25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * CDDL HEADER START
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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 * 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 * __k_cosl(long double x, long double y)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * kernel cos 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 cos(-x) = cos(x), we may replace x by |x|
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * 2. if x < 25/128 = [0x3ffc4000, 0] = 0.15625 , then
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * if x < 2^-57 (hx < 0x3fc60000 0), return 1.0 with inexact if x != 0
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * if x <= 1/128 = 2**-7 = 0.0078125
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * cos(x)=1.0+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))))
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * cos(x)=1.0+z*(q1+ ... z*q8)
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 * = cos(t)cos(x')-sin(t)sin(x')
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * = cos(t)(1+z*(qq1+z*qq2))-[sin(t)]*x*(1+z*(pp1+z*pp2))
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * = cos(t) + [cos(t)]*(z*(qq1+z*qq2))-
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * [sin(t)]*x*(1+z*(pp1+z*pp2))
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * let a= _TBL_cos_hi[i], b = _TBL_cos_lo[i], c= _TBL_sin_hi[i],
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * cos(t+x) = a+(b+ (-c*x*(1+z*(pp1+z*pp2))+a*(z*(qq1+z*qq2)))
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisextern const long double _TBL_cosl_hi[], _TBL_cosl_lo[], _TBL_sinl_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 * 2 16 -117.11
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * |cos(x) - (1+q1*x + ... + q8*x )| <= 2 for |x|<= 0.15625
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis q1 = -4.999999999999999999999999999999756416975e-0001L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis q2 = +4.166666666666666666666666664006066577258e-0002L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis q3 = -1.388888888888888888888877700363937169637e-0003L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis q4 = +2.480158730158730158494468463031814083559e-0005L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis q5 = -2.755731922398586276322819250356005542871e-0007L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis q6 = +2.087675698767424261441959760729854017855e-0009L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis q7 = -1.147074481239662089072452129010790774761e-0011L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis q8 = +4.777761647399651599730663422263531034782e-0014L,
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 if ((i = (int) x) == 0)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis return one + z * (qq1 + z * (qq2 + z * (qq3 +
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis return one + z * (q1 + z * (q2 + z * (q3 +
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_lo[i] - (_TBL_sinl_hi[i] * w - a * t);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis return (a + t);