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glibc  2.9
Functions | Variables
e_acosl.c File Reference
#include "math.h"
#include "math_private.h"

Go to the source code of this file.

Functions

long double __ieee754_acosl (long double x)

Variables

static long double one = 1.0L
static long double pio2_hi = 1.5707963267948966192313216916397514420986L
static long double pio2_lo = 4.3359050650618905123985220130216759843812E-35L
static long double rS0 = 5.619049346208901520945464704848780243887E0L
static long double rS1 = -4.460504162777731472539175700169871920352E1L
static long double rS2 = 1.317669505315409261479577040530751477488E2L
static long double rS3 = -1.626532582423661989632442410808596009227E2L
static long double rS4 = 3.144806644195158614904369445440583873264E1L
static long double rS5 = 9.806674443470740708765165604769099559553E1L
static long double rS6 = -5.708468492052010816555762842394927806920E1L
static long double rS7 = -1.396540499232262112248553357962639431922E1L
static long double rS8 = 1.126243289311910363001762058295832610344E1L
static long double rS9 = 4.956179821329901954211277873774472383512E-1L
static long double rS10 = -3.313227657082367169241333738391762525780E-1L
static long double sS0 = -4.645814742084009935700221277307007679325E0L
static long double sS1 = 3.879074822457694323970438316317961918430E1L
static long double sS2 = -1.221986588013474694623973554726201001066E2L
static long double sS3 = 1.658821150347718105012079876756201905822E2L
static long double sS4 = -4.804379630977558197953176474426239748977E1L
static long double sS5 = -1.004296417397316948114344573811562952793E2L
static long double sS6 = 7.530281592861320234941101403870010111138E1L
static long double sS7 = 1.270735595411673647119592092304357226607E1L
static long double sS8 = -1.815144839646376500705105967064792930282E1L
static long double sS9 = -7.821597334910963922204235247786840828217E-2L
static long double acosr5625 = 9.7338991014954640492751132535550279812151E-1L
static long double pimacosr5625 = 2.1682027434402468335351320579240000860757E0L
static long double P0 = 2.177690192235413635229046633751390484892E0L
static long double P1 = -2.848698225706605746657192566166142909573E1L
static long double P2 = 1.040076477655245590871244795403659880304E2L
static long double P3 = -1.400087608918906358323551402881238180553E2L
static long double P4 = 2.221047917671449176051896400503615543757E1L
static long double P5 = 9.643714856395587663736110523917499638702E1L
static long double P6 = -5.158406639829833829027457284942389079196E1L
static long double P7 = -1.578651828337585944715290382181219741813E1L
static long double P8 = 1.093632715903802870546857764647931045906E1L
static long double P9 = 5.448925479898460003048760932274085300103E-1L
static long double P10 = -3.315886001095605268470690485170092986337E-1L
static long double Q0 = -1.958219113487162405143608843774587557016E0L
static long double Q1 = 2.614577866876185080678907676023269360520E1L
static long double Q2 = -9.990858606464150981009763389881793660938E1L
static long double Q3 = 1.443958741356995763628660823395334281596E2L
static long double Q4 = -3.206441012484232867657763518369723873129E1L
static long double Q5 = -1.048560885341833443564920145642588991492E2L
static long double Q6 = 6.745883931909770880159915641984874746358E1L
static long double Q7 = 1.806809656342804436118449982647641392951E1L
static long double Q8 = -1.770150690652438294290020775359580915464E1L
static long double Q9 = -5.659156469628629327045433069052560211164E-1L
static long double acosr4375 = 1.1179797320499710475919903296900511518755E0L
static long double pimacosr4375 = 2.0236129215398221908706530535894517323217E0L
static long double pS0 = -8.358099012470680544198472400254596543711E2L
static long double pS1 = 3.674973957689619490312782828051860366493E3L
static long double pS2 = -6.730729094812979665807581609853656623219E3L
static long double pS3 = 6.643843795209060298375552684423454077633E3L
static long double pS4 = -3.817341990928606692235481812252049415993E3L
static long double pS5 = 1.284635388402653715636722822195716476156E3L
static long double pS6 = -2.410736125231549204856567737329112037867E2L
static long double pS7 = 2.219191969382402856557594215833622156220E1L
static long double pS8 = -7.249056260830627156600112195061001036533E-1L
static long double pS9 = 1.055923570937755300061509030361395604448E-3L
static long double qS0 = -5.014859407482408326519083440151745519205E3L
static long double qS1 = 2.430653047950480068881028451580393430537E4L
static long double qS2 = -4.997904737193653607449250593976069726962E4L
static long double qS3 = 5.675712336110456923807959930107347511086E4L
static long double qS4 = -3.881523118339661268482937768522572588022E4L
static long double qS5 = 1.634202194895541569749717032234510811216E4L
static long double qS6 = -4.151452662440709301601820849901296953752E3L
static long double qS7 = 5.956050864057192019085175976175695342168E2L
static long double qS8 = -4.175375777334867025769346564600396877176E1L

Function Documentation

long double __ieee754_acosl ( long double  x)

Definition at line 160 of file e_acosl.c.

