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 #include <sys/cdefs.h> 13 14 #include "namespace.h" 15 16 #include <float.h> 17 #include <machine/ieee.h> 18 19 #include "math.h" 20 #include "math_private.h" 21 22 #ifdef __weak_alias 23 __weak_alias(atanl, _atanl) 24 #endif 25 26 #ifdef __HAVE_LONG_DOUBLE 27 28 /* 29 * See comments in s_atan.c. 30 * Converted to long double by David Schultz <das@FreeBSD.ORG>. 31 */ 32 33 34 #if LDBL_MANT_DIG == 64 35 #include "../ld80/invtrig.h" 36 #elif LDBL_MANT_DIG == 113 37 #include "../ld128/invtrig.h" 38 #else 39 #error "Unsupported long double format" 40 #endif 41 42 #ifdef LDBL_IMPLICIT_NBIT 43 #define LDBL_NBIT 0 44 #endif 45 46 static const long double 47 one = 1.0, 48 huge = 1.0e300; 49 50 long double 51 atanl(long double x) 52 { 53 union ieee_ext_u u; 54 long double w,s1,s2,z; 55 int id; 56 int16_t expsign, expt; 57 int32_t expman; 58 59 u.extu_ld = x; 60 expsign = GET_EXPSIGN(&u); 61 expt = expsign & 0x7fff; 62 if(expt >= ATAN_CONST) { /* if |x| is large, atan(x)~=pi/2 */ 63 if(expt == BIAS + LDBL_MAX_EXP && 64 ((u.extu_frach&~LDBL_NBIT)|u.extu_fracl)!=0) 65 return x+x; /* NaN */ 66 if(expsign>0) return atanhi[3]+atanlo[3]; 67 else return -atanhi[3]-atanlo[3]; 68 } 69 /* Extract the exponent and the first few bits of the mantissa. */ 70 /* XXX There should be a more convenient way to do this. */ 71 expman = (expt << 8) | ((u.extu_frach >> (MANH_SIZE - 9)) & 0xff); 72 if (expman < ((BIAS - 2) << 8) + 0xc0) { /* |x| < 0.4375 */ 73 if (expt < ATAN_LINEAR) { /* if |x| is small, atanl(x)~=x */ 74 if(huge+x>one) return x; /* raise inexact */ 75 } 76 id = -1; 77 } else { 78 x = fabsl(x); 79 if (expman < (BIAS << 8) + 0x30) { /* |x| < 1.1875 */ 80 if (expman < ((BIAS - 1) << 8) + 0x60) { /* 7/16 <=|x|<11/16 */ 81 id = 0; x = (2.0*x-one)/(2.0+x); 82 } else { /* 11/16<=|x|< 19/16 */ 83 id = 1; x = (x-one)/(x+one); 84 } 85 } else { 86 if (expman < ((BIAS + 1) << 8) + 0x38) { /* |x| < 2.4375 */ 87 id = 2; x = (x-1.5)/(one+1.5*x); 88 } else { /* 2.4375 <= |x| < 2^ATAN_CONST */ 89 id = 3; x = -1.0/x; 90 } 91 }} 92 /* end of argument reduction */ 93 z = x*x; 94 w = z*z; 95 /* break sum aT[i]z**(i+1) into odd and even poly */ 96 s1 = z*T_even(w); 97 s2 = w*T_odd(w); 98 if (id<0) return x - x*(s1+s2); 99 else { 100 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); 101 return (expsign<0)? -z:z; 102 } 103 } 104 #else 105 long double 106 atanl(long double x) 107 { 108 return atan(x); 109 } 110 #endif 111