* c2 = h * (s + s1/2); */
	118	add_shift_mulh (s[3], x, co, c[2], 0, 1); /* s3 = h * (c - c2); */
	119	add_shift_mulh (c[3], x, si, s[2], 0, 0); /* c3 = h * (s + s2); */
	120	summ (si, si, s, 0); /* s = s + (s0+2s1+2s2+s3)/6; */
	121	summ (co, co, c, 1); /* c = c - (c0+2c1+2c2+c3)/6; */
	122	}
	123	#undef add_shift_mulh
	124	#undef summ
	125	}
126
127	static int
128	mpn_bitsize (const mp_limb_t *SRC_PTR, mp_size_t SIZE)
129	{
130	int i, j;
131	for (i = SIZE - 1; i > 0; i--)
132	if (SRC_PTR[i] != 0)
133	break;
b259e746 UD	134	for (j = mpbpl - 1; j >= 0; j--)
b259e746 UD	135	if ((SRC_PTR[i] & (mp_limb_t)1 << j) != 0)
9a0a462c UD	136	break;
9a0a462c UD	137
b259e746	138	return i * mpbpl + j;
9a0a462c UD	139	}
	140
	141	int
	142	main (void)
	143	{
	144	mp1 si, co, x, ox, xt, s2, c2, s3, c3;
	145	int i;
	146	int sin_errors = 0, cos_errors = 0;
	147	int sin_failures = 0, cos_failures = 0;
	148	mp1 sin_maxerror, cos_maxerror;
	149	int sin_maxerror_s = 0, cos_maxerror_s = 0;
	150	const double sf = pow (2, mpbpl);
	151
	152	/* assert(mpbpl == mp_bits_per_limb); */
	153	assert(FRAC / mpbpl * mpbpl == FRAC);
	154
	155	memset (sin_maxerror, 0, sizeof (mp1));
	156	memset (cos_maxerror, 0, sizeof (mp1));
	157	memset (xt, 0, sizeof (mp1));
69bf5f75	158	xt[(FRAC - N2) / mpbpl] = (mp_limb_t)1 << (FRAC - N2) % mpbpl;
9a0a462c UD	159
	160	for (i = 0; i < 1 << N2; i++)
	161	{
	162	int s2s, s3s, c2s, c3s, j;
	163	double ds2,dc2;
	164
	165	mpn_mul_1 (x, xt, SZ, i);
	166	sincosx_mpn (si, co, x, i == 0 ? NULL : ox);
	167	memcpy (ox, x, sizeof (mp1));
	168	ds2 = sin (i / (double) (1 << N2));
	169	dc2 = cos (i / (double) (1 << N2));
	170	for (j = SZ-1; j >= 0; j--)
	171	{
	172	s2[j] = (mp_limb_t) ds2;
	173	ds2 = (ds2 - s2[j]) * sf;
	174	c2[j] = (mp_limb_t) dc2;
	175	dc2 = (dc2 - c2[j]) * sf;
	176	}
	177	if (mpn_cmp (si, s2, SZ) >= 0)
	178	mpn_sub_n (s3, si, s2, SZ);
	179	else
	180	mpn_sub_n (s3, s2, si, SZ);
	181	if (mpn_cmp (co, c2, SZ) >= 0)
	182	mpn_sub_n (c3, co, c2, SZ);
	183	else
	184	mpn_sub_n (c3, c2, co, SZ);
	185
	186	s2s = mpn_bitsize (s2, SZ);
	187	s3s = mpn_bitsize (s3, SZ);
	188	c2s = mpn_bitsize (c2, SZ);
	189	c3s = mpn_bitsize (c3, SZ);
04795ad9 UD	190	if ((s3s >= 0 && s2s - s3s < 54)
04795ad9 UD	191	\|\| (c3s >= 0 && c2s - c3s < 54)
9a0a462c UD	192	\|\| 0)
	193	{
	194	#if PRINT_ERRORS
	195	printf ("%06x ", i * (0x100000 / (1 << N2)));
	196	print_mpn_hex(si, (FRAC / 4) + 1);
	197	putchar (' ');
	198	print_mpn_hex (co, (FRAC / 4) + 1);
	199	putchar ('\n');
	200	fputs (" ", stdout);
	201	print_mpn_hex (s2, (FRAC / 4) + 1);
