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Diffstat (limited to 'usr/src/lib/libm/common/LD/__tanl.c')
| -rw-r--r-- | usr/src/lib/libm/common/LD/__tanl.c | 171 |
1 files changed, 171 insertions, 0 deletions
diff --git a/usr/src/lib/libm/common/LD/__tanl.c b/usr/src/lib/libm/common/LD/__tanl.c new file mode 100644 index 0000000000..fffa457212 --- /dev/null +++ b/usr/src/lib/libm/common/LD/__tanl.c @@ -0,0 +1,171 @@ +/* + * 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 2011 Nexenta Systems, Inc. All rights reserved. + */ +/* + * Copyright 2006 Sun Microsystems, Inc. All rights reserved. + * Use is subject to license terms. + */ + +/* INDENT OFF */ +/* + * __k_tanl( long double x; long double y; int k ) + * kernel tan/cotan 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. + * Input k indicate -- tan if k=0; else -1/tan + * + * Table look up algorithm + * 1. by tan(-x) = -tan(x), need only to consider positive x + * 2. if x < 5/32 = [0x3ffc4000, 0] = 0.15625 , then + * if x < 2^-57 (hx < 0x3fc40000 0), set w=x with inexact if x != 0 + * else + * z = x*x; + * w = x + (y+(x*z)*(t1+z*(t2+z*(t3+z*(t4+z*(t5+z*t6)))))) + * return (k == 0 ? w : 1/w); + * 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 + * tan(t+x') + * = (tan(t)+tan(x'))/(1-tan(x')tan(t)) + * We have + * sin(x')+tan(t)*(tan(t)*sin(x')) + * = tan(t) + ------------------------------- for k=0 + * cos(x') - tan(t)*sin(x') + * + * cos(x') - tan(t)*sin(x') + * = - -------------------------------------- for k=1 + * tan(t) + tan(t)*(cos(x')-1) + sin(x') + * + * + * where tan(t) is from the table, + * sin(x') = x + pp1*x^3 + ...+ pp5*x^11 + * cos(x') = 1 + qq1*x^2 + ...+ qq5*x^10 + */ + +#include "libm.h" + +#include <sys/isa_defs.h> + +extern const long double _TBL_tanl_hi[], _TBL_tanl_lo[]; +static const long double +one = 1.0, +/* + * |sin(x) - (x+pp1*x^3+...+ pp5*x^11)| <= 2^-122.32 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 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, +/* + * |tan(x) - (x+t1*x^3+...+t6*x^13)| + * |------------------------------ | <= 2^-59.73 for |x|<0.15625 + * | x | + */ +t1 = 3.333333333333333333333333333333423342490e-0001L, +t2 = 1.333333333333333333333333333093838744537e-0001L, +t3 = 5.396825396825396825396827906318682662250e-0002L, +t4 = 2.186948853615520282185576976994418486911e-0002L, +t5 = 8.863235529902196573354554519991152936246e-0003L, +t6 = 3.592128036572480064652191427543994878790e-0003L, +t7 = 1.455834387051455257856833807581901305474e-0003L, +t8 = 5.900274409318599857829983256201725587477e-0004L, +t9 = 2.391291152117265181501116961901122362937e-0004L, +t10 = 9.691533169382729742394024173194981882375e-0005L, +t11 = 3.927994733186415603228178184225780859951e-0005L, +t12 = 1.588300018848323824227640064883334101288e-0005L, +t13 = 6.916271223396808311166202285131722231723e-0006L; +/* INDENT ON */ +long double +__k_tanl(long double x, long double y, int k) { + long double a, t, z, w = 0.0, s, c; + int *pt = (int *) &t, *px = (int *) &x; + int i, j, hx, ix; + + t = 1.0; +#if defined(__i386) || defined(__amd64) + XTOI(px, hx); +#else + hx = px[0]; +#endif + ix = hx & 0x7fffffff; + if (ix < 0x3ffc4000) { + if (ix < 0x3fc60000) { + if ((i = (int) x) == 0) /* generate inexact */ + w = x; + } else { + z = x * x; + if (ix < 0x3ff30000) /* 2**-12 */ + t = z * (t1 + z * (t2 + z * (t3 + z * t4))); + else + t = z * (t1 + z * (t2 + z * (t3 + z * (t4 + + z * (t5 + z * (t6 + z * (t7 + z * + (t8 + z * (t9 + z * (t10 + z * (t11 + + z * (t12 + z * t13)))))))))))); + t = y + x * t; + w = x + t; + } + return (k == 0 ? w : -one / w); + } + j = (ix + 0x400) & 0x7ffff800; + i = (j - 0x3ffc4000) >> 11; +#if defined(__i386) || defined(__amd64) + ITOX(j, pt); +#else + pt[0] = j; +#endif + if (hx > 0) + x = y - (t - x); + else + x = (-y) - (t + x); + a = _TBL_tanl_hi[i]; + z = x * x; + /* cos(x)-1 */ + t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5)))); + /* sin(x) */ + s = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z * + pp5))))); + if (k == 0) { + w = a * s; + t = _TBL_tanl_lo[i] + (s + a * w) / (one - (w - t)); + return (hx < 0 ? -a - t : a + t); + } else { + w = s + a * t; + c = w + _TBL_tanl_lo[i]; + z = (one - (a * s - t)); + return (hx >= 0 ? z / (-a - c) : z / (a + c)); + } +} |