25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * CDDL HEADER START
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * The contents of this file are subject to the terms of the
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
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * and limitations under the License.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * When distributing Covered Code, include this CDDL HEADER in each
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * If applicable, add the following below this CDDL HEADER, with the
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * fields enclosed by brackets "[]" replaced with your own identifying
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * information: Portions Copyright [yyyy] [name of copyright owner]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * CDDL HEADER END
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_tanl(long double x; long double y, int k);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * kernel tan/cotan 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 * Input k indicate -- tan if k=0; else -1/tan
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Table look up algorithm
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * 1. by tan(-x) = -tan(x), need only to consider positive x
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * 2. if x < 5/32 = [0x3ffc4000, 0] = 0.15625 , then
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * if x < 2^-57 (hx < 0x3fc40000 0), set w=x with inexact if x != 0
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * w = x + (y+(x*z)*(t1+z*(t2+z*(t3+z*(t4+z*(t5+z*t6))))))
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * return (k == 0)? w: 1/w;
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 * = (tan(t)+tan(x'))/(1-tan(x')tan(t))
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * sin(x')+tan(t)*(tan(t)*sin(x'))
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * = tan(t) + ------------------------------- for k=0
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * cos(x') - tan(t)*sin(x')
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * cos(x') - tan(t)*sin(x')
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * = - -------------------------------------- for k=1
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * tan(t) + tan(t)*(cos(x')-1) + sin(x')
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * where tan(t) is from the table,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * sin(x') = x + pp1*x^3 + ...+ pp5*x^11
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * cos(x') = 1 + qq1*x^2 + ...+ qq5*x^10
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisextern const long double _TBL_tanl_hi[], _TBL_tanl_lo[];
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 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 * |tan(x) - (x+t1*x^3+...+t6*x^13)|
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * |------------------------------ | <= 2^-59.73 for |x|<0.15625
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t1 = +3.333333333333333333333333333333423342490e-0001L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t2 = +1.333333333333333333333333333093838744537e-0001L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t3 = +5.396825396825396825396827906318682662250e-0002L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t4 = +2.186948853615520282185576976994418486911e-0002L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t5 = +8.863235529902196573354554519991152936246e-0003L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t6 = +3.592128036572480064652191427543994878790e-0003L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t7 = +1.455834387051455257856833807581901305474e-0003L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t8 = +5.900274409318599857829983256201725587477e-0004L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t9 = +2.391291152117265181501116961901122362937e-0004L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t10 = +9.691533169382729742394024173194981882375e-0005L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t11 = +3.927994733186415603228178184225780859951e-0005L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t12 = +1.588300018848323824227640064883334101288e-0005L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t13 = +6.916271223396808311166202285131722231723e-0006L;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis__k_tanl(long double x, long double y, int k) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis long double a, t, z, w = 0, s, c;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *(3 - i0 + (int *) &t) = 1; /* make t = one+ulp */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis if (((int) (x * t)) < 1) /* generate inexact */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis w = x; /* generate underflow if subnormal */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t = z * (t1 + z * (t2 + z * (t3 + z * t4)));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t = z * (t1 + z * (t2 + z * (t3 + z * (t4 +
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t = y + x * t;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis return (k == 0 ? w : -one / w);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis x = y - (t - x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis x = (-y) - (t + x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis /* cos(x)-1 */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis s = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z * pp5)))));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t = _TBL_tanl_lo[i] + (s + a * w) / (one - (w - t));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis return (hx < 0 ? -a - t : a + t);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis w = s + a * t;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis z = one - (a * s - t);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis return (hx >= 0 ? z / (-a - c) : z / (a + c));