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 __cacosl = cacosl
  32 
  33 #include "libm.h"       /* acosl/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 = 3.141592653589793238295968524909085317631252110004425048828125L,
  48         pi_l = 1.666748583704175665659172893706807721468195923078e-19L,
  49         pi_2 = 1.5707963267948966191479842624545426588156260L,
  50         pi_2_l = 8.3337429185208783282958644685340386073409796e-20L,
  51         pi_4 = 0.78539816339744830957399213122727132940781302750110626220703125L,
  52         pi_4_l = 4.166871459260439164147932234267019303670489807695410e-20L,
  53         pi3_4 = 2.35619449019234492872197639368181398822343908250331878662109375L,
  54         pi3_4_l = 1.250061437778131749244379670280105791101146942308e-19L;
  55 #else
  56         E = 9.6296497219361792652798897129246365926905e-35L,    /* 2**-113 */
  57         pi = 3.1415926535897932384626433832795027974790680981372955730045043318L,
  58         pi_l = 8.6718101301237810247970440260433519687623233462565303417759356862e-35L,
  59         pi_2 = 1.5707963267948966192313216916397513987395340L,
  60         pi_2_l = 4.3359050650618905123985220130216759843811616e-35L,
  61         pi_4 = 0.785398163397448309615660845819875699369767024534323893251126L,
  62         pi_4_l = 2.167952532530945256199261006510837992190580836564132585443e-35L,
  63         pi3_4 = 2.35619449019234492884698253745962709810930107360297167975337824L,
  64         pi3_4_l = 6.503857597592835768597783019532513976571742509692397756331e-35L;
  65 #endif
  66 /* END CSTYLED */
  67 
  68 #if defined(__x86)
  69 static const int ip1 = 0x40400000;      /* 2**65 */
  70 #else
  71 static const int ip1 = 0x40710000;      /* 2**114 */
  72 #endif
  73 
  74 ldcomplex
  75 cacosl(ldcomplex z)
  76 {
  77         long double x, y, t, R, S, A, Am1, B, y2, xm1, xp1, Apx;
  78         int ix, iy, hx, hy;
  79         ldcomplex ans;
  80 
  81         x = LD_RE(z);
  82         y = LD_IM(z);
  83         hx = HI_XWORD(x);
  84         hy = HI_XWORD(y);
  85         ix = hx & 0x7fffffff;
  86         iy = hy & 0x7fffffff;
  87 
  88         /* x is 0 */
  89         if (x == zero) {
  90                 if (y == zero || (iy >= 0x7fff0000)) {
  91                         LD_RE(ans) = pi_2 + pi_2_l;
  92                         LD_IM(ans) = -y;
  93                         return (ans);
  94                 }
  95         }
  96 
  97         /* |y| is inf or NaN */
  98         if (iy >= 0x7fff0000) {
  99                 if (isinfl(y)) {        /* cacos(x + i inf) =  pi/2 - i inf */
 100                         LD_IM(ans) = -y;
 101 
 102                         if (ix < 0x7fff0000) {
 103                                 LD_RE(ans) = pi_2 + pi_2_l;
 104                         } else if (isinfl(x)) {
 105                                 if (hx >= 0)
 106                                         LD_RE(ans) = pi_4 + pi_4_l;
 107                                 else
 108                                         LD_RE(ans) = pi3_4 + pi3_4_l;
 109                         } else {
 110                                 LD_RE(ans) = x;
 111                         }
 112                 } else {                /* cacos(x + i NaN) = NaN  + i NaN */
 113                         LD_RE(ans) = y + x;
 114 
 115                         if (isinfl(x))
 116                                 LD_IM(ans) = -fabsl(x);
 117                         else
 118                                 LD_IM(ans) = y;
 119                 }
 120 
 121                 return (ans);
 122         }
 123 
 124         y = fabsl(y);
 125 
 126         if (ix >= 0x7fff0000) {              /* x is inf or NaN */
 127                 if (isinfl(x)) {        /* x is INF */
 128                         LD_IM(ans) = -fabsl(x);
 129 
 130                         if (iy >= 0x7fff0000) {
 131                                 if (isinfl(y)) {
 132                                         /*
 133                                          * cacos(inf + i inf) = pi/4 - i inf
 134                                          * cacos(-inf+ i inf) =3pi/4 - i inf
 135                                          */
 136                                         if (hx >= 0)
 137                                                 LD_RE(ans) = pi_4 + pi_4_l;
 138                                         else
 139                                                 LD_RE(ans) = pi3_4 + pi3_4_l;
 140                                 } else {
 141                                         /*
 142                                          * cacos(inf + i NaN) = NaN  - i inf
 143                                          */
 144                                         LD_RE(ans) = y + y;
 145                                 }
 146                         } else {
 147                                 /*
 148                                  * cacos(inf + iy ) = 0  - i inf
 149                                  * cacos(-inf+ iy  ) = pi - i inf
 150                                  */
 151                                 if (hx >= 0)
 152                                         LD_RE(ans) = zero;
 153                                 else
 154                                         LD_RE(ans) = pi + pi_l;
 155                         }
 156                 } else {                /* x is NaN */
 157 
 158                         /*
 159                          * cacos(NaN + i inf) = NaN  - i inf
 160                          * cacos(NaN + i y  ) = NaN  + i NaN
 161                          * cacos(NaN + i NaN) = NaN  + i NaN
 162                          */
 163                         LD_RE(ans) = x + y;
 164 
