Print this page
11210 libm should be cstyle(1ONBLD) clean


   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 /*
  31  * long double __k_sincos(long double x, long double y, long double *c);
  32  * kernel sincosl function on [-pi/4, pi/4], pi/4 ~ 0.785398164
  33  * Input x is assumed to be bounded by ~pi/4 in magnitude.
  34  * Input y is the tail of x.
  35  * return sinl(x) with *c = cosl(x)
  36  *
  37  * Table look up algorithm
  38  *      see __k_sinl and __k_cosl
  39  */
  40 
  41 #include "libm.h"
  42 
  43 extern const long double _TBL_sinl_hi[], _TBL_sinl_lo[],
  44         _TBL_cosl_hi[], _TBL_cosl_lo[];
  45 static const long double
  46         one     = 1.0L,
  47 /*
  48  *                   3           11       -122.32
  49  * |sin(x) - (x+pp1*x +...+ pp5*x  )| <= 2        for |x|<1/64
  50  */

  51         pp1     = -1.666666666666666666666666666586782940810e-0001L,
  52         pp2     = +8.333333333333333333333003723660929317540e-0003L,
  53         pp3     = -1.984126984126984076045903483778337804470e-0004L,
  54         pp4     = +2.755731922361906641319723106210900949413e-0006L,
  55         pp5     = -2.505198398570947019093998469135012057673e-0008L,

  56 /*
  57  * |(sin(x) - (x+p1*x^3+...+p8*x^17)|
  58  * |------------------------------- | <= 2^-116.17 for |x|<0.1953125
  59  * |                 x              |
  60  */

  61         p1      = -1.666666666666666666666666666666211262297e-0001L,
  62         p2      = +8.333333333333333333333333301497876908541e-0003L,
  63         p3      = -1.984126984126984126984041302881180621922e-0004L,
  64         p4      = +2.755731922398589064100587351307269621093e-0006L,
  65         p5      = -2.505210838544163129378906953765595393873e-0008L,
  66         p6      = +1.605904383643244375050998243778534074273e-0010L,
  67         p7      = -7.647162722800685516901456114270824622699e-0013L,
  68         p8      = +2.810046428661902961725428841068844462603e-0015L,

  69 /*
  70  *                   2           10       -123.84
  71  * |cos(x) - (1+qq1*x +...+ qq5*x  )| <= 2        for |x|<=1/128
  72  */

  73         qq1     = -4.999999999999999999999999999999378373641e-0001L,
  74         qq2     = +4.166666666666666666666665478399327703130e-0002L,
  75         qq3     = -1.388888888888888888058211230618051613494e-0003L,
  76         qq4     = +2.480158730156105377771585658905303111866e-0005L,
  77         qq5     = -2.755728099762526325736488376695157008736e-0007L,

  78 /*
  79  *                  2            16       -117.11
  80  * |cos(x) - (1+q1*x + ... + q8*x  )| <= 2        for |x|<= 0.15625
  81  */

  82         q1      = -4.999999999999999999999999999999756416975e-0001L,
  83         q2      = +4.166666666666666666666666664006066577258e-0002L,
  84         q3      = -1.388888888888888888888877700363937169637e-0003L,
  85         q4      = +2.480158730158730158494468463031814083559e-0005L,
  86         q5      = -2.755731922398586276322819250356005542871e-0007L,
  87         q6      = +2.087675698767424261441959760729854017855e-0009L,
  88         q7      = -1.147074481239662089072452129010790774761e-0011L,
  89         q8      = +4.777761647399651599730663422263531034782e-0014L;
  90 
  91 #define i0      0
  92 
  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 = 1.0L;
 100         hx = px[i0];
 101         ix = hx & 0x7fffffff;

 102         if (ix < 0x3ffc4000) {
 103                 if (ix < 0x3fc60000)
 104                         if (((int) x) == 0) {
 105                                 *c = one;
 106                                 return (x);
 107                         }       /* generate inexact */


 108                 z = x * x;
 109 
 110                 if (ix < 0x3ff80000) {
 111                         *c = one + z * (qq1 + z * (qq2 + z * (qq3 +
 112                                 z * (qq4 + z * qq5))));
 113                         t = z * (p1 + z * (p2 + z * (p3 + z * (p4 +
 114                                 z * (p5 + z * p6)))));
 115                 } else {
 116                         *c = one + z * (q1 + z * (q2 + z * (q3 + z * (q4 +
 117                                 z * (q5 + z * (q6 + z * (q7 + z * q8)))))));
 118                         t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * (p5 +
 119                                 z * (p6 + z * (p7 + z * p8)))))));
 120                 }
 121 
 122                 t = y + x * t;
 123                 return (x + t);
 124         }

 125         j = (ix + 0x400) & 0x7ffff800;
 126         i = (j - 0x3ffc4000) >> 11;
 127         pt[i0] = j;

 128         if (hx > 0)
 129                 x = y - (t - x);
 130         else
 131                 x = (-y) - (t + x);

 132         a1 = _TBL_sinl_hi[i];
 133         z = x * x;
 134         t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
 135         w = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z * pp5)))));
 136         a2 = _TBL_cosl_hi[i];
 137         t2 = _TBL_cosl_lo[i] - (a1 * w - a2 * t);
 138         *c = a2 + t2;
 139         t1 = a2 * w + a1 * t;
 140         t1 += _TBL_sinl_lo[i];

