exp2.c

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-----------
 
Copyright (c) 2002-2019 Advanced Micro Devices, Inc.
 
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#include "libm.h"
#include "libm_util.h"
 
#define USE_SPLITEXP
#define USE_SCALEDOUBLE_1
#define USE_SCALEDOUBLE_2
#define USE_ZERO_WITH_FLAGS
#define USE_INFINITY_WITH_FLAGS
#define USE_HANDLE_ERROR
 
#include "libm_inlines.h"
#undef USE_ZERO_WITH_FLAGS
#undef USE_SPLITEXP
#undef USE_SCALEDOUBLE_1
#undef USE_SCALEDOUBLE_2
#undef USE_INFINITY_WITH_FLAGS
#undef USE_HANDLE_ERROR
 
#include "libm_errno.h"
 
/* exp2 is only provided for use by powf under Windows, so give
   it a leading underscore. */
double FN_PROTOTYPE(_exp2)(double x)
{
  static const double
    max_exp2_arg = 1024.0,  /* 0x4090000000000000 */
    min_exp2_arg = -1074.0, /* 0xc090c80000000000 */
    log2 = 6.931471805599453094178e-01, /* 0x3fe62e42fefa39ef */
    log2_lead = 6.93147167563438415527E-01, /* 0x3fe62e42f8000000 */
    log2_tail = 1.29965068938898869640E-08, /* 0x3e4be8e7bcd5e4f1 */
    one_by_32_lead = 0.03125;
 
  double y, z1, z2, z, hx, tx, y1, y2;
  int m;
  unsigned long long ux, ax;
 
  /*
    Computation of exp2(x).
 
    We compute the values m, z1, and z2 such that
    exp2(x) = 2**m * (z1 + z2),  where exp2(x) is 2**x.
 
    Computations needed in order to obtain m, z1, and z2
    involve three steps.
 
    First, we reduce the argument x to the form
    x = n/32 + remainder,
    where n has the value of an integer and |remainder| <= 1/64.
    The value of n = x * 32 rounded to the nearest integer and
    the remainder = x - n/32.
 
    Second, we approximate exp2(r1 + r2) - 1 where r1 is the leading
    part of the remainder and r2 is the trailing part of the remainder.
 
    Third, we reconstruct exp2(x) so that
    exp2(x) = 2**m * (z1 + z2).
  */
 
 
  GET_BITS_DP64(x, ux);
  ax = ux & (~SIGNBIT_DP64);
 
  if (ax >= 0x4090000000000000) /* abs(x) >= 1024.0 */
    {
      if(ax >= 0x7ff0000000000000)
        {
          /* x is either NaN or infinity */
          if (ux & MANTBITS_DP64)
            /* x is NaN */
            return _handle_error("exp2", OP_EXP, ux|0x0008000000000000, _DOMAIN,
                                0, EDOM, x, 0.0, 1);
          else if (ux & SIGNBIT_DP64)
            /* x is negative infinity; return 0.0 with no flags. */
            return 0.0;
          else
            /* x is positive infinity */
            return x;
        }
      if (x > max_exp2_arg)
        /* Return +infinity with overflow flag */
        return _handle_error("exp2", OP_EXP, PINFBITPATT_DP64, _OVERFLOW,
                            AMD_F_OVERFLOW | AMD_F_INEXACT, ERANGE, x, 0.0, 1);
      else if (x < min_exp2_arg)
        /* x is negative. Return +zero with underflow and inexact flags */
        return _handle_error("exp2", OP_EXP, 0, _UNDERFLOW,
                            AMD_F_UNDERFLOW | AMD_F_INEXACT, ERANGE, x, 0.0, 1);
    }
 
 
  /* Handle small arguments separately */
  if (ax < 0x3fb7154764ee6c2f)   /* abs(x) < 1/(16*log2) */
    {
      if (ax < 0x3c00000000000000)   /* abs(x) < 2^(-63) */
        return 1.0 + x; /* Raises inexact if x is non-zero */
      else
        {
          /* Split x into hx (head) and tx (tail). */
          unsigned long long u;
          hx = x;
          GET_BITS_DP64(hx, u);
          u &= 0xfffffffff8000000;
          PUT_BITS_DP64(u, hx);
          tx = x - hx;
          /* Carefully multiply x by log2. y1 is the most significant
             part of the result, and y2 the least significant part */
          y1 = x * log2_lead;
          y2 = (((hx * log2_lead - y1) + hx * log2_tail) +
                  tx * log2_lead) + tx * log2_tail;
 
          y = y1 + y2;
        z = (9.99564649780173690e-1 +
             (1.61251249355268050e-5 +
              (2.37986978239838493e-2 +
                2.68724774856111190e-7*y)*y)*y)/
            (9.99564649780173692e-1 +
             (-4.99766199765151309e-1 +
              (1.070876894098586184e-1 +
               (-1.189773642681502232e-2 +
             5.9480622371960190616e-4*y)*y)*y)*y);
          z = ((z * y1) + (z * y2)) + 1.0;
        }
    }
  else
    {
      /* Find m, z1 and z2 such that exp2(x) = 2**m * (z1 + z2) */
 
      splitexp(x, log2, 32.0, one_by_32_lead, 0.0, &m, &z1, &z2);
 
      /* Scale (z1 + z2) by 2.0**m */
      if (m > EMIN_DP64 && m < EMAX_DP64)
    z = scaleDouble_1((z1+z2),m);
      else
    z = scaleDouble_2((z1+z2),m);
    }
  return z;
}