1194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg/* s_atanf.c -- float version of s_atan.c. 2194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 3194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg */ 4194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg 5194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg/* 6194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg * ==================================================== 7194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 8194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg * 9194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg * Developed at SunPro, a Sun Microsystems, Inc. business. 10194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg * Permission to use, copy, modify, and distribute this 11194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg * software is freely granted, provided that this notice 12194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg * is preserved. 13194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg * ==================================================== 14194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg */ 15194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg 16194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg#include <sys/cdefs.h> 17194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg__FBSDID("$FreeBSD$"); 18194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg 19194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg#include "math.h" 20f805306b53d82eef67d8891a5dd5c32d3794a3abAlexey Polyudov#include <math_private.h> 21194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg 22194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinbergstatic const float atanhi[] = { 23194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */ 24194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */ 25194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */ 26194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg 1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */ 27194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg}; 28194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg 29194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinbergstatic const float atanlo[] = { 30194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg 5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */ 31194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg 3.7748947079e-08, /* atan(1.0)lo 0x33222168 */ 32194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg 3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */ 33194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg 7.5497894159e-08, /* atan(inf)lo 0x33a22168 */ 34194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg}; 35194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg 36194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinbergstatic const float aT[] = { 37194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg 3.3333328366e-01, 38194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg -1.9999158382e-01, 39194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg 1.4253635705e-01, 40194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg -1.0648017377e-01, 41194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg 6.1687607318e-02, 42194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg}; 43194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg 44194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinbergstatic const float 45194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinbergone = 1.0, 46194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberghuge = 1.0e30; 47194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg 48194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinbergfloat 49194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinbergatanf(float x) 50194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg{ 51194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg float w,s1,s2,z; 52194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg int32_t ix,hx,id; 53194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg 54194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg GET_FLOAT_WORD(hx,x); 55194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg ix = hx&0x7fffffff; 56194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg if(ix>=0x4c800000) { /* if |x| >= 2**26 */ 57194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg if(ix>0x7f800000) 58194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg return x+x; /* NaN */ 59194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg if(hx>0) return atanhi[3]+*(volatile float *)&atanlo[3]; 60194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg else return -atanhi[3]-*(volatile float *)&atanlo[3]; 61194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg } if (ix < 0x3ee00000) { /* |x| < 0.4375 */ 62194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg if (ix < 0x39800000) { /* |x| < 2**-12 */ 63194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg if(huge+x>one) return x; /* raise inexact */ 64194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg } 65194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg id = -1; 66194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg } else { 67194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg x = fabsf(x); 68194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg if (ix < 0x3f980000) { /* |x| < 1.1875 */ 69194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */ 70194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg id = 0; x = ((float)2.0*x-one)/((float)2.0+x); 71194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg } else { /* 11/16<=|x|< 19/16 */ 72194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg id = 1; x = (x-one)/(x+one); 73194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg } 74194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg } else { 75194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg if (ix < 0x401c0000) { /* |x| < 2.4375 */ 76194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg id = 2; x = (x-(float)1.5)/(one+(float)1.5*x); 77194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg } else { /* 2.4375 <= |x| < 2**26 */ 78194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg id = 3; x = -(float)1.0/x; 79194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg } 80194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg }} 81194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg /* end of argument reduction */ 82194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg z = x*x; 83194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg w = z*z; 84194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ 85194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg s1 = z*(aT[0]+w*(aT[2]+w*aT[4])); 86194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg s2 = w*(aT[1]+w*aT[3]); 87194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg if (id<0) return x - x*(s1+s2); 88194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg else { 89194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); 90194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg return (hx<0)? -z:z; 91194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg } 92194b0b02d0013c6bb1e1e1b10957aad50a0b4870Dmitry Grinberg} 93