mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-22 13:00:06 +00:00
Fix ctan, ctanh overflow (bug 11521).
This commit is contained in:
Joseph Myers
parent
8a1fbaaf75
commit
bcc8d6617b
16
ChangeLog
16
ChangeLog
@ -1,3 +1,19 @@
|
||||
2012-04-09 Joseph Myers <joseph@codesourcery.com>
|
||||
|
||||
[BZ #11521]
|
||||
* math/s_ctan.c: Include <float.h>.
|
||||
(__ctan): Avoid internal overflow or cancellation in calculating
|
||||
denominator.
|
||||
* math/s_ctanf.c: Likewise.
|
||||
* math/s_ctanl.c: Likewise.
|
||||
* math/s_ctanh.c: Likewise.
|
||||
* math/s_ctanhf.c: Likewise.
|
||||
* math/s_ctanhl.c: Likewise.
|
||||
* math/libm-test.inc (ctan_test): Add more tests.
|
||||
(ctanh_test): Likewise.
|
||||
* sysdeps/i386/fpu/libm-test-ulps: Update.
|
||||
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
|
||||
|
||||
2012-04-09 Andreas Jaeger <aj@suse.de>
|
||||
|
||||
[BZ #6894]
|
||||
|
||||
14
NEWS
14
NEWS
@ -14,13 +14,13 @@ Version 2.16
|
||||
4596, 4822, 5077, 5461, 5805, 5993, 6471, 6486, 6578, 6649, 6730, 6770,
|
||||
6884, 6890, 6894, 6895, 6907, 6911, 9739, 9902, 10110, 10135, 10140,
|
||||
10153, 10210, 10254, 10346, 10545, 10716, 11174, 11322, 11365, 11451,
|
||||
11494, 12047, 12340, 13058, 13525, 13526, 13527, 13528, 13529, 13530,
|
||||
13531, 13532, 13533, 13547, 13551, 13552, 13553, 13555, 13559, 13566,
|
||||
13583, 13592, 13618, 13637, 13656, 13658, 13673, 13691, 13695, 13704,
|
||||
13705, 13706, 13726, 13738, 13760, 13761, 13786, 13792, 13806, 13824,
|
||||
13840, 13841, 13844, 13846, 13851, 13852, 13854, 13871, 13873, 13879,
|
||||
13883, 13892, 13895, 13908, 13910, 13911, 13912, 13913, 13915, 13916,
|
||||
13917, 13918, 13919, 13920, 13921, 13926, 13928, 13938, 13963
|
||||
11494, 11521, 12047, 12340, 13058, 13525, 13526, 13527, 13528, 13529,
|
||||
13530, 13531, 13532, 13533, 13547, 13551, 13552, 13553, 13555, 13559,
|
||||
13566, 13583, 13592, 13618, 13637, 13656, 13658, 13673, 13691, 13695,
|
||||
13704, 13705, 13706, 13726, 13738, 13760, 13761, 13786, 13792, 13806,
|
||||
13824, 13840, 13841, 13844, 13846, 13851, 13852, 13854, 13871, 13873,
|
||||
13879, 13883, 13892, 13895, 13908, 13910, 13911, 13912, 13913, 13915,
|
||||
13916, 13917, 13918, 13919, 13920, 13921, 13926, 13928, 13938, 13963
|
||||
|
||||
* ISO C11 support:
|
||||
|
||||
|
||||
@ -2840,6 +2840,36 @@ ctan_test (void)
|
||||
TEST_c_c (ctan, 0.75L, 1.25L, 0.160807785916206426725166058173438663L, 0.975363285031235646193581759755216379L);
|
||||
TEST_c_c (ctan, -2, -3, 0.376402564150424829275122113032269084e-2L, -1.00323862735360980144635859782192726L);
|
||||
|
||||
TEST_c_c (ctan, 1, 45, 1.490158918874345552942703234806348520895e-39L, 1.000000000000000000000000000000000000001L);
|
||||
TEST_c_c (ctan, 1, 47, 2.729321264492904590777293425576722354636e-41L, 1.0);
|
||||
|
||||
#ifndef TEST_FLOAT
|
||||
TEST_c_c (ctan, 1, 355, 8.140551093483276762350406321792653551513e-309L, 1.0);
|
||||
TEST_c_c (ctan, 1, 365, 1.677892637497921890115075995898773550884e-317L, 1.0);
|
||||
#endif
|
||||
|
||||
#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
|
||||
