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Diffstat (limited to 'sysdeps/ieee754/ldbl-96/k_cosl.c')
| -rw-r--r-- | sysdeps/ieee754/ldbl-96/k_cosl.c | 123 |
1 files changed, 123 insertions, 0 deletions
diff --git a/sysdeps/ieee754/ldbl-96/k_cosl.c b/sysdeps/ieee754/ldbl-96/k_cosl.c new file mode 100644 index 0000000000..9e8f33a283 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/k_cosl.c @@ -0,0 +1,123 @@ +/* Extended-precision floating point cosine on <-pi/4,pi/4>. + Copyright (C) 1999-2012 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Based on quad-precision cosine 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 <math.h> +#include <math_private.h> + +/* The polynomials have not been optimized for extended-precision and + may contain more terms than needed. */ + +static const long double c[] = { +#define ONE c[0] + 1.00000000000000000000000000000000000E+00L, + +/* 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-01L, + 4.16666666666666666666666666556146073E-02L, +-1.38888888888888888888309442601939728E-03L, + 2.48015873015862382987049502531095061E-05L, +-2.75573112601362126593516899592158083E-07L, + +/* 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-01L, + 4.16666666666666666666666666651287795E-02L, +-1.38888888888888888888888742314300284E-03L, + 2.48015873015873015867694002851118210E-05L, +-2.75573192239858811636614709689300351E-07L, + 2.08767569877762248667431926878073669E-09L, +-1.14707451049343817400420280514614892E-11L, + 4.77810092804389587579843296923533297E-14L, + +/* 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-01L, + 8.33333333333333333333333333146298442E-03L, +-1.98412698412698412697726277416810661E-04L, + 2.75573192239848624174178393552189149E-06L, +-2.50521016467996193495359189395805639E-08L, +}; + +#define SINCOSL_COS_HI 0 +#define SINCOSL_COS_LO 1 +#define SINCOSL_SIN_HI 2 +#define SINCOSL_SIN_LO 3 +extern const long double __sincosl_table[]; + +long double +__kernel_cosl(long double x, long double y) +{ + long double h, l, z, sin_l, cos_l_m1; + int index; + + if (signbit (x)) + { + x = -x; + y = -y; + } + if (x < 0.1484375L) + { + /* Argument is small enough to approximate it by a Chebyshev + polynomial of degree 16. */ + if (x < 0x1p-33L) + 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 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 + cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l). */ + index = (int) (128 * (x - (0.1484375L - 1.0L / 256.0L))); + h = 0.1484375L + index / 128.0; + index *= 4; + 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 __sincosl_table [index + SINCOSL_COS_HI] + + (__sincosl_table [index + SINCOSL_COS_LO] + - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l + - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1)); + } +} |