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glibc  2.9
Functions | Variables
s_log1pl.c File Reference
#include "math.h"
#include "math_private.h"
#include <math_ldbl_opt.h>

Go to the source code of this file.

Functions

long double __log1pl (long double xm1)
 long_double_symbol (libm, __log1pl, log1pl)

Variables

static const long double P12 = 1.538612243596254322971797716843006400388E-6L
static const long double P11 = 4.998469661968096229986658302195402690910E-1L
static const long double P10 = 2.321125933898420063925789532045674660756E1L
static const long double P9 = 4.114517881637811823002128927449878962058E2L
static const long double P8 = 3.824952356185897735160588078446136783779E3L
static const long double P7 = 2.128857716871515081352991964243375186031E4L
static const long double P6 = 7.594356839258970405033155585486712125861E4L
static const long double P5 = 1.797628303815655343403735250238293741397E5L
static const long double P4 = 2.854829159639697837788887080758954924001E5L
static const long double P3 = 3.007007295140399532324943111654767187848E5L
static const long double P2 = 2.014652742082537582487669938141683759923E5L
static const long double P1 = 7.771154681358524243729929227226708890930E4L
static const long double P0 = 1.313572404063446165910279910527789794488E4L
static const long double Q11 = 4.839208193348159620282142911143429644326E1L
static const long double Q10 = 9.104928120962988414618126155557301584078E2L
static const long double Q9 = 9.147150349299596453976674231612674085381E3L
static const long double Q8 = 5.605842085972455027590989944010492125825E4L
static const long double Q7 = 2.248234257620569139969141618556349415120E5L
static const long double Q6 = 6.132189329546557743179177159925690841200E5L
static const long double Q5 = 1.158019977462989115839826904108208787040E6L
static const long double Q4 = 1.514882452993549494932585972882995548426E6L
static const long double Q3 = 1.347518538384329112529391120390701166528E6L
static const long double Q2 = 7.777690340007566932935753241556479363645E5L
static const long double Q1 = 2.626900195321832660448791748036714883242E5L
static const long double Q0 = 3.940717212190338497730839731583397586124E4L
static const long double R5 = -8.828896441624934385266096344596648080902E-1L
static const long double R4 = 8.057002716646055371965756206836056074715E1L
static const long double R3 = -2.024301798136027039250415126250455056397E3L
static const long double R2 = 2.048819892795278657810231591630928516206E4L
static const long double R1 = -8.977257995689735303686582344659576526998E4L
static const long double R0 = 1.418134209872192732479751274970992665513E5L
static const long double S5 = -1.186359407982897997337150403816839480438E2L
static const long double S4 = 3.998526750980007367835804959888064681098E3L
static const long double S3 = -5.748542087379434595104154610899551484314E4L
static const long double S2 = 4.001557694070773974936904547424676279307E5L
static const long double S1 = -1.332535117259762928288745111081235577029E6L
static const long double S0 = 1.701761051846631278975701529965589676574E6L
static const long double C1 = 6.93145751953125E-1L
static const long double C2 = 1.428606820309417232121458176568075500134E-6L
static const long double sqrth = 0.7071067811865475244008443621048490392848L
static const long double maxlog = 1.1356523406294143949491931077970764891253E4L
static const long double big = 2e300L
static const long double zero = 0.0L

Function Documentation

long double __log1pl ( long double  xm1)

Definition at line 126 of file s_log1pl.c.

