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Side by Side Diff: fusl/src/math/atan.c

Issue 1714623002: [fusl] clang-format fusl (Closed) Base URL: git@github.com:domokit/mojo.git@master
Patch Set: headers too Created 4 years, 10 months ago
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1 /* origin: FreeBSD /usr/src/lib/msun/src/s_atan.c */ 1 /* origin: FreeBSD /usr/src/lib/msun/src/s_atan.c */
2 /* 2 /*
3 * ==================================================== 3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 * 5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business. 6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this 7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice 8 * software is freely granted, provided that this notice
9 * is preserved. 9 * is preserved.
10 * ==================================================== 10 * ====================================================
(...skipping 11 matching lines...) Expand all
22 * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) ) 22 * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
23 * [39/16,INF] atan(x) = atan(INF) + atan( -1/t ) 23 * [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
24 * 24 *
25 * Constants: 25 * Constants:
26 * The hexadecimal values are the intended ones for the following 26 * The hexadecimal values are the intended ones for the following
27 * constants. The decimal values may be used, provided that the 27 * constants. The decimal values may be used, provided that the
28 * compiler will convert from decimal to binary accurately enough 28 * compiler will convert from decimal to binary accurately enough
29 * to produce the hexadecimal values shown. 29 * to produce the hexadecimal values shown.
30 */ 30 */
31 31
32
33 #include "libm.h" 32 #include "libm.h"
34 33
35 static const double atanhi[] = { 34 static const double atanhi[] = {
36 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ 35 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
37 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */ 36 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
38 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */ 37 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
39 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */ 38 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
40 }; 39 };
41 40
42 static const double atanlo[] = { 41 static const double atanlo[] = {
43 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ 42 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
44 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */ 43 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
45 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ 44 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
46 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */ 45 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
47 }; 46 };
48 47
49 static const double aT[] = { 48 static const double aT[] = {
50 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */ 49 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
51 -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */ 50 -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
52 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */ 51 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
53 -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */ 52 -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
54 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */ 53 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
55 -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */ 54 -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
56 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */ 55 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
57 -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ 56 -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
58 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ 57 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
59 -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ 58 -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
60 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ 59 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
61 }; 60 };
62 61
63 double atan(double x) 62 double atan(double x) {
64 { 63 double_t w, s1, s2, z;
65 » double_t w,s1,s2,z; 64 uint32_t ix, sign;
66 » uint32_t ix,sign; 65 int id;
67 » int id;
68 66
69 » GET_HIGH_WORD(ix, x); 67 GET_HIGH_WORD(ix, x);
70 » sign = ix >> 31; 68 sign = ix >> 31;
71 » ix &= 0x7fffffff; 69 ix &= 0x7fffffff;
72 » if (ix >= 0x44100000) { /* if |x| >= 2^66 */ 70 if (ix >= 0x44100000) { /* if |x| >= 2^66 */
73 » » if (isnan(x)) 71 if (isnan(x))
74 » » » return x; 72 return x;
75 » » z = atanhi[3] + 0x1p-120f; 73 z = atanhi[3] + 0x1p-120f;
76 » » return sign ? -z : z; 74 return sign ? -z : z;
77 » } 75 }
78 » if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ 76 if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
79 » » if (ix < 0x3e400000) { /* |x| < 2^-27 */ 77 if (ix < 0x3e400000) { /* |x| < 2^-27 */
80 » » » if (ix < 0x00100000) 78 if (ix < 0x00100000)
81 » » » » /* raise underflow for subnormal x */ 79 /* raise underflow for subnormal x */
82 » » » » FORCE_EVAL((float)x); 80 FORCE_EVAL((float)x);
83 » » » return x; 81 return x;
84 » » } 82 }
85 » » id = -1; 83 id = -1;
86 » } else { 84 } else {
87 » » x = fabs(x); 85 x = fabs(x);
88 » » if (ix < 0x3ff30000) { /* |x| < 1.1875 */ 86 if (ix < 0x3ff30000) { /* |x| < 1.1875 */
89 » » » if (ix < 0x3fe60000) { /* 7/16 <= |x| < 11/16 */ 87 if (ix < 0x3fe60000) { /* 7/16 <= |x| < 11/16 */
90 » » » » id = 0; 88 id = 0;
91 » » » » x = (2.0*x-1.0)/(2.0+x); 89 x = (2.0 * x - 1.0) / (2.0 + x);
92 » » » } else { /* 11/16 <= |x| < 19/16 */ 90 } else { /* 11/16 <= |x| < 19/16 */
93 » » » » id = 1; 91 id = 1;
94 » » » » x = (x-1.0)/(x+1.0); 92 x = (x - 1.0) / (x + 1.0);
95 » » » } 93 }
96 » » } else { 94 } else {
97 » » » if (ix < 0x40038000) { /* |x| < 2.4375 */ 95 if (ix < 0x40038000) { /* |x| < 2.4375 */
98 » » » » id = 2; 96 id = 2;
99 » » » » x = (x-1.5)/(1.0+1.5*x); 97 x = (x - 1.5) / (1.0 + 1.5 * x);
100 » » » } else { /* 2.4375 <= |x| < 2^66 */ 98 } else { /* 2.4375 <= |x| < 2^66 */
101 » » » » id = 3; 99 id = 3;
102 » » » » x = -1.0/x; 100 x = -1.0 / x;
103 » » » } 101 }
104 » » } 102 }
105 » } 103 }
106 » /* end of argument reduction */ 104 /* end of argument reduction */
107 » z = x*x; 105 z = x * x;
108 » w = z*z; 106 w = z * z;
109 » /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ 107 /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
110 » s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); 108 s1 = z * (aT[0] +
111 » s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); 109 w * (aT[2] + w * (aT[4] + w * (aT[6] + w * (aT[8] + w * aT[10])))));
112 » if (id < 0) 110 s2 = w * (aT[1] + w * (aT[3] + w * (aT[5] + w * (aT[7] + w * aT[9]))));
113 » » return x - x*(s1+s2); 111 if (id < 0)
114 » z = atanhi[id] - (x*(s1+s2) - atanlo[id] - x); 112 return x - x * (s1 + s2);
115 » return sign ? -z : z; 113 z = atanhi[id] - (x * (s1 + s2) - atanlo[id] - x);
114 return sign ? -z : z;
116 } 115 }
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