usr/src/lib/libm/common/complex/cacosl.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 __cacosl = cacosl
  31
  32 #include "libm.h"               /* acosl/atanl/fabsl/isinfl/log1pl/logl/sqrtl */
  33 #include "complex_wrapper.h"
  34 #include "longdouble.h"
  35
  36 /* INDENT OFF */
  37 static const long double
  38 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 /* INDENT ON */
  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         long double x, y, t, R, S, A, Am1, B, y2, xm1, xp1, Apx;
  77         int ix, iy, hx, hy;
  78         ldcomplex ans;
  79
  80         x = LD_RE(z);
  81         y = LD_IM(z);
  82         hx = HI_XWORD(x);
  83         hy = HI_XWORD(y);
  84         ix = hx & 0x7fffffff;
  85         iy = hy & 0x7fffffff;
  86
  87         /* x is 0 */
  88         if (x == zero) {
  89                 if (y == zero || (iy >= 0x7fff0000)) {
  90                         LD_RE(ans) = pi_2 + pi_2_l;
  91                         LD_IM(ans) = -y;
  92                         return (ans);
  93                 }
  94         }
  95
  96         /* |y| is inf or NaN */
  97         if (iy >= 0x7fff0000) {
  98                 if (isinfl(y)) {        /* cacos(x + i inf) =  pi/2 - i inf */
  99                         LD_IM(ans) = -y;
 100                         if (ix < 0x7fff0000) {
 101                                 LD_RE(ans) = pi_2 + pi_2_l;
 102                         } else if (isinfl(x)) {
 103                                 if (hx >= 0)
 104                                         LD_RE(ans) = pi_4 + pi_4_l;
 105                                 else
 106                                         LD_RE(ans) = pi3_4 + pi3_4_l;
 107                         } else {
 108                                 LD_RE(ans) = x;
 109                         }
 110                 } else {                /* cacos(x + i NaN) = NaN  + i NaN */
 111                         LD_RE(ans) = y + x;
 112                         if (isinfl(x))
 113                                 LD_IM(ans) = -fabsl(x);
 114                         else
 115                                 LD_IM(ans) = y;
 116                 }
 117                 return (ans);
 118         }
 119
 120         y = fabsl(y);
 121
 122         if (ix >= 0x7fff0000) { /* x is inf or NaN */
 123                 if (isinfl(x)) {        /* x is INF */
 124                         LD_IM(ans) = -fabsl(x);
 125                         if (iy >= 0x7fff0000) {
 126                                 if (isinfl(y)) {
 127                                         /* INDENT OFF */
 128                                         /* cacos(inf + i inf) = pi/4 - i inf */
 129                                         /* cacos(-inf+ i inf) =3pi/4 - i inf */
 130                                         /* INDENT ON */
 131                                         if (hx >= 0)
 132                                                 LD_RE(ans) = pi_4 + pi_4_l;
 133                                         else
 134                                                 LD_RE(ans) = pi3_4 + pi3_4_l;
 135                                 } else
 136                                         /* INDENT OFF */
 137                                         /* cacos(inf + i NaN) = NaN  - i inf  */
 138                                         /* INDENT ON */
 139                                         LD_RE(ans) = y + y;
 140                         } else {
 141                                 /* INDENT OFF */
 142                                 /* cacos(inf + iy ) = 0  - i inf */
 143                                 /* cacos(-inf+ iy  ) = pi - i inf */
 144                                 /* INDENT ON */
 145                                 if (hx >= 0)
 146                                         LD_RE(ans) = zero;
 147                                 else
 148                                         LD_RE(ans) = pi + pi_l;
 149                         }
 150                 } else {                /* x is NaN */
 151                         /* INDENT OFF */
 152                         /*
 153                          * cacos(NaN + i inf) = NaN  - i inf
 154                          * cacos(NaN + i y  ) = NaN  + i NaN
 155                          * cacos(NaN + i NaN) = NaN  + i NaN
 156                          */
 157                         /* INDENT ON */
 158                         LD_RE(ans) = x + y;
 159                         if (iy >= 0x7fff0000) {
 160                                 LD_IM(ans) = -y;
 161                         } else {
 162                                 LD_IM(ans) = x;
 163                         }
 164                 }
 165                 if (hy < 0)
 166                         LD_IM(ans) = -LD_IM(ans);
 167                 return (ans);
 168         }
 169
 170         if (y == zero) {        /* region 1: y=0 */
 171                 if (ix < 0x3fff0000) {  /* |x| < 1 */
 172                         LD_RE(ans) = acosl(x);
 173                         LD_IM(ans) = zero;
