1 /* $NetBSD: s_atanl.c,v 1.8 2024/07/17 12:00:48 riastradh Exp $ */ 2 3 /* FreeBSD: head/lib/msun/src/s_atan.c 176451 2008-02-22 02:30:36Z das */ 4 /* 5 * ==================================================== 6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 7 * 8 * Developed at SunPro, a Sun Microsystems, Inc. business. 9 * Permission to use, copy, modify, and distribute this 10 * software is freely granted, provided that this notice 11 * is preserved. 12 * ==================================================== 13 */ 14 15 #include <sys/cdefs.h> 16 __RCSID("$NetBSD: s_atanl.c,v 1.8 2024/07/17 12:00:48 riastradh Exp $"); 17 18 #include "namespace.h" 19 20 #include <float.h> 21 #include <machine/ieee.h> 22 23 #include "math.h" 24 #include "math_private.h" 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 __weak_alias(atanl, _atanl) 34 35 #if LDBL_MANT_DIG == 64 36 #include "../ld80/invtrig.h" 37 #elif LDBL_MANT_DIG == 113 38 #include "../ld128/invtrig.h" 39 #else 40 #error "Unsupported long double format" 41 #endif 42 43 #ifdef LDBL_IMPLICIT_NBIT 44 #define LDBL_NBIT 0 45 #endif 46 47 static const long double 48 one = 1.0, 49 huge = 1.0e300; 50 51 long double 52 atanl(long double x) 53 { 54 union ieee_ext_u u; 55 long double w,s1,s2,z; 56 int id; 57 int16_t expsign, expt; 58 int32_t expman; 59 60 u.extu_ld = x; 61 expsign = GET_EXPSIGN(&u); 62 expt = expsign & 0x7fff; 63 if(expt >= ATAN_CONST) { /* if |x| is large, atan(x)~=pi/2 */ 64 if(expt == BIAS + LDBL_MAX_EXP && 65 ((u.extu_frach&~LDBL_NBIT)|u.extu_fracl)!=0) 66 return x+x; /* NaN */ 67 if(expsign>0) return atanhi[3]+atanlo[3]; 68 else return -atanhi[3]-atanlo[3]; 69 } 70 /* Extract the exponent and the first few bits of the significand. */ 71 /* XXX There should be a more convenient way to do this. */ 72 expman = (expt << 8) | ((u.extu_frach >> (MANH_SIZE - 9)) & 0xff); 73 if (expman < ((BIAS - 2) << 8) + 0xc0) { /* |x| < 0.4375 */ 74 if (expt < ATAN_LINEAR) { /* if |x| is small, atanl(x)~=x */ 75 if(huge+x>one) return x; /* raise inexact */ 76 } 77 id = -1; 78 } else { 79 x = fabsl(x); 80 if (expman < (BIAS << 8) + 0x30) { /* |x| < 1.1875 */ 81 if (expman < ((BIAS - 1) << 8) + 0x60) { /* 7/16 <=|x|<11/16 */ 82 id = 0; x = (2.0*x-one)/(2.0+x); 83 } else { /* 11/16<=|x|< 19/16 */ 84 id = 1; x = (x-one)/(x+one); 85 } 86 } else { 87 if (expman < ((BIAS + 1) << 8) + 0x38) { /* |x| < 2.4375 */ 88 id = 2; x = (x-1.5)/(one+1.5*x); 89 } else { /* 2.4375 <= |x| < 2^ATAN_CONST */ 90 id = 3; x = -1.0/x; 91 } 92 }} 93 /* end of argument reduction */ 94 z = x*x; 95 w = z*z; 96 /* break sum aT[i]z**(i+1) into odd and even poly */ 97 s1 = z*T_even(w); 98 s2 = w*T_odd(w); 99 if (id<0) return x - x*(s1+s2); 100 else { 101 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); 102 return (expsign<0)? -z:z; 103 } 104 } 105 #endif 106