1/* $NetBSD: s_atan.c,v 1.13 2024/06/09 13:35:38 riastradh Exp $ */ 2 3/* @(#)s_atan.c 5.1 93/09/24 */ 4/* 5 * ==================================================== 6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 7 * 8 * Developed at SunPro, a Sun Microsystems, Inc. business. 9 * Permission to use, copy, modify, and distribute this 10 * software is freely granted, provided that this notice 11 * is preserved. 12 * ==================================================== 13 */ 14 15#include <sys/cdefs.h> 16#if defined(LIBM_SCCS) && !defined(lint) 17__RCSID("$NetBSD: s_atan.c,v 1.13 2024/06/09 13:35:38 riastradh Exp $"); 18#endif 19 20/* atan(x) 21 * Method 22 * 1. Reduce x to positive by atan(x) = -atan(-x). 23 * 2. According to the integer k=4t+0.25 chopped, t=x, the argument 24 * is further reduced to one of the following intervals and the 25 * arctangent of t is evaluated by the corresponding formula: 26 * 27 * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) 28 * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) ) 29 * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) ) 30 * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) ) 31 * [39/16,INF] atan(x) = atan(INF) + atan( -1/t ) 32 * 33 * Constants: 34 * The hexadecimal values are the intended ones for the following 35 * constants. The decimal values may be used, provided that the 36 * compiler will convert from decimal to binary accurately enough 37 * to produce the hexadecimal values shown. 38 */ 39 40#include "namespace.h" 41 42#include "math.h" 43#include "math_private.h" 44 45#ifndef __HAVE_LONG_DOUBLE 46__weak_alias(atanl, _atanl) 47__strong_alias(_atanl, _atan) 48#endif 49 50__weak_alias(atan, _atan) 51 52static const double atanhi[] = { 53 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ 54 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */ 55 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */ 56 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */ 57}; 58 59static const double atanlo[] = { 60 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ 61 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */ 62 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ 63 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */ 64}; 65 66static const double aT[] = { 67 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */ 68 -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */ 69 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */ 70 -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */ 71 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */ 72 -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */ 73 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */ 74 -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ 75 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ 76 -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ 77 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ 78}; 79 80 static const double 81one = 1.0, 82huge = 1.0e300; 83 84double 85atan(double x) 86{ 87 double w,s1,s2,z; 88 int32_t ix,hx,id; 89 90 GET_HIGH_WORD(hx,x); 91 ix = hx&0x7fffffff; 92 if(ix>=0x44100000) { /* if |x| >= 2^66 */ 93 u_int32_t low; 94 GET_LOW_WORD(low,x); 95 if(ix>0x7ff00000|| 96 (ix==0x7ff00000&&(low!=0))) 97 return x+x; /* NaN */ 98 if(hx>0) return atanhi[3]+atanlo[3]; 99 else return -atanhi[3]-atanlo[3]; 100 } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ 101 if (ix < 0x3e200000) { /* |x| < 2^-29 */ 102 if(huge+x>one) return x; /* raise inexact */ 103 } 104 id = -1; 105 } else { 106 x = fabs(x); 107 if (ix < 0x3ff30000) { /* |x| < 1.1875 */ 108 if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */ 109 id = 0; x = (2.0*x-one)/(2.0+x); 110 } else { /* 11/16<=|x|< 19/16 */ 111 id = 1; x = (x-one)/(x+one); 112 } 113 } else { 114 if (ix < 0x40038000) { /* |x| < 2.4375 */ 115 id = 2; x = (x-1.5)/(one+1.5*x); 116 } else { /* 2.4375 <= |x| < 2^66 */ 117 id = 3; x = -1.0/x; 118 } 119 }} 120 /* end of argument reduction */ 121 z = x*x; 122 w = z*z; 123 /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ 124 s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); 125 s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); 126 if (id<0) return x - x*(s1+s2); 127 else { 128 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); 129 return (hx<0)? -z:z; 130 } 131} 132