 174                 } else {
 175                         LD_RE(ans) = zero;
 176                         x = fabsl(x);
 177                         if (ix >= ip1)  /* i386 ? 2**65 : 2**114 */
 178                                 LD_IM(ans) = ln2 + logl(x);
 179                         else if (ix >= 0x3fff8000)      /* x > Acrossover */
 180                                 LD_IM(ans) = logl(x + sqrtl((x - one) * (x +
 181                                         one)));
 182                         else {
 183                                 xm1 = x - one;
 184                                 LD_IM(ans) = log1pl(xm1 + sqrtl(xm1 * (x +
 185                                         one)));
 186                         }
 187                 }
 188         } else if (y <= E * fabsl(fabsl(x) - one)) {
 189                 /* region 2: y < tiny*||x|-1| */
 190                 if (ix < 0x3fff0000) {  /* x < 1 */
 191                         LD_RE(ans) = acosl(x);
 192                         x = fabsl(x);
 193                         LD_IM(ans) = y / sqrtl((one + x) * (one - x));
 194                 } else if (ix >= ip1) { /* i386 ? 2**65 : 2**114 */
 195                         if (hx >= 0)
 196                                 LD_RE(ans) = y / x;
 197                         else {
 198                                 if (ix >= ip1 + 0x00040000)
 199                                         LD_RE(ans) = pi + pi_l;
 200                                 else {
 201                                         t = pi_l + y / x;
 202                                         LD_RE(ans) = pi + t;
 203                                 }
 204                         }
 205                         LD_IM(ans) = ln2 + logl(fabsl(x));
 206                 } else {
 207                         x = fabsl(x);
 208                         t = sqrtl((x - one) * (x + one));
 209                         LD_RE(ans) = (hx >= 0)? y / t : pi - (y / t - pi_l);
 210                         if (ix >= 0x3fff8000)   /* x > Acrossover */
 211                                 LD_IM(ans) = logl(x + t);
 212                         else
 213                                 LD_IM(ans) = log1pl(t - (one - x));
 214                 }
 215         } else if (y < Foursqrtu) {     /* region 3 */
 216                 t = sqrtl(y);
 217                 LD_RE(ans) = (hx >= 0)? t : pi + pi_l;
 218                 LD_IM(ans) = t;
 219         } else if (E * y - one >= fabsl(x)) {   /* region 4 */
 220                 LD_RE(ans) = pi_2 + pi_2_l;
 221                 LD_IM(ans) = ln2 + logl(y);
 222         } else if (ix >= 0x5ffb0000 || iy >= 0x5ffb0000) {
 223                 /* region 5: x+1 and y are both (>= sqrt(max)/8) i.e. 2**8188 */
 224                 t = x / y;
 225                 LD_RE(ans) = atan2l(y, x);
 226                 LD_IM(ans) = ln2 + logl(y) + half * log1pl(t * t);
 227         } else if (fabsl(x) < Foursqrtu) {
 228                 /* region 6: x is very small, < 4sqrt(min) */
 229                 LD_RE(ans) = pi_2 + pi_2_l;
 230                 A = sqrtl(one + y * y);
 231                 if (iy >= 0x3fff8000)   /* if y > Acrossover */
 232                         LD_IM(ans) = logl(y + A);
 233                 else
 234                         LD_IM(ans) = half * log1pl((y + y) * (y + A));
 235         } else {        /* safe region */
 236                 t = fabsl(x);
 237                 y2 = y * y;
 238                 xp1 = t + one;
 239                 xm1 = t - one;
 240                 R = sqrtl(xp1 * xp1 + y2);
 241                 S = sqrtl(xm1 * xm1 + y2);
 242                 A = half * (R + S);
 243                 B = t / A;
 244
 245                 if (B <= Bcrossover)
 246                         LD_RE(ans) = (hx >= 0)? acosl(B) : acosl(-B);
 247                 else {          /* use atan and an accurate approx to a-x */
 248                         Apx = A + t;
 249                         if (t <= one)
 250                                 LD_RE(ans) = atan2l(sqrtl(half * Apx * (y2 /
 251                                         (R + xp1) + (S - xm1))), x);
 252                         else
 253                                 LD_RE(ans) = atan2l((y * sqrtl(half * (Apx /
 254                                         (R + xp1) + Apx / (S + xm1)))), x);
 255                 }
 256                 if (A <= Acrossover) {
 257                         /* use log1p and an accurate approx to A-1 */
 258                         if (ix < 0x3fff0000)
 259                                 Am1 = half * (y2 / (R + xp1) + y2 / (S - xm1));
 260                         else
 261                                 Am1 = half * (y2 / (R + xp1) + (S + xm1));
 262                         LD_IM(ans) = log1pl(Am1 + sqrtl(Am1 * (A + one)));
 263                 } else {
 264                         LD_IM(ans) = logl(A + sqrtl(A * A - one));
 265                 }
 266         }
 267
 268         if (hy >= 0)
 269                 LD_IM(ans) = -LD_IM(ans);
 270
 271         return (ans);
 272 }