| 1 | /* @(#)s_atan.c 5.1 93/09/24 */
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| 2 | /*
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| 3 | * ====================================================
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| 4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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| 5 | *
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| 6 | * Developed at SunPro, a Sun Microsystems, Inc. business.
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| 7 | * Permission to use, copy, modify, and distribute this
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| 8 | * software is freely granted, provided that this notice
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| 9 | * is preserved.
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| 10 | * ====================================================
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| 11 | */
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| 12 |
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| 13 | #ifndef lint
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| 14 | static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_atan.c,v 1.9 2003/07/23 04:53:46 peter Exp $";
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| 15 | #endif
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| 16 |
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| 17 | /* atan(x)
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| 18 | * Method
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| 19 | * 1. Reduce x to positive by atan(x) = -atan(-x).
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| 20 | * 2. According to the integer k=4t+0.25 chopped, t=x, the argument
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| 21 | * is further reduced to one of the following intervals and the
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| 22 | * arctangent of t is evaluated by the corresponding formula:
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| 23 | *
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| 24 | * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
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| 25 | * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
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| 26 | * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
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| 27 | * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
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| 28 | * [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
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| 29 | *
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| 30 | * Constants:
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| 31 | * The hexadecimal values are the intended ones for the following
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| 32 | * constants. The decimal values may be used, provided that the
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| 33 | * compiler will convert from decimal to binary accurately enough
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| 34 | * to produce the hexadecimal values shown.
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| 35 | */
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| 36 |
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| 37 | #include "math.h"
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| 38 | #include "math_private.h"
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| 39 |
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| 40 | static const double atanhi[] = {
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| 41 | 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
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| 42 | 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
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| 43 | 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
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| 44 | 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
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| 45 | };
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| 46 |
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| 47 | static const double atanlo[] = {
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| 48 | 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
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| 49 | 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
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| 50 | 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
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| 51 | 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
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| 52 | };
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| 53 |
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| 54 | static const double aT[] = {
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| 55 | 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
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| 56 | -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
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| 57 | 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
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| 58 | -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
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| 59 | 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
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| 60 | -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
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| 61 | 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
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| 62 | -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
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| 63 | 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
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| 64 | -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
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| 65 | 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
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| 66 | };
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| 67 |
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| 68 | static const double
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| 69 | one = 1.0,
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| 70 | huge = 1.0e300;
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| 71 |
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| 72 | double
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| 73 | atan(double x)
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| 74 | {
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| 75 | double w,s1,s2,z;
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| 76 | int32_t ix,hx,id;
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| 77 |
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| 78 | GET_HIGH_WORD(hx,x);
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| 79 | ix = hx&0x7fffffff;
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| 80 | if(ix>=0x44100000) { /* if |x| >= 2^66 */
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| 81 | u_int32_t low;
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| 82 | GET_LOW_WORD(low,x);
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| 83 | if(ix>0x7ff00000||
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| 84 | (ix==0x7ff00000&&(low!=0)))
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| 85 | return x+x; /* NaN */
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| 86 | if(hx>0) return atanhi[3]+atanlo[3];
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| 87 | else return -atanhi[3]-atanlo[3];
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| 88 | } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
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| 89 | if (ix < 0x3e200000) { /* |x| < 2^-29 */
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| 90 | if(huge+x>one) return x; /* raise inexact */
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| 91 | }
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| 92 | id = -1;
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| 93 | } else {
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| 94 | x = fabs(x);
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| 95 | if (ix < 0x3ff30000) { /* |x| < 1.1875 */
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| 96 | if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */
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| 97 | id = 0; x = (2.0*x-one)/(2.0+x);
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| 98 | } else { /* 11/16<=|x|< 19/16 */
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| 99 | id = 1; x = (x-one)/(x+one);
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| 100 | }
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| 101 | } else {
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| 102 | if (ix < 0x40038000) { /* |x| < 2.4375 */
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| 103 | id = 2; x = (x-1.5)/(one+1.5*x);
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| 104 | } else { /* 2.4375 <= |x| < 2^66 */
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| 105 | id = 3; x = -1.0/x;
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| 106 | }
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| 107 | }}
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| 108 | /* end of argument reduction */
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| 109 | z = x*x;
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| 110 | w = z*z;
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| 111 | /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
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| 112 | s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
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| 113 | s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
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| 114 | if (id<0) return x - x*(s1+s2);
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| 115 | else {
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| 116 | z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
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| 117 | return (hx<0)? -z:z;
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| 118 | }
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| 119 | }
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