25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * CDDL HEADER START
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25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Common Development and Distribution License (the "License").
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * You may not use this file except in compliance with the License.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * or http://www.opensolaris.org/os/licensing.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * See the License for the specific language governing permissions
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25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
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25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Use is subject to license terms.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * long double __k_sinl(long double x, long double y);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.785398164
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Input x is assumed to be bounded by ~pi/4 in magnitude.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Input y is the tail of x.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Table look up algorithm
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * 1. by sin(-x) = -sin(x), need only to consider positive x
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * 2. if x < 25/128 = [0x3ffc9000,0,0,0] = 0.1953125 , then
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * if x < 2^-57 (hx < 0x3fc60000,0,0,0), return x (inexact if x != 0)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * if x <= 1/64 = 2**-6
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * sin(x) = x + (y+(x*z)*(p1 + z*p2))
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * sin(x) = x + (y+(x*z)*(p1 + z*(p2 + z*(p3 + z*p4))))
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * ht = (hx + 0x400)&0x7ffff800 (round x to a break point t)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * i = (hy-0x3ffc4000)>>11; (i<=64)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * x' = (x - t)+y (|x'| ~<= 2^-7
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * = sin(t)cos(x')+cos(t)sin(x')
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * = sin(t)(1+z*(qq1+z*qq2))+[cos(t)]*x*(1+z*(pp1+z*pp2))
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * = sin(t) + [sin(t)]*(z*(qq1+z*qq2))+
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * [cos(t)]*x*(1+z*(pp1+z*pp2))
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * let a= _TBL_sin_hi[i], b = _TBL_sin_lo[i], c= _TBL_cos_hi[i],
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * sin(t+x) = a+(b+ ((c*x)*(1+z*(pp1+z*pp2))+a*(z*(qq1+z*qq2)))
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisextern const long double _TBL_sinl_hi[], _TBL_sinl_lo[], _TBL_cosl_hi[];
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisstatic const long double
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * 3 11 -122.32
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * |sin(x) - (x+pp1*x +...+ pp5*x )| <= 2 for |x|<1/64
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis pp1 = -1.666666666666666666666666666586782940810e-0001L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis pp2 = +8.333333333333333333333003723660929317540e-0003L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis pp3 = -1.984126984126984076045903483778337804470e-0004L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis pp4 = +2.755731922361906641319723106210900949413e-0006L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis pp5 = -2.505198398570947019093998469135012057673e-0008L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * |(sin(x) - (x+p1*x^3+...+p8*x^17)|
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * |------------------------------- | <= 2^-116.17 for |x|<0.1953125
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis p1 = -1.666666666666666666666666666666211262297e-0001L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis p2 = +8.333333333333333333333333301497876908541e-0003L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis p3 = -1.984126984126984126984041302881180621922e-0004L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis p4 = +2.755731922398589064100587351307269621093e-0006L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis p5 = -2.505210838544163129378906953765595393873e-0008L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis p6 = +1.605904383643244375050998243778534074273e-0010L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis p7 = -7.647162722800685516901456114270824622699e-0013L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis p8 = +2.810046428661902961725428841068844462603e-0015L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * 2 10 -123.84
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * |cos(x) - (1+qq1*x +...+ qq5*x )| <= 2 for |x|<=1/128
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis qq1 = -4.999999999999999999999999999999378373641e-0001L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis qq2 = +4.166666666666666666666665478399327703130e-0002L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis qq3 = -1.388888888888888888058211230618051613494e-0003L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis qq4 = +2.480158730156105377771585658905303111866e-0005L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis qq5 = -2.755728099762526325736488376695157008736e-0007L;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis long double a, t, z, w;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *(3 - i0 + (int *) &t) = -1; /* one-ulp */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis if (((int) (x * t)) < 1)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis return (x); /* inexact and underflow */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * (p5 +
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t = y + x * t;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis return (x + t);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis x = y - (t - x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis x = (-y) - (t + x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis w = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z * pp5)))));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t = _TBL_cosl_hi[i] * w + a * t;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis return (-a - t);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis return (a + t);