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Fix ctan, ctanh overflow (bug 11521).

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This commit is contained in:
Joseph Myers
2012-04-09 22:31:35 +00:00
parent 8a1fbaaf75
commit bcc8d6617b
11 changed files with 404 additions and 98 deletions
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45
math/s_ctanl.c
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@ -1,5 +1,5 @@
/* Complex tangent function for long double.
Copyright (C) 1997, 2005, 2011 Free Software Foundation, Inc.
Copyright (C) 1997-2012 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
@ -20,9 +20,8 @@
#include <complex.h>
#include <fenv.h>
#include <math.h>
#include <math_private.h>
#include <float.h>
__complex__ long double
__ctanl (__complex__ long double x)
@ -51,25 +50,45 @@ __ctanl (__complex__ long double x)
}
else
{
long double sin2rx, cos2rx;
long double sinrx, cosrx;
long double den;
const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2);
__sincosl (2.0 * __real__ x, &sin2rx, &cos2rx);
/* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
= (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
den = cos2rx + __ieee754_coshl (2.0 * __imag__ x);
__sincosl (__real__ x, &sinrx, &cosrx);
if (den == 0.0)
if (fabsl (__imag__ x) > t)
{
__complex__ long double ez = __cexpl (1.0i * x);
__complex__ long double emz = __cexpl (-1.0i * x);
/* Avoid intermediate overflow when the real part of the
result may be subnormal. Ignoring negligible terms, the
imaginary part is +/- 1, the real part is
sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */
long double exp_2t = __ieee754_expl (2 * t);
res = (ez - emz) / (ez + emz) * -1.0i;
__imag__ res = __copysignl (1.0, __imag__ x);
__real__ res = 4 * sinrx * cosrx;
__imag__ x = fabsl (__imag__ x);
__imag__ x -= t;
__real__ res /= exp_2t;
if (__imag__ x > t)
{
/* Underflow (original imaginary part of x has absolute
value > 2t). */
__real__ res /= exp_2t;
}
else
__real__ res /= __ieee754_expl (2 * __imag__ x);
}
else
{
__real__ res = sin2rx / den;
__imag__ res = __ieee754_sinhl (2.0 * __imag__ x) / den;
long double sinhix = __ieee754_sinhl (__imag__ x);
long double coshix = __ieee754_coshl (__imag__ x);
den = cosrx * cosrx + sinhix * sinhix;
__real__ res = sinrx * cosrx / den;
__imag__ res = sinhix * coshix / den;
}
}