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117 lines
3.8 KiB
117 lines
3.8 KiB
7 years ago
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/* origin: FreeBSD /usr/src/lib/msun/src/s_atan.c */
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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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/* atan(x)
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* Method
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* 1. Reduce x to positive by atan(x) = -atan(-x).
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* 2. According to the integer k=4t+0.25 chopped, t=x, the argument
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* is further reduced to one of the following intervals and the
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* arctangent of t is evaluated by the corresponding formula:
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*
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* [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
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* [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
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* [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
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* [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
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* [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
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*
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* Constants:
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* The hexadecimal values are the intended ones for the following
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* constants. The decimal values may be used, provided that the
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* compiler will convert from decimal to binary accurately enough
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* to produce the hexadecimal values shown.
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*/
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#include "libm.h"
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static const double atanhi[] = {
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4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
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7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
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9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
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1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
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};
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static const double atanlo[] = {
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2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
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3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
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1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
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6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
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};
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static const double aT[] = {
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3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
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-1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
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1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
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-1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
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9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
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-7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
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6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
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-5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
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4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
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-3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
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1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
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};
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double atan(double x)
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{
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double_t w,s1,s2,z;
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uint32_t ix,sign;
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int id;
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GET_HIGH_WORD(ix, x);
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sign = ix >> 31;
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ix &= 0x7fffffff;
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if (ix >= 0x44100000) { /* if |x| >= 2^66 */
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if (isnan(x))
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return x;
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z = atanhi[3] + 0x1p-120f;
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return sign ? -z : z;
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}
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if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
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if (ix < 0x3e400000) { /* |x| < 2^-27 */
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if (ix < 0x00100000)
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/* raise underflow for subnormal x */
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FORCE_EVAL((float)x);
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return x;
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}
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id = -1;
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} else {
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x = fabs(x);
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if (ix < 0x3ff30000) { /* |x| < 1.1875 */
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if (ix < 0x3fe60000) { /* 7/16 <= |x| < 11/16 */
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id = 0;
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x = (2.0*x-1.0)/(2.0+x);
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} else { /* 11/16 <= |x| < 19/16 */
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id = 1;
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x = (x-1.0)/(x+1.0);
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}
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} else {
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if (ix < 0x40038000) { /* |x| < 2.4375 */
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id = 2;
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x = (x-1.5)/(1.0+1.5*x);
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} else { /* 2.4375 <= |x| < 2^66 */
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id = 3;
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x = -1.0/x;
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}
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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]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
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s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
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if (id < 0)
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return x - x*(s1+s2);
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z = atanhi[id] - (x*(s1+s2) - atanlo[id] - x);
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return sign ? -z : z;
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}
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