src/libm/s_atan.c
 changeset 4873 67ad1c88dda0 child 6044 35448a5ea044
```     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/src/libm/s_atan.c	Sun Aug 29 16:51:48 2010 -0700
1.3 @@ -0,0 +1,114 @@
1.4 +/*
1.5 + * ====================================================
1.7 + *
1.8 + * Developed at SunPro, a Sun Microsystems, Inc. business.
1.9 + * Permission to use, copy, modify, and distribute this
1.10 + * software is freely granted, provided that this notice
1.11 + * is preserved.
1.12 + * ====================================================
1.13 + */
1.14 +
1.15 +/* atan(x)
1.16 + * Method
1.17 + *   1. Reduce x to positive by atan(x) = -atan(-x).
1.18 + *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
1.19 + *      is further reduced to one of the following intervals and the
1.20 + *      arctangent of t is evaluated by the corresponding formula:
1.21 + *
1.22 + *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
1.23 + *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
1.24 + *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
1.25 + *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
1.26 + *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
1.27 + *
1.28 + * Constants:
1.29 + * The hexadecimal values are the intended ones for the following
1.30 + * constants. The decimal values may be used, provided that the
1.31 + * compiler will convert from decimal to binary accurately enough
1.32 + * to produce the hexadecimal values shown.
1.33 + */
1.34 +
1.35 +#include "math.h"
1.36 +#include "math_private.h"
1.37 +
1.38 +static const double atanhi[] = {
1.39 +  4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
1.40 +  7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
1.41 +  9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
1.42 +  1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
1.43 +};
1.44 +
1.45 +static const double atanlo[] = {
1.46 +  2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
1.47 +  3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
1.48 +  1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
1.49 +  6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
1.50 +};
1.51 +
1.52 +static const double aT[] = {
1.53 +  3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
1.54 + -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
1.55 +  1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
1.56 + -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
1.57 +  9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
1.58 + -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
1.59 +  6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
1.60 + -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
1.61 +  4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
1.62 + -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
1.63 +  1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
1.64 +};
1.65 +
1.66 +static const double
1.67 +one   = 1.0,
1.68 +huge   = 1.0e300;
1.69 +
1.70 +double atan(double x)
1.71 +{
1.72 +	double w,s1,s2,z;
1.73 +	int32_t ix,hx,id;
1.74 +
1.75 +	GET_HIGH_WORD(hx,x);
1.76 +	ix = hx&0x7fffffff;
1.77 +	if(ix>=0x44100000) {	/* if |x| >= 2^66 */
1.78 +	    u_int32_t low;
1.79 +	    GET_LOW_WORD(low,x);
1.80 +	    if(ix>0x7ff00000||
1.81 +		(ix==0x7ff00000&&(low!=0)))
1.82 +		return x+x;		/* NaN */
1.83 +	    if(hx>0) return  atanhi[3]+atanlo[3];
1.84 +	    else     return -atanhi[3]-atanlo[3];
1.85 +	} if (ix < 0x3fdc0000) {	/* |x| < 0.4375 */
1.86 +	    if (ix < 0x3e200000) {	/* |x| < 2^-29 */
1.87 +		if(huge+x>one) return x;	/* raise inexact */
1.88 +	    }
1.89 +	    id = -1;
1.90 +	} else {
1.91 +	x = fabs(x);
1.92 +	if (ix < 0x3ff30000) {		/* |x| < 1.1875 */
1.93 +	    if (ix < 0x3fe60000) {	/* 7/16 <=|x|<11/16 */
1.94 +		id = 0; x = (2.0*x-one)/(2.0+x);
1.95 +	    } else {			/* 11/16<=|x|< 19/16 */
1.96 +		id = 1; x  = (x-one)/(x+one);
1.97 +	    }
1.98 +	} else {
1.99 +	    if (ix < 0x40038000) {	/* |x| < 2.4375 */
1.100 +		id = 2; x  = (x-1.5)/(one+1.5*x);
1.101 +	    } else {			/* 2.4375 <= |x| < 2^66 */
1.102 +		id = 3; x  = -1.0/x;
1.103 +	    }
1.104 +	}}
1.105 +    /* end of argument reduction */
1.106 +	z = x*x;
1.107 +	w = z*z;
1.108 +    /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
1.109 +	s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
1.110 +	s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
1.111 +	if (id<0) return x - x*(s1+s2);
1.112 +	else {
1.113 +	    z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
1.114 +	    return (hx<0)? -z:z;
1.115 +	}
1.116 +}
1.117 +libm_hidden_def(atan)
```