atan.c File Reference

#include "prim.h"
#include "math.h"

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Functions
double	atan (double x)
	Inverse trigonometric tangent function. More...

Variables
static const double	atanhi []
static const double	atanlo []
static const double	aT []
static const double	one = 1.0
static const double	huge = 1.0e300

Function Documentation

double atan

(

double

x

)

Inverse trigonometric tangent function.

Version

1.3

Date

95/01/18

Method
  1. Reduce x to positive by atan(x) = -atan(-x).
  2. According to the integer k=4t+0.25 chopped, t=x, the argument
     is further reduced to one of the following intervals and the
     arctangent of t is evaluated by the corresponding formula:

     [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
     [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
     [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
     [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
     [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )

Constants:
The hexadecimal values are the intended ones for the following
constants. The decimal values may be used, provided that the
compiler will convert from decimal to binary accurately enough
to produce the hexadecimal values shown.

Copyright

Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. Developed at SunSoft, a Sun Microsystems, Inc. business. Permission to use, copy, modify, and distribute this software is freely granted, provided that this notice is preserved.

Definition at line 109 of file atan.c.

References aT, atanhi, atanlo, huge, and one.

Referenced by RealNumber::ArcCotangent(), RealNumber::ArcTangent(), and atan2().

{
    double w,s1,s2,z;
    sword ix,hx,id;

    GET_HIGH_WORD(hx,x);
    ix = hx&0x7fffffff;
    if(ix>=0x44100000) {    /* if |x| >= 2^66 */
        uword low;

        GET_LOW_WORD(low,x);
        if(ix>0x7ff00000||
                (ix==0x7ff00000&&(low!=0)))
            return x+x;     /* NaN */
        if(hx>0) return  atanhi[3]+atanlo[3];
        else     return -atanhi[3]-atanlo[3];
    }
    if (ix < 0x3fdc0000) {  /* |x| < 0.4375 */
        if (ix < 0x3e200000) {  /* |x| < 2^-29 */
            if(huge+x>one) return x;    /* raise inexact */
        }
        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-one)/(2.0+x);
            } else {            /* 11/16<=|x|< 19/16 */
                id = 1;
                x  = (x-one)/(x+one);
            }
        } else {
            if (ix < 0x40038000) {  /* |x| < 2.4375 */
                id = 2;
                x  = (x-1.5)/(one+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);
    else {
        z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
        return (hx<0)? -z:z;
    }
}

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Variable Documentation

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 61 of file atan.c.

Referenced by atan().

const double atanhi[]

static

Initial value:

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

Definition at line 47 of file atan.c.

Referenced by atan().

const double atanlo[]

static

Initial value:

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

Definition at line 54 of file atan.c.

Referenced by atan().

const double huge = 1.0e300

static

Definition at line 77 of file atan.c.

Referenced by atan().

const double one = 1.0

static

Definition at line 76 of file atan.c.

Referenced by atan().