| /*- |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. |
| * |
| * Developed at SunSoft, a Sun Microsystems, Inc. business. |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| * |
| * k_sinl.c and k_cosl.c merged by Steven G. Kargl |
| */ |
| |
| #include <sys/cdefs.h> |
| __FBSDID("$FreeBSD$"); |
| |
| #if LDBL_MANT_DIG == 64 /* ld80 version of k_sincosl.c. */ |
| |
| #if defined(__amd64__) || defined(__i386__) |
| /* Long double constants are slow on these arches, and broken on i386. */ |
| static const volatile double |
| C1hi = 0.041666666666666664, /* 0x15555555555555.0p-57 */ |
| C1lo = 2.2598839032744733e-18, /* 0x14d80000000000.0p-111 */ |
| S1hi = -0.16666666666666666, /* -0x15555555555555.0p-55 */ |
| S1lo = -9.2563760475949941e-18; /* -0x15580000000000.0p-109 */ |
| #define S1 ((long double)S1hi + S1lo) |
| #define C1 ((long double)C1hi + C1lo) |
| #else |
| static const long double |
| C1 = 0.0416666666666666666136L, /* 0xaaaaaaaaaaaaaa9b.0p-68 */ |
| S1 = -0.166666666666666666671L; /* -0xaaaaaaaaaaaaaaab.0p-66 */ |
| #endif |
| |
| static const double |
| C2 = -0.0013888888888888874, /* -0x16c16c16c16c10.0p-62 */ |
| C3 = 0.000024801587301571716, /* 0x1a01a01a018e22.0p-68 */ |
| C4 = -0.00000027557319215507120, /* -0x127e4fb7602f22.0p-74 */ |
| C5 = 0.0000000020876754400407278, /* 0x11eed8caaeccf1.0p-81 */ |
| C6 = -1.1470297442401303e-11, /* -0x19393412bd1529.0p-89 */ |
| C7 = 4.7383039476436467e-14, /* 0x1aac9d9af5c43e.0p-97 */ |
| S2 = 0.0083333333333333332, /* 0x11111111111111.0p-59 */ |
| S3 = -0.00019841269841269427, /* -0x1a01a01a019f81.0p-65 */ |
| S4 = 0.0000027557319223597490, /* 0x171de3a55560f7.0p-71 */ |
| S5 = -0.000000025052108218074604, /* -0x1ae64564f16cad.0p-78 */ |
| S6 = 1.6059006598854211e-10, /* 0x161242b90243b5.0p-85 */ |
| S7 = -7.6429779983024564e-13, /* -0x1ae42ebd1b2e00.0p-93 */ |
| S8 = 2.6174587166648325e-15; /* 0x179372ea0b3f64.0p-101 */ |
| |
| static inline void |
| __kernel_sincosl(long double x, long double y, int iy, long double *sn, |
| long double *cs) |
| { |
| long double hz, r, v, w, z; |
| |
| z = x * x; |
| v = z * x; |
| /* |
| * XXX Replace Horner scheme with an algorithm suitable for CPUs |
| * with more complex pipelines. |
| */ |
| r = S2 + z * (S3 + z * (S4 + z * (S5 + z * (S6 + z * (S7 + z * S8))))); |
| |
| if (iy == 0) |
| *sn = x + v * (S1 + z * r); |
| else |
| *sn = x - ((z * (y / 2 - v * r) - y) - v * S1); |
| |
| hz = z / 2; |
| w = 1 - hz; |
| r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * (C6 + |
| z * C7)))))); |
| *cs = w + (((1 - w) - hz) + (z * r - x * y)); |
| } |
| |
| #elif LDBL_MANT_DIG == 113 /* ld128 version of k_sincosl.c. */ |
| |
| static const long double |
| S1 = -0.16666666666666666666666666666666666606732416116558L, |
| S2 = 0.0083333333333333333333333333333331135404851288270047L, |
| S3 = -0.00019841269841269841269841269839935785325638310428717L, |
| S4 = 0.27557319223985890652557316053039946268333231205686e-5L, |
| S5 = -0.25052108385441718775048214826384312253862930064745e-7L, |
| S6 = 0.16059043836821614596571832194524392581082444805729e-9L, |
| S7 = -0.76471637318198151807063387954939213287488216303768e-12L, |
| S8 = 0.28114572543451292625024967174638477283187397621303e-14L; |
| |
| static const double |
| S9 = -0.82206352458348947812512122163446202498005154296863e-17, |
| S10 = 0.19572940011906109418080609928334380560135358385256e-19, |
| S11 = -0.38680813379701966970673724299207480965452616911420e-22, |
| S12 = 0.64038150078671872796678569586315881020659912139412e-25; |
| |
| static const long double |
| C1 = 4.16666666666666666666666666666666667e-02L, |
| C2 = -1.38888888888888888888888888888888834e-03L, |
| C3 = 2.48015873015873015873015873015446795e-05L, |
| C4 = -2.75573192239858906525573190949988493e-07L, |
| C5 = 2.08767569878680989792098886701451072e-09L, |
| C6 = -1.14707455977297247136657111139971865e-11L, |
| C7 = 4.77947733238738518870113294139830239e-14L, |
| C8 = -1.56192069685858079920640872925306403e-16L, |
| C9 = 4.11031762320473354032038893429515732e-19L, |
| C10= -8.89679121027589608738005163931958096e-22L, |
| C11= 1.61171797801314301767074036661901531e-24L, |
| C12= -2.46748624357670948912574279501044295e-27L; |
| |
| static inline void |
| __kernel_sincosl(long double x, long double y, int iy, long double *sn, |
| long double *cs) |
| { |
| long double hz, r, v, w, z; |
| |
| z = x * x; |
| v = z * x; |
| /* |
| * XXX Replace Horner scheme with an algorithm suitable for CPUs |
| * with more complex pipelines. |
| */ |
| r = S2 + z * (S3 + z * (S4 + z * (S5 + z * (S6 + z * (S7 + z * (S8 + |
| z * (S9 + z * (S10 + z * (S11 + z * S12))))))))); |
| |
| if (iy == 0) |
| *sn = x + v * (S1 + z * r); |
| else |
| *sn = x - ((z * (y / 2 - v * r) - y) - v * S1); |
| |
| hz = z / 2; |
| w = 1 - hz; |
| r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * (C6 + |
| z * (C7 + z * (C8 + z * (C9 + z * (C10 + z * (C11+z*C12))))))))))); |
| |
| *cs = w + (((1 - w) - hz) + (z * r - x * y)); |
| } |
| #else |
| #error "Unsupported long double format" |
| #endif |
