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/* $OpenBSD: s_atanl.c,v 1.2 2016/09/12 19:47:02 guenther Exp $ */ |
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/* @(#)s_atan.c 5.1 93/09/24 */ |
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/* FreeBSD: head/lib/msun/src/s_atan.c 176451 2008-02-22 02:30:36Z das */ |
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/* |
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* ==================================================== |
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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* |
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* Developed at SunPro, a Sun Microsystems, Inc. business. |
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* Permission to use, copy, modify, and distribute this |
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* software is freely granted, provided that this notice |
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* is preserved. |
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* ==================================================== |
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*/ |
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/* |
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* See comments in s_atan.c. |
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* Converted to long double by David Schultz <das@FreeBSD.ORG>. |
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* Adapted for OpenBSD by Martynas Venckus <martynas@openbsd.org>. |
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*/ |
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#include <float.h> |
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#include <math.h> |
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#include "invtrig.h" |
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#include "math_private.h" |
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#ifdef EXT_IMPLICIT_NBIT |
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#define LDBL_NBIT 0 |
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#else /* EXT_IMPLICIT_NBIT */ |
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#define LDBL_NBIT 0x80000000 |
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#endif /* EXT_IMPLICIT_NBIT */ |
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static const long double |
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one = 1.0, |
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huge = 1.0e300; |
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long double |
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atanl(long double x) |
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{ |
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union { |
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long double e; |
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struct ieee_ext bits; |
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} u; |
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long double w,s1,s2,z; |
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int id; |
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int16_t expsign, expt; |
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int32_t expman; |
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u.e = x; |
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expsign = (u.bits.ext_sign << 15) | u.bits.ext_exp; |
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expt = expsign & 0x7fff; |
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✗✓ |
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if(expt >= ATAN_CONST) { /* if |x| is large, atan(x)~=pi/2 */ |
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if(expt == BIAS + LDBL_MAX_EXP && |
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((u.bits.ext_frach&~LDBL_NBIT) |
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#ifdef EXT_FRACHMBITS |
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| u.bits.ext_frachm |
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#endif /* EXT_FRACHMBITS */ |
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#ifdef EXT_FRACLMBITS |
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| u.bits.ext_fraclm |
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#endif /* EXT_FRACLMBITS */ |
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| u.bits.ext_fracl)!=0) |
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return x+x; /* NaN */ |
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if(expsign>0) return atanhi[3]+atanlo[3]; |
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else return -atanhi[3]-atanlo[3]; |
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} |
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/* Extract the exponent and the first few bits of the mantissa. */ |
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/* XXX There should be a more convenient way to do this. */ |
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expman = (expt << 8) | |
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((u.bits.ext_frach >> (EXT_FRACHBITS - 9)) & 0xff); |
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✓✓ |
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if (expman < ((BIAS - 2) << 8) + 0xc0) { /* |x| < 0.4375 */ |
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✓✓ |
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if (expt < ATAN_LINEAR) { /* if |x| is small, atanl(x)~=x */ |
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✓✗ |
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if(huge+x>one) return x; /* raise inexact */ |
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} |
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id = -1; |
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} else { |
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x = fabsl(x); |
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✓✓ |
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if (expman < (BIAS << 8) + 0x30) { /* |x| < 1.1875 */ |
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✓✓ |
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if (expman < ((BIAS - 1) << 8) + 0x60) { /* 7/16 <=|x|<11/16 */ |
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id = 0; x = (2.0*x-one)/(2.0+x); |
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} else { /* 11/16<=|x|< 19/16 */ |
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id = 1; x = (x-one)/(x+one); |
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} |
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} else { |
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✓✓ |
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if (expman < ((BIAS + 1) << 8) + 0x38) { /* |x| < 2.4375 */ |
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id = 2; x = (x-1.5)/(one+1.5*x); |
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} else { /* 2.4375 <= |x| < 2^ATAN_CONST */ |
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id = 3; x = -1.0/x; |
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} |
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}} |
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/* end of argument reduction */ |
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z = x*x; |
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w = z*z; |
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/* break sum aT[i]z**(i+1) into odd and even poly */ |
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s1 = z*T_even(w); |
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s2 = w*T_odd(w); |
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✓✓ |
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if (id<0) return x - x*(s1+s2); |
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else { |
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z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); |
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return (expsign<0)? -z:z; |
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} |
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} |
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DEF_STD(atanl); |