/* Copyright (C) 1997-2018 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_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 __attribute__ ((unused));

   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 300

#define TEST_FUNCTION do_test ()

#include "../test-skeleton.c"