atan.c File Reference

#include "libm.h"

Include dependency graph for atan.c:

Go to the source code of this file.

Functions
double	atan (double x)

Variables
static const double	atanhi []
static const double	atanlo []
static const double	aT []

Function Documentation

atan()

double atan

(

double

x

)

Definition at line 77 of file atan.c.

{
    double_t w,s1,s2,z;
    uint32_t ix,sign;
    int id;
 
    GET_HIGH_WORD(ix, x);
    sign = ix >> 31;
    ix &= 0x7fffffff;
    if (ix >= 0x44100000) {   /* if |x| >= 2^66 */
        if (isnan(x))
            return x;
        z = atanhi[3] + 0x1p-120f;
        return sign ? -z : z;
    }
    if (ix < 0x3fdc0000) {    /* |x| < 0.4375 */
        if (ix < 0x3e400000) {  /* |x| < 2^-27 */
            if (ix < 0x00100000)
                /* raise underflow for subnormal x */
                FORCE_EVAL((float)x);
            return x;
        }
        id = -1;
    } else {
        x = fabs(x);
        if (ix < 0x3ff30000) {  /* |x| < 1.1875 */
            if (ix < 0x3fe60000) {  /*  7/16 <= |x| < 11/16 */
                id = 0;
                x = (2.0*x-1.0)/(2.0+x);
            } else {                /* 11/16 <= |x| < 19/16 */
                id = 1;
                x = (x-1.0)/(x+1.0);
            }
        } else {
            if (ix < 0x40038000) {  /* |x| < 2.4375 */
                id = 2;
                x = (x-1.5)/(1.0+1.5*x);
            } else {                /* 2.4375 <= |x| < 2^66 */
                id = 3;
                x = -1.0/x;
            }
        }
    }
    /* end of argument reduction */
    z = x*x;
    w = z*z;
    /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
    s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
    s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
    if (id < 0)
        return x - x*(s1+s2);
    z = atanhi[id] - (x*(s1+s2) - atanlo[id] - x);
    return sign ? -z : z;
}

Variable Documentation

aT

const double aT[]

static

Initial value:

= {
  3.33333333333329318027e-01, 
 -1.99999999998764832476e-01, 
  1.42857142725034663711e-01, 
 -1.11111104054623557880e-01, 
  9.09088713343650656196e-02, 
 -7.69187620504482999495e-02, 
  6.66107313738753120669e-02, 
 -5.83357013379057348645e-02, 
  4.97687799461593236017e-02, 
 -3.65315727442169155270e-02, 
  1.62858201153657823623e-02, 
}

Definition at line 63 of file atan.c.

Referenced by atan().

atanhi

const double atanhi[]

static

Initial value:

= {
  4.63647609000806093515e-01, 
  7.85398163397448278999e-01, 
  9.82793723247329054082e-01, 
  1.57079632679489655800e+00, 
}

Definition at line 49 of file atan.c.

Referenced by atan().

atanlo

const double atanlo[]

static

Initial value:

= {
  2.26987774529616870924e-17, 
  3.06161699786838301793e-17, 
  1.39033110312309984516e-17, 
  6.12323399573676603587e-17, 
}

Definition at line 56 of file atan.c.

Referenced by atan().