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1 /* origin: FreeBSD /usr/src/lib/msun/ld80/k_sinl.c */ | 1 /* origin: FreeBSD /usr/src/lib/msun/ld80/k_sinl.c */ |
2 /* origin: FreeBSD /usr/src/lib/msun/ld128/k_sinl.c */ | 2 /* origin: FreeBSD /usr/src/lib/msun/ld128/k_sinl.c */ |
3 /* | 3 /* |
4 * ==================================================== | 4 * ==================================================== |
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. | 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
6 * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. | 6 * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. |
7 * | 7 * |
8 * Developed at SunSoft, a Sun Microsystems, Inc. business. | 8 * Developed at SunSoft, a Sun Microsystems, Inc. business. |
9 * Permission to use, copy, modify, and distribute this | 9 * Permission to use, copy, modify, and distribute this |
10 * software is freely granted, provided that this notice | 10 * software is freely granted, provided that this notice |
11 * is preserved. | 11 * is preserved. |
12 * ==================================================== | 12 * ==================================================== |
13 */ | 13 */ |
14 | 14 |
15 #include "libm.h" | 15 #include "libm.h" |
16 | 16 |
17 #if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 | 17 #if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 |
18 #if LDBL_MANT_DIG == 64 | 18 #if LDBL_MANT_DIG == 64 |
19 /* | 19 /* |
20 * ld80 version of __sin.c. See __sin.c for most comments. | 20 * ld80 version of __sin.c. See __sin.c for most comments. |
21 */ | 21 */ |
22 /* | 22 /* |
23 * Domain [-0.7854, 0.7854], range ~[-1.89e-22, 1.915e-22] | 23 * Domain [-0.7854, 0.7854], range ~[-1.89e-22, 1.915e-22] |
24 * |sin(x)/x - s(x)| < 2**-72.1 | 24 * |sin(x)/x - s(x)| < 2**-72.1 |
25 * | 25 * |
26 * See __cosl.c for more details about the polynomial. | 26 * See __cosl.c for more details about the polynomial. |
27 */ | 27 */ |
28 static const long double | 28 static const long double S1 = |
29 S1 = -0.166666666666666666671L; /* -0xaaaaaaaaaaaaaaab.0p-66 */ | 29 -0.166666666666666666671L; /* -0xaaaaaaaaaaaaaaab.0p-66 */ |
30 static const double | 30 static const double S2 = 0.0083333333333333332, /* 0x11111111111111.0p-59 */ |
31 S2 = 0.0083333333333333332, /* 0x11111111111111.0p-59 */ | 31 S3 = -0.00019841269841269427, /* -0x1a01a01a019f81.0p-65 */ |
32 S3 = -0.00019841269841269427, /* -0x1a01a01a019f81.0p-65 */ | 32 S4 = 0.0000027557319223597490, /* 0x171de3a55560f7.0p-71 */ |
33 S4 = 0.0000027557319223597490, /* 0x171de3a55560f7.0p-71 */ | 33 S5 = -0.000000025052108218074604, /* -0x1ae64564f16cad.0p-78 */ |
34 S5 = -0.000000025052108218074604, /* -0x1ae64564f16cad.0p-78 */ | 34 S6 = 1.6059006598854211e-10, /* 0x161242b90243b5.0p-85 */ |
35 S6 = 1.6059006598854211e-10, /* 0x161242b90243b5.0p-85 */ | 35 S7 = -7.6429779983024564e-13, /* -0x1ae42ebd1b2e00.0p-93 */ |
36 S7 = -7.6429779983024564e-13, /* -0x1ae42ebd1b2e00.0p-93 */ | 36 S8 = 2.6174587166648325e-15; /* 0x179372ea0b3f64.0p-101 */ |
37 S8 = 2.6174587166648325e-15; /* 0x179372ea0b3f64.0p-101 */ | 37 #define POLY(z) \ |
38 #define POLY(z) (S2+z*(S3+z*(S4+z*(S5+z*(S6+z*(S7+z*S8)))))) | 38 (S2 + z * (S3 + z * (S4 + z * (S5 + z * (S6 + z * (S7 + z * S8)))))) |
