s_atan.c revision 97409
155714Skris/* @(#)s_atan.c 5.1 93/09/24 */ 255714Skris/* 355714Skris * ==================================================== 455714Skris * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 555714Skris * 655714Skris * Developed at SunPro, a Sun Microsystems, Inc. business. 755714Skris * Permission to use, copy, modify, and distribute this 8296341Sdelphij * software is freely granted, provided that this notice 955714Skris * is preserved. 1055714Skris * ==================================================== 1155714Skris */ 1255714Skris 1355714Skris#ifndef lint 1455714Skrisstatic char rcsid[] = "$FreeBSD: head/lib/msun/src/s_atan.c 97409 2002-05-28 17:51:46Z alfred $"; 15296341Sdelphij#endif 1655714Skris 1755714Skris/* atan(x) 1855714Skris * Method 1955714Skris * 1. Reduce x to positive by atan(x) = -atan(-x). 2055714Skris * 2. According to the integer k=4t+0.25 chopped, t=x, the argument 2155714Skris * is further reduced to one of the following intervals and the 22296341Sdelphij * arctangent of t is evaluated by the corresponding formula: 2355714Skris * 2455714Skris * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) 2555714Skris * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) ) 2655714Skris * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) ) 2755714Skris * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) ) 2855714Skris * [39/16,INF] atan(x) = atan(INF) + atan( -1/t ) 2955714Skris * 3055714Skris * Constants: 3155714Skris * The hexadecimal values are the intended ones for the following 3255714Skris * constants. The decimal values may be used, provided that the 3355714Skris * compiler will convert from decimal to binary accurately enough 3455714Skris * to produce the hexadecimal values shown. 3555714Skris */ 3655714Skris 37296341Sdelphij#include "math.h" 3855714Skris#include "math_private.h" 3955714Skris 40296341Sdelphijstatic const double atanhi[] = { 4155714Skris 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ 4255714Skris 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */ 4355714Skris 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */ 4455714Skris 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */ 4555714Skris}; 4655714Skris 4755714Skrisstatic const double atanlo[] = { 4855714Skris 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ 4955714Skris 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */ 5055714Skris 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ 5155714Skris 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */ 52296341Sdelphij}; 5355714Skris 5455714Skrisstatic const double aT[] = { 5555714Skris 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */ 5655714Skris -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */ 5755714Skris 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */ 5855714Skris -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */ 5955714Skris 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */ 6055714Skris -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */ 6155714Skris 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */ 62296341Sdelphij -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ 63296341Sdelphij 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ 64296341Sdelphij -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ 65296341Sdelphij 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ 6655714Skris}; 6755714Skris 68109998Smarkm static const double 69296341Sdelphijone = 1.0, 7068651Skrishuge = 1.0e300; 7155714Skris 7255714Skris double __generic_atan(double x) 73109998Smarkm{ 7455714Skris double w,s1,s2,z; 7555714Skris int32_t ix,hx,id; 76296341Sdelphij 77296341Sdelphij GET_HIGH_WORD(hx,x); 78296341Sdelphij ix = hx&0x7fffffff; 79296341Sdelphij if(ix>=0x44100000) { /* if |x| >= 2^66 */ 80296341Sdelphij u_int32_t low; 81296341Sdelphij GET_LOW_WORD(low,x); 82296341Sdelphij if(ix>0x7ff00000|| 83296341Sdelphij (ix==0x7ff00000&&(low!=0))) 84296341Sdelphij return x+x; /* NaN */ 85296341Sdelphij if(hx>0) return atanhi[3]+atanlo[3]; 86296341Sdelphij else return -atanhi[3]-atanlo[3]; 87296341Sdelphij } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ 88296341Sdelphij if (ix < 0x3e200000) { /* |x| < 2^-29 */ 89296341Sdelphij if(huge+x>one) return x; /* raise inexact */ 90296341Sdelphij } 91296341Sdelphij id = -1; 92296341Sdelphij } else { 93296341Sdelphij x = fabs(x); 94296341Sdelphij if (ix < 0x3ff30000) { /* |x| < 1.1875 */ 95296341Sdelphij if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */ 96296341Sdelphij id = 0; x = (2.0*x-one)/(2.0+x); 97296341Sdelphij } else { /* 11/16<=|x|< 19/16 */ 98296341Sdelphij id = 1; x = (x-one)/(x+one); 99296341Sdelphij } 10055714Skris } else { 10155714Skris if (ix < 0x40038000) { /* |x| < 2.4375 */ 102296341Sdelphij id = 2; x = (x-1.5)/(one+1.5*x); 103296341Sdelphij } else { /* 2.4375 <= |x| < 2^66 */ 104296341Sdelphij id = 3; x = -1.0/x; 10555714Skris } 106296341Sdelphij }} 107296341Sdelphij /* end of argument reduction */ 108296341Sdelphij z = x*x; 109296341Sdelphij w = z*z; 110296341Sdelphij /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ 111296341Sdelphij s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); 11255714Skris s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); 11355714Skris if (id<0) return x - x*(s1+s2); 114296341Sdelphij else { 115296341Sdelphij z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); 116296341Sdelphij return (hx<0)? -z:z; 117296341Sdelphij } 118296341Sdelphij} 11955714Skris