usr/src/lib/libm/common/C/acos.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 #pragma weak __acos = acos
  31
  32 /* INDENT OFF */
  33 /*
  34  * acos(x)
  35  * Method :
  36  *      acos(x)  = pi/2 - asin(x)
  37  *      acos(-x) = pi/2 + asin(x)
  38  * For |x|<=0.5
  39  *      acos(x) = pi/2 - (x + x*x^2*R(x^2))     (see asin.c)
  40  * For x>0.5
  41  *      acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
  42  *              = 2asin(sqrt((1-x)/2))
  43  *              = 2s + 2s*z*R(z)        ...z=(1-x)/2, s=sqrt(z)
  44  *              = 2f + (2c + 2s*z*R(z))
  45  *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
  46  *     for f so that f+c ~ sqrt(z).
  47  * For x<-0.5
  48  *      acos(x) = pi - 2asin(sqrt((1-|x|)/2))
  49  *              = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
  50  *
  51  * Special cases:
  52  *      if x is NaN, return x itself;
  53  *      if |x|>1, return NaN with invalid signal.
  54  *
  55  * Function needed: sqrt
  56  */
  57 /* INDENT ON */
  58
  59 #include "libm_protos.h"        /* _SVID_libm_error */
  60 #include "libm_macros.h"
  61 #include <math.h>
  62
  63 /* INDENT OFF */
  64 static const double xxx[] = {
  65 /* one */        1.00000000000000000000e+00,    /* 3FF00000, 00000000 */
  66 /* pi */         3.14159265358979311600e+00,    /* 400921FB, 54442D18 */
  67 /* pio2_hi */    1.57079632679489655800e+00,    /* 3FF921FB, 54442D18 */
  68 /* pio2_lo */    6.12323399573676603587e-17,    /* 3C91A626, 33145C07 */
  69 /* pS0 */        1.66666666666666657415e-01,    /* 3FC55555, 55555555 */
  70 /* pS1 */       -3.25565818622400915405e-01,    /* BFD4D612, 03EB6F7D */
  71 /* pS2 */        2.01212532134862925881e-01,    /* 3FC9C155, 0E884455 */
  72 /* pS3 */       -4.00555345006794114027e-02,    /* BFA48228, B5688F3B */
  73 /* pS4 */        7.91534994289814532176e-04,    /* 3F49EFE0, 7501B288 */
  74 /* pS5 */        3.47933107596021167570e-05,    /* 3F023DE1, 0DFDF709 */
  75 /* qS1 */       -2.40339491173441421878e+00,    /* C0033A27, 1C8A2D4B */
  76 /* qS2 */        2.02094576023350569471e+00,    /* 40002AE5, 9C598AC8 */
  77 /* qS3 */       -6.88283971605453293030e-01,    /* BFE6066C, 1B8D0159 */
  78 /* qS4 */        7.70381505559019352791e-02     /* 3FB3B8C5, B12E9282 */
  79 };
  80 #define one     xxx[0]
  81 #define pi      xxx[1]
  82 #define pio2_hi xxx[2]
  83 #define pio2_lo xxx[3]
  84 #define pS0     xxx[4]
  85 #define pS1     xxx[5]
  86 #define pS2     xxx[6]
  87 #define pS3     xxx[7]
  88 #define pS4     xxx[8]
  89 #define pS5     xxx[9]
  90 #define qS1     xxx[10]
  91 #define qS2     xxx[11]
  92 #define qS3     xxx[12]
  93 #define qS4     xxx[13]
  94 /* INDENT ON */
  95
  96 double
  97 acos(double x) {
  98         double z, p, q, r, w, s, c, df;
  99         int hx, ix;
 100
 101         hx = ((int *) &x)[HIWORD];
 102         ix = hx & 0x7fffffff;
 103         if (ix >= 0x3ff00000) { /* |x| >= 1 */
 104                 if (((ix - 0x3ff00000) | ((int *) &x)[LOWORD]) == 0) {
 105                         /* |x| == 1 */
 106                         if (hx > 0)     /* acos(1) = 0 */
 107                                 return (0.0);
 108                         else            /* acos(-1) = pi */
 109                                 return (pi + 2.0 * pio2_lo);
 110                 } else if (isnan(x))
 111 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
 112                         return (ix >= 0x7ff80000 ? x : (x - x) / (x - x));
 113                         /* assumes sparc-like QNaN */
 114 #else
 115                         return (x - x) / (x - x);       /* acos(|x|>1) is NaN */
 116 #endif
 117                 else
 118                         return (_SVID_libm_err(x, x, 1));
 119         }
 120         if (ix < 0x3fe00000) {  /* |x| < 0.5 */
 121                 if (ix <= 0x3c600000)
 122                         return (pio2_hi + pio2_lo);     /* if |x| < 2**-57 */
 123                 z = x * x;
 124                 p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 +
 125                         z * (pS4 + z * pS5)))));
 126                 q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
 127                 r = p / q;
 128                 return (pio2_hi - (x - (pio2_lo - x * r)));
 129         } else if (hx < 0) {
 130                 /* x < -0.5 */
 131                 z = (one + x) * 0.5;
 132                 p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 +
 133                         z * (pS4 + z * pS5)))));
 134                 q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
 135                 s = sqrt(z);
 136                 r = p / q;
 137                 w = r * s - pio2_lo;
 138                 return (pi - 2.0 * (s + w));
 139         } else {
 140                 /* x > 0.5 */
 141                 z = (one - x) * 0.5;
 142                 s = sqrt(z);
 143                 df = s;
 144                 ((int *) &df)[LOWORD] = 0;
 145                 c = (z - df * df) / (s + df);
 146                 p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 +
 147                         z * (pS4 + z * pS5)))));
 148                 q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
 149                 r = p / q;
 150                 w = r * s + c;
 151                 return (2.0 * (df + w));
 152         }
 153 }