[thirdparty/glibc.git] / math / atest-exp2.c

/* 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>
#include <stdlib.h>

#define PRINT_ERRORS 0

#define TOL 80
#define N2 18
#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];

#if BITS_PER_MP_LIMB == 64
# define LIMB64(L, H) 0x ## H ## L
#elif BITS_PER_MP_LIMB == 32
# define LIMB64(L, H) 0x ## L, 0x ## H
#else
# error
#endif

/* Once upon a time these constants were generated to 400 bits.
   We only need FRAC bits (128) at present, but we retain 384 bits
   in the text Just In Case.  */
#define CONSTSZ(INT, F1, F2, F3, F4, F5, F6, F7, F8, F9, Fa, Fb, Fc) \
	LIMB64(F4, F3), LIMB64(F2, F1), INT

static const mp1 mp_exp1 = {
  CONSTSZ (2, b7e15162, 8aed2a6a, bf715880, 9cf4f3c7, 62e7160f, 38b4da56,
           a784d904, 5190cfef, 324e7738, 926cfbe5, f4bf8d8d, 8c31d763)
};

static const mp1 mp_exp_m1 = {
  CONSTSZ (0, 5e2d58d8, b3bcdf1a, badec782, 9054f90d, da9805aa, b56c7733,
           3024b9d0, a507daed, b16400bf, 472b4215, b8245b66, 9d90d27a)
};

static const mp1 mp_log2 = {
  CONSTSZ (0, b17217f7, d1cf79ab, c9e3b398, 03f2f6af, 40f34326, 7298b62d,
           8a0d175b, 8baafa2b, e7b87620, 6debac98, 559552fb, 4afa1b10)
};

static void
print_mpn_fp (const mp_limb_t *x, unsigned int dp, unsigned int base)
{
   static const char hexdig[16] = "0123456789abcdef";
   unsigned int i;
   mp1 tx;

   memcpy (tx, x, sizeof (mp1));
   if (base == 16)
     fputs ("0x", stdout);
   assert (x[SZ-1] < base);
   fputc (hexdig[x[SZ - 1]], stdout);
   fputc ('.', stdout);
   for (i = 0; i < dp; i++)
     {
       tx[SZ - 1] = 0;
       mpn_mul_1 (tx, tx, SZ, base);
       assert (tx[SZ - 1] < base);
       fputc (hexdig[tx[SZ - 1]], stdout);
     }
}

/* Compute e^x.  */
static void
exp_mpn (mp1 ex, mp1 x)
{
   unsigned int n;
   mp1 xp;
   mp2 tmp;
   mp_limb_t chk;
   mp1 tol;

   memset (xp, 0, sizeof (mp1));
   memset (ex, 0, sizeof (mp1));
   xp[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
   memset (tol, 0, sizeof (mp1));
   tol[(FRAC - TOL) / mpbpl] = (mp_limb_t)1 << (FRAC - TOL) % mpbpl;

   n = 0;

   do
     {
       /* Calculate sum(x^n/n!) until the next term is sufficiently small.  */

       mpn_mul_n (tmp, xp, x, SZ);
       assert(tmp[SZ * 2 - 1] == 0);
       if (n > 0)
	 mpn_divmod_1 (xp, tmp + FRAC / mpbpl, SZ, n);
       chk = mpn_add_n (ex, ex, xp, SZ);
       assert (chk == 0);
       ++n;
       assert (n < 80); /* Catch too-high TOL.  */
     }
   while (n < 10 || mpn_cmp (xp, tol, SZ) >= 0);
}

/* Calculate 2^x.  */
static void
exp2_mpn (mp1 ex, mp1 x)
{
  mp2 tmp;
  mpn_mul_n (tmp, x, mp_log2, SZ);
  assert(tmp[SZ * 2 - 1] == 0);
  exp_mpn (ex, tmp + FRAC / mpbpl);
}


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;
}

static int
do_test (void)
{
  mp1 ex, x, xt, e2, e3;
  int i;
  int errors = 0;
  int failures = 0;
  mp1 maxerror;
  int maxerror_s = 0;
  const double sf = pow (2, mpbpl);

