131 lines
4.3 KiB
C
131 lines
4.3 KiB
C
/* Quad-precision floating point sine on <-pi/4,pi/4>.
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Copyright (C) 1999-2022 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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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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<https://www.gnu.org/licenses/>. */
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/* The polynomials have not been optimized for extended-precision and
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may contain more terms than needed. */
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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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#include <math-underflow.h>
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/* The polynomials have not been optimized for extended-precision and
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may contain more terms than needed. */
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static const long double c[] = {
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#define ONE c[0]
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1.00000000000000000000000000000000000E+00L,
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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,
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4.16666666666666666666666666556146073E-02L,
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-1.38888888888888888888309442601939728E-03L,
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2.48015873015862382987049502531095061E-05L,
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-2.75573112601362126593516899592158083E-07L,
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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[6]
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#define SIN2 c[7]
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#define SIN3 c[8]
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#define SIN4 c[9]
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#define SIN5 c[10]
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#define SIN6 c[11]
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#define SIN7 c[12]
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#define SIN8 c[13]
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-1.66666666666666666666666666666666538e-01L,
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8.33333333333333333333333333307532934e-03L,
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-1.98412698412698412698412534478712057e-04L,
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2.75573192239858906520896496653095890e-06L,
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-2.50521083854417116999224301266655662e-08L,
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1.60590438367608957516841576404938118e-10L,
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-7.64716343504264506714019494041582610e-13L,
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2.81068754939739570236322404393398135e-15L,
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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,
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8.33333333333333333333333333146298442E-03L,
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-1.98412698412698412697726277416810661E-04L,
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2.75573192239848624174178393552189149E-06L,
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-2.50521016467996193495359189395805639E-08L,
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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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long double
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__kernel_sinl(long double x, long double y, int iy)
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{
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long double absx, h, l, z, sin_l, cos_l_m1;
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int index;
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absx = fabsl (x);
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if (absx < 0.1484375L)
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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 17. */
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if (absx < 0x1p-33L)
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{
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math_check_force_underflow (x);
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if (!((int)x)) return x; /* generate inexact */
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}
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z = x * x;
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return 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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}
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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). */
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index = (int) (128 * (absx - (0.1484375L - 1.0L / 256.0L)));
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h = 0.1484375L + index / 128.0;
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index *= 4;
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if (iy)
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l = (x < 0 ? -y : y) - (h - absx);
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else
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l = absx - 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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return (x < 0) ? -z : z;
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}
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}
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