86 lines
2.3 KiB
C
86 lines
2.3 KiB
C
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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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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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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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*/
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#include <float.h>
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#include "invtrig.h"
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#include "math.h"
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#include "math_private.h"
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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 IEEEl2bits 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.xbits.expsign;
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expt = expsign & 0x7fff;
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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.manh&~LDBL_NBIT)|u.bits.manl)!=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) | ((u.bits.manh >> (MANH_SIZE - 9)) & 0xff);
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if (expman < ((BIAS - 2) << 8) + 0xc0) { /* |x| < 0.4375 */
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if (expt < ATAN_LINEAR) { /* if |x| is small, atanl(x)~=x */
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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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if (expman < (BIAS << 8) + 0x30) { /* |x| < 1.1875 */
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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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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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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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