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Side by Side Diff: fusl/src/math/__tan.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/k_tan.c */ 1 /* origin: FreeBSD /usr/src/lib/msun/src/k_tan.c */
2 /* 2 /*
3 * ==================================================== 3 * ====================================================
4 * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. 4 * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved.
5 * 5 *
6 * Permission to use, copy, modify, and distribute this 6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice 7 * software is freely granted, provided that this notice
8 * is preserved. 8 * is preserved.
9 * ==================================================== 9 * ====================================================
10 */ 10 */
11 /* __tan( x, y, k ) 11 /* __tan( x, y, k )
12 * kernel tan function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854 12 * kernel tan function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854
13 * Input x is assumed to be bounded by ~pi/4 in magnitude. 13 * Input x is assumed to be bounded by ~pi/4 in magnitude.
14 * Input y is the tail of x. 14 * Input y is the tail of x.
15 * Input odd indicates whether tan (if odd = 0) or -1/tan (if odd = 1) is return ed. 15 * Input odd indicates whether tan (if odd = 0) or -1/tan (if odd = 1) is
16 * returned.
16 * 17 *
17 * Algorithm 18 * Algorithm
18 * 1. Since tan(-x) = -tan(x), we need only to consider positive x. 19 * 1. Since tan(-x) = -tan(x), we need only to consider positive x.
19 * 2. Callers must return tan(-0) = -0 without calling here since our 20 * 2. Callers must return tan(-0) = -0 without calling here since our
20 * odd polynomial is not evaluated in a way that preserves -0. 21 * odd polynomial is not evaluated in a way that preserves -0.
21 * Callers may do the optimization tan(x) ~ x for tiny x. 22 * Callers may do the optimization tan(x) ~ x for tiny x.
22 * 3. tan(x) is approximated by a odd polynomial of degree 27 on 23 * 3. tan(x) is approximated by a odd polynomial of degree 27 on
23 * [0,0.67434] 24 * [0,0.67434]
24 * 3 27 25 * 3 27
25 * tan(x) ~ x + T1*x + ... + T13*x 26 * tan(x) ~ x + T1*x + ... + T13*x
(...skipping 12 matching lines...) Expand all
38 * 3 2 39 * 3 2
39 * tan(x+y) = x + (T1*x + (x *(r+y)+y)) 40 * tan(x+y) = x + (T1*x + (x *(r+y)+y))
40 * 41 *
41 * 4. For x in [0.67434,pi/4], let y = pi/4 - x, then 42 * 4. For x in [0.67434,pi/4], let y = pi/4 - x, then
42 * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y)) 43 * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
43 * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) 44 * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
44 */ 45 */
45 46
46 #include "libm.h" 47 #include "libm.h"
47 48
48 static const double T[] = { 49 static const double T[] =
49 3.33333333333334091986e-01, /* 3FD55555, 55555563 */ 50 {
50 1.33333333333201242699e-01, /* 3FC11111, 1110FE7A */ 51 3.33333333333334091986e-01, /* 3FD55555, 55555563 */
51 5.39682539762260521377e-02, /* 3FABA1BA, 1BB341FE */ 52 1.33333333333201242699e-01, /* 3FC11111, 1110FE7A */
52 2.18694882948595424599e-02, /* 3F9664F4, 8406D637 */ 53 5.39682539762260521377e-02, /* 3FABA1BA, 1BB341FE */
53 8.86323982359930005737e-03, /* 3F8226E3, E96E8493 */ 54 2.18694882948595424599e-02, /* 3F9664F4, 8406D637 */
54 3.59207910759131235356e-03, /* 3F6D6D22, C9560328 */ 55 8.86323982359930005737e-03, /* 3F8226E3, E96E8493 */
