| /* Quad-precision floating point sine and cosine on <-pi/4,pi/4>. |
| Copyright (C) 1999-2017 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 */ |
| { |
| math_check_force_underflow (x); |
| 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 cosq(h) and sinq(h) in |
| pre-computed tables, compute cosq(l) and sinq(l) using a |
| Chebyshev polynomial of degree 10(11) and compute |
| sinq(h+l) = sinq(h)cosq(l) + cosq(h)sinq(l) and |
| cosq(h+l) = cosq(h)cosq(l) - sinq(h)sinq(l). */ |
| index = 0x3ffe - (tix >> 16); |
| hix = (tix + (0x200 << index)) & (0xfffffc00 << index); |
| if (signbitq (x)) |
| { |
| x = -x; |
| y = -y; |
| } |
| 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)); |
| } |
| } |