	202	putchar (' ');
	203	print_mpn_hex (c2, (FRAC / 4) + 1);
	204	putchar ('\n');
	205	printf (" %c%c ",
b259e746 UD	206	s3s >= 0 && s2s-s3s < 54 ? s2s - s3s == 53 ? 'e' : 'F' : 'P',
b259e746 UD	207	c3s >= 0 && c2s-c3s < 54 ? c2s - c3s == 53 ? 'e' : 'F' : 'P');
9a0a462c UD	208	print_mpn_hex (s3, (FRAC / 4) + 1);
	209	putchar (' ');
	210	print_mpn_hex (c3, (FRAC / 4) + 1);
	211	putchar ('\n');
	212	#endif
	213	sin_errors += s2s - s3s == 53;
	214	cos_errors += c2s - c3s == 53;
	215	sin_failures += s2s - s3s < 53;
	216	cos_failures += c2s - c3s < 53;
	217	}
	218	if (s3s >= sin_maxerror_s
	219	&& mpn_cmp (s3, sin_maxerror, SZ) > 0)
	220	{
	221	memcpy (sin_maxerror, s3, sizeof (mp1));
	222	sin_maxerror_s = s3s;
	223	}
	224	if (c3s >= cos_maxerror_s
	225	&& mpn_cmp (c3, cos_maxerror, SZ) > 0)
	226	{
	227	memcpy (cos_maxerror, c3, sizeof (mp1));
	228	cos_maxerror_s = c3s;
	229	}
	230	}
	231
	232	/* Check Range-Kutta against precomputed values of sin(1) and cos(1). */
	233	memset (x, 0, sizeof (mp1));
69bf5f75	234	x[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
9a0a462c UD	235	sincosx_mpn (si, co, x, ox);
	236
	237	memset (s2, 0, sizeof (mp1));
	238	memset (c2, 0, sizeof (mp1));
	239	for (i = 0; i < 100 && i < FRAC / 4; i++)
	240	{
11bf311e UD	241	s2[(FRAC - i * 4 - 4) / mpbpl] \|= ((mp_limb_t) (strchr (hexdig, sin1[i])
	242	- hexdig)
	243	<< (FRAC - i * 4 - 4) % mpbpl);
	244	c2[(FRAC - i * 4 - 4) / mpbpl] \|= ((mp_limb_t) (strchr (hexdig, cos1[i])
	245	- hexdig)
9a0a462c UD	246	<< (FRAC - i * 4 - 4) % mpbpl);
	247	}
	248
	249	if (mpn_cmp (si, s2, SZ) >= 0)
	250	mpn_sub_n (s3, si, s2, SZ);
	251	else
	252	mpn_sub_n (s3, s2, si, SZ);
	253	if (mpn_cmp (co, c2, SZ) >= 0)
	254	mpn_sub_n (c3, co, c2, SZ);
	255	else
	256	mpn_sub_n (c3, c2, co, SZ);
	257
	258	printf ("sin:\n");
	259	printf ("%d failures; %d errors; error rate %0.2f%%\n",
	260	sin_failures, sin_errors, sin_errors * 100.0 / (double) (1 << N2));
	261	fputs ("maximum error: ", stdout);
	262	print_mpn_hex (sin_maxerror, (FRAC / 4) + 1);
	263	fputs ("\nerror in sin(1): ", stdout);
	264	print_mpn_hex (s3, (FRAC / 4) + 1);
	265
	266	fputs ("\n\ncos:\n", stdout);
	267	printf ("%d failures; %d errors; error rate %0.2f%%\n",
	268	cos_failures, cos_errors, cos_errors * 100.0 / (double) (1 << N2));
	269	fputs ("maximum error: ", stdout);
	270	print_mpn_hex (cos_maxerror, (FRAC / 4) + 1);
	271	fputs ("\nerror in cos(1): ", stdout);
	272	print_mpn_hex (c3, (FRAC / 4) + 1);
	273	putchar ('\n');
	274
	275	return (sin_failures == 0 && cos_failures == 0) ? 0 : 1;
	276	}