12aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm/* @(#)s_atan.c 5.1 93/09/24 */ 22aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm/* 32aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm * ==================================================== 42aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 52aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm * 62aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm * Developed at SunPro, a Sun Microsystems, Inc. business. 72aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm * Permission to use, copy, modify, and distribute this 82aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm * software is freely granted, provided that this notice 92aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm * is preserved. 102aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm * ==================================================== 112aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm */ 122aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm#include <LibConfig.h> 132aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm#include <sys/EfiCdefs.h> 142aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm#if defined(LIBM_SCCS) && !defined(lint) 152aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm__RCSID("$NetBSD: s_atan.c,v 1.11 2002/05/26 22:01:54 wiz Exp $"); 162aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm#endif 172aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm 182aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm/* atan(x) 192aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm * Method 202aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm * 1. Reduce x to positive by atan(x) = -atan(-x). 212aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm * 2. According to the integer k=4t+0.25 chopped, t=x, the argument 222aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm * is further reduced to one of the following intervals and the 232aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm * arctangent of t is evaluated by the corresponding formula: 242aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm * 252aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) 262aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) ) 272aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) ) 282aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) ) 292aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm * [39/16,INF] atan(x) = atan(INF) + atan( -1/t ) 302aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm * 312aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm * Constants: 322aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm * The hexadecimal values are the intended ones for the following 332aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm * constants. The decimal values may be used, provided that the 342aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm * compiler will convert from decimal to binary accurately enough 352aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm * to produce the hexadecimal values shown. 362aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm */ 372aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm 382aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm#include "math.h" 392aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm#include "math_private.h" 402aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm 412aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylmstatic const double atanhi[] = { 422aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ 432aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */ 442aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */ 452aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */ 462aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm}; 472aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm 482aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylmstatic const double atanlo[] = { 492aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ 502aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */ 512aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ 522aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */ 532aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm}; 542aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm 552aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylmstatic const double aT[] = { 562aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */ 572aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */ 582aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */ 592aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */ 602aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */ 612aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */ 622aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */ 632aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ 642aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ 652aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ 662aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ 672aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm}; 682aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm 692aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm static const double 702aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylmone = 1.0, 712aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylmhuge = 1.0e300; 722aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm 732aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylmdouble 742aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylmatan(double x) 752aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm{ 762aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm double w,s1,s2,z; 772aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm int32_t ix,hx,id; 782aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm 792aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm GET_HIGH_WORD(hx,x); 802aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm ix = hx&0x7fffffff; 812aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm if(ix>=0x44100000) { /* if |x| >= 2^66 */ 822aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm u_int32_t low; 832aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm GET_LOW_WORD(low,x); 842aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm if(ix>0x7ff00000|| 852aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm (ix==0x7ff00000&&(low!=0))) 862aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm return x+x; /* NaN */ 872aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm if(hx>0) return atanhi[3]+atanlo[3]; 882aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm else return -atanhi[3]-atanlo[3]; 892aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ 902aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm if (ix < 0x3e200000) { /* |x| < 2^-29 */ 912aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm if(huge+x>one) return x; /* raise inexact */ 922aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm } 932aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm id = -1; 942aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm } else { 952aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm x = fabs(x); 962aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm if (ix < 0x3ff30000) { /* |x| < 1.1875 */ 972aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */ 982aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm id = 0; x = (2.0*x-one)/(2.0+x); 992aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm } else { /* 11/16<=|x|< 19/16 */ 1002aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm id = 1; x = (x-one)/(x+one); 1012aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm } 1022aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm } else { 1032aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm if (ix < 0x40038000) { /* |x| < 2.4375 */ 1042aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm id = 2; x = (x-1.5)/(one+1.5*x); 1052aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm } else { /* 2.4375 <= |x| < 2^66 */ 1062aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm id = 3; x = -1.0/x; 1072aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm } 1082aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm }} 1092aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm /* end of argument reduction */ 1102aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm z = x*x; 1112aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm w = z*z; 1122aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ 1132aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); 1142aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); 1152aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm if (id<0) return x - x*(s1+s2); 1162aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm else { 1172aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); 1182aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm return (hx<0)? -z:z; 1192aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm } 1202aa62f2bc9a9654687b377d9ca8a8c2c860a3852darylm} 121