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

  memset (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 e2s, e3s, j;
      double de2;

      mpn_mul_1 (x, xt, SZ, i);
      exp2_mpn (ex, x);
      de2 = exp2 (i / (double) (1 << N2));
      for (j = SZ - 1; j >= 0; --j)
	{
	  e2[j] = (mp_limb_t) de2;
	  de2 = (de2 - e2[j]) * sf;
	}
      if (mpn_cmp (ex, e2, SZ) >= 0)
	mpn_sub_n (e3, ex, e2, SZ);
      else
	mpn_sub_n (e3, e2, ex, SZ);

      e2s = mpn_bitsize (e2, SZ);
      e3s = mpn_bitsize (e3, SZ);
      if (e3s >= 0 && e2s - e3s < 54)
	{
#if PRINT_ERRORS
	  printf ("%06x ", i * (0x100000 / (1 << N2)));
	  print_mpn_fp (ex, (FRAC / 4) + 1, 16);
	  putchar ('\n');
	  fputs ("       ",stdout);
	  print_mpn_fp (e2, (FRAC / 4) + 1, 16);
	  putchar ('\n');
	  printf (" %c     ",
		  e2s - e3s < 54 ? e2s - e3s == 53 ? 'e' : 'F' : 'P');
	  print_mpn_fp (e3, (FRAC / 4) + 1, 16);
	  putchar ('\n');
#endif
	  errors += (e2s - e3s == 53);
	  failures += (e2s - e3s < 53);
	}
      if (e3s >= maxerror_s
	  && mpn_cmp (e3, maxerror, SZ) > 0)
	{
	  memcpy (maxerror, e3, sizeof (mp1));
	  maxerror_s = e3s;
	}
    }

  /* Check exp_mpn against precomputed value of exp(1).  */
  memset (x, 0, sizeof (mp1));
  x[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
  exp_mpn (ex, x);
  if (mpn_cmp (ex, mp_exp1, SZ) >= 0)
    mpn_sub_n (e3, ex, mp_exp1, SZ);
  else
    mpn_sub_n (e3, mp_exp1, ex, SZ);

  printf ("%d failures; %d errors; error rate %0.2f%%\n", failures, errors,
	  errors * 100.0 / (double) (1 << N2));
  fputs ("maximum error:   ", stdout);
  print_mpn_fp (maxerror, (FRAC / 4) + 1, 16);
  putchar ('\n');
  fputs ("error in exp(1): ", stdout);
  print_mpn_fp (e3, (FRAC / 4) + 1, 16);
  putchar ('\n');

