s_atan.c revision 176451
12116Sjkh/* @(#)s_atan.c 5.1 93/09/24 */ 22116Sjkh/* 32116Sjkh * ==================================================== 42116Sjkh * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 52116Sjkh * 62116Sjkh * Developed at SunPro, a Sun Microsystems, Inc. business. 72116Sjkh * Permission to use, copy, modify, and distribute this 88870Srgrimes * software is freely granted, provided that this notice 92116Sjkh * is preserved. 102116Sjkh * ==================================================== 112116Sjkh */ 122116Sjkh 13176451Sdas#include <sys/cdefs.h> 14176451Sdas__FBSDID("$FreeBSD: head/lib/msun/src/s_atan.c 176451 2008-02-22 02:30:36Z das $"); 152116Sjkh 162116Sjkh/* atan(x) 172116Sjkh * Method 182116Sjkh * 1. Reduce x to positive by atan(x) = -atan(-x). 192116Sjkh * 2. According to the integer k=4t+0.25 chopped, t=x, the argument 202116Sjkh * is further reduced to one of the following intervals and the 212116Sjkh * arctangent of t is evaluated by the corresponding formula: 222116Sjkh * 232116Sjkh * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) 242116Sjkh * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) ) 252116Sjkh * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) ) 262116Sjkh * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) ) 272116Sjkh * [39/16,INF] atan(x) = atan(INF) + atan( -1/t ) 282116Sjkh * 292116Sjkh * Constants: 308870Srgrimes * The hexadecimal values are the intended ones for the following 318870Srgrimes * constants. The decimal values may be used, provided that the 328870Srgrimes * compiler will convert from decimal to binary accurately enough 332116Sjkh * to produce the hexadecimal values shown. 342116Sjkh */ 352116Sjkh 362116Sjkh#include "math.h" 372116Sjkh#include "math_private.h" 382116Sjkh 392116Sjkhstatic const double atanhi[] = { 402116Sjkh 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ 412116Sjkh 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */ 422116Sjkh 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */ 432116Sjkh 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */ 442116Sjkh}; 452116Sjkh 462116Sjkhstatic const double atanlo[] = { 472116Sjkh 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ 482116Sjkh 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */ 492116Sjkh 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ 502116Sjkh 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */ 512116Sjkh}; 522116Sjkh 532116Sjkhstatic const double aT[] = { 542116Sjkh 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */ 552116Sjkh -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */ 562116Sjkh 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */ 572116Sjkh -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */ 582116Sjkh 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */ 592116Sjkh -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */ 602116Sjkh 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */ 612116Sjkh -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ 622116Sjkh 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ 632116Sjkh -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ 642116Sjkh 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ 652116Sjkh}; 662116Sjkh 678870Srgrimes static const double 682116Sjkhone = 1.0, 692116Sjkhhuge = 1.0e300; 702116Sjkh 7197413Salfreddouble 72117912Speteratan(double x) 732116Sjkh{ 742116Sjkh double w,s1,s2,z; 752116Sjkh int32_t ix,hx,id; 762116Sjkh 772116Sjkh GET_HIGH_WORD(hx,x); 782116Sjkh ix = hx&0x7fffffff; 792116Sjkh if(ix>=0x44100000) { /* if |x| >= 2^66 */ 802116Sjkh u_int32_t low; 812116Sjkh GET_LOW_WORD(low,x); 822116Sjkh if(ix>0x7ff00000|| 832116Sjkh (ix==0x7ff00000&&(low!=0))) 842116Sjkh return x+x; /* NaN */ 852116Sjkh if(hx>0) return atanhi[3]+atanlo[3]; 862116Sjkh else return -atanhi[3]-atanlo[3]; 872116Sjkh } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ 882116Sjkh if (ix < 0x3e200000) { /* |x| < 2^-29 */ 892116Sjkh if(huge+x>one) return x; /* raise inexact */ 902116Sjkh } 912116Sjkh id = -1; 922116Sjkh } else { 932116Sjkh x = fabs(x); 942116Sjkh if (ix < 0x3ff30000) { /* |x| < 1.1875 */ 952116Sjkh if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */ 968870Srgrimes id = 0; x = (2.0*x-one)/(2.0+x); 972116Sjkh } else { /* 11/16<=|x|< 19/16 */ 988870Srgrimes id = 1; x = (x-one)/(x+one); 992116Sjkh } 1002116Sjkh } else { 1012116Sjkh if (ix < 0x40038000) { /* |x| < 2.4375 */ 1022116Sjkh id = 2; x = (x-1.5)/(one+1.5*x); 1032116Sjkh } else { /* 2.4375 <= |x| < 2^66 */ 1042116Sjkh id = 3; x = -1.0/x; 1052116Sjkh } 1062116Sjkh }} 1072116Sjkh /* end of argument reduction */ 1082116Sjkh z = x*x; 1092116Sjkh w = z*z; 1102116Sjkh /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ 1112116Sjkh s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); 1122116Sjkh s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); 1132116Sjkh if (id<0) return x - x*(s1+s2); 1142116Sjkh else { 1152116Sjkh z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); 1162116Sjkh return (hx<0)? -z:z; 1172116Sjkh } 1182116Sjkh} 119