TEST_c_c (ctan, 1, 5680, 4.725214596136812019616700920476949798307e-4934L, 1.0);
|
||||
TEST_c_c (ctan, 1, 5690, 9.739393181626937151720816611272607059057e-4943L, 1.0);
|
||||
#endif
|
||||
|
||||
TEST_c_c (ctan, 0x3.243f6cp-1, 0, -2.287733242885645987394874673945769518150e7L, 0.0);
|
||||
|
||||
TEST_c_c (ctan, 0x1p127, 1, 0.2446359391192790896381501310437708987204L, 0.9101334047676183761532873794426475906201L);
|
||||
|
||||
#ifndef TEST_FLOAT
|
||||
TEST_c_c (ctan, 0x1p1023, 1, -0.2254627924997545057926782581695274244229L, 0.8786063118883068695462540226219865087189L);
|
||||
#endif
|
||||
|
||||
#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
|
||||
TEST_c_c (ctan, 0x1p16383L, 1, 0.1608598776370396607204448234354670036772L, 0.8133818522051542536316746743877629761488L);
|
||||
#endif
|
||||
|
||||
TEST_c_c (ctan, 50000, 50000, plus_zero, 1.0);
|
||||
TEST_c_c (ctan, 50000, -50000, plus_zero, -1.0);
|
||||
TEST_c_c (ctan, -50000, 50000, minus_zero, 1.0);
|
||||
TEST_c_c (ctan, -50000, -50000, minus_zero, -1.0);
|
||||
|
||||
END (ctan, complex);
|
||||
}
|
||||
|
||||
@ -2899,6 +2929,36 @@ ctanh_test (void)
|
||||
TEST_c_c (ctanh, 0.75L, 1.25L, 1.37260757053378320258048606571226857L, 0.385795952609750664177596760720790220L);
|
||||
TEST_c_c (ctanh, -2, -3, -0.965385879022133124278480269394560686L, 0.988437503832249372031403430350121098e-2L);
|
||||
|
||||
TEST_c_c (ctanh, 45, 1, 1.000000000000000000000000000000000000001L, 1.490158918874345552942703234806348520895e-39L);
|
||||
TEST_c_c (ctanh, 47, 1, 1.0, 2.729321264492904590777293425576722354636e-41L);
|
||||
|
||||
#ifndef TEST_FLOAT
|
||||
TEST_c_c (ctanh, 355, 1, 1.0, 8.140551093483276762350406321792653551513e-309L);
|
||||
TEST_c_c (ctanh, 365, 1, 1.0, 1.677892637497921890115075995898773550884e-317L);
|
||||
#endif
|
||||
|
||||
#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
|
||||
TEST_c_c (ctanh, 5680, 1, 1.0, 4.725214596136812019616700920476949798307e-4934L);
|
||||
TEST_c_c (ctanh, 5690, 1, 1.0, 9.739393181626937151720816611272607059057e-4943L);
|
||||
#endif
|
||||
|
||||
TEST_c_c (ctanh, 0, 0x3.243f6cp-1, 0.0, -2.287733242885645987394874673945769518150e7L);
|
||||
|
||||
TEST_c_c (ctanh, 1, 0x1p127, 0.9101334047676183761532873794426475906201L, 0.2446359391192790896381501310437708987204L);
|
||||
|
||||
#ifndef TEST_FLOAT
|
||||
TEST_c_c (ctanh, 1, 0x1p1023, 0.8786063118883068695462540226219865087189L, -0.2254627924997545057926782581695274244229L);
|
||||
#endif
|
||||
|
||||
#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
|
||||
TEST_c_c (ctanh, 1, 0x1p16383L, 0.8133818522051542536316746743877629761488L, 0.1608598776370396607204448234354670036772L);
|
||||
#endif
|
||||
|
||||
TEST_c_c (ctanh, 50000, 50000, 1.0, plus_zero);
|
||||
TEST_c_c (ctanh, 50000, -50000, 1.0, minus_zero);
|
||||
TEST_c_c (ctanh, -50000, 50000, -1.0, plus_zero);
|
||||
TEST_c_c (ctanh, -50000, -50000, -1.0, minus_zero);
|
||||
|
||||
END (ctanh, complex);
|
||||
}
|
||||
|
||||
|
||||
@ -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;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
@ -1,5 +1,5 @@
|
||||
/* Complex tangent function for float.
