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Diffstat (limited to 'usr/src/libm/src/Q/__cosl.c')
| -rw-r--r-- | usr/src/libm/src/Q/__cosl.c | 137 |
1 files changed, 137 insertions, 0 deletions
diff --git a/usr/src/libm/src/Q/__cosl.c b/usr/src/libm/src/Q/__cosl.c new file mode 100644 index 0000000..1bd86de --- /dev/null +++ b/usr/src/libm/src/Q/__cosl.c @@ -0,0 +1,137 @@ +/* + * CDDL HEADER START + * + * The contents of this file are subject to the terms of the + * Common Development and Distribution License (the "License"). + * You may not use this file except in compliance with the License. + * + * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE + * or http://www.opensolaris.org/os/licensing. + * See the License for the specific language governing permissions + * and limitations under the License. + * + * When distributing Covered Code, include this CDDL HEADER in each + * file and include the License file at usr/src/OPENSOLARIS.LICENSE. + * If applicable, add the following below this CDDL HEADER, with the + * fields enclosed by brackets "[]" replaced with your own identifying + * information: Portions Copyright [yyyy] [name of copyright owner] + * + * CDDL HEADER END + */ + +/* + * Copyright 2006 Sun Microsystems, Inc. All rights reserved. + * Use is subject to license terms. + */ + +#pragma ident "@(#)__cosl.c 1.8 06/01/31 SMI" + +/* + * __k_cosl(long double x, long double y) + * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * + * Table look up algorithm + * 1. by cos(-x) = cos(x), we may replace x by |x| + * 2. if x < 25/128 = [0x3ffc4000, 0] = 0.15625 , then + * if x < 2^-57 (hx < 0x3fc60000 0), return 1.0 with inexact if x!= 0 + * z = x*x; + * if x <= 1/128 = 2**-7 = 0.0078125 + * cos(x)=1.0+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))) + * else + * cos(x)=1.0+z*(q1+ ... z*q8) + * 3. else + * ht = (hx + 0x400)&0x7ffff800 (round x to a break point t) + * lt = 0 + * i = (hy-0x3ffc4000)>>11; (i<=64) + * x' = (x - t)+y (|x'| ~<= 2^-7 + * By + * cos(t+x') + * = cos(t)cos(x')-sin(t)sin(x') + * = cos(t)(1+z*(qq1+z*qq2))-[sin(t)]*x*(1+z*(pp1+z*pp2)) + * = cos(t) + [cos(t)]*(z*(qq1+z*qq2))- + * [sin(t)]*x*(1+z*(pp1+z*pp2)) + * + * Thus, + * let a= _TBL_cos_hi[i], b = _TBL_cos_lo[i], c= _TBL_sin_hi[i], + * x = (x-t)+y + * z = x*x; + * cos(t+x) = a+(b+ (-c*x*(1+z*(pp1+z*pp2))+a*(z*(qq1+z*qq2))) + */ + +#include "libm.h" + +extern const long double _TBL_cosl_hi[], _TBL_cosl_lo[], _TBL_sinl_hi[]; +static const long double + one = 1.0L, +/* + * 3 11 -122.32 + * |sin(x) - (x+pp1*x +...+ pp5*x )| <= 2 for |x|<1/64 + */ + pp1 = -1.666666666666666666666666666586782940810e-0001L, + pp2 = +8.333333333333333333333003723660929317540e-0003L, + pp3 = -1.984126984126984076045903483778337804470e-0004L, + pp4 = +2.755731922361906641319723106210900949413e-0006L, + pp5 = -2.505198398570947019093998469135012057673e-0008L, +/* + * 2 16 -117.11 + * |cos(x) - (1+q1*x + ... + q8*x )| <= 2 for |x|<= 0.15625 + */ + q1 = -4.999999999999999999999999999999756416975e-0001L, + q2 = +4.166666666666666666666666664006066577258e-0002L, + q3 = -1.388888888888888888888877700363937169637e-0003L, + q4 = +2.480158730158730158494468463031814083559e-0005L, + q5 = -2.755731922398586276322819250356005542871e-0007L, + q6 = +2.087675698767424261441959760729854017855e-0009L, + q7 = -1.147074481239662089072452129010790774761e-0011L, + q8 = +4.777761647399651599730663422263531034782e-0014L, +/* + * 2 10 -123.84 + * |cos(x) - (1+qq1*x +...+ qq5*x )| <= 2 for |x|<=1/128 + */ + qq1 = -4.999999999999999999999999999999378373641e-0001L, + qq2 = +4.166666666666666666666665478399327703130e-0002L, + qq3 = -1.388888888888888888058211230618051613494e-0003L, + qq4 = +2.480158730156105377771585658905303111866e-0005L, + qq5 = -2.755728099762526325736488376695157008736e-0007L; + +#define i0 0 + +long double +__k_cosl(long double x, long double y) { + long double a, t, z, w; + int *pt = (int *) &t, *px = (int *) &x; + int i, j, hx, ix; + + t = 1.0L; + hx = px[i0]; + ix = hx & 0x7fffffff; + if (ix < 0x3ffc4000) { + if (ix < 0x3fc60000) + if ((i = (int) x) == 0) + return (one); /* generate inexact */ + z = x * x; + + if (ix < 0x3ff80000) /* 0.0078125 */ + return one + z * (qq1 + z * (qq2 + z * (qq3 + + z * (qq4 + z * qq5)))); + else + return one + z * (q1 + z * (q2 + z * (q3 + + z * (q4 + z * (q5 + z * (q6 + z * (q7 + + z * q8))))))); + } + j = (ix + 0x400) & 0x7ffff800; + i = (j - 0x3ffc4000) >> 11; + pt[i0] = j; + if (hx > 0) + x = y - (t - x); + else + x = (-y) - (t + x); + a = _TBL_cosl_hi[i]; + z = x * x; + t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5)))); + w = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z * pp5))))); + t = _TBL_cosl_lo[i] - (_TBL_sinl_hi[i] * w - a * t); + return (a + t); +} |