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 } 273