|
||||
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.
|
||||
|
||||
@ -21,7 +21,7 @@
|
||||
#include <fenv.h>
|
||||
#include <math.h>
|
||||
#include <math_private.h>
|
||||
|
||||
#include <float.h>
|
||||
|
||||
__complex__ float
|
||||
__ctanf (__complex__ float x)
|
||||
@ -50,25 +50,45 @@ __ctanf (__complex__ float x)
|
||||
}
|
||||
else
|
||||
{
|
||||
float sin2rx, cos2rx;
|
||||
float sinrx, cosrx;
|
||||
float den;
|
||||
const int t = (int) ((FLT_MAX_EXP - 1) * M_LN2 / 2);
|
||||
|
||||
__sincosf (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_coshf (2.0 * __imag__ x);
|
||||
__sincosf (__real__ x, &sinrx, &cosrx);
|
||||
|
||||
|
||||
if (den == 0.0)
|
||||
if (fabsf (__imag__ x) > t)
|
||||
{
|
||||
__complex__ float ez = __cexpf (1.0i * x);
|
||||
__complex__ float emz = __cexpf (-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). */
|
||||
float exp_2t = __ieee754_expf (2 * t);
|
||||
|
||||
res = (ez - emz) / (ez + emz) * -1.0i;
|
||||
__imag__ res = __copysignf (1.0, __imag__ x);
|
||||
__real__ res = 4 * sinrx * cosrx;
|
||||
__imag__ x = fabsf (__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_expf (2 * __imag__ x);
|
||||
}
|
||||
else
|
||||
{
|
||||
__real__ res = sin2rx / den;
|
||||
__imag__ res = __ieee754_sinhf (2.0 * __imag__ x) / den;
|
||||
float sinhix = __ieee754_sinhf (__imag__ x);
|
||||
float coshix = __ieee754_coshf (__imag__ x);
|
||||
|
||||
den = cosrx * cosrx + sinhix * sinhix;
|
||||
__real__ res = sinrx * cosrx / den;
|
||||
__imag__ res = sinhix * coshix / den;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
@ -1,5 +1,5 @@
|
||||
/* Complex hyperbole tangent 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.