 141         if (hx < 0)
 142                 return (-a1 - t1);
 143         else
 144                 return (a1 + t1);
 145 }


   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 /*
  27  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
  28  * Use is subject to license terms.
  29  */
  30 
  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 extern const long double _TBL_sinl_hi[], _TBL_sinl_lo[], _TBL_cosl_hi[],
  45         _TBL_cosl_lo[];
  46 static const long double one = 1.0L;
  47 
  48 /*
  49  *                   3           11       -122.32
  50  * |sin(x) - (x+pp1*x +...+ pp5*x  )| <= 2        for |x|<1/64
  51  */
  52 static const long double
  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 /*
  60  * |(sin(x) - (x+p1*x^3+...+p8*x^17)|
  61  * |------------------------------- | <= 2^-116.17 for |x|<0.1953125
  62  * |                 x              |
  63  */
  64 static const long double
  65         p1 = -1.666666666666666666666666666666211262297e-0001L,
  66         p2 = +8.333333333333333333333333301497876908541e-0003L,
  67         p3 = -1.984126984126984126984041302881180621922e-0004L,
  68         p4 = +2.755731922398589064100587351307269621093e-0006L,
  69         p5 = -2.505210838544163129378906953765595393873e-0008L,
  70         p6 = +1.605904383643244375050998243778534074273e-0010L,
  71         p7 = -7.647162722800685516901456114270824622699e-0013L,
  72         p8 = +2.810046428661902961725428841068844462603e-0015L;
  73 
  74 /*
  75  *                   2           10       -123.84
  76  * |cos(x) - (1+qq1*x +...+ qq5*x  )| <= 2        for |x|<=1/128
  77  */
  78 static const long double
  79         qq1 = -4.999999999999999999999999999999378373641e-0001L,
  80         qq2 = +4.166666666666666666666665478399327703130e-0002L,
  81         qq3 = -1.388888888888888888058211230618051613494e-0003L,
  82         qq4 = +2.480158730156105377771585658905303111866e-0005L,
  83         qq5 = -2.755728099762526325736488376695157008736e-0007L;
  84 
  85 /*
  86  *                  2            16       -117.11
  87  * |cos(x) - (1+q1*x + ... + q8*x  )| <= 2        for |x|<= 0.15625
  88  */
  89 static const long double
  90         q1 = -4.999999999999999999999999999999756416975e-0001L,
  91         q2 = +4.166666666666666666666666664006066577258e-0002L,
  92         q3 = -1.388888888888888888888877700363937169637e-0003L,
  93         q4 = +2.480158730158730158494468463031814083559e-0005L,
  94         q5 = -2.755731922398586276322819250356005542871e-0007L,
  95         q6 = +2.087675698767424261441959760729854017855e-0009L,
  96         q7 = -1.147074481239662089072452129010790774761e-0011L,
  97         q8 = +4.777761647399651599730663422263531034782e-0014L;
  98 
  99 #define i0      0
 100 
 101 long double
 102 __k_sincosl(long double x, long double y, long double *c)
 103 {
 104         long double a1, a2, t, t1, t2, z, w;
 105         int *pt = (int *)&t, *px = (int *)&x;
 106         int i, j, hx, ix;
 107 
 108         t = 1.0L;
 109         hx = px[i0];
 110         ix = hx & 0x7fffffff;
 111 
 112         if (ix < 0x3ffc4000) {
 113                 if (ix < 0x3fc60000) {
 114                         if (((int)x) == 0) {
 115                                 *c = one;
 116                                 return (x);
 117                         }               /* generate inexact */
 118                 }
 119 
 120                 z = x * x;
 121 
 122                 if (ix < 0x3ff80000) {
 123                         *c = one + z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 +
 124                             z * qq5))));
 125                         t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * (p5 +
 126                             z * p6)))));
 127                 } else {
 128                         *c = one + z * (q1 + z * (q2 + z * (q3 + z * (q4 + z *
 129                             (q5 + z * (q6 + z * (q7 + z * q8)))))));
 130                         t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * (p5 +
 131                             z * (p6 + z * (p7 + z * p8)))))));
 132                 }
 133 
 134                 t = y + x * t;
 135                 return (x + t);
 136         }
 137 
 138         j = (ix + 0x400) & 0x7ffff800;
 139         i = (j - 0x3ffc4000) >> 11;
 140         pt[i0] = j;
 141 
 142         if (hx > 0)
 143                 x = y - (t - x);
 144         else
 145                 x = (-y) - (t + x);
 146 
 147         a1 = _TBL_sinl_hi[i];
 148         z = x * x;
 149         t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
 150         w = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z * pp5)))));
 151         a2 = _TBL_cosl_hi[i];
 152         t2 = _TBL_cosl_lo[i] - (a1 * w - a2 * t);
 153         *c = a2 + t2;
 154         t1 = a2 * w + a1 * t;
 155         t1 += _TBL_sinl_lo[i];
 156 
 157         if (hx < 0)
 158                 return (-a1 - t1);
 159         else
 160                 return (a1 + t1);
 161 }