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 <sys/cdefs.h> 15 /* 16 * See comments in s_atan.c. 17 * Converted to long double by David Schultz <das@FreeBSD.ORG>. 18 */ 19 20 #include <float.h> 21 22 #include "invtrig.h" 23 #include "math.h" 24 #include "math_private.h" 25 26 static const long double 27 one = 1.0, 28 huge = 1.0e300; 29 30 long double 31 atanl(long double x) 32 { 33 union IEEEl2bits u; 34 long double w,s1,s2,z; 35 int id; 36 int16_t expsign, expt; 37 int32_t expman; 38 39 u.e = x; 40 expsign = u.xbits.expsign; 41 expt = expsign & 0x7fff; 42 if(expt >= ATAN_CONST) { /* if |x| is large, atan(x)~=pi/2 */ 43 if(expt == BIAS + LDBL_MAX_EXP && 44 ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)!=0) 45 return x+x; /* NaN */ 46 if(expsign>0) return atanhi[3]+atanlo[3]; 47 else return -atanhi[3]-atanlo[3]; 48 } 49 /* Extract the exponent and the first few bits of the mantissa. */ 50 /* XXX There should be a more convenient way to do this. */ 51 expman = (expt << 8) | ((u.bits.manh >> (MANH_SIZE - 9)) & 0xff); 52 if (expman < ((BIAS - 2) << 8) + 0xc0) { /* |x| < 0.4375 */ 53 if (expt < ATAN_LINEAR) { /* if |x| is small, atanl(x)~=x */ 54 if(huge+x>one) return x; /* raise inexact */ 55 } 56 id = -1; 57 } else { 58 x = fabsl(x); 59 if (expman < (BIAS << 8) + 0x30) { /* |x| < 1.1875 */ 60 if (expman < ((BIAS - 1) << 8) + 0x60) { /* 7/16 <=|x|<11/16 */ 61 id = 0; x = (2.0*x-one)/(2.0+x); 62 } else { /* 11/16<=|x|< 19/16 */ 63 id = 1; x = (x-one)/(x+one); 64 } 65 } else { 66 if (expman < ((BIAS + 1) << 8) + 0x38) { /* |x| < 2.4375 */ 67 id = 2; x = (x-1.5)/(one+1.5*x); 68 } else { /* 2.4375 <= |x| < 2^ATAN_CONST */ 69 id = 3; x = -1.0/x; 70 } 71 }} 72 /* end of argument reduction */ 73 z = x*x; 74 w = z*z; 75 /* break sum aT[i]z**(i+1) into odd and even poly */ 76 s1 = z*T_even(w); 77 s2 = w*T_odd(w); 78 if (id<0) return x - x*(s1+s2); 79 else { 80 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); 81 return (expsign<0)? -z:z; 82 } 83 } 84