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glibc  2.9
Defines | Typedefs | Functions | Variables
atest-exp2.c File Reference
#include <stdio.h>
#include <math.h>
#include <gmp.h>
#include <string.h>
#include <limits.h>
#include <assert.h>
#include <stdlib.h>

Go to the source code of this file.

Defines

#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)

Typedefs

typedef mp_limb_t mp1 [SZ]
typedef mp_limb_t mp2 [SZ *2]

Functions

static void print_mpn_fp (const mp_limb_t *x, unsigned int dp, unsigned int base)
static void read_mpn_hex (mp_limb_t *x, const char *str)
static mp_limb_tget_log2 (void)
static void exp_mpn (mp1 ex, mp1 x)
static void exp2_mpn (mp1 ex, mp1 x)
static int mpn_bitsize (const mp_limb_t *SRC_PTR, mp_size_t SIZE)
int main (void)

Variables

static const char exp1 [102] = "84d9045190cfef324e7738926cfbe5f4bf8d8d8c31d763da07"
static const char exp_m1 [102] = "24b9d0a507daedb16400bf472b4215b8245b669d90d27a5aea"
static const char hexdig [] = "0123456789abcdef"

Define Documentation

#define FRAC   (32*4)

Definition at line 32 of file atest-exp2.c.

#define mpbpl   (CHAR_BIT * sizeof (mp_limb_t))

Definition at line 34 of file atest-exp2.c.

#define N2   18

Definition at line 31 of file atest-exp2.c.

#define PRINT_ERRORS   0

Definition at line 28 of file atest-exp2.c.

#define SZ   (FRAC / mpbpl + 1)

Definition at line 35 of file atest-exp2.c.

#define TOL   80

Definition at line 30 of file atest-exp2.c.


Typedef Documentation

typedef mp_limb_t mp1[SZ]

Definition at line 36 of file atest-exp2.c.

typedef mp_limb_t mp2[SZ *2]

Definition at line 36 of file atest-exp2.c.


Function Documentation

static void exp2_mpn ( mp1  ex,
mp1  x 
) [static]

Definition at line 135 of file atest-exp2.c.

{
  mp2 tmp;
  mpn_mul_n (tmp, x, get_log2 (), SZ);
  assert(tmp[SZ * 2 - 1] == 0);
  exp_mpn (ex, tmp + FRAC / mpbpl);
}

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static void exp_mpn ( mp1  ex,
mp1  x 
) [static]

Definition at line 101 of file atest-exp2.c.

{
   unsigned int n;
   mp1 xp;
   mp2 tmp;
   mp_limb_t chk, round;
   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)
        round = 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);
}

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static mp_limb_t* get_log2 ( void  ) [static]

Definition at line 81 of file atest-exp2.c.

{
  static mp1 log2_m;
  static int log2_m_inited = 0;
  static const char log2[102] = "0" /* point */
    "b17217f7d1cf79abc9e3b39803f2f6af40f343267298b62d8a"
    "0d175b8baafa2be7b876206debac98559552fb4afa1b10ed2e";

  if (!log2_m_inited)
    {
      read_mpn_hex (log2_m, log2);
      log2_m_inited = 1;
    }
  return log2_m;
}

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int main ( void  )

Definition at line 159 of file atest-exp2.c.

{
  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);
  read_mpn_hex (e2, exp1);
  if (mpn_cmp (ex, e2, SZ) >= 0)
    mpn_sub_n (e3, ex, e2, SZ);
  else
    mpn_sub_n (e3, e2, 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;
}

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static int mpn_bitsize ( const mp_limb_t SRC_PTR,
mp_size_t  SIZE 
) [static]

Definition at line 145 of file atest-exp2.c.

{
  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;
}

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static void print_mpn_fp ( const mp_limb_t x,
unsigned int  dp,
unsigned int  base 
) [static]

Definition at line 49 of file atest-exp2.c.

{
   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);
     }
}

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static void read_mpn_hex ( mp_limb_t x,
const char *  str 
) [static]

Definition at line 70 of file atest-exp2.c.

{
  int i;

  memset (x, 0, sizeof (mp1));
  for (i = -1; i < 100 && i < FRAC / 4; ++i)
    x[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (hexdig, str[i + 1])
                                             - hexdig)
                                  << (FRAC - i * 4 - 4) % mpbpl);
}

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Variable Documentation

const char exp1[102] = "84d9045190cfef324e7738926cfbe5f4bf8d8d8c31d763da07" [static]

Definition at line 39 of file atest-exp2.c.

const char exp_m1[102] = "24b9d0a507daedb16400bf472b4215b8245b669d90d27a5aea" [static]

Definition at line 42 of file atest-exp2.c.

const char hexdig[] = "0123456789abcdef" [static]

Definition at line 46 of file atest-exp2.c.