{
  long double z, r, w, p, q, s, t, f2;
  int32_t ix, sign;
  ieee854_long_double_shape_type u;

  u.value = x;
  sign = u.parts32.w0;
  ix = sign & 0x7fffffff;
  u.parts32.w0 = ix;        /* |x| */
  if (ix >= 0x3fff0000)            /* |x| >= 1 */
    {
      if (ix == 0x3fff0000
         && (u.parts32.w1 | u.parts32.w2 | u.parts32.w3) == 0)
       {                    /* |x| == 1 */
         if ((sign & 0x80000000) == 0)
           return 0.0;             /* acos(1) = 0  */
         else
           return (2.0 * pio2_hi) + (2.0 * pio2_lo);    /* acos(-1)= pi */
       }
      return (x - x) / (x - x);    /* acos(|x| > 1) is NaN */
    }
  else if (ix < 0x3ffe0000) /* |x| < 0.5 */
    {
      if (ix < 0x3fc60000)  /* |x| < 2**-57 */
       return pio2_hi + pio2_lo;
      if (ix < 0x3ffde000)  /* |x| < .4375 */
       {
         /* Arcsine of x.  */
         z = x * x;
         p = (((((((((pS9 * z
                     + pS8) * z
                    + pS7) * z
                   + pS6) * z
                  + pS5) * z
                 + pS4) * z
                + pS3) * z
               + pS2) * z
              + pS1) * z
              + pS0) * z;
         q = (((((((( z
                     + qS8) * z
                   + qS7) * z
                  + qS6) * z
                 + qS5) * z
                + qS4) * z
               + qS3) * z
              + qS2) * z
              + qS1) * z
           + qS0;
         r = x + x * p / q;
         z = pio2_hi - (r - pio2_lo);
         return z;
       }
      /* .4375 <= |x| < .5 */
      t = u.value - 0.4375L;
      p = ((((((((((P10 * t
                  + P9) * t
                 + P8) * t
                + P7) * t
               + P6) * t
              + P5) * t
              + P4) * t
             + P3) * t
            + P2) * t
           + P1) * t
          + P0) * t;

      q = (((((((((t
                 + Q9) * t
                + Q8) * t
               + Q7) * t
              + Q6) * t
              + Q5) * t
             + Q4) * t
            + Q3) * t
           + Q2) * t
          + Q1) * t
       + Q0;
      r = p / q;
      if (sign & 0x80000000)
       r = pimacosr4375 - r;
      else
       r = acosr4375 + r;
      return r;
    }
  else if (ix < 0x3ffe4000) /* |x| < 0.625 */
    {
      t = u.value - 0.5625L;
      p = ((((((((((rS10 * t
                  + rS9) * t
                 + rS8) * t
                + rS7) * t
               + rS6) * t
              + rS5) * t
              + rS4) * t
             + rS3) * t
            + rS2) * t
           + rS1) * t
          + rS0) * t;

      q = (((((((((t
                 + sS9) * t
                + sS8) * t
               + sS7) * t
              + sS6) * t
              + sS5) * t
             + sS4) * t
            + sS3) * t
           + sS2) * t
          + sS1) * t
       + sS0;
      if (sign & 0x80000000)
       r = pimacosr5625 - p / q;
      else
       r = acosr5625 + p / q;
      return r;
    }
  else
    {                       /* |x| >= .625 */
      z = (one - u.value) * 0.5;
      s = __ieee754_sqrtl (z);
      /* Compute an extended precision square root from
        the Newton iteration  s -> 0.5 * (s + z / s).
         The change w from s to the improved value is
           w = 0.5 * (s + z / s) - s  = (s^2 + z)/2s - s = (z - s^2)/2s.
          Express s = f1 + f2 where f1 * f1 is exactly representable.
         w = (z - s^2)/2s = (z - f1^2 - 2 f1 f2 - f2^2)/2s .
          s + w has extended precision.  */
      u.value = s;
      u.parts32.w2 = 0;
      u.parts32.w3 = 0;
      f2 = s - u.value;
      w = z - u.value * u.value;
      w = w - 2.0 * u.value * f2;
      w = w - f2 * f2;
      w = w / (2.0 * s);
      /* Arcsine of s.  */
      p = (((((((((pS9 * z
                 + pS8) * z
                + pS7) * z
               + pS6) * z
              + pS5) * z
              + pS4) * z
             + pS3) * z
            + pS2) * z
           + pS1) * z
          + pS0) * z;
      q = (((((((( z
                 + qS8) * z
               + qS7) * z
              + qS6) * z
              + qS5) * z
             + qS4) * z
            + qS3) * z
           + qS2) * z
          + qS1) * z
       + qS0;
      r = s + (w + s * p / q);

