s_atanl.c revision 181074
1124524Sume/* @(#)s_atan.c 5.1 93/09/24 */ 266776Skris/* FreeBSD: head/lib/msun/src/s_atan.c 176451 2008-02-22 02:30:36Z das */ 355163Sshin/* 455163Sshin * ==================================================== 555163Sshin * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 662632Skris * 755163Sshin * Developed at SunPro, a Sun Microsystems, Inc. business. 855163Sshin * Permission to use, copy, modify, and distribute this 955163Sshin * software is freely granted, provided that this notice 1055163Sshin * is preserved. 1155163Sshin * ==================================================== 1255163Sshin */ 1355163Sshin 1455163Sshin#include <sys/cdefs.h> 1555163Sshin__FBSDID("$FreeBSD: head/lib/msun/src/s_atanl.c 181074 2008-07-31 22:41:26Z das $"); 1655163Sshin 1755163Sshin/* 1862632Skris * See comments in s_atan.c. 1955163Sshin * Converted to long double by David Schultz <das@FreeBSD.ORG>. 2055163Sshin */ 2155163Sshin 2255163Sshin#include <float.h> 2355163Sshin 2455163Sshin#include "invtrig.h" 2555163Sshin#include "math.h" 2655163Sshin#include "math_private.h" 2755163Sshin 2855163Sshinstatic const long double 2955163Sshinone = 1.0, 3055163Sshinhuge = 1.0e300; 3155163Sshin 3255163Sshinlong double 3355163Sshinatanl(long double x) 3455163Sshin{ 3555163Sshin union IEEEl2bits u; 3655163Sshin long double w,s1,s2,z; 3755163Sshin int id; 3866776Skris int16_t expsign, expt; 3955163Sshin int32_t expman; 4055163Sshin 4155163Sshin u.e = x; 4255163Sshin expsign = u.xbits.expsign; 4355163Sshin expt = expsign & 0x7fff; 4455163Sshin if(expt >= ATAN_CONST) { /* if |x| is large, atan(x)~=pi/2 */ 4555163Sshin if(expt == BIAS + LDBL_MAX_EXP && 46118787Sume ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)!=0) 4755163Sshin return x+x; /* NaN */ 4855163Sshin if(expsign>0) return atanhi[3]+atanlo[3]; 4955163Sshin else return -atanhi[3]-atanlo[3]; 5055163Sshin } 5155163Sshin /* Extract the exponent and the first few bits of the mantissa. */ 5255163Sshin /* XXX There should be a more convenient way to do this. */ 5355163Sshin expman = (expt << 8) | ((u.bits.manh >> (MANH_SIZE - 9)) & 0xff); 5455163Sshin if (expman < ((BIAS - 2) << 8) + 0xc0) { /* |x| < 0.4375 */ 5555163Sshin if (expt < ATAN_LINEAR) { /* if |x| is small, atanl(x)~=x */ 5655163Sshin if(huge+x>one) return x; /* raise inexact */ 5755163Sshin } 5855163Sshin id = -1; 5955163Sshin } else { 6062632Skris x = fabsl(x); 6155163Sshin if (expman < (BIAS << 8) + 0x30) { /* |x| < 1.1875 */ 6255163Sshin if (expman < ((BIAS - 1) << 8) + 0x60) { /* 7/16 <=|x|<11/16 */ 6362632Skris id = 0; x = (2.0*x-one)/(2.0+x); 6455163Sshin } else { /* 11/16<=|x|< 19/16 */ 6555163Sshin id = 1; x = (x-one)/(x+one); 66118998Sume } 67118998Sume } else { 6855163Sshin if (expman < ((BIAS + 1) << 8) + 0x38) { /* |x| < 2.4375 */ 6955163Sshin id = 2; x = (x-1.5)/(one+1.5*x); 70124524Sume } else { /* 2.4375 <= |x| < 2^ATAN_CONST */ 7155163Sshin id = 3; x = -1.0/x; 7262632Skris } 7355163Sshin }} 7455163Sshin /* end of argument reduction */ 7555163Sshin z = x*x; 7655163Sshin w = z*z; 7755163Sshin /* break sum aT[i]z**(i+1) into odd and even poly */ 7855163Sshin s1 = z*T_even(w); 7955163Sshin s2 = w*T_odd(w); 8055163Sshin if (id<0) return x - x*(s1+s2); 8162632Skris else { 8255163Sshin z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); 83119027Sume return (expsign<0)? -z:z; 8455163Sshin } 8555163Sshin} 86118660Sume