1 /* @(#)s_atan.c 5.1 93/09/24 */ 2 /* FreeBSD: head/lib/msun/src/s_atan.c 176451 2008-02-22 02:30:36Z das */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunPro, a Sun Microsystems, Inc. business. 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 */ 13 14 #include "cdefs-compat.h" 15 //__FBSDID("$FreeBSD: src/lib/msun/src/s_atanl.c,v 1.1 2008/07/31 22:41:26 das Exp $"); 16 17 /* 18 * See comments in s_atan.c. 19 * Converted to long double by David Schultz <das@FreeBSD.ORG>. 20 */ 21 22 #include <float.h> 23 #include <openlibm.h> 24 25 #include "invtrig.h" 26 #include "math_private.h" 27 28 static const long double 29 one = 1.0, 30 huge = 1.0e300; 31 32 DLLEXPORT long double 33 atanl(long double x) 34 { 35 union IEEEl2bits u; 36 long double w,s1,s2,z; 37 int id; 38 int16_t expsign, expt; 39 int32_t expman; 40 41 u.e = x; 42 expsign = u.xbits.expsign; 43 expt = expsign & 0x7fff; 44 if(expt >= ATAN_CONST) { /* if |x| is large, atan(x)~=pi/2 */ 45 if(expt == BIAS + LDBL_MAX_EXP && 46 ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)!=0) 47 return x+x; /* NaN */ 48 if(expsign>0) return atanhi[3]+atanlo[3]; 49 else return -atanhi[3]-atanlo[3]; 50 } 51 /* Extract the exponent and the first few bits of the mantissa. */ 52 /* XXX There should be a more convenient way to do this. */ 53 expman = (expt << 8) | ((u.bits.manh >> (MANH_SIZE - 9)) & 0xff); 54 if (expman < ((BIAS - 2) << 8) + 0xc0) { /* |x| < 0.4375 */ 55 if (expt < ATAN_LINEAR) { /* if |x| is small, atanl(x)~=x */ 56 if(huge+x>one) return x; /* raise inexact */ 57 } 58 id = -1; 59 } else { 60 x = fabsl(x); 61 if (expman < (BIAS << 8) + 0x30) { /* |x| < 1.1875 */ 62 if (expman < ((BIAS - 1) << 8) + 0x60) { /* 7/16 <=|x|<11/16 */ 63 id = 0; x = (2.0*x-one)/(2.0+x); 64 } else { /* 11/16<=|x|< 19/16 */ 65 id = 1; x = (x-one)/(x+one); 66 } 67 } else { 68 if (expman < ((BIAS + 1) << 8) + 0x38) { /* |x| < 2.4375 */ 69 id = 2; x = (x-1.5)/(one+1.5*x); 70 } else { /* 2.4375 <= |x| < 2^ATAN_CONST */ 71 id = 3; x = -1.0/x; 72 } 73 }} 74 /* end of argument reduction */ 75 z = x*x; 76 w = z*z; 77 /* break sum aT[i]z**(i+1) into odd and even poly */ 78 s1 = z*T_even(w); 79 s2 = w*T_odd(w); 80 if (id<0) return x - x*(s1+s2); 81 else { 82 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); 83 return (expsign<0)? -z:z; 84 } 85 } 86