      if (sign & 0x80000000)
       w = pio2_hi + (pio2_lo - r);
      else
       w = r;
      return 2.0 * w;
    }
}

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Variable Documentation

long double acosr4375 = 1.1179797320499710475919903296900511518755E0L [static]

Definition at line 127 of file e_acosl.c.

long double acosr5625 = 9.7338991014954640492751132535550279812151E-1L [static]

Definition at line 97 of file e_acosl.c.

long double one = 1.0L [static]

Definition at line 65 of file e_acosl.c.

long double P0 = 2.177690192235413635229046633751390484892E0L [static]

Definition at line 104 of file e_acosl.c.

long double P1 = -2.848698225706605746657192566166142909573E1L [static]

Definition at line 105 of file e_acosl.c.

long double P10 = -3.315886001095605268470690485170092986337E-1L [static]

Definition at line 114 of file e_acosl.c.

long double P2 = 1.040076477655245590871244795403659880304E2L [static]

Definition at line 106 of file e_acosl.c.

long double P3 = -1.400087608918906358323551402881238180553E2L [static]

Definition at line 107 of file e_acosl.c.

long double P4 = 2.221047917671449176051896400503615543757E1L [static]

Definition at line 108 of file e_acosl.c.

long double P5 = 9.643714856395587663736110523917499638702E1L [static]

Definition at line 109 of file e_acosl.c.

long double P6 = -5.158406639829833829027457284942389079196E1L [static]

Definition at line 110 of file e_acosl.c.

long double P7 = -1.578651828337585944715290382181219741813E1L [static]

Definition at line 111 of file e_acosl.c.

long double P8 = 1.093632715903802870546857764647931045906E1L [static]

Definition at line 112 of file e_acosl.c.

long double P9 = 5.448925479898460003048760932274085300103E-1L [static]

Definition at line 113 of file e_acosl.c.

long double pimacosr4375 = 2.0236129215398221908706530535894517323217E0L [static]

Definition at line 128 of file e_acosl.c.

long double pimacosr5625 = 2.1682027434402468335351320579240000860757E0L [static]

Definition at line 98 of file e_acosl.c.

long double pio2_hi = 1.5707963267948966192313216916397514420986L [static]

Definition at line 66 of file e_acosl.c.

long double pio2_lo = 4.3359050650618905123985220130216759843812E-35L [static]

Definition at line 67 of file e_acosl.c.

long double pS0 = -8.358099012470680544198472400254596543711E2L [static]

Definition at line 133 of file e_acosl.c.

long double pS1 = 3.674973957689619490312782828051860366493E3L [static]

Definition at line 134 of file e_acosl.c.

long double pS2 = -6.730729094812979665807581609853656623219E3L [static]

Definition at line 135 of file e_acosl.c.

long double pS3 = 6.643843795209060298375552684423454077633E3L [static]

Definition at line 136 of file e_acosl.c.

long double pS4 = -3.817341990928606692235481812252049415993E3L [static]

Definition at line 137 of file e_acosl.c.

long double pS5 = 1.284635388402653715636722822195716476156E3L [static]

Definition at line 138 of file e_acosl.c.

long double pS6 = -2.410736125231549204856567737329112037867E2L [static]

Definition at line 139 of file e_acosl.c.

long double pS7 = 2.219191969382402856557594215833622156220E1L [static]

Definition at line 140 of file e_acosl.c.

long double pS8 = -7.249056260830627156600112195061001036533E-1L [static]

Definition at line 141 of file e_acosl.c.

long double pS9 = 1.055923570937755300061509030361395604448E-3L [static]

Definition at line 142 of file e_acosl.c.

long double Q0 = -1.958219113487162405143608843774587557016E0L [static]

Definition at line 115 of file e_acosl.c.

long double Q1 = 2.614577866876185080678907676023269360520E1L [static]

Definition at line 116 of file e_acosl.c.

long double Q2 = -9.990858606464150981009763389881793660938E1L [static]

