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Diffstat (limited to 'libquadmath/math/sincosq_kernel.c')
| -rw-r--r-- | libquadmath/math/sincosq_kernel.c | 163 |
1 files changed, 163 insertions, 0 deletions
diff --git a/libquadmath/math/sincosq_kernel.c b/libquadmath/math/sincosq_kernel.c new file mode 100644 index 000000000..578d1828f --- /dev/null +++ b/libquadmath/math/sincosq_kernel.c @@ -0,0 +1,163 @@ +/* Quad-precision floating point sine and cosine on <-pi/4,pi/4>. + Copyright (C) 1999 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jj@ultra.linux.cz> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, write to the Free + Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA + 02111-1307 USA. */ + +#include "quadmath-imp.h" + +static const __float128 c[] = { +#define ONE c[0] + 1.00000000000000000000000000000000000E+00Q, /* 3fff0000000000000000000000000000 */ + +/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 ) + x in <0,1/256> */ +#define SCOS1 c[1] +#define SCOS2 c[2] +#define SCOS3 c[3] +#define SCOS4 c[4] +#define SCOS5 c[5] +-5.00000000000000000000000000000000000E-01Q, /* bffe0000000000000000000000000000 */ + 4.16666666666666666666666666556146073E-02Q, /* 3ffa5555555555555555555555395023 */ +-1.38888888888888888888309442601939728E-03Q, /* bff56c16c16c16c16c16a566e42c0375 */ + 2.48015873015862382987049502531095061E-05Q, /* 3fefa01a01a019ee02dcf7da2d6d5444 */ +-2.75573112601362126593516899592158083E-07Q, /* bfe927e4f5dce637cb0b54908754bde0 */ + +/* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 ) + x in <0,0.1484375> */ +#define COS1 c[6] +#define COS2 c[7] +#define COS3 c[8] +#define COS4 c[9] +#define COS5 c[10] +#define COS6 c[11] +#define COS7 c[12] +#define COS8 c[13] +-4.99999999999999999999999999999999759E-01Q, /* bffdfffffffffffffffffffffffffffb */ + 4.16666666666666666666666666651287795E-02Q, /* 3ffa5555555555555555555555516f30 */ +-1.38888888888888888888888742314300284E-03Q, /* bff56c16c16c16c16c16c16a463dfd0d */ + 2.48015873015873015867694002851118210E-05Q, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */ +-2.75573192239858811636614709689300351E-07Q, /* bfe927e4fb7789f5aa8142a22044b51f */ + 2.08767569877762248667431926878073669E-09Q, /* 3fe21eed8eff881d1e9262d7adff4373 */ +-1.14707451049343817400420280514614892E-11Q, /* bfda9397496922a9601ed3d4ca48944b */ + 4.77810092804389587579843296923533297E-14Q, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */ + +/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 ) + x in <0,1/256> */ +#define SSIN1 c[14] +#define SSIN2 c[15] +#define SSIN3 c[16] +#define SSIN4 c[17] +#define SSIN5 c[18] +-1.66666666666666666666666666666666659E-01Q, /* bffc5555555555555555555555555555 */ + 8.33333333333333333333333333146298442E-03Q, /* 3ff81111111111111111111110fe195d */ +-1.98412698412698412697726277416810661E-04Q, /* bff2a01a01a01a01a019e7121e080d88 */ + 2.75573192239848624174178393552189149E-06Q, /* 3fec71de3a556c640c6aaa51aa02ab41 */ +-2.50521016467996193495359189395805639E-08Q, /* bfe5ae644ee90c47dc71839de75b2787 */ + +/* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 ) + x in <0,0.1484375> */ +#define SIN1 c[19] +#define SIN2 c[20] +#define SIN3 c[21] +#define SIN4 c[22] +#define SIN5 c[23] +#define SIN6 c[24] +#define SIN7 c[25] +#define SIN8 c[26] +-1.66666666666666666666666666666666538e-01Q, /* bffc5555555555555555555555555550 */ + 8.33333333333333333333333333307532934e-03Q, /* 3ff811111111111111111111110e7340 */ +-1.98412698412698412698412534478712057e-04Q, /* bff2a01a01a01a01a01a019e7a626296 */ + 2.75573192239858906520896496653095890e-06Q, /* 3fec71de3a556c7338fa38527474b8f5 */ +-2.50521083854417116999224301266655662e-08Q, /* bfe5ae64567f544e16c7de65c2ea551f */ + 1.60590438367608957516841576404938118e-10Q, /* 3fde6124613a811480538a9a41957115 */ +-7.64716343504264506714019494041582610e-13Q, /* bfd6ae7f3d5aef30c7bc660b060ef365 */ + 2.81068754939739570236322404393398135e-15Q, /* 3fce9510115aabf87aceb2022a9a9180 */ +}; + +#define SINCOSQ_COS_HI 0 +#define SINCOSQ_COS_LO 1 +#define SINCOSQ_SIN_HI 2 +#define SINCOSQ_SIN_LO 3 +extern const __float128 __sincosq_table[]; + +void +__quadmath_kernel_sincosq(__float128 x, __float128 y, __float128 *sinx, + __float128 *cosx, int iy) +{ + __float128 h, l, z, sin_l, cos_l_m1; + int64_t ix; + uint32_t tix, hix, index; + GET_FLT128_MSW64 (ix, x); + tix = ((uint64_t)ix) >> 32; + tix &= ~0x80000000; /* tix = |x|'s high 32 bits */ + if (tix < 0x3ffc3000) /* |x| < 0.1484375 */ + { + /* Argument is small enough to approximate it by a Chebyshev + polynomial of degree 16(17). */ + if (tix < 0x3fc60000) /* |x| < 2^-57 */ + if (!((int)x)) /* generate inexact */ + { + *sinx = x; + *cosx = ONE; + return; + } + z = x * x; + *sinx = x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+ + z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8))))))))); + *cosx = ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+ + z*(COS5+z*(COS6+z*(COS7+z*COS8)))))))); + } + else + { + /* So that we don't have to use too large polynomial, we find + l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83 + possible values for h. We look up cosl(h) and sinl(h) in + pre-computed tables, compute cosl(l) and sinl(l) using a + Chebyshev polynomial of degree 10(11) and compute + sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l) and + cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l). */ + index = 0x3ffe - (tix >> 16); + hix = (tix + (0x200 << index)) & (0xfffffc00 << index); + x = fabsq (x); + switch (index) + { + case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break; + case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break; + default: + case 2: index = (hix - 0x3ffc3000) >> 10; break; + } + + SET_FLT128_WORDS64(h, ((uint64_t)hix) << 32, 0); + if (iy) + l = y - (h - x); + else + l = x - h; + z = l * l; + sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5))))); + cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5)))); + z = __sincosq_table [index + SINCOSQ_SIN_HI] + + (__sincosq_table [index + SINCOSQ_SIN_LO] + + (__sincosq_table [index + SINCOSQ_SIN_HI] * cos_l_m1) + + (__sincosq_table [index + SINCOSQ_COS_HI] * sin_l)); + *sinx = (ix < 0) ? -z : z; + *cosx = __sincosq_table [index + SINCOSQ_COS_HI] + + (__sincosq_table [index + SINCOSQ_COS_LO] + - (__sincosq_table [index + SINCOSQ_SIN_HI] * sin_l + - __sincosq_table [index + SINCOSQ_COS_HI] * cos_l_m1)); + } +} |