/* 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>

#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;

}

static int

do_test (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;

}

#define TIMEOUT 600

#define TEST_FUNCTION do_test ()

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