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 __casinl = casinl 31 32 #include "libm.h" /* asinl/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_4 = 0.7853981633974483095739921312272713294078130L, 48 pi_4_l = 4.1668714592604391641479322342670193036704898e-20L, 49 pi_2 = 1.5707963267948966191479842624545426588156260L, 50 pi_2_l = 8.3337429185208783282958644685340386073409796e-20L; 51 52 #else 53 E = 9.6296497219361792652798897129246365926905e-35L, /* 2**-113 */ 54 pi_4 = 0.7853981633974483096156608458198756993697670L, 55 pi_4_l = 2.1679525325309452561992610065108379921905808e-35L, 56 pi_2 = 1.5707963267948966192313216916397513987395340L, 57 pi_2_l = 4.3359050650618905123985220130216759843811616e-35L; 58 59 #endif 60 /* INDENT ON */ 61 62 #if defined(__x86) 63 static const int ip1 = 0x40400000; /* 2**65 */ 64 #else 65 static const int ip1 = 0x40710000; /* 2**114 */ 66 #endif 67 68 ldcomplex 69 casinl(ldcomplex z) { 70 long double x, y, t, R, S, A, Am1, B, y2, xm1, xp1, Apx; 71 int ix, iy, hx, hy; 72 ldcomplex ans; 73 74 x = LD_RE(z); 75 y = LD_IM(z); 76 hx = HI_XWORD(x); 77 hy = HI_XWORD(y); 78 ix = hx & 0x7fffffff; 79 iy = hy & 0x7fffffff; 80 x = fabsl(x); 81 y = fabsl(y); 82 83 /* special cases */ 84 85 /* x is inf or NaN */ 86 if (ix >= 0x7fff0000) { /* x is inf or NaN */ 87 if (isinfl(x)) { /* x is INF */ 88 LD_IM(ans) = x; 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 } else { /* x is NaN */ 98 if (iy >= 0x7fff0000) { 99 /* INDENT OFF */ 100 /* 101 * casin(NaN + i inf) = NaN + i inf 102 * casin(NaN + i NaN) = NaN + i NaN 103 */ 104 /* INDENT ON */ 105 LD_IM(ans) = y + y; 106 LD_RE(ans) = x + x; 107 } else { 108 /* INDENT OFF */ 109 /* casin(NaN + i y ) = NaN + i NaN */ 110 /* INDENT ON */ 111 LD_IM(ans) = LD_RE(ans) = x + y; 112 } 113 } 114 if (hx < 0) 115 LD_RE(ans) = -LD_RE(ans); 116 if (hy < 0) 117 LD_IM(ans) = -LD_IM(ans); 118 return (ans); 119 } 120 121 /* casin(+0 + i 0) = 0 + i 0. */ 122 if (x == zero && y == zero) 123 return (z); 124 125 if (iy >= 0x7fff0000) { /* y is inf or NaN */ 126 if (isinfl(y)) { /* casin(x + i inf) = 0 + i inf */ 127 LD_IM(ans) = y; 128 LD_RE(ans) = zero; 129 } else { /* casin(x + i NaN) = NaN + i NaN */ 130 LD_IM(ans) = x + y; 131 if (x == zero) 132 LD_RE(ans) = x; 133 else 134 LD_RE(ans) = y; 135 } 136 if (hx < 0) 137 LD_RE(ans) = -LD_RE(ans); 138 if (hy < 0) 139 LD_IM(ans) = -LD_IM(ans); 140 return (ans); 141 } 142 143 if (y == zero) { /* region 1: y=0 */ 144 if (ix < 0x3fff0000) { /* |x| < 1 */ 145 LD_RE(ans) = asinl(x); 146 LD_IM(ans) = zero; 147 } else { 148 LD_RE(ans) = pi_2 + pi_2_l; 149 if (ix >= ip1) /* |x| >= i386 ? 