  return failures == 0 ? 0 : 1;
}

#define TIMEOUT 10
#define TEST_FUNCTION do_test ()
#include "../test-skeleton.c"
Commit	Line	Data
d4697bc9	1	/* Copyright (C) 1997-2014 Free Software Foundation, Inc.
650425ce 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.
650425ce 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.
650425ce	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/>. */
650425ce UD	18
	19	#include <stdio.h>
	20	#include <math.h>
48896b9d	21	#include <gmp.h>
650425ce UD	22	#include <string.h>
	23	#include <limits.h>
	24	#include <assert.h>
	25	#include <stdlib.h>
	26
	27	#define PRINT_ERRORS 0
	28
	29	#define TOL 80
	30	#define N2 18
	31	#define FRAC (32*4)
	32
	33	#define mpbpl (CHAR_BIT * sizeof (mp_limb_t))
	34	#define SZ (FRAC / mpbpl + 1)
	35	typedef mp_limb_t mp1[SZ], mp2[SZ * 2];
	36
e6e49e59 RH	37	#if BITS_PER_MP_LIMB == 64
	38	# define LIMB64(L, H) 0x ## H ## L
	39	#elif BITS_PER_MP_LIMB == 32
	40	# define LIMB64(L, H) 0x ## L, 0x ## H
	41	#else
	42	# error
	43	#endif
	44
	45	/* Once upon a time these constants were generated to 400 bits.
	46	We only need FRAC bits (128) at present, but we retain 384 bits
	47	in the text Just In Case. */
	48	#define CONSTSZ(INT, F1, F2, F3, F4, F5, F6, F7, F8, F9, Fa, Fb, Fc) \
	49	LIMB64(F4, F3), LIMB64(F2, F1), INT
	50
	51	static const mp1 mp_exp1 = {
	52	CONSTSZ (2, b7e15162, 8aed2a6a, bf715880, 9cf4f3c7, 62e7160f, 38b4da56,
	53	a784d904, 5190cfef, 324e7738, 926cfbe5, f4bf8d8d, 8c31d763)
	54	};
650425ce	55
e6e49e59 RH	56	static const mp1 mp_exp_m1 = {
	57	CONSTSZ (0, 5e2d58d8, b3bcdf1a, badec782, 9054f90d, da9805aa, b56c7733,
	58	3024b9d0, a507daed, b16400bf, 472b4215, b8245b66, 9d90d27a)
	59	};
	60
	61	static const mp1 mp_log2 = {
	62	CONSTSZ (0, b17217f7, d1cf79ab, c9e3b398, 03f2f6af, 40f34326, 7298b62d,
	63	8a0d175b, 8baafa2b, e7b87620, 6debac98, 559552fb, 4afa1b10)
	64	};
650425ce	65
767b6275	66	static void
650425ce UD	67	print_mpn_fp (const mp_limb_t *x, unsigned int dp, unsigned int base)
650425ce UD	68	{
e6e49e59	69	static const char hexdig[16] = "0123456789abcdef";
650425ce UD	70	unsigned int i;
	71	mp1 tx;
	72
	73	memcpy (tx, x, sizeof (mp1));
	74	if (base == 16)
	75	fputs ("0x", stdout);
	76	assert (x[SZ-1] < base);
	77	fputc (hexdig[x[SZ - 1]], stdout);
	78	fputc ('.', stdout);
	79	for (i = 0; i < dp; i++)
	80	{
	81	tx[SZ - 1] = 0;
	82	mpn_mul_1 (tx, tx, SZ, base);
	83	assert (tx[SZ - 1] < base);
	84	fputc (hexdig[tx[SZ - 1]], stdout);
	85	}
	86	}
	87
650425ce	88	/* Compute e^x. */
767b6275	89	static void
650425ce UD	90	exp_mpn (mp1 ex, mp1 x)
	91	{
	92	unsigned int n;
	93	mp1 xp;
	94	mp2 tmp;
e4f22324	95	mp_limb_t chk;
650425ce UD	96	mp1 tol;
	97
	98	memset (xp, 0, sizeof (mp1));
	99	memset (ex, 0, sizeof (mp1));
69bf5f75	100	xp[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
650425ce	101	memset (tol, 0, sizeof (mp1));
69bf5f75	102	tol[(FRAC - TOL) / mpbpl] = (mp_limb_t)1 << (FRAC - TOL) % mpbpl;
650425ce UD	103
	104	n = 0;
	105
	106	do
	107	{
	108	/* Calculate sum(x^n/n!) until the next term is sufficiently small. */
	109
	110	mpn_mul_n (tmp, xp, x, SZ);
	111	assert(tmp[SZ * 2 - 1] == 0);
	112	if (n > 0)
e4f22324	113	mpn_divmod_1 (xp, tmp + FRAC / mpbpl, SZ, n);
650425ce UD	114	chk = mpn_add_n (ex, ex, xp, SZ);
	115	assert (chk == 0);
	116	++n;
