usr/src/lib/libm/common/LD/__sinl.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  * __k_sinl( long double x;  long double y )
  33  * kernel sin 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  *
  37  * Table look up algorithm
  38  *      1. by sin(-x) = -sin(x), need only to consider positive x
  39  *      2. if x < 25/128 = [0x3ffc9000,0,0,0] = 0.1953125 , then
  40  *           if x < 2^-57 (hx < 0x3fc60000,0,0,0), return x (inexact if x !=  0)
  41  *           z = x*x;
  42  *           if x <= 1/64 = 2**-6
  43  *              sin(x) = x + (y+(x*z)*(p1 + z*p2))
  44  *           else
  45  *              sin(x) = x + (y+(x*z)*(p1 + z*(p2 + z*(p3 + z*p4))))
  46  *      3. else
  47  *              ht = (hx + 0x400)&0x7ffff800    (round x to a break point t)
  48  *              lt = 0
  49  *              i  = (hy-0x3ffc4000)>>11;       (i<=64)
  50  *              x' = (x - t)+y                  (|x'| ~<= 2^-7
  51  *         By
  52  *              sin(t+x')
  53  *                = sin(t)cos(x')+cos(t)sin(x')
  54  *                = sin(t)(1+z*(qq1+z*qq2))+[cos(t)]*x*(1+z*(pp1+z*pp2))
  55  *                = sin(t) + [sin(t)]*(z*(qq1+z*qq2))+
  56  *                              [cos(t)]*x*(1+z*(pp1+z*pp2))
  57  *
  58  *         Thus,
  59  *              let a= _TBL_sin_hi[i], b = _TBL_sin_lo[i], c= _TBL_cos_hi[i],
  60  *              x = (x-t)+y
  61  *              z = x*x;
  62  *              sin(t+x) = a+(b+ ((c*x)*(1+z*(pp1+z*pp2))+a*(z*(qq1+z*qq2)))
  63  */
  64
  65 #include "libm.h"
  66
  67 #include <sys/isa_defs.h>
  68
  69 extern const long double _TBL_sinl_hi[], _TBL_sinl_lo[], _TBL_cosl_hi[];
  70 static const long double
  71 one     = 1.0,
  72 /*
  73  * |sin(x) - (x+pp1*x^3+...+ pp5*x^11)| <= 2^-122.32 for |x|<1/64
  74  */
  75 pp1     = -1.666666666666666666666666666586782940810e-0001L,
  76 pp2     =  8.333333333333333333333003723660929317540e-0003L,
  77 pp3     = -1.984126984126984076045903483778337804470e-0004L,
  78 pp4     =  2.755731922361906641319723106210900949413e-0006L,
  79 pp5     = -2.505198398570947019093998469135012057673e-0008L,
  80 /*
  81  * |(sin(x) - (x+p1*x^3+...+p8*x^17)|
  82  * |------------------------------- | <= 2^-116.17 for |x|<0.1953125
  83  * |                 x              |
  84  */
  85 p1      = -1.666666666666666666666666666666211262297e-0001L,
  86 p2      =  8.333333333333333333333333301497876908541e-0003L,
  87 p3      = -1.984126984126984126984041302881180621922e-0004L,
  88 p4      =  2.755731922398589064100587351307269621093e-0006L,
  89 p5      = -2.505210838544163129378906953765595393873e-0008L,
  90 p6      =  1.605904383643244375050998243778534074273e-0010L,
  91 p7      = -7.647162722800685516901456114270824622699e-0013L,
  92 p8      =  2.810046428661902961725428841068844462603e-0015L,
  93 /*
  94  *                   2           10        -123.84
  95  * |cos(x) - (1+qq1*x +...+ qq5*x  )| <= 2        for |x|<=1/128
  96  */
  97 qq1     = -4.999999999999999999999999999999378373641e-0001L,
  98 qq2     =  4.166666666666666666666665478399327703130e-0002L,
  99 qq3     = -1.388888888888888888058211230618051613494e-0003L,
 100 qq4     =  2.480158730156105377771585658905303111866e-0005L,
 101 qq5     = -2.755728099762526325736488376695157008736e-0007L;
 102 /* INDENT ON */
 103 long double
 104 __k_sinl(long double x, long double y) {
 105         long double a, t, z, w;
 106         int *pt = (int *) &t, *px = (int *) &x;
 107         int i, j, hx, ix;
 108
 109         t = 1.0L;
 110 #if defined(__i386) || defined(__amd64)
 111         XTOI(px, hx);
 112 #else
 113         hx = px[0];
 114 #endif
 115         ix = hx & 0x7fffffff;
 116         if (ix < 0x3ffc9000) {
 117                 if (ix < 0x3fc60000)
 118                         if (((int) x) == 0)
 119                                 return (x);     /* generate inexact */
 120                 z = x * x;
 121                 t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * (p5 + z *
 122                         (p6 + z * (p7 + z * p8)))))));
 123                 t = y + x * t;
 124                 return (x + t);
 125         }
 126         j = (ix + 0x400) & 0x7ffff800;
 127         i = (j - 0x3ffc4000) >> 11;
 128 #if defined(__i386) || defined(__amd64)
 129         ITOX(j, pt);
 130 #else
 131         pt[0] = j;
 132 #endif
 133         if (hx > 0)
 134                 x = y - (t - x);
 135         else
 136                 x = (-y) - (t + x);
 137         a = _TBL_sinl_hi[i];
 138         z = x * x;
 139         t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
 140         w = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z *
 141                 pp5)))));
 142         t = _TBL_cosl_hi[i] * w + a * t;
 143         t += _TBL_sinl_lo[i];
 144         if (hx < 0)
 145                 return (-a - t);
 146         else
 147                 return (a + t);
 148 }