Definition at line 117 of file e_acosl.c.

long double Q3 = 1.443958741356995763628660823395334281596E2L [static]

Definition at line 118 of file e_acosl.c.

long double Q4 = -3.206441012484232867657763518369723873129E1L [static]

Definition at line 119 of file e_acosl.c.

long double Q5 = -1.048560885341833443564920145642588991492E2L [static]

Definition at line 120 of file e_acosl.c.

long double Q6 = 6.745883931909770880159915641984874746358E1L [static]

Definition at line 121 of file e_acosl.c.

long double Q7 = 1.806809656342804436118449982647641392951E1L [static]

Definition at line 122 of file e_acosl.c.

long double Q8 = -1.770150690652438294290020775359580915464E1L [static]

Definition at line 123 of file e_acosl.c.

long double Q9 = -5.659156469628629327045433069052560211164E-1L [static]

Definition at line 124 of file e_acosl.c.

long double qS0 = -5.014859407482408326519083440151745519205E3L [static]

Definition at line 144 of file e_acosl.c.

long double qS1 = 2.430653047950480068881028451580393430537E4L [static]

Definition at line 145 of file e_acosl.c.

long double qS2 = -4.997904737193653607449250593976069726962E4L [static]

Definition at line 146 of file e_acosl.c.

long double qS3 = 5.675712336110456923807959930107347511086E4L [static]

Definition at line 147 of file e_acosl.c.

long double qS4 = -3.881523118339661268482937768522572588022E4L [static]

Definition at line 148 of file e_acosl.c.

long double qS5 = 1.634202194895541569749717032234510811216E4L [static]

Definition at line 149 of file e_acosl.c.

long double qS6 = -4.151452662440709301601820849901296953752E3L [static]

Definition at line 150 of file e_acosl.c.

long double qS7 = 5.956050864057192019085175976175695342168E2L [static]

Definition at line 151 of file e_acosl.c.

long double qS8 = -4.175375777334867025769346564600396877176E1L [static]

Definition at line 152 of file e_acosl.c.

long double rS0 = 5.619049346208901520945464704848780243887E0L [static]

Definition at line 73 of file e_acosl.c.

long double rS1 = -4.460504162777731472539175700169871920352E1L [static]

Definition at line 74 of file e_acosl.c.

long double rS10 = -3.313227657082367169241333738391762525780E-1L [static]

Definition at line 83 of file e_acosl.c.

long double rS2 = 1.317669505315409261479577040530751477488E2L [static]

Definition at line 75 of file e_acosl.c.

long double rS3 = -1.626532582423661989632442410808596009227E2L [static]

Definition at line 76 of file e_acosl.c.

long double rS4 = 3.144806644195158614904369445440583873264E1L [static]

Definition at line 77 of file e_acosl.c.

long double rS5 = 9.806674443470740708765165604769099559553E1L [static]

Definition at line 78 of file e_acosl.c.

long double rS6 = -5.708468492052010816555762842394927806920E1L [static]

Definition at line 79 of file e_acosl.c.

long double rS7 = -1.396540499232262112248553357962639431922E1L [static]

Definition at line 80 of file e_acosl.c.

long double rS8 = 1.126243289311910363001762058295832610344E1L [static]

Definition at line 81 of file e_acosl.c.

long double rS9 = 4.956179821329901954211277873774472383512E-1L [static]

Definition at line 82 of file e_acosl.c.

long double sS0 = -4.645814742084009935700221277307007679325E0L [static]

Definition at line 85 of file e_acosl.c.

long double sS1 = 3.879074822457694323970438316317961918430E1L [static]

Definition at line 86 of file e_acosl.c.

long double sS2 = -1.221986588013474694623973554726201001066E2L [static]

Definition at line 87 of file e_acosl.c.

long double sS3 = 1.658821150347718105012079876756201905822E2L [static]

Definition at line 88 of file e_acosl.c.

long double sS4 = -4.804379630977558197953176474426239748977E1L [static]

Definition at line 89 of file e_acosl.c.

long double sS5 = -1.004296417397316948114344573811562952793E2L [static]

Definition at line 90 of file e_acosl.c.

long double sS6 = 7.530281592861320234941101403870010111138E1L [static]

Definition at line 91 of file e_acosl.c.

long double sS7 = 1.270735595411673647119592092304357226607E1L [static]

Definition at line 92 of file e_acosl.c.

long double sS8 = -1.815144839646376500705105967064792930282E1L [static]

Definition at line 93 of file e_acosl.c.

long double sS9 = -7.821597334910963922204235247786840828217E-2L [static]

Definition at line 94 of file e_acosl.c.