	117	assert (n < 80); /* Catch too-high TOL. */
	118	}
	119	while (n < 10 \|\| mpn_cmp (xp, tol, SZ) >= 0);
	120	}
	121
	122	/* Calculate 2^x. */
767b6275	123	static void
650425ce UD	124	exp2_mpn (mp1 ex, mp1 x)
	125	{
	126	mp2 tmp;
e6e49e59	127	mpn_mul_n (tmp, x, mp_log2, SZ);
650425ce UD	128	assert(tmp[SZ * 2 - 1] == 0);
	129	exp_mpn (ex, tmp + FRAC / mpbpl);
	130	}
	131
	132
	133	static int
	134	mpn_bitsize(const mp_limb_t *SRC_PTR, mp_size_t SIZE)
	135	{
	136	int i, j;
	137	for (i = SIZE - 1; i > 0; --i)
	138	if (SRC_PTR[i] != 0)
	139	break;
b259e746 UD	140	for (j = mpbpl - 1; j >= 0; --j)
b259e746 UD	141	if ((SRC_PTR[i] & (mp_limb_t)1 << j) != 0)
650425ce UD	142	break;
650425ce UD	143
b259e746	144	return i * mpbpl + j;
650425ce UD	145	}
650425ce UD	146
29955b5d AS	147	static int
29955b5d AS	148	do_test (void)
650425ce UD	149	{
	150	mp1 ex, x, xt, e2, e3;
	151	int i;
	152	int errors = 0;
	153	int failures = 0;
	154	mp1 maxerror;
	155	int maxerror_s = 0;
	156	const double sf = pow (2, mpbpl);
	157
	158	/* assert(mpbpl == mp_bits_per_limb); */
	159	assert(FRAC / mpbpl * mpbpl == FRAC);
	160
	161	memset (maxerror, 0, sizeof (mp1));
	162	memset (xt, 0, sizeof (mp1));
69bf5f75	163	xt[(FRAC - N2) / mpbpl] = (mp_limb_t)1 << (FRAC - N2) % mpbpl;
650425ce UD	164
	165	for (i = 0; i < (1 << N2); ++i)
	166	{
	167	int e2s, e3s, j;
	168	double de2;
	169
	170	mpn_mul_1 (x, xt, SZ, i);
	171	exp2_mpn (ex, x);
	172	de2 = exp2 (i / (double) (1 << N2));
	173	for (j = SZ - 1; j >= 0; --j)
	174	{
	175	e2[j] = (mp_limb_t) de2;
	176	de2 = (de2 - e2[j]) * sf;
	177	}
	178	if (mpn_cmp (ex, e2, SZ) >= 0)
	179	mpn_sub_n (e3, ex, e2, SZ);
	180	else
	181	mpn_sub_n (e3, e2, ex, SZ);
	182
	183	e2s = mpn_bitsize (e2, SZ);
	184	e3s = mpn_bitsize (e3, SZ);
b259e746	185	if (e3s >= 0 && e2s - e3s < 54)
650425ce UD	186	{
	187	#if PRINT_ERRORS
	188	printf ("%06x ", i * (0x100000 / (1 << N2)));
	189	print_mpn_fp (ex, (FRAC / 4) + 1, 16);
	190	putchar ('\n');
	191	fputs (" ",stdout);
	192	print_mpn_fp (e2, (FRAC / 4) + 1, 16);
	193	putchar ('\n');
	194	printf (" %c ",
	195	e2s - e3s < 54 ? e2s - e3s == 53 ? 'e' : 'F' : 'P');
	196	print_mpn_fp (e3, (FRAC / 4) + 1, 16);
	197	putchar ('\n');
	198	#endif
	199	errors += (e2s - e3s == 53);
	200	failures += (e2s - e3s < 53);
	201	}
	202	if (e3s >= maxerror_s
	203	&& mpn_cmp (e3, maxerror, SZ) > 0)
	204	{
	205	memcpy (maxerror, e3, sizeof (mp1));
	206	maxerror_s = e3s;
	207	}
	208	}
	209
	210	/* Check exp_mpn against precomputed value of exp(1). */
	211	memset (x, 0, sizeof (mp1));
69bf5f75	212	x[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
650425ce	213	exp_mpn (ex, x);
e6e49e59 RH	214	if (mpn_cmp (ex, mp_exp1, SZ) >= 0)
e6e49e59 RH	215	mpn_sub_n (e3, ex, mp_exp1, SZ);
650425ce	216	else
e6e49e59	217	mpn_sub_n (e3, mp_exp1, ex, SZ);
650425ce UD	218
	219	printf ("%d failures; %d errors; error rate %0.2f%%\n", failures, errors,
	220	errors * 100.0 / (double) (1 << N2));
	221	fputs ("maximum error: ", stdout);
	222	print_mpn_fp (maxerror, (FRAC / 4) + 1, 16);
	223	putchar ('\n');
	224	fputs ("error in exp(1): ", stdout);
	225	print_mpn_fp (e3, (FRAC / 4) + 1, 16);
	226	putchar ('\n');
	227
	228	return failures == 0 ? 0 : 1;
	229	}
29955b5d	230
4ef91cdc	231	#define TIMEOUT 10
29955b5d AS	232	#define TEST_FUNCTION do_test ()
29955b5d AS	233	#include "../test-skeleton.c"