diff options
Diffstat (limited to 'lib/msun/src/k_sincosl.h')
-rw-r--r-- | lib/msun/src/k_sincosl.h | 134 |
1 files changed, 134 insertions, 0 deletions
diff --git a/lib/msun/src/k_sincosl.h b/lib/msun/src/k_sincosl.h new file mode 100644 index 0000000..3a609bc --- /dev/null +++ b/lib/msun/src/k_sincosl.h @@ -0,0 +1,134 @@ +/*- + * ==================================================== + * 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 +C1 = 0.04166666666666666666666666666666658424671L, +C2 = -0.001388888888888888888888888888863490893732L, +C3 = 0.00002480158730158730158730158600795304914210L, +C4 = -0.2755731922398589065255474947078934284324e-6L, +C5 = 0.2087675698786809897659225313136400793948e-8L, +C6 = -0.1147074559772972315817149986812031204775e-10L, +C7 = 0.4779477332386808976875457937252120293400e-13L, +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 +C8 = -0.1561920696721507929516718307820958119868e-15, +C9 = 0.4110317413744594971475941557607804508039e-18, +C10 = -0.8896592467191938803288521958313920156409e-21, +C11 = 0.1601061435794535138244346256065192782581e-23, +S9 = -0.82206352458348947812512122163446202498005154296863e-17, +S10 = 0.19572940011906109418080609928334380560135358385256e-19, +S11 = -0.38680813379701966970673724299207480965452616911420e-22, +S12 = 0.64038150078671872796678569586315881020659912139412e-25; + +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 + *cs = 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)))))))))); + + *cs = w + (((1 - w) - hz) + (z * r - x * y)); +} +#else +#error "Unsupported long double format" +#endif |