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glibc  2.9
Functions | Variables
s_expm1l.c File Reference
#include "math.h"
#include "math_private.h"
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Go to the source code of this file.

Functions

long double __expm1l (long double x)

Variables

static const long double P0 = 2.943520915569954073888921213330863757240E8L
static const long double P1 = -5.722847283900608941516165725053359168840E7L
static const long double P2 = 8.944630806357575461578107295909719817253E6L
static const long double P3 = -7.212432713558031519943281748462837065308E5L
static const long double P4 = 4.578962475841642634225390068461943438441E4L
static const long double P5 = -1.716772506388927649032068540558788106762E3L
static const long double P6 = 4.401308817383362136048032038528753151144E1L
static const long double P7 = -4.888737542888633647784737721812546636240E-1L
static const long double Q0 = 1.766112549341972444333352727998584753865E9L
static const long double Q1 = -7.848989743695296475743081255027098295771E8L
static const long double Q2 = 1.615869009634292424463780387327037251069E8L
static const long double Q3 = -2.019684072836541751428967854947019415698E7L
static const long double Q4 = 1.682912729190313538934190635536631941751E6L
static const long double Q5 = -9.615511549171441430850103489315371768998E4L
static const long double Q6 = 3.697714952261803935521187272204485251835E3L
static const long double Q7 = -8.802340681794263968892934703309274564037E1L
static const long double C1 = 6.93145751953125E-1L
static const long double C2 = 1.428606820309417232121458176568075500134E-6L
static const long double maxlog = 1.1356523406294143949491931077970764891253E4L
static const long double minarg = -7.9018778583833765273564461846232128760607E1L
static const long double big = 2e4932L

Function Documentation

long double __expm1l ( long double  x)

Definition at line 92 of file s_expm1l.c.

{
  long double px, qx, xx;
  int32_t ix, sign;
  ieee854_long_double_shape_type u;
  int k;

  /* Detect infinity and NaN.  */
  u.value = x;
  ix = u.parts32.w0;
  sign = ix & 0x80000000;
  ix &= 0x7fffffff;
  if (ix >= 0x7fff0000)
    {
      /* Infinity. */
      if (((ix & 0xffff) | u.parts32.w1 | u.parts32.w2 | u.parts32.w3) == 0)
       {
         if (sign)
           return -1.0L;
         else
           return x;
       }
      /* NaN. No invalid exception. */
      return x;
    }

  /* expm1(+- 0) = +- 0.  */
  if ((ix == 0) && (u.parts32.w1 | u.parts32.w2 | u.parts32.w3) == 0)
    return x;

  /* Overflow.  */
  if (x > maxlog)
    return (big * big);

  /* Minimum value.  */
  if (x < minarg)
    return (4.0/big - 1.0L);

  /* Express x = ln 2 (k + remainder), remainder not exceeding 1/2. */
  xx = C1 + C2;                    /* ln 2. */
  px = __floorl (0.5 + x / xx);
  k = px;
  /* remainder times ln 2 */
  x -= px * C1;
  x -= px * C2;

  /* Approximate exp(remainder ln 2).  */
  px = (((((((P7 * x
             + P6) * x
            + P5) * x + P4) * x + P3) * x + P2) * x + P1) * x + P0) * x;

  qx = (((((((x
             + Q7) * x
            + Q6) * x + Q5) * x + Q4) * x + Q3) * x + Q2) * x + Q1) * x + Q0;

  xx = x * x;
  qx = x + (0.5 * xx + xx * px / qx);

  /* exp(x) = exp(k ln 2) exp(remainder ln 2) = 2^k exp(remainder ln 2).

  We have qx = exp(remainder ln 2) - 1, so
  exp(x) - 1 = 2^k (qx + 1) - 1
             = 2^k qx + 2^k - 1.  */

  px = __ldexpl (1.0L, k);
  x = px * qx + (px - 1.0);
  return x;
}

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Variable Documentation

const long double big = 2e4932L [static]

Definition at line 88 of file s_expm1l.c.

const long double C1 = 6.93145751953125E-1L [static]

Definition at line 83 of file s_expm1l.c.

const long double C2 = 1.428606820309417232121458176568075500134E-6L [static]

Definition at line 84 of file s_expm1l.c.

const long double maxlog = 1.1356523406294143949491931077970764891253E4L [static]

Definition at line 86 of file s_expm1l.c.

const long double minarg = -7.9018778583833765273564461846232128760607E1L [static]

Definition at line 88 of file s_expm1l.c.

const long double P0 = 2.943520915569954073888921213330863757240E8L [static]

Definition at line 64 of file s_expm1l.c.

const long double P1 = -5.722847283900608941516165725053359168840E7L [static]

Definition at line 65 of file s_expm1l.c.

const long double P2 = 8.944630806357575461578107295909719817253E6L [static]

Definition at line 66 of file s_expm1l.c.

const long double P3 = -7.212432713558031519943281748462837065308E5L [static]

Definition at line 67 of file s_expm1l.c.

const long double P4 = 4.578962475841642634225390068461943438441E4L [static]

Definition at line 68 of file s_expm1l.c.

const long double P5 = -1.716772506388927649032068540558788106762E3L [static]

Definition at line 69 of file s_expm1l.c.

const long double P6 = 4.401308817383362136048032038528753151144E1L [static]

Definition at line 70 of file s_expm1l.c.

const long double P7 = -4.888737542888633647784737721812546636240E-1L [static]

Definition at line 71 of file s_expm1l.c.

const long double Q0 = 1.766112549341972444333352727998584753865E9L [static]

Definition at line 72 of file s_expm1l.c.

const long double Q1 = -7.848989743695296475743081255027098295771E8L [static]

Definition at line 73 of file s_expm1l.c.

const long double Q2 = 1.615869009634292424463780387327037251069E8L [static]

Definition at line 74 of file s_expm1l.c.

const long double Q3 = -2.019684072836541751428967854947019415698E7L [static]

Definition at line 75 of file s_expm1l.c.

const long double Q4 = 1.682912729190313538934190635536631941751E6L [static]

Definition at line 76 of file s_expm1l.c.

const long double Q5 = -9.615511549171441430850103489315371768998E4L [static]

Definition at line 77 of file s_expm1l.c.

const long double Q6 = 3.697714952261803935521187272204485251835E3L [static]

Definition at line 78 of file s_expm1l.c.

const long double Q7 = -8.802340681794263968892934703309274564037E1L [static]

Definition at line 79 of file s_expm1l.c.