 165                         if (iy >= 0x7fff0000)
 166                                 LD_IM(ans) = -y;
 167                         else
 168                                 LD_IM(ans) = x;
 169                 }
 170 
 171                 if (hy < 0)
 172                         LD_IM(ans) = -LD_IM(ans);
 173 
 174                 return (ans);
 175         }
 176 
 177         if (y == zero) {                /* region 1: y=0 */
 178                 if (ix < 0x3fff0000) {       /* |x| < 1 */
 179                         LD_RE(ans) = acosl(x);
 180                         LD_IM(ans) = zero;
 181                 } else {
 182                         LD_RE(ans) = zero;
 183                         x = fabsl(x);
 184 
 185                         if (ix >= ip1) { /* i386 ? 2**65 : 2**114 */
 186                                 LD_IM(ans) = ln2 + logl(x);
 187                         } else if (ix >= 0x3fff8000) {       /* x > Acrossover */
 188                                 LD_IM(ans) = logl(x + sqrtl((x - one) * (x +
 189                                     one)));
 190                         } else {
 191                                 xm1 = x - one;
 192                                 LD_IM(ans) = log1pl(xm1 + sqrtl(xm1 * (x +
 193                                     one)));
 194                         }
 195                 }
 196         } else if (y <= E * fabsl(fabsl(x) - one)) {
 197                 /* region 2: y < tiny*||x|-1| */
 198                 if (ix < 0x3fff0000) {       /* x < 1 */
 199                         LD_RE(ans) = acosl(x);
 200                         x = fabsl(x);
 201                         LD_IM(ans) = y / sqrtl((one + x) * (one - x));
 202                 } else if (ix >= ip1) {      /* i386 ? 2**65 : 2**114 */
 203                         if (hx >= 0) {
 204                                 LD_RE(ans) = y / x;
 205                         } else {
 206                                 if (ix >= ip1 + 0x00040000) {
 207                                         LD_RE(ans) = pi + pi_l;
 208                                 } else {
 209                                         t = pi_l + y / x;
 210                                         LD_RE(ans) = pi + t;
 211                                 }
 212                         }
 213 
 214                         LD_IM(ans) = ln2 + logl(fabsl(x));
 215                 } else {
 216                         x = fabsl(x);
 217                         t = sqrtl((x - one) * (x + one));
 218                         LD_RE(ans) = (hx >= 0) ? y / t : pi - (y / t - pi_l);
 219 
 220                         if (ix >= 0x3fff8000)        /* x > Acrossover */
 221                                 LD_IM(ans) = logl(x + t);
 222                         else
 223                                 LD_IM(ans) = log1pl(t - (one - x));
 224                 }
 225         } else if (y < Foursqrtu) {  /* region 3 */
 226                 t = sqrtl(y);
 227                 LD_RE(ans) = (hx >= 0) ? t : pi + pi_l;
 228                 LD_IM(ans) = t;
 229         } else if (E * y - one >= fabsl(x)) {        /* region 4 */
 230                 LD_RE(ans) = pi_2 + pi_2_l;
 231                 LD_IM(ans) = ln2 + logl(y);
 232         } else if (ix >= 0x5ffb0000 || iy >= 0x5ffb0000) {
 233                 /* region 5: x+1 and y are both (>= sqrt(max)/8) i.e. 2**8188 */
 234                 t = x / y;
 235                 LD_RE(ans) = atan2l(y, x);
 236                 LD_IM(ans) = ln2 + logl(y) + half * log1pl(t * t);
 237         } else if (fabsl(x) < Foursqrtu) {
 238                 /* region 6: x is very small, < 4sqrt(min) */
 239                 LD_RE(ans) = pi_2 + pi_2_l;
 240                 A = sqrtl(one + y * y);
 241 
 242                 if (iy >= 0x3fff8000)        /* if y > Acrossover */
 243                         LD_IM(ans) = logl(y + A);
 244                 else
 245                         LD_IM(ans) = half * log1pl((y + y) * (y + A));
 246         } else {                        /* safe region */
 247                 t = fabsl(x);
 248                 y2 = y * y;
 249                 xp1 = t + one;
 250                 xm1 = t - one;
 251                 R = sqrtl(xp1 * xp1 + y2);
 252                 S = sqrtl(xm1 * xm1 + y2);
 253                 A = half * (R + S);
 254                 B = t / A;
 255 
 256                 if (B <= Bcrossover) {
 257                         LD_RE(ans) = (hx >= 0) ? acosl(B) : acosl(-B);
 258                 } else {        /* use atan and an accurate approx to a-x */
 259                         Apx = A + t;
 260 
 261                         if (t <= one)
 262                                 LD_RE(ans) = atan2l(sqrtl(half * Apx * (y2 /
 263                                     (R + xp1) + (S - xm1))), x);
 264                         else
 265                                 LD_RE(ans) = atan2l((y * sqrtl(half * (Apx /
 266                                     (R + xp1) + Apx / (S + xm1)))), x);
 267                 }
 268 
 269                 if (A <= Acrossover) {
 270                         /* use log1p and an accurate approx to A-1 */
 271                         if (ix < 0x3fff0000)
 272                                 Am1 = half * (y2 / (R + xp1) + y2 / (S - xm1));
 273                         else
 274                                 Am1 = half * (y2 / (R + xp1) + (S + xm1));
 275 
 276                         LD_IM(ans) = log1pl(Am1 + sqrtl(Am1 * (A + one)));
 277                 } else {
 278                         LD_IM(ans) = logl(A + sqrtl(A * A - one));
 279                 }
 280         }
 281 
 282         if (hy >= 0)
 283                 LD_IM(ans) = -LD_IM(ans);
 284 
 285         return (ans);
 286 }