diff options
Diffstat (limited to 'math/s_ctan.c')
| -rw-r--r-- | math/s_ctan.c | 44 |
1 files changed, 32 insertions, 12 deletions
diff --git a/math/s_ctan.c b/math/s_ctan.c index c838fadebb..78117b3103 100644 --- a/math/s_ctan.c +++ b/math/s_ctan.c @@ -1,5 +1,5 @@ /* Complex tangent function for 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__ double __ctan (__complex__ double x) @@ -51,24 +50,45 @@ __ctan (__complex__ double x) } else { - double sin2rx, cos2rx; + double sinrx, cosrx; double den; + const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2); - __sincos (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_cosh (2.0 * __imag__ x); + __sincos (__real__ x, &sinrx, &cosrx); - if (den == 0.0) + if (fabs (__imag__ x) > t) { - __complex__ double ez = __cexp (1.0i * x); - __complex__ double emz = __cexp (-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). */ + double exp_2t = __ieee754_exp (2 * t); - res = (ez - emz) / (ez + emz) * -1.0i; + __imag__ res = __copysign (1.0, __imag__ x); + __real__ res = 4 * sinrx * cosrx; + __imag__ x = fabs (__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_exp (2 * __imag__ x); } else { - __real__ res = sin2rx / den; - __imag__ res = __ieee754_sinh (2.0 * __imag__ x) / den; + double sinhix = __ieee754_sinh (__imag__ x); + double coshix = __ieee754_cosh (__imag__ x); + + den = cosrx * cosrx + sinhix * sinhix; + __real__ res = sinrx * cosrx / den; + __imag__ res = sinhix * coshix / den; } } |