|
||||
|
||||
@ -21,7 +21,7 @@
|
||||
#include <fenv.h>
|
||||
#include <math.h>
|
||||
#include <math_private.h>
|
||||
|
||||
#include <float.h>
|
||||
|
||||
__complex__ double
|
||||
__ctanh (__complex__ double x)
|
||||
@ -50,24 +50,45 @@ __ctanh (__complex__ double x)
|
||||
}
|
||||
else
|
||||
{
|
||||
double sin2ix, cos2ix;
|
||||
double sinix, cosix;
|
||||
double den;
|
||||
const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2);
|
||||
|
||||
__sincos (2.0 * __imag__ x, &sin2ix, &cos2ix);
|
||||
/* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
|
||||
= (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */
|
||||
|
||||
den = (__ieee754_cosh (2.0 * __real__ x) + cos2ix);
|
||||
__sincos (__imag__ x, &sinix, &cosix);
|
||||
|
||||
if (den == 0.0)
|
||||
if (fabs (__real__ x) > t)
|
||||
{
|
||||
__complex__ double ez = __cexp (x);
|
||||
__complex__ double emz = __cexp (-x);
|
||||
/* Avoid intermediate overflow when the imaginary part of
|
||||
the result may be subnormal. Ignoring negligible terms,
|
||||
the real part is +/- 1, the imaginary part is
|
||||
sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */
|
||||
double exp_2t = __ieee754_exp (2 * t);
|
||||
|
||||
res = (ez - emz) / (ez + emz);
|
||||
__real__ res = __copysign (1.0, __real__ x);
|
||||
__imag__ res = 4 * sinix * cosix;
|
||||
__real__ x = fabs (__real__ x);
|
||||
__real__ x -= t;
|
||||
__imag__ res /= exp_2t;
|
||||
if (__real__ x > t)
|
||||
{
|
||||
/* Underflow (original real part of x has absolute value
|
||||
> 2t). */
|
||||
__imag__ res /= exp_2t;
|
||||
}
|
||||
else
|
||||
__imag__ res /= __ieee754_exp (2 * __real__ x);
|
||||
}
|
||||
else
|
||||
{
|
||||
__real__ res = __ieee754_sinh (2.0 * __real__ x) / den;
|
||||
__imag__ res = sin2ix / den;
|
||||
double sinhrx = __ieee754_sinh (__real__ x);
|
||||
double coshrx = __ieee754_cosh (__real__ x);
|
||||
|
||||
den = sinhrx * sinhrx + cosix * cosix;
|
||||
__real__ res = sinhrx * coshrx / den;
|
||||
__imag__ res = sinix * cosix / den;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
@ -1,5 +1,5 @@
|
||||
/* Complex hyperbole tangent for float.
|
||||
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.
|
||||
|
||||
@ -21,7 +21,7 @@
|
||||
#include <fenv.h>
|
||||
#include <math.h>
|
||||
#include <math_private.h>
|
||||
|
||||
#include <float.h>
|
||||
|
||||
__complex__ float
|
||||
__ctanhf (__complex__ float x)
|
||||
@ -50,24 +50,45 @@ __ctanhf (__complex__ float x)
|
||||
}
|
||||
else
|
||||
{
|
||||
float sin2ix, cos2ix;
|
||||
float sinix, cosix;
|
||||
float den;
|
||||
const int t = (int) ((FLT_MAX_EXP - 1) * M_LN2 / 2);
|
||||
|
||||
__sincosf (2.0 * __imag__ x, &sin2ix, &cos2ix);
|
||||
/* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
|
||||
= (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */
|
||||
|
||||
den = (__ieee754_coshf (2.0 * __real__ x) + cos2ix);
|
||||
__sincosf (__imag__ x, &sinix, &cosix);
|
||||
|
||||
if (den == 0.0f)
|
||||
if (fabsf (__real__ x) > t)
|
||||
{
|
||||
__complex__ float ez = __cexpf (x);
|
||||
__complex__ float emz = __cexpf (-x);
|
||||
/* Avoid intermediate overflow when the imaginary part of
|
||||
the result may be subnormal. Ignoring negligible terms,
|
||||
the real part is +/- 1, the imaginary part is
|
||||
sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */
|
||||
float exp_2t = __ieee754_expf (2 * t);
|
||||
|
||||
res = (ez - emz) / (ez + emz);
|
||||
__real__ res = __copysignf (1.0, __real__ x);
|
||||
__imag__ res = 4 * sinix * cosix;
|
||||
__real__ x = fabsf (__real__ x);
|
||||
__real__ x -= t;
|
||||
__imag__ res /= exp_2t;
|
||||
if (__real__ x > t)
|
||||
{
|
||||
/* Underflow (original real part of x has absolute value
|
||||
> 2t). */
|
||||
__imag__ res /= exp_2t;
|
||||
}
|
||||
else
|
||||
__imag__ res /= __ieee754_expf (2 * __real__ x);
|
||||
}
|
||||
else
|
||||
{
|
||||
__real__ res = __ieee754_sinhf (2.0 * __real__ x) / den;
|
||||
__imag__ res = sin2ix / den;
|
||||
float sinhrx = __ieee754_sinhf (__real__ x);
|
||||
float coshrx = __ieee754_coshf (__real__ x);
|
||||
|
||||
den = sinhrx * sinhrx + cosix * cosix;
|
||||
__real__ res = sinhrx * coshrx / den;
|
||||
__imag__ res = sinix * cosix / den;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
@ -1,5 +1,5 @@
|
||||
/* Complex hyperbole tangent 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.
