src/libm/s_atan.c
author Ryan C. Gordon <icculus@icculus.org>
Tue, 26 May 2015 21:19:23 -0400
changeset 9649 d7762e30ba24
parent 8056 abd9434c5d3e
child 11683 48bcba563d9c
permissions -rw-r--r--
Stack hint should look for 0, not -1, and not care about environment variables.
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/*
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 * ====================================================
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 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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 *
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 * Developed at SunPro, a Sun Microsystems, Inc. business.
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 * Permission to use, copy, modify, and distribute this
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 * software is freely granted, provided that this notice
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 * is preserved.
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 * ====================================================
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 */
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/* atan(x)
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 * Method
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 *   1. Reduce x to positive by atan(x) = -atan(-x).
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 *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
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 *      is further reduced to one of the following intervals and the
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 *      arctangent of t is evaluated by the corresponding formula:
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 *
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 *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
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 *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
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 *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
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 *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
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 *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
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 *
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 * Constants:
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 * The hexadecimal values are the intended ones for the following
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 * constants. The decimal values may be used, provided that the
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 * compiler will convert from decimal to binary accurately enough
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 * to produce the hexadecimal values shown.
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 */
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#include "math_libm.h"
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#include "math_private.h"
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static const double atanhi[] = {
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  4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
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  7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
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  9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
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  1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
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};
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static const double atanlo[] = {
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  2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
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  3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
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  1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
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  6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
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};
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static const double aT[] = {
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  3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
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 -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
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  1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
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 -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
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  9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
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 -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
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  6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
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 -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
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  4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
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 -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
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  1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
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};
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static const double
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one   = 1.0,
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huge   = 1.0e300;
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double atan(double x)
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{
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	double w,s1,s2,z;
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	int32_t ix,hx,id;
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	GET_HIGH_WORD(hx,x);
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	ix = hx&0x7fffffff;
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	if(ix>=0x44100000) {	/* if |x| >= 2^66 */
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	    u_int32_t low;
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	    GET_LOW_WORD(low,x);
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	    if(ix>0x7ff00000||
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		(ix==0x7ff00000&&(low!=0)))
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		return x+x;		/* NaN */
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	    if(hx>0) return  atanhi[3]+atanlo[3];
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	    else     return -atanhi[3]-atanlo[3];
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	} if (ix < 0x3fdc0000) {	/* |x| < 0.4375 */
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	    if (ix < 0x3e200000) {	/* |x| < 2^-29 */
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		if(huge+x>one) return x;	/* raise inexact */
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	    }
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	    id = -1;
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	} else {
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	x = fabs(x);
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	if (ix < 0x3ff30000) {		/* |x| < 1.1875 */
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	    if (ix < 0x3fe60000) {	/* 7/16 <=|x|<11/16 */
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		id = 0; x = (2.0*x-one)/(2.0+x);
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	    } else {			/* 11/16<=|x|< 19/16 */
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		id = 1; x  = (x-one)/(x+one);
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	    }
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	} else {
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	    if (ix < 0x40038000) {	/* |x| < 2.4375 */
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		id = 2; x  = (x-1.5)/(one+1.5*x);
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	    } else {			/* 2.4375 <= |x| < 2^66 */
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		id = 3; x  = -1.0/x;
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	    }
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	}}
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    /* end of argument reduction */
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	z = x*x;
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	w = z*z;
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    /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
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	s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
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	s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
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	if (id<0) return x - x*(s1+s2);
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	else {
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	    z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
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	    return (hx<0)? -z:z;
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	}
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}
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libm_hidden_def(atan)
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