{
  long double x, y, z, r, s;
  ieee854_long_double_shape_type u;
  int32_t hx;
  int e;

  /* Test for NaN or infinity input. */
  u.value = xm1;
  hx = u.parts32.w0;
  if (hx >= 0x7ff00000)
    return xm1;

  /* log1p(+- 0) = +- 0.  */
  if (((hx & 0x7fffffff) == 0)
      && (u.parts32.w1 | (u.parts32.w2 & 0x7fffffff) | u.parts32.w3) == 0)
    return xm1;

  x = xm1 + 1.0L;

  /* log1p(-1) = -inf */
  if (x <= 0.0L)
    {
      if (x == 0.0L)
       return (-1.0L / (x - x));
      else
       return (zero / (x - x));
    }

  /* Separate mantissa from exponent.  */

  /* Use frexp used so that denormal numbers will be handled properly.  */
  x = __frexpl (x, &e);

  /* Logarithm using log(x) = z + z^3 P(z^2)/Q(z^2),
     where z = 2(x-1)/x+1).  */
  if ((e > 2) || (e < -2))
    {
      if (x < sqrth)
       {                    /* 2( 2x-1 )/( 2x+1 ) */
         e -= 1;
         z = x - 0.5L;
         y = 0.5L * z + 0.5L;
       }
      else
       {                    /*  2 (x-1)/(x+1)   */
         z = x - 0.5L;
         z -= 0.5L;
         y = 0.5L * x + 0.5L;
       }
      x = z / y;
      z = x * x;
      r = ((((R5 * z
             + R4) * z
            + R3) * z
           + R2) * z
          + R1) * z
       + R0;
      s = (((((z
              + S5) * z
             + S4) * z
            + S3) * z
           + S2) * z
          + S1) * z
       + S0;
      z = x * (z * r / s);
      z = z + e * C2;
      z = z + x;
      z = z + e * C1;
      return (z);
    }


  /* Logarithm using log(1+x) = x - .5x^2 + x^3 P(x)/Q(x). */

  if (x < sqrth)
    {
      e -= 1;
      if (e != 0)
       x = 2.0L * x - 1.0L; /*  2x - 1  */
      else
       x = xm1;
    }
  else
    {
      if (e != 0)
       x = x - 1.0L;
      else
       x = xm1;
    }
  z = x * x;
  r = (((((((((((P12 * x
               + P11) * x
              + P10) * x
              + P9) * x
             + P8) * x
            + P7) * x
           + P6) * x
          + P5) * x
         + P4) * x
        + P3) * x
       + P2) * x
       + P1) * x
    + P0;
  s = (((((((((((x
               + Q11) * x
              + Q10) * x
              + Q9) * x
             + Q8) * x
            + Q7) * x
           + Q6) * x
          + Q5) * x
         + Q4) * x
        + Q3) * x
       + Q2) * x
       + Q1) * x
    + Q0;
  y = x * (z * r / s);
  y = y + e * C2;
  z = y - 0.5L * z;
  z = z + x;
  z = z + e * C1;
  return (z);
}

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long_double_symbol ( libm  ,
__log1pl  ,
log1pl   
)

Variable Documentation

const long double big = 2e300L [static]

Definition at line 121 of file s_log1pl.c.

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

Definition at line 115 of file s_log1pl.c.

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

Definition at line 116 of file s_log1pl.c.

const long double maxlog = 1.1356523406294143949491931077970764891253E4L [static]

Definition at line 120 of file s_log1pl.c.

const long double P0 = 1.313572404063446165910279910527789794488E4L [static]

Definition at line 78 of file s_log1pl.c.

const long double P1 = 7.771154681358524243729929227226708890930E4L [static]

Definition at line 77 of file s_log1pl.c.

const long double P10 = 2.321125933898420063925789532045674660756E1L [static]

Definition at line 68 of file s_log1pl.c.

const long double P11 = 4.998469661968096229986658302195402690910E-1L [static]

Definition at line 67 of file s_log1pl.c.

const long double P12 = 1.538612243596254322971797716843006400388E-6L [static]

Definition at line 66 of file s_log1pl.c.

const long double P2 = 2.014652742082537582487669938141683759923E5L [static]

Definition at line 76 of file s_log1pl.c.

const long double P3 = 3.007007295140399532324943111654767187848E5L [static]

Definition at line 75 of file s_log1pl.c.

const long double P4 = 2.854829159639697837788887080758954924001E5L [static]