39 #elif LDBL_MANT_DIG == 113 | 39 #elif LDBL_MANT_DIG == 113 |
40 /* | 40 /* |
41 * ld128 version of __sin.c. See __sin.c for most comments. | 41 * ld128 version of __sin.c. See __sin.c for most comments. |
42 */ | 42 */ |
43 /* | 43 /* |
44 * Domain [-0.7854, 0.7854], range ~[-1.53e-37, 1.659e-37] | 44 * Domain [-0.7854, 0.7854], range ~[-1.53e-37, 1.659e-37] |
45 * |sin(x)/x - s(x)| < 2**-122.1 | 45 * |sin(x)/x - s(x)| < 2**-122.1 |
46 * | 46 * |
47 * See __cosl.c for more details about the polynomial. | 47 * See __cosl.c for more details about the polynomial. |
48 */ | 48 */ |
49 static const long double | 49 static const long double |
50 S1 = -0.16666666666666666666666666666666666606732416116558L, | 50 S1 = -0.16666666666666666666666666666666666606732416116558L, |
51 S2 = 0.0083333333333333333333333333333331135404851288270047L, | 51 S2 = 0.0083333333333333333333333333333331135404851288270047L, |
52 S3 = -0.00019841269841269841269841269839935785325638310428717L, | 52 S3 = -0.00019841269841269841269841269839935785325638310428717L, |
53 S4 = 0.27557319223985890652557316053039946268333231205686e-5L, | 53 S4 = 0.27557319223985890652557316053039946268333231205686e-5L, |
54 S5 = -0.25052108385441718775048214826384312253862930064745e-7L, | 54 S5 = -0.25052108385441718775048214826384312253862930064745e-7L, |
55 S6 = 0.16059043836821614596571832194524392581082444805729e-9L, | 55 S6 = 0.16059043836821614596571832194524392581082444805729e-9L, |
56 S7 = -0.76471637318198151807063387954939213287488216303768e-12L, | 56 S7 = -0.76471637318198151807063387954939213287488216303768e-12L, |
57 S8 = 0.28114572543451292625024967174638477283187397621303e-14L; | 57 S8 = 0.28114572543451292625024967174638477283187397621303e-14L; |
58 static const double | 58 static const double |
59 S9 = -0.82206352458348947812512122163446202498005154296863e-17, | 59 S9 = -0.82206352458348947812512122163446202498005154296863e-17, |
60 S10 = 0.19572940011906109418080609928334380560135358385256e-19, | 60 S10 = 0.19572940011906109418080609928334380560135358385256e-19, |
61 S11 = -0.38680813379701966970673724299207480965452616911420e-22, | 61 S11 = -0.38680813379701966970673724299207480965452616911420e-22, |
62 S12 = 0.64038150078671872796678569586315881020659912139412e-25; | 62 S12 = 0.64038150078671872796678569586315881020659912139412e-25; |
63 #define POLY(z) (S2+z*(S3+z*(S4+z*(S5+z*(S6+z*(S7+z*(S8+ \ | 63 #define POLY(z) \ |
64 » z*(S9+z*(S10+z*(S11+z*S12)))))))))) | 64 (S2 + \ |
| 65 z * (S3 + \ |
| 66 z * (S4 + \ |
| 67 z * (S5 + \ |
| 68 z * (S6 + \ |
| 69 z * (S7 + \ |
| 70 z * (S8 + \ |
| 71 z * (S9 + \ |
| 72 z * (S10 + z * (S11 + z * S12)))))))))) |
65 #endif | 73 #endif |
66 | 74 |
67 long double __sinl(long double x, long double y, int iy) | 75 long double __sinl(long double x, long double y, int iy) { |
68 { | 76 long double z, r, v; |
69 » long double z,r,v; | |
70 | 77 |
71 » z = x*x; | 78 z = x * x; |
72 » v = z*x; | 79 v = z * x; |
73 » r = POLY(z); | 80 r = POLY(z); |
74 » if (iy == 0) | 81 if (iy == 0) |
75 » » return x+v*(S1+z*r); | 82 return x + v * (S1 + z * r); |
76 » return x-((z*(0.5*y-v*r)-y)-v*S1); | 83 return x - ((z * (0.5 * y - v * r) - y) - v * S1); |
77 } | 84 } |
78 #endif | 85 #endif |
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