usr/src/lib/libm/common/LD/__sincosl.c

   1 /*
   2  * CDDL HEADER START
   3  *
   4  * The contents of this file are subject to the terms of the
   5  * Common Development and Distribution License (the "License").
   6  * You may not use this file except in compliance with the License.
   7  *
   8  * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
   9  * or http://www.opensolaris.org/os/licensing.
  10  * See the License for the specific language governing permissions
  11  * and limitations under the License.
  12  *
  13  * When distributing Covered Code, include this CDDL HEADER in each
  14  * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
  15  * If applicable, add the following below this CDDL HEADER, with the
  16  * fields enclosed by brackets "[]" replaced with your own identifying
  17  * information: Portions Copyright [yyyy] [name of copyright owner]
  18  *
  19  * CDDL HEADER END
  20  */
  21
  22 /*
  23  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
  24  */
  25 /*
  26  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
  27  * Use is subject to license terms.
  28  */
  29
  30 /* INDENT OFF */
  31 /*
  32  * long double __k_sincos( long double x, long double y, long double *c )
  33  * kernel sincosl function on [-pi/4, pi/4], pi/4 ~ 0.785398164
  34  * Input x is assumed to be bounded by ~pi/4 in magnitude.
  35  * Input y is the tail of x.
  36  * return sinl(x) with *c = cosl(x)
  37  *
  38  * Table look up algorithm
  39  *      see __k_sinl() and __k_cosl()
  40  */
  41
  42 #include "libm.h"
  43
  44 #include <sys/isa_defs.h>
  45
  46 extern const long double _TBL_sinl_hi[], _TBL_sinl_lo[], _TBL_cosl_hi[],
  47         _TBL_cosl_lo[];
  48 static const long double
  49 one     = 1.0,
  50 /*
  51  * |sin(x) - (x+pp1*x^3+...+pp5*x^11)| <= 2^-122.32 for |x|<1/64
  52  */
  53 pp1     = -1.666666666666666666666666666586782940810e-0001L,
  54 pp2     =  8.333333333333333333333003723660929317540e-0003L,
  55 pp3     = -1.984126984126984076045903483778337804470e-0004L,
  56 pp4     =  2.755731922361906641319723106210900949413e-0006L,
  57 pp5     = -2.505198398570947019093998469135012057673e-0008L,
  58 /*
  59  * |(sin(x) - (x+p1*x^3+...+p8*x^17)|
  60  * |------------------------------- | <= 2^-116.17 for |x|<0.1953125
  61  * |                 x              |
  62  */
  63 p1      =  -1.666666666666666666666666666666211262297e-0001L,
  64 p2      =   8.333333333333333333333333301497876908541e-0003L,
  65 p3      =  -1.984126984126984126984041302881180621922e-0004L,
  66 p4      =   2.755731922398589064100587351307269621093e-0006L,
  67 p5      =  -2.505210838544163129378906953765595393873e-0008L,
  68 p6      =   1.605904383643244375050998243778534074273e-0010L,
  69 p7      =  -7.647162722800685516901456114270824622699e-0013L,
  70 p8      =   2.810046428661902961725428841068844462603e-0015L,
  71 /*
  72  *
  73  * |cos(x) - (1+qq1*x^2+...+ qq5*x^10)| <= 2^-123.84 for |x|<=1/128
  74  */
  75 qq1     =  -4.999999999999999999999999999999378373641e-0001L,
  76 qq2     =   4.166666666666666666666665478399327703130e-0002L,
  77 qq3     =  -1.388888888888888888058211230618051613494e-0003L,
  78 qq4     =   2.480158730156105377771585658905303111866e-0005L,
  79 qq5     =  -2.755728099762526325736488376695157008736e-0007L,
  80 /*
  81  *
  82  * |cos(x) - (1+q1*x^2+...+ q8*x^16)| <= 2^-117.11 for |x|<= 0.15625
  83  */
  84 q1      =  -4.999999999999999999999999999999756416975e-0001L,
  85 q2      =   4.166666666666666666666666664006066577258e-0002L,
  86 q3      =  -1.388888888888888888888877700363937169637e-0003L,
  87 q4      =   2.480158730158730158494468463031814083559e-0005L,
  88 q5      =  -2.755731922398586276322819250356005542871e-0007L,
  89 q6      =   2.087675698767424261441959760729854017855e-0009L,
  90 q7      =  -1.147074481239662089072452129010790774761e-0011L,
  91 q8      =   4.777761647399651599730663422263531034782e-0014L;
  92 /* INDENT ON */
  93 long double
  94 __k_sincosl(long double x, long double y, long double *c) {
  95         long double a1, a2, t, t1, t2, z, w;
  96         int *pt = (int *) &t, *px = (int *) &x;
  97         int i, j, hx, ix;
  98
  99         t = 1.0;
 100 #if defined(__i386) || defined(__amd64)
 101         XTOI(px, hx);
 102 #else
 103         hx = px[0];
 104 #endif
 105         ix = hx & 0x7fffffff;
 106         if (ix < 0x3ffc4000) {
 107                 if (ix < 0x3fc60000)
 108                         if (((int) x) == 0) {
 109                                 *c = one;
 110                                 return (x);
 111                         }       /* generate inexact */
 112                 z = x * x;
 113
 114                 if (ix < 0x3ff80000) {
 115                         *c = one + z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 +
 116                                 z * qq5))));
 117                         t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * (p5 +
 118                                 z * p6)))));
 119                 } else {
 120                         *c = one + z * (q1 + z * (q2 + z * (q3 + z * (q4 + z *
 121                                 (q5 + z * (q6 + z * (q7 + z * q8)))))));
 122                         t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * (p5 +
 123                                 z * (p6 + z * (p7 + z * p8)))))));
 124                 }
 125
 126                 t = y + x * t;
 127                 return (x + t);
 128         }
 129         j = (ix + 0x400) & 0x7ffff800;
 130         i = (j - 0x3ffc4000) >> 11;
 131 #if defined(__i386) || defined(__amd64)
 132         ITOX(j, pt);
 133 #else
 134         pt[0] = j;
 135 #endif
 136         if (hx > 0)
 137                 x = y - (t - x);
 138         else
 139                 x = (-y) - (t + x);
 140         a1 = _TBL_sinl_hi[i];
 141         z = x * x;
 142         t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
 143         w = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z *
 144                 pp5)))));
 145         a2 = _TBL_cosl_hi[i];
 146         t2 = _TBL_cosl_lo[i] - (a1 * w - a2 * t);
 147         *c = a2 + t2;
 148         t1 = a2 * w + a1 * t;
 149         t1 += _TBL_sinl_lo[i];
 150         if (hx < 0)
 151                 return (-a1 - t1);
 152         else
 153                 return (a1 + t1);
 154 }