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Similar to various other bugs in this area, some sin and sincos implementations do not raise the underflow exception for subnormal arguments, when the result is tiny and inexact. This patch forces the exception in a similar way to previous fixes. Tested for x86_64, x86, mips64 and powerpc. [BZ #16526] [BZ #16538] * sysdeps/ieee754/dbl-64/s_sin.c: Include <float.h>. (__sin): Force underflow exception for arguments with small absolute value. * sysdeps/ieee754/flt-32/k_sinf.c: Include <float.h>. (__kernel_sinf): Force underflow exception for arguments with small absolute value. * sysdeps/ieee754/ldbl-128/k_sincosl.c: Include <float.h>. (__kernel_sincosl): Force underflow exception for arguments with small absolute value. * sysdeps/ieee754/ldbl-128/k_sinl.c: Include <float.h>. (__kernel_sinl): Force underflow exception for arguments with small absolute value. * sysdeps/ieee754/ldbl-128ibm/k_sincosl.c: Include <float.h>. (__kernel_sincosl): Force underflow exception for arguments with small absolute value. * sysdeps/ieee754/ldbl-128ibm/k_sinl.c: Include <float.h>. (__kernel_sinl): Force underflow exception for arguments with small absolute value. * sysdeps/ieee754/ldbl-96/k_sinl.c: Include <float.h>. (__kernel_sinl): Force underflow exception for arguments with small absolute value. * sysdeps/powerpc/fpu/k_sinf.c: Include <float.h>. (__kernel_sinf): Force underflow exception for arguments with small absolute value. * math/auto-libm-test-in: Add more tests of sin and sincos. * math/auto-libm-test-out: Regenerated.
198 lines
7.4 KiB
C
198 lines
7.4 KiB
C
/* Quad-precision floating point sine and cosine on <-pi/4,pi/4>.
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Copyright (C) 1999-2015 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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Contributed by Jakub Jelinek <jj@ultra.linux.cz>
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<http://www.gnu.org/licenses/>. */
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#include <float.h>
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#include <math.h>
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#include <math_private.h>
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static const long double c[] = {
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#define ONE c[0]
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1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */
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/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
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x in <0,1/256> */
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#define SCOS1 c[1]
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#define SCOS2 c[2]
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#define SCOS3 c[3]
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#define SCOS4 c[4]
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#define SCOS5 c[5]
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-5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */
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4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */
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-1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */
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2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */
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-2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */
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/* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 )
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x in <0,0.1484375> */
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#define COS1 c[6]
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#define COS2 c[7]
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#define COS3 c[8]
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#define COS4 c[9]
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#define COS5 c[10]
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#define COS6 c[11]
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#define COS7 c[12]
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#define COS8 c[13]
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-4.99999999999999999999999999999999759E-01L, /* bffdfffffffffffffffffffffffffffb */
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4.16666666666666666666666666651287795E-02L, /* 3ffa5555555555555555555555516f30 */
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-1.38888888888888888888888742314300284E-03L, /* bff56c16c16c16c16c16c16a463dfd0d */
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2.48015873015873015867694002851118210E-05L, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */
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-2.75573192239858811636614709689300351E-07L, /* bfe927e4fb7789f5aa8142a22044b51f */
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2.08767569877762248667431926878073669E-09L, /* 3fe21eed8eff881d1e9262d7adff4373 */
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-1.14707451049343817400420280514614892E-11L, /* bfda9397496922a9601ed3d4ca48944b */
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4.77810092804389587579843296923533297E-14L, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */
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/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
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x in <0,1/256> */
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#define SSIN1 c[14]
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#define SSIN2 c[15]
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#define SSIN3 c[16]
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#define SSIN4 c[17]
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#define SSIN5 c[18]
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-1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */
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8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */
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-1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */
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2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */
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-2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */
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/* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
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x in <0,0.1484375> */
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#define SIN1 c[19]
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#define SIN2 c[20]
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#define SIN3 c[21]
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#define SIN4 c[22]
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#define SIN5 c[23]
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#define SIN6 c[24]
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#define SIN7 c[25]
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#define SIN8 c[26]
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-1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */
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8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */
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-1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */
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2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */
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-2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */
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1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */
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-7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
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2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */
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};
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#define SINCOSL_COS_HI 0
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#define SINCOSL_COS_LO 1
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#define SINCOSL_SIN_HI 2
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#define SINCOSL_SIN_LO 3
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extern const long double __sincosl_table[];
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void
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__kernel_sincosl(long double x, long double y, long double *sinx, long double *cosx, int iy)
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{
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long double h, l, z, sin_l, cos_l_m1;
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int64_t ix;
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uint32_t tix, hix, index;
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double xhi, hhi;
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xhi = ldbl_high (x);
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EXTRACT_WORDS64 (ix, xhi);
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tix = ((uint64_t)ix) >> 32;
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tix &= ~0x80000000; /* tix = |x|'s high 32 bits */
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if (tix < 0x3fc30000) /* |x| < 0.1484375 */
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{
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/* Argument is small enough to approximate it by a Chebyshev
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polynomial of degree 16(17). */
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if (tix < 0x3c600000) /* |x| < 2^-57 */
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{
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if (fabsl (x) < LDBL_MIN)
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{
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long double force_underflow = x * x;
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math_force_eval (force_underflow);
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}
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if (!((int)x)) /* generate inexact */
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{
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*sinx = x;
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*cosx = ONE;
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return;
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}
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}
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z = x * x;
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*sinx = x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
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z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
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*cosx = ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
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z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
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}
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else
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{
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/* So that we don't have to use too large polynomial, we find
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l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
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possible values for h. We look up cosl(h) and sinl(h) in
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pre-computed tables, compute cosl(l) and sinl(l) using a
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Chebyshev polynomial of degree 10(11) and compute
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sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l) and
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cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l). */
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int six = tix;
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tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000;
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index = 0x3ffe - (tix >> 16);
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hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
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x = fabsl (x);
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switch (index)
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{
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case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
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case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
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default:
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case 2: index = (hix - 0x3ffc3000) >> 10; break;
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}
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hix = (hix << 4) & 0x3fffffff;
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/*
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The following should work for double but generates the wrong index.
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For now the code above converts double to ieee extended to compute
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the index back to double for the h value.
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index = 0x3fe - (tix >> 20);
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hix = (tix + (0x2000 << index)) & (0xffffc000 << index);
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if (signbit (x))
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{
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x = -x;
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y = -y;
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}
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switch (index)
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{
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case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break;
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case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break;
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default:
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case 2: index = (hix - 0x3fc30000) >> 14; break;
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}
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*/
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INSERT_WORDS64 (hhi, ((uint64_t)hix) << 32);
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h = hhi;
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if (iy)
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l = y - (h - x);
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else
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l = x - h;
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z = l * l;
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sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
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cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
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z = __sincosl_table [index + SINCOSL_SIN_HI]
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+ (__sincosl_table [index + SINCOSL_SIN_LO]
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+ (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1)
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+ (__sincosl_table [index + SINCOSL_COS_HI] * sin_l));
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*sinx = (ix < 0) ? -z : z;
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*cosx = __sincosl_table [index + SINCOSL_COS_HI]
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+ (__sincosl_table [index + SINCOSL_COS_LO]
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- (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l
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- __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1));
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}
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}
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