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 #include <sys/cdefs.h> 14 /* 15 * See comments in s_atan.c. 16 * Converted to long double by David Schultz <das@FreeBSD.ORG>. 17 */ 18 19 #include <float.h> 20 21 #include "invtrig.h" 22 #include "math.h" 23 #include "math_private.h" 24 25 static const long double 26 one = 1.0, 27 huge = 1.0e300; 28 29 long double 30 atanl(long double x) 31 { 32 union IEEEl2bits u; 33 long double w,s1,s2,z; 34 int id; 35 int16_t expsign, expt; 36 int32_t expman; 37 38 u.e = x; 39 expsign = u.xbits.expsign; 40 expt = expsign & 0x7fff; 41 if(expt >= ATAN_CONST) { /* if |x| is large, atan(x)~=pi/2 */ 42 if(expt == BIAS + LDBL_MAX_EXP && 43 ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)!=0) 44 return x+x; /* NaN */ 45 if(expsign>0) return atanhi[3]+atanlo[3]; 46 else return -atanhi[3]-atanlo[3]; 47 } 48 /* Extract the exponent and the first few bits of the mantissa. */ 49 /* XXX There should be a more convenient way to do this. */ 50 expman = (expt << 8) | ((u.bits.manh >> (MANH_SIZE - 9)) & 0xff); 51 if (expman < ((BIAS - 2) << 8) + 0xc0) { /* |x| < 0.4375 */ 52 if (expt < ATAN_LINEAR) { /* if |x| is small, atanl(x)~=x */ 53 if(huge+x>one) return x; /* raise inexact */ 54 } 55 id = -1; 56 } else { 57 x = fabsl(x); 58 if (expman < (BIAS << 8) + 0x30) { /* |x| < 1.1875 */ 59 if (expman < ((BIAS - 1) << 8) + 0x60) { /* 7/16 <=|x|<11/16 */ 60 id = 0; x = (2.0*x-one)/(2.0+x); 61 } else { /* 11/16<=|x|< 19/16 */ 62 id = 1; x = (x-one)/(x+one); 63 } 64 } else { 65 if (expman < ((BIAS + 1) << 8) + 0x38) { /* |x| < 2.4375 */ 66 id = 2; x = (x-1.5)/(one+1.5*x); 67 } else { /* 2.4375 <= |x| < 2^ATAN_CONST */ 68 id = 3; x = -1.0/x; 69 } 70 }} 71 /* end of argument reduction */ 72 z = x*x; 73 w = z*z; 74 /* break sum aT[i]z**(i+1) into odd and even poly */ 75 s1 = z*T_even(w); 76 s2 = w*T_odd(w); 77 if (id<0) return x - x*(s1+s2); 78 else { 79 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); 80 return (expsign<0)? -z:z; 81 } 82 } 83