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 ctanh = __ctanh 31 32 /* INDENT OFF */ 33 /* 34 * dcomplex ctanh(dcomplex z); 35 * 36 * tanh x + i tan y sinh 2x + i sin 2y 37 * ctanh z = --------------------- = -------------------- 38 * 1 + i tanh(x)tan(y) cosh 2x + cos 2y 39 * 40 * For |x| >= prec/2 (14,28,34,60 for single, double, double extended, quad), 41 * we use 42 * 43 * 1 2x 2 sin 2y 44 * cosh 2x = sinh 2x = --- e and hence ctanh z = 1 + i -----------; 45 * 2 2x 46 * e 47 * 48 * otherwise, to avoid cancellation, for |x| < prec/2, 49 * 2x 2 50 * (e - 1) 2 2 51 * cosh 2x + cos 2y = 1 + ------------ + cos y - sin y 52 * 2x 53 * 2 e 54 * 55 * 1 2x 2 -2x 2 56 * = --- (e - 1) e + 2 cos y 57 * 2 58 * and 59 * 60 * [ 2x ] 61 * 1 [ 2x e - 1 ] 62 * sinh 2x = --- [ e - 1 + --------- ] 63 * 2 [ 2x ] 64 * [ e ] 65 * 2x 66 * Implementation notes: let t = expm1(2x) = e - 1, then 67 * 68 * 1 [ t*t 2 ] 1 [ t ] 69 * cosh 2x + cos 2y = --- * [ ----- + 4 cos y ]; sinh 2x = --- * [ t + --- ] 70 * 2 [ t+1 ] 2 [ t+1 ] 71 * 72 * Hence, 73 * 74 * 75 * t*t+2t [4(t+1)(cos y)]*(sin y) 76 * ctanh z = --------------------------- + i -------------------------- 77 * t*t+[4(t+1)(cos y)](cos y) t*t+[4(t+1)(cos y)](cos y) 78 * 79 * EXCEPTION (conform to ISO/IEC 9899:1999(E)): 80 * ctanh(0,0)=(0,0) 81 * ctanh(x,inf) = (NaN,NaN) for finite x 82 * ctanh(x,NaN) = (NaN,NaN) for finite x 83 * ctanh(inf,y) = 1+ i*0*sin(2y) for positive-signed finite y 84 * ctanh(inf,inf) = (1, +-0) 85 * ctanh(inf,NaN) = (1, +-0) 86 * ctanh(NaN,0) = (NaN,0) 87 * ctanh(NaN,y) = (NaN,NaN) for non-zero y 88 * ctanh(NaN,NaN) = (NaN,NaN) 89 */ 90 /* INDENT ON */ 91 92 #include "libm.h" /* exp/expm1/fabs/sin/tanh/sincos */ 93 #include "complex_wrapper.h" 94 95 static const double four = 4.0, two = 2.0, one = 1.0, zero = 0.0; 96 97 dcomplex 98 ctanh(dcomplex z) { 99 double t, r, v, u, x, y, S, C; 100 int hx, ix, lx, hy, iy, ly; 101 dcomplex ans; 102 103 x = D_RE(z); 104 y = D_IM(z); 105 hx = HI_WORD(x); 106 lx = LO_WORD(x); 107 ix = hx & 0x7fffffff; 108 hy = HI_WORD(y); 109 ly = LO_WORD(y); 110 iy = hy & 0x7fffffff; 111 x = fabs(x); 112 y = fabs(y); 113 114 if ((iy | ly) == 0) { /* ctanh(x,0) = (x,0) for x = 0 or NaN */ 115 D_RE(ans) = tanh(x); 116 D_IM(ans) = zero; 117 } else if (iy >= 0x7ff00000) { /* y is inf or NaN */ 118 if (ix < 0x7ff00000) /* catanh(finite x,inf/nan) is nan */ 119 D_RE(ans) = D_IM(ans) = y - y; 120 else if (((ix - 0x7ff00000) | lx) == 0) { /* x is inf */ 121 D_RE(ans) = one; 122 D_IM(ans) = zero; 123 } else { 124 D_RE(ans) = x + y; 125 D_IM(ans) = y - y; 126 } 127 } else if (ix >= 0x403c0000) { 128 /* 129 * |x| > 28 = prec/2 (14,28,34,60) 130 * ctanh z ~ 1 + i (sin2y)/(exp(2x)) 131 */ 132 D_RE(ans) = one; 133 if (iy < 0x7fe00000) /* t = sin(2y) */ 134 S = sin(y + y); 135 else { 136 (void) sincos(y, &S, &C); 137 S = (S + S) * C; 138 } 139 if (ix >= 0x7fe00000) { /* |x| > max/2 */ 140 if (ix >= 0x7ff00000) { /* |x| is inf or NaN */ 141 if (((ix - 0x7ff00000) | lx) != 0) 142 D_RE(ans) = D_IM(ans) = x + y; 143 /* x is NaN */ 144 else 145 D_IM(ans) = zero * S; /* x is inf */ 146 } else 147 D_IM(ans) = S * exp(-x); /* underflow */ 148 } else 149 D_IM(ans) = (S + S) * exp(-(x + x)); 150 /* 2 sin 2y / exp(2x) */ 151 } else { 152 /* INDENT OFF */ 153 /* 154 * t*t+2t 155 * ctanh z = --------------------------- + 156 * t*t+[4(t+1)(cos y)](cos y) 157 * 158 * [4(t+1)(cos y)]*(sin y) 159 * i -------------------------- 160 * t*t+[4(t+1)(cos y)](cos y) 161 */ 162 /* INDENT ON */ 163 (void) sincos(y, &S, &C); 164 t = expm1(x + x); 165 r = (four * C) * (t + one); 166 u = t * t; 167 v = one / (u + r * C); 168 D_RE(ans) = (u + two * t) * v; 169 D_IM(ans) = (r * S) * v; 170 } 171 if (hx < 0) 172 D_RE(ans) = -D_RE(ans); 173 if (hy < 0) 174 D_IM(ans) = -D_IM(ans); 175 return (ans); 176 } 177