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 /*
  27  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
  28  * Use is subject to license terms.
  29  */
  30 
  31 #pragma weak __casinl = casinl
  32 
  33 #include "libm.h"       /* asinl/atanl/fabsl/isinfl/log1pl/logl/sqrtl */
  34 #include "complex_wrapper.h"
  35 #include "longdouble.h"
  36 
  37 /* BEGIN CSTYLED */
  38 static const long double zero = 0.0L,
  39         one = 1.0L,
  40         Acrossover = 1.5L,
  41         Bcrossover = 0.6417L,
  42         half = 0.5L,
  43         ln2 = 6.931471805599453094172321214581765680755e-0001L,
  44         Foursqrtu = 7.3344154702193886624856495681939326638255e-2466L,  /* 2**-8189 */
  45 #if defined(__x86)
  46         E = 5.4210108624275221700372640043497085571289e-20L,    /* 2**-64 */
  47         pi_4 = 0.7853981633974483095739921312272713294078130L,
  48         pi_4_l = 4.1668714592604391641479322342670193036704898e-20L,
  49         pi_2 = 1.5707963267948966191479842624545426588156260L,
  50         pi_2_l = 8.3337429185208783282958644685340386073409796e-20L;
  51 #else
  52         E = 9.6296497219361792652798897129246365926905e-35L,    /* 2**-113 */
  53         pi_4 = 0.7853981633974483096156608458198756993697670L,
  54         pi_4_l = 2.1679525325309452561992610065108379921905808e-35L,
  55         pi_2 = 1.5707963267948966192313216916397513987395340L,
  56         pi_2_l = 4.3359050650618905123985220130216759843811616e-35L;
  57 #endif
  58 /* END CSTYLED */
  59 
  60 #if defined(__x86)
  61 static const int ip1 = 0x40400000;      /* 2**65 */
  62 #else
  63 static const int ip1 = 0x40710000;      /* 2**114 */
  64 #endif
  65 
  66 ldcomplex
  67 casinl(ldcomplex z)
  68 {
  69         long double x, y, t, R, S, A, Am1, B, y2, xm1, xp1, Apx;
  70         int ix, iy, hx, hy;
  71         ldcomplex ans;
  72 
  73         x = LD_RE(z);
  74         y = LD_IM(z);
  75         hx = HI_XWORD(x);
  76         hy = HI_XWORD(y);
  77         ix = hx & 0x7fffffff;
  78         iy = hy & 0x7fffffff;
  79         x = fabsl(x);
  80         y = fabsl(y);
  81 
  82         /* special cases */
  83 
  84         /* x is inf or NaN */
  85         if (ix >= 0x7fff0000) {              /* x is inf or NaN */
  86                 if (isinfl(x)) {        /* x is INF */
  87                         LD_IM(ans) = x;
  88 
  89                         if (iy >= 0x7fff0000) {
  90                                 if (isinfl(y))
  91                                         /* casin(inf + i inf) = pi/4 + i inf */
  92                                         LD_RE(ans) = pi_4 + pi_4_l;
  93                                 else    /* casin(inf + i NaN) = NaN + i inf */
  94                                         LD_RE(ans) = y + y;
  95                         } else { /* casin(inf + iy) = pi/2 + i inf */
  96                                 LD_RE(ans) = pi_2 + pi_2_l;
  97                         }
  98                 } else {                /* x is NaN */
  99                         if (iy >= 0x7fff0000) {
 100 
 101                                 /*
 102                                  * casin(NaN + i inf) = NaN  + i inf
 103                                  * casin(NaN + i NaN) = NaN  + i NaN
 104                                  */
 105                                 LD_IM(ans) = y + y;
 106                                 LD_RE(ans) = x + x;
 107                         } else {
 108                                 /*
 109                                  * casin(NaN + i y ) = NaN  + i NaN
 110                                  */
 111                                 LD_IM(ans) = LD_RE(ans) = x + y;
 112                         }
 113                 }
 114 
 115                 if (hx < 0)
 116                         LD_RE(ans) = -LD_RE(ans);
 117 
 118                 if (hy < 0)
 119                         LD_IM(ans) = -LD_IM(ans);
 120 
 121                 return (ans);
 122         }
 123 
 124         /* casin(+0 + i 0) = 0 + i 0. */
 125         if (x == zero && y == zero)
 126                 return (z);
 127 
 128         if (iy >= 0x7fff0000) {              /* y is inf or NaN */
 129                 if (isinfl(y)) {        /* casin(x + i inf) = 0 + i inf */
 130                         LD_IM(ans) = y;
 131                         LD_RE(ans) = zero;
 132                 } else {                /* casin(x + i NaN) = NaN + i NaN */
 133                         LD_IM(ans) = x + y;
 134 
 135                         if (x == zero)
 136                                 LD_RE(ans) = x;
 137                         else
 138                                 LD_RE(ans) = y;
 139                 }
 140 
 141                 if (hx < 0)
 142                         LD_RE(ans) = -LD_RE(ans);
 143 
 144                 if (hy < 0)
 145                         LD_IM(ans) = -LD_IM(ans);