Definition at line 74 of file s_log1pl.c.

const long double P5 = 1.797628303815655343403735250238293741397E5L [static]

Definition at line 73 of file s_log1pl.c.

const long double P6 = 7.594356839258970405033155585486712125861E4L [static]

Definition at line 72 of file s_log1pl.c.

const long double P7 = 2.128857716871515081352991964243375186031E4L [static]

Definition at line 71 of file s_log1pl.c.

const long double P8 = 3.824952356185897735160588078446136783779E3L [static]

Definition at line 70 of file s_log1pl.c.

const long double P9 = 4.114517881637811823002128927449878962058E2L [static]

Definition at line 69 of file s_log1pl.c.

const long double Q0 = 3.940717212190338497730839731583397586124E4L [static]

Definition at line 91 of file s_log1pl.c.

const long double Q1 = 2.626900195321832660448791748036714883242E5L [static]

Definition at line 90 of file s_log1pl.c.

const long double Q10 = 9.104928120962988414618126155557301584078E2L [static]

Definition at line 81 of file s_log1pl.c.

const long double Q11 = 4.839208193348159620282142911143429644326E1L [static]

Definition at line 80 of file s_log1pl.c.

const long double Q2 = 7.777690340007566932935753241556479363645E5L [static]

Definition at line 89 of file s_log1pl.c.

const long double Q3 = 1.347518538384329112529391120390701166528E6L [static]

Definition at line 88 of file s_log1pl.c.

const long double Q4 = 1.514882452993549494932585972882995548426E6L [static]

Definition at line 87 of file s_log1pl.c.

const long double Q5 = 1.158019977462989115839826904108208787040E6L [static]

Definition at line 86 of file s_log1pl.c.

const long double Q6 = 6.132189329546557743179177159925690841200E5L [static]

Definition at line 85 of file s_log1pl.c.

const long double Q7 = 2.248234257620569139969141618556349415120E5L [static]

Definition at line 84 of file s_log1pl.c.

const long double Q8 = 5.605842085972455027590989944010492125825E4L [static]

Definition at line 83 of file s_log1pl.c.

const long double Q9 = 9.147150349299596453976674231612674085381E3L [static]

Definition at line 82 of file s_log1pl.c.

const long double R0 = 1.418134209872192732479751274970992665513E5L [static]

Definition at line 105 of file s_log1pl.c.

const long double R1 = -8.977257995689735303686582344659576526998E4L [static]

Definition at line 104 of file s_log1pl.c.

const long double R2 = 2.048819892795278657810231591630928516206E4L [static]

Definition at line 103 of file s_log1pl.c.

const long double R3 = -2.024301798136027039250415126250455056397E3L [static]

Definition at line 102 of file s_log1pl.c.

const long double R4 = 8.057002716646055371965756206836056074715E1L [static]

Definition at line 101 of file s_log1pl.c.

const long double R5 = -8.828896441624934385266096344596648080902E-1L [static]

Definition at line 100 of file s_log1pl.c.

const long double S0 = 1.701761051846631278975701529965589676574E6L [static]

Definition at line 112 of file s_log1pl.c.

const long double S1 = -1.332535117259762928288745111081235577029E6L [static]

Definition at line 111 of file s_log1pl.c.

const long double S2 = 4.001557694070773974936904547424676279307E5L [static]

Definition at line 110 of file s_log1pl.c.

const long double S3 = -5.748542087379434595104154610899551484314E4L [static]

Definition at line 109 of file s_log1pl.c.

const long double S4 = 3.998526750980007367835804959888064681098E3L [static]

Definition at line 108 of file s_log1pl.c.

const long double S5 = -1.186359407982897997337150403816839480438E2L [static]

Definition at line 107 of file s_log1pl.c.

const long double sqrth = 0.7071067811865475244008443621048490392848L [static]

Definition at line 118 of file s_log1pl.c.

const long double zero = 0.0L [static]

Definition at line 122 of file s_log1pl.c.