2edbbc3997
- Adjust several constants for float precision. Some thresholds
that were appropriate for double precision were never changed
when these routines were converted to float precision. This
has an impact on performance but not accuracy. (Submitted by bde.)
- Reduce the degrees of the polynomials used. A smaller degree
suffices for float precision.
- In asinf(), use double arithmetic in part of the calculation to
avoid a corner case and some complicated arithmetic involving a
division and some buggy constants. This improves performance and
accuracy.
Max error (ulps):
asinf acosf atanf
before 0.925 0.782 0.852
after 0.743 0.804 0.852
As bde points out, it's cheaper for asin*() and acos*() to use
polynomials instead of rational functions, but that's a task for
another day.
93 lines
2.4 KiB
C
93 lines
2.4 KiB
C
/* s_atanf.c -- float version of s_atan.c.
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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*/
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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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#include "math.h"
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#include "math_private.h"
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static const float atanhi[] = {
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4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
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7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
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9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
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1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
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};
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static const float atanlo[] = {
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5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
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3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
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3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
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7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
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};
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static const float aT[] = {
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3.3333328366e-01,
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-1.9999158382e-01,
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1.4253635705e-01,
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-1.0648017377e-01,
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6.1687607318e-02,
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};
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static const float
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one = 1.0,
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huge = 1.0e30;
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float
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atanf(float x)
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{
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float w,s1,s2,z;
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int32_t ix,hx,id;
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GET_FLOAT_WORD(hx,x);
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ix = hx&0x7fffffff;
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if(ix>=0x4c800000) { /* if |x| >= 2**26 */
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if(ix>0x7f800000)
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return x+x; /* NaN */
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if(hx>0) return atanhi[3]+*(volatile float *)&atanlo[3];
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else return -atanhi[3]-*(volatile float *)&atanlo[3];
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} if (ix < 0x3ee00000) { /* |x| < 0.4375 */
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if (ix < 0x39800000) { /* |x| < 2**-12 */
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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 = fabsf(x);
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if (ix < 0x3f980000) { /* |x| < 1.1875 */
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if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */
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id = 0; x = ((float)2.0*x-one)/((float)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 (ix < 0x401c0000) { /* |x| < 2.4375 */
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id = 2; x = (x-(float)1.5)/(one+(float)1.5*x);
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} else { /* 2.4375 <= |x| < 2**26 */
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id = 3; x = -(float)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 from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
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s1 = z*(aT[0]+w*(aT[2]+w*aT[4]));
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s2 = w*(aT[1]+w*aT[3]);
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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 (hx<0)? -z:z;
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}
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}
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