 146 
 147                 return (ans);
 148         }
 149 
 150         if (y == zero) {                /* region 1: y=0 */
 151                 if (ix < 0x3fff0000) {       /* |x| < 1 */
 152                         LD_RE(ans) = asinl(x);
 153                         LD_IM(ans) = zero;
 154                 } else {
 155                         LD_RE(ans) = pi_2 + pi_2_l;
 156 
 157                         if (ix >= ip1) { /* |x| >= i386 ? 2**65 : 2**114 */
 158                                 LD_IM(ans) = ln2 + logl(x);
 159                         } else if (ix >= 0x3fff8000) {       /* x > Acrossover */
 160                                 LD_IM(ans) = logl(x + sqrtl((x - one) * (x +
 161                                     one)));
 162                         } else {
 163                                 xm1 = x - one;
 164                                 LD_IM(ans) = log1pl(xm1 + sqrtl(xm1 * (x +
 165                                     one)));
 166                         }
 167                 }
 168         } else if (y <= E * fabsl(x - one)) {        /* region 2: y < tiny*|x-1| */
 169                 if (ix < 0x3fff0000) {               /* x < 1 */
 170                         LD_RE(ans) = asinl(x);
 171                         LD_IM(ans) = y / sqrtl((one + x) * (one - x));
 172                 } else {
 173                         LD_RE(ans) = pi_2 + pi_2_l;
 174 
 175                         if (ix >= ip1) /* i386 ? 2**65 : 2**114 */
 176                                 LD_IM(ans) = ln2 + logl(x);
 177                         else if (ix >= 0x3fff8000)   /* x > Acrossover */
 178                                 LD_IM(ans) = logl(x + sqrtl((x - one) * (x +
 179                                     one)));
 180                         else
 181                                 LD_IM(ans) = log1pl((x - one) + sqrtl((x -
 182                                     one) * (x + one)));
 183                 }
 184         } else if (y < Foursqrtu) {  /* region 3 */
 185                 t = sqrtl(y);
 186                 LD_RE(ans) = pi_2 - (t - pi_2_l);
 187                 LD_IM(ans) = t;
 188         } else if (E * y - one >= x) {       /* region 4 */
 189                 LD_RE(ans) = x / y;     /* need to fix underflow cases */
 190                 LD_IM(ans) = ln2 + logl(y);
 191         } else if (ix >= 0x5ffb0000 || iy >= 0x5ffb0000) {
 192                 /* region 5: x+1 and y are both (>= sqrt(max)/8) i.e. 2**8188 */
 193                 t = x / y;
 194                 LD_RE(ans) = atanl(t);
 195                 LD_IM(ans) = ln2 + logl(y) + half * log1pl(t * t);
 196         } else if (x < Foursqrtu) {
 197                 /* region 6: x is very small, < 4sqrt(min) */
 198                 A = sqrtl(one + y * y);
 199                 LD_RE(ans) = x / A;     /* may underflow */
 200 
 201                 if (iy >= 0x3fff8000)        /* if y > Acrossover */
 202                         LD_IM(ans) = logl(y + A);
 203                 else
 204                         LD_IM(ans) = half * log1pl((y + y) * (y + A));
 205         } else {                        /* safe region */
 206                 y2 = y * y;
 207                 xp1 = x + one;
 208                 xm1 = x - one;
 209                 R = sqrtl(xp1 * xp1 + y2);
 210                 S = sqrtl(xm1 * xm1 + y2);
 211                 A = half * (R + S);
 212                 B = x / A;
 213 
 214                 if (B <= Bcrossover) {
 215                         LD_RE(ans) = asinl(B);
 216                 } else {        /* use atan and an accurate approx to a-x */
 217                         Apx = A + x;
 218 
 219                         if (x <= one)
 220                                 LD_RE(ans) = atanl(x / sqrtl(half * Apx * (y2 /
 221                                     (R + xp1) + (S - xm1))));
 222                         else
 223                                 LD_RE(ans) = atanl(x / (y * sqrtl(half * (Apx /
 224                                     (R + xp1) + Apx / (S + xm1)))));
 225                 }
 226 
 227                 if (A <= Acrossover) {
 228                         /* use log1p and an accurate approx to A-1 */
 229                         if (x < one)
 230                                 Am1 = half * (y2 / (R + xp1) + y2 / (S - xm1));
 231                         else
 232                                 Am1 = half * (y2 / (R + xp1) + (S + xm1));
 233 
 234                         LD_IM(ans) = log1pl(Am1 + sqrtl(Am1 * (A + one)));
 235                 } else {
 236                         LD_IM(ans) = logl(A + sqrtl(A * A - one));
 237                 }
 238         }
 239 
 240         if (hx < 0)
 241                 LD_RE(ans) = -LD_RE(ans);
 242 
 243         if (hy < 0)
 244                 LD_IM(ans) = -LD_IM(ans);
 245 
 246         return (ans);
 247 }