usr/src/lib/libm/common/LD/__cosl.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_cosl( long double x;  long double y )
  33  * kernel cos 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 cos(-x) = cos(x), we may replace x by |x|
  39  *      2. if x < 25/128 = [0x3ffc4000, 0] = 0.15625 , then
  40  *           if x < 2^-57 (hx < 0x3fc60000 0), return 1.0 with inexact if x !=  0
  41  *           z = x*x;
  42  *           if x <= 1/128 = 2**-7 = 0.0078125
  43  *              cos(x)=1.0+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))))
  44  *           else
  45  *              cos(x)=1.0+z*(q1+ ... z*q8)
  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  *              cos(t+x')
  53  *                = cos(t)cos(x')-sin(t)sin(x')
  54  *                = cos(t)(1+z*(qq1+z*qq2))-[sin(t)]*x*(1+z*(pp1+z*pp2))
  55  *                = cos(t) + [cos(t)]*(z*(qq1+z*qq2))-
  56  *                              [sin(t)]*x*(1+z*(pp1+z*pp2))
  57  *
  58  *         Thus,
  59  *              let a= _TBL_cos_hi[i], b = _TBL_cos_lo[i], c= _TBL_sin_hi[i],
  60  *              x = (x-t)+y
  61  *              z = x*x;
  62  *              cos(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_cosl_hi[], _TBL_cosl_lo[], _TBL_sinl_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  *
  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 /*
  93  *
  94  * |cos(x) - (1+qq1*x^2+...+ qq5*x^10)| <= 2^-123.84 for |x|<=1/128
  95  */
  96 qq1     =  -4.999999999999999999999999999999378373641e-0001L,
  97 qq2     =   4.166666666666666666666665478399327703130e-0002L,
  98 qq3     =  -1.388888888888888888058211230618051613494e-0003L,
  99 qq4     =   2.480158730156105377771585658905303111866e-0005L,
 100 qq5     =  -2.755728099762526325736488376695157008736e-0007L;
 101 /* INDENT ON */
 102 long double
 103 __k_cosl(long double x, long double y) {
 104         long double a, t, z, w;
 105         int *pt = (int *) &t, *px = (int *) &x;
 106         int i, j, hx, ix;
 107
 108         t = 1.0;
 109 #if defined(__i386) || defined(__amd64)
 110         XTOI(px, hx);
 111 #else
 112         hx = px[0];
 113 #endif
 114         ix = hx & 0x7fffffff;
 115         if (ix < 0x3ffc4000) {
 116                 if (ix < 0x3fc60000)
 117                         if ((i = (int) x) == 0)
 118                                 return (one);   /* generate inexact */
 119                 z = x * x;
 120
 121                 if (ix < 0x3ff80000)    /* 0.0078125 */
 122                         return (one + z * (qq1 + z * (qq2 + z * (qq3 + z *
 123                                 (qq4 + z * qq5)))));
 124                 else
 125                         return (one + z * (q1 + z * (q2 + z * (q3 + z * (q4 +
 126                                 z * (q5 + z * (q6 + z * (q7 + z * q8))))))));
 127         }
 128         j = (ix + 0x400) & 0x7ffff800;
 129         i = (j - 0x3ffc4000) >> 11;
 130 #if defined(__i386) || defined(__amd64)
 131         ITOX(j, pt);
 132 #else
 133         pt[0] = j;
 134 #endif
 135         if (hx > 0)
 136                 x = y - (t - x);
 137         else
 138                 x = (-y) - (t + x);
 139         a = _TBL_cosl_hi[i];
 140         z = x * x;
 141         t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
 142         w = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z *
 143                 pp5)))));
 144         t = _TBL_cosl_lo[i] - (_TBL_sinl_hi[i] * w - a * t);
 145         return (a + t);
 146 }