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