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- /* Quad-precision floating point cosine on <-pi/4,pi/4>.
- Copyright (C) 1999-2018 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, see
- <http://www.gnu.org/licenses/>. */
- #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 */
- };
- #define SINCOSL_COS_HI 0
- #define SINCOSL_COS_LO 1
- #define SINCOSL_SIN_HI 2
- #define SINCOSL_SIN_LO 3
- extern const __float128 __sincosq_table[];
- __float128
- __quadmath_kernel_cosq(__float128 x, __float128 y)
- {
- __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. */
- if (tix < 0x3fc60000) /* |x| < 2^-57 */
- if (!((int)x)) return ONE; /* generate inexact */
- z = x * x;
- return 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 fabsq(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
- 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);
- l = y - (h - x);
- 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))));
- return __sincosq_table [index + SINCOSL_COS_HI]
- + (__sincosq_table [index + SINCOSL_COS_LO]
- - (__sincosq_table [index + SINCOSL_SIN_HI] * sin_l
- - __sincosq_table [index + SINCOSL_COS_HI] * cos_l_m1));
- }
- }
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