55 1.45620945432529025516e-03, /* 3F57DBC8, FEE08315 */ 56 3.59207910759131235356e-03, /* 3F6D6D22, C9560328 */
56 5.88041240820264096874e-04, /* 3F4344D8, F2F26501 */ 57 1.45620945432529025516e-03, /* 3F57DBC8, FEE08315 */
57 2.46463134818469906812e-04, /* 3F3026F7, 1A8D1068 */ 58 5.88041240820264096874e-04, /* 3F4344D8, F2F26501 */
58 7.81794442939557092300e-05, /* 3F147E88, A03792A6 */ 59 2.46463134818469906812e-04, /* 3F3026F7, 1A8D1068 */
59 7.14072491382608190305e-05, /* 3F12B80F, 32F0A7E9 */ 60 7.81794442939557092300e-05, /* 3F147E88, A03792A6 */
60 -1.85586374855275456654e-05, /* BEF375CB, DB605373 */ 61 7.14072491382608190305e-05, /* 3F12B80F, 32F0A7E9 */
61 2.59073051863633712884e-05, /* 3EFB2A70, 74BF7AD4 */ 62 -1.85586374855275456654e-05, /* BEF375CB, DB605373 */
63 2.59073051863633712884e-05, /* 3EFB2A70, 74BF7AD4 */
62 }, 64 },
63 pio4 = 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */ 65 pio4 = 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */
64 pio4lo = 3.06161699786838301793e-17; /* 3C81A626, 33145C07 */ 66 pio4lo = 3.06161699786838301793e-17; /* 3C81A626, 33145C07 */
65 67
66 double __tan(double x, double y, int odd) 68 double __tan(double x, double y, int odd) {
67 { 69 double_t z, r, v, w, s, a;
68 » double_t z, r, v, w, s, a; 70 double w0, a0;
69 » double w0, a0; 71 uint32_t hx;
70 » uint32_t hx; 72 int big, sign;
71 » int big, sign;
72 73
73 » GET_HIGH_WORD(hx,x); 74 GET_HIGH_WORD(hx, x);
74 » big = (hx&0x7fffffff) >= 0x3FE59428; /* |x| >= 0.6744 */ 75 big = (hx & 0x7fffffff) >= 0x3FE59428; /* |x| >= 0.6744 */
75 » if (big) { 76 if (big) {
76 » » sign = hx>>31; 77 sign = hx >> 31;
77 » » if (sign) { 78 if (sign) {
78 » » » x = -x; 79 x = -x;
79 » » » y = -y; 80 y = -y;
80 » » } 81 }
81 » » x = (pio4 - x) + (pio4lo - y); 82 x = (pio4 - x) + (pio4lo - y);
82 » » y = 0.0; 83 y = 0.0;
83 » } 84 }
84 » z = x * x; 85 z = x * x;
85 » w = z * z; 86 w = z * z;
86 » /* 87 /*
87 » * Break x^5*(T[1]+x^2*T[2]+...) into 88 * Break x^5*(T[1]+x^2*T[2]+...) into
88 » * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + 89 * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
89 » * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) 90 * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
90 » */ 91 */
91 » r = T[1] + w*(T[3] + w*(T[5] + w*(T[7] + w*(T[9] + w*T[11])))); 92 r = T[1] + w * (T[3] + w * (T[5] + w * (T[7] + w * (T[9] + w * T[11]))));
92 » v = z*(T[2] + w*(T[4] + w*(T[6] + w*(T[8] + w*(T[10] + w*T[12]))))); 93 v = z *
93 » s = z * x; 94 (T[2] + w * (T[4] + w * (T[6] + w * (T[8] + w * (T[10] + w * T[12])))));
94 » r = y + z*(s*(r + v) + y) + s*T[0]; 95 s = z * x;
95 » w = x + r; 96 r = y + z * (s * (r + v) + y) + s * T[0];
96 » if (big) { 97 w = x + r;
97 » » s = 1 - 2*odd; 98 if (big) {
98 » » v = s - 2.0 * (x + (r - w*w/(w + s))); 99 s = 1 - 2 * odd;
99 » » return sign ? -v : v; 100 v = s - 2.0 * (x + (r - w * w / (w + s)));
100 » } 101 return sign ? -v : v;
101 » if (!odd) 102 }
102 » » return w; 103 if (!odd)
103 » /* -1.0/(x+r) has up to 2ulp error, so compute it accurately */ 104 return w;
104 » w0 = w; 105 /* -1.0/(x+r) has up to 2ulp error, so compute it accurately */
105 » SET_LOW_WORD(w0, 0); 106 w0 = w;
106 » v = r - (w0 - x); /* w0+v = r+x */ 107 SET_LOW_WORD(w0, 0);
107 » a0 = a = -1.0 / w; 108 v = r - (w0 - x); /* w0+v = r+x */
108 » SET_LOW_WORD(a0, 0); 109 a0 = a = -1.0 / w;
109 » return a0 + a*(1.0 + a0*w0 + a0*v); 110 SET_LOW_WORD(a0, 0);
111 return a0 + a * (1.0 + a0 * w0 + a0 * v);
110 } 112 }
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