/* * CDDL HEADER START * * The contents of this file are subject to the terms of the * Common Development and Distribution License (the "License"). * You may not use this file except in compliance with the License. * * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE * or http://www.opensolaris.org/os/licensing. * See the License for the specific language governing permissions * and limitations under the License. * * When distributing Covered Code, include this CDDL HEADER in each * file and include the License file at usr/src/OPENSOLARIS.LICENSE. * If applicable, add the following below this CDDL HEADER, with the * fields enclosed by brackets "[]" replaced with your own identifying * information: Portions Copyright [yyyy] [name of copyright owner] * * CDDL HEADER END */ /* * Copyright 2011 Nexenta Systems, Inc. All rights reserved. */ /* * Copyright 2006 Sun Microsystems, Inc. All rights reserved. * Use is subject to license terms. */ #pragma weak __ctanh = ctanh /* INDENT OFF */ /* * dcomplex ctanh(dcomplex z); * * tanh x + i tan y sinh 2x + i sin 2y * ctanh z = --------------------- = -------------------- * 1 + i tanh(x)tan(y) cosh 2x + cos 2y * * For |x| >= prec/2 (14,28,34,60 for single, double, double extended, quad), * we use * * 1 2x 2 sin 2y * cosh 2x = sinh 2x = --- e and hence ctanh z = 1 + i -----------; * 2 2x * e * * otherwise, to avoid cancellation, for |x| < prec/2, * 2x 2 * (e - 1) 2 2 * cosh 2x + cos 2y = 1 + ------------ + cos y - sin y * 2x * 2 e * * 1 2x 2 -2x 2 * = --- (e - 1) e + 2 cos y * 2 * and * * [ 2x ] * 1 [ 2x e - 1 ] * sinh 2x = --- [ e - 1 + --------- ] * 2 [ 2x ] * [ e ] * 2x * Implementation notes: let t = expm1(2x) = e - 1, then * * 1 [ t*t 2 ] 1 [ t ] * cosh 2x + cos 2y = --- * [ ----- + 4 cos y ]; sinh 2x = --- * [ t + --- ] * 2 [ t+1 ] 2 [ t+1 ] * * Hence, * * * t*t+2t [4(t+1)(cos y)]*(sin y) * ctanh z = --------------------------- + i -------------------------- * t*t+[4(t+1)(cos y)](cos y) t*t+[4(t+1)(cos y)](cos y) * * EXCEPTION (conform to ISO/IEC 9899:1999(E)): * ctanh(0,0)=(0,0) * ctanh(x,inf) = (NaN,NaN) for finite x * ctanh(x,NaN) = (NaN,NaN) for finite x * ctanh(inf,y) = 1+ i*0*sin(2y) for positive-signed finite y * ctanh(inf,inf) = (1, +-0) * ctanh(inf,NaN) = (1, +-0) * ctanh(NaN,0) = (NaN,0) * ctanh(NaN,y) = (NaN,NaN) for non-zero y * ctanh(NaN,NaN) = (NaN,NaN) */ /* INDENT ON */ #include "libm.h" /* exp/expm1/fabs/sin/tanh/sincos */ #include "complex_wrapper.h" static const double four = 4.0, two = 2.0, one = 1.0, zero = 0.0; dcomplex ctanh(dcomplex z) { double t, r, v, u, x, y, S, C; int hx, ix, lx, hy, iy, ly; dcomplex ans; x = D_RE(z); y = D_IM(z); hx = HI_WORD(x); lx = LO_WORD(x); ix = hx & 0x7fffffff; hy = HI_WORD(y); ly = LO_WORD(y); iy = hy & 0x7fffffff; x = fabs(x); y = fabs(y); if ((iy | ly) == 0) { /* ctanh(x,0) = (x,0) for x = 0 or NaN */ D_RE(ans) = tanh(x); D_IM(ans) = zero; } else if (iy >= 0x7ff00000) { /* y is inf or NaN */ if (ix < 0x7ff00000) /* catanh(finite x,inf/nan) is nan */ D_RE(ans) = D_IM(ans) = y - y; else if (((ix - 0x7ff00000) | lx) == 0) { /* x is inf */ D_RE(ans) = one; D_IM(ans) = zero; } else { D_RE(ans) = x + y; D_IM(ans) = y - y; } } else if (ix >= 0x403c0000) { /* * |x| > 28 = prec/2 (14,28,34,60) * ctanh z ~ 1 + i (sin2y)/(exp(2x)) */ D_RE(ans) = one; if (iy < 0x7fe00000) /* t = sin(2y) */ S = sin(y + y); else { (void) sincos(y, &S, &C); S = (S + S) * C; } if (ix >= 0x7fe00000) { /* |x| > max/2 */ if (ix >= 0x7ff00000) { /* |x| is inf or NaN */ if (((ix - 0x7ff00000) | lx) != 0) D_RE(ans) = D_IM(ans) = x + y; /* x is NaN */ else D_IM(ans) = zero * S; /* x is inf */ } else D_IM(ans) = S * exp(-x); /* underflow */ } else D_IM(ans) = (S + S) * exp(-(x + x)); /* 2 sin 2y / exp(2x) */ } else { /* INDENT OFF */ /* * t*t+2t * ctanh z = --------------------------- + * t*t+[4(t+1)(cos y)](cos y) * * [4(t+1)(cos y)]*(sin y) * i -------------------------- * t*t+[4(t+1)(cos y)](cos y) */ /* INDENT ON */ (void) sincos(y, &S, &C); t = expm1(x + x); r = (four * C) * (t + one); u = t * t; v = one / (u + r * C); D_RE(ans) = (u + two * t) * v; D_IM(ans) = (r * S) * v; } if (hx < 0) D_RE(ans) = -D_RE(ans); if (hy < 0) D_IM(ans) = -D_IM(ans); return (ans); }