2**65 : 2**114 */ 150 LD_IM(ans) = ln2 + logl(x); 151 else if (ix >= 0x3fff8000) /* x > Acrossover */ 152 LD_IM(ans) = logl(x + sqrtl((x - one) * (x + 153 one))); 154 else { 155 xm1 = x - one; 156 LD_IM(ans) = log1pl(xm1 + sqrtl(xm1 * (x + 157 one))); 158 } 159 } 160 } else if (y <= E * fabsl(x - one)) { /* region 2: y < tiny*|x-1| */ 161 if (ix < 0x3fff0000) { /* x < 1 */ 162 LD_RE(ans) = asinl(x); 163 LD_IM(ans) = y / sqrtl((one + x) * (one - x)); 164 } else { 165 LD_RE(ans) = pi_2 + pi_2_l; 166 if (ix >= ip1) /* i386 ? 2**65 : 2**114 */ 167 LD_IM(ans) = ln2 + logl(x); 168 else if (ix >= 0x3fff8000) /* x > Acrossover */ 169 LD_IM(ans) = logl(x + sqrtl((x - one) * (x + 170 one))); 171 else 172 LD_IM(ans) = log1pl((x - one) + sqrtl((x - 173 one) * (x + one))); 174 } 175 } else if (y < Foursqrtu) { /* region 3 */ 176 t = sqrtl(y); 177 LD_RE(ans) = pi_2 - (t - pi_2_l); 178 LD_IM(ans) = t; 179 } else if (E * y - one >= x) { /* region 4 */ 180 LD_RE(ans) = x / y; /* need to fix underflow cases */ 181 LD_IM(ans) = ln2 + logl(y); 182 } else if (ix >= 0x5ffb0000 || iy >= 0x5ffb0000) { 183 /* region 5: x+1 and y are both (>= sqrt(max)/8) i.e. 2**8188 */ 184 t = x / y; 185 LD_RE(ans) = atanl(t); 186 LD_IM(ans) = ln2 + logl(y) + half * log1pl(t * t); 187 } else if (x < Foursqrtu) { 188 /* region 6: x is very small, < 4sqrt(min) */ 189 A = sqrtl(one + y * y); 190 LD_RE(ans) = x / A; /* may underflow */ 191 if (iy >= 0x3fff8000) /* if y > Acrossover */ 192 LD_IM(ans) = logl(y + A); 193 else 194 LD_IM(ans) = half * log1pl((y + y) * (y + A)); 195 } else { /* safe region */ 196 y2 = y * y; 197 xp1 = x + one; 198 xm1 = x - one; 199 R = sqrtl(xp1 * xp1 + y2); 200 S = sqrtl(xm1 * xm1 + y2); 201 A = half * (R + S); 202 B = x / A; 203 if (B <= Bcrossover) 204 LD_RE(ans) = asinl(B); 205 else { /* use atan and an accurate approx to a-x */ 206 Apx = A + x; 207 if (x <= one) 208 LD_RE(ans) = atanl(x / sqrtl(half * Apx * (y2 / 209 (R + xp1) + (S - xm1)))); 210 else 211 LD_RE(ans) = atanl(x / (y * sqrtl(half * (Apx / 212 (R + xp1) + Apx / (S + xm1))))); 213 } 214 if (A <= Acrossover) { 215 /* use log1p and an accurate approx to A-1 */ 216 if (x < one) 217 Am1 = half * (y2 / (R + xp1) + y2 / (S - xm1)); 218 else 219 Am1 = half * (y2 / (R + xp1) + (S + xm1)); 220 LD_IM(ans) = log1pl(Am1 + sqrtl(Am1 * (A + one))); 221 } else { 222 LD_IM(ans) = logl(A + sqrtl(A * A - one)); 223 } 224 } 225 226 if (hx < 0) 227 LD_RE(ans) = -LD_RE(ans); 228 if (hy < 0) 229 LD_IM(ans) = -LD_IM(ans); 230 231 return (ans); 232 } 233