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Diffstat (limited to 'math/k_sin.c')
-rw-r--r-- | math/k_sin.c | 88 |
1 files changed, 88 insertions, 0 deletions
diff --git a/math/k_sin.c b/math/k_sin.c new file mode 100644 index 0000000..3b97028 --- /dev/null +++ b/math/k_sin.c @@ -0,0 +1,88 @@ +/* + * k_sin.c + * + * Copyright (C) 1998-2015, ARM Limited, All Rights Reserved + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the "License"); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + * + * This file is part of the Optimized Routines project + */ + +/* @(#)k_sin.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __kernel_sin( x, y, iy) + * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). + * + * Algorithm + * 1. Since sin(-x) = -sin(x), we need only to consider positive x. + * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. + * 3. sin(x) is approximated by a polynomial of degree 13 on + * [0,pi/4] + * 3 13 + * sin(x) ~ x + S1*x + ... + S6*x + * where + * + * |sin(x) 2 4 6 8 10 12 | -58 + * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 + * | x | + * + * 4. sin(x+y) = sin(x) + sin'(x')*y + * ~ sin(x) + (1-x*x/2)*y + * For better accuracy, let + * 3 2 2 2 2 + * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) + * then 3 2 + * sin(x) = x + (S1*x + (x *(r-y/2)+y)) + */ + +#include "arm_math.h" +#include "math_private.h" +#include <math.h> + +static const double + half = 0x1p-1, /* 5.00000000000000000000e-01 */ + S1 = -0x1.5555555555549p-3, /* -1.66666666666666324348e-01 */ + S[] = { 0x1.111111110f8a6p-7, /* 8.33333333332248946124e-03 */ + -0x1.a01a019c161d5p-13, /* -1.98412698298579493134e-04 */ + 0x1.71de357b1fe7dp-19, /* 2.75573137070700676789e-06 */ + -0x1.ae5e68a2b9cebp-26, /* -2.50507602534068634195e-08 */ + 0x1.5d93a5acfd57cp-33, /* 1.58969099521155010221e-10 */ }; + +double +ARM__kernel_sin(double x, double y, int iy) +{ + double z,r,v; + int ix; + ix = __HI(x)&0x7fffffff; /* high word of x */ + if(ix<0x3e400000) /* |x| < 2**-27 */ + return DOUBLE_CHECKDENORM(x); + z = x*x; + v = z*x; + r = ARM__kernel_poly(S,5,z); + if(iy==0) return x+v*(S1+z*r); + else return x-((z*(half*y-v*r)-y)-v*S1); +} |