|
||||
|
||||
@ -21,7 +21,7 @@
|
||||
#include <fenv.h>
|
||||
#include <math.h>
|
||||
#include <math_private.h>
|
||||
|
||||
#include <float.h>
|
||||
|
||||
__complex__ long double
|
||||
__ctanhl (__complex__ long double x)
|
||||
@ -50,24 +50,45 @@ __ctanhl (__complex__ long double x)
|
||||
}
|
||||
else
|
||||
{
|
||||
long double sin2ix, cos2ix;
|
||||
long double sinix, cosix;
|
||||
long double den;
|
||||
const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2);
|
||||
|
||||
__sincosl (2.0 * __imag__ x, &sin2ix, &cos2ix);
|
||||
/* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
|
||||
= (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */
|
||||
|
||||
den = (__ieee754_coshl (2.0 * __real__ x) + cos2ix);
|
||||
__sincosl (__imag__ x, &sinix, &cosix);
|
||||
|
||||
if (den == 0.0L)
|
||||
if (fabsl (__real__ x) > t)
|
||||
{
|
||||
__complex__ long double ez = __cexpl (x);
|
||||
__complex__ long double emz = __cexpl (-x);
|
||||
/* Avoid intermediate overflow when the imaginary part of
|
||||
the result may be subnormal. Ignoring negligible terms,
|
||||
the real part is +/- 1, the imaginary part is
|
||||
sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */
|
||||
long double exp_2t = __ieee754_expl (2 * t);
|
||||
|
||||
res = (ez - emz) / (ez + emz);
|
||||
__real__ res = __copysignl (1.0, __real__ x);
|
||||
__imag__ res = 4 * sinix * cosix;
|
||||
__real__ x = fabsl (__real__ x);
|
||||
__real__ x -= t;
|
||||
__imag__ res /= exp_2t;
|
||||
if (__real__ x > t)
|
||||
{
|
||||
/* Underflow (original real part of x has absolute value
|
||||
> 2t). */
|
||||
__imag__ res /= exp_2t;
|
||||
}
|
||||
else
|
||||
__imag__ res /= __ieee754_expl (2 * __real__ x);
|
||||
}
|
||||
else
|
||||
{
|
||||
__real__ res = __ieee754_sinhl (2.0 * __real__ x) / den;
|
||||
__imag__ res = sin2ix / den;
|
||||
long double sinhrx = __ieee754_sinhl (__real__ x);
|
||||
long double coshrx = __ieee754_coshl (__real__ x);
|
||||
|
||||
den = sinhrx * sinhrx + cosix * cosix;
|
||||
__real__ res = sinhrx * coshrx / den;
|
||||
__imag__ res = sinix * cosix / den;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
@ -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;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
@ -1009,9 +1009,33 @@ idouble: 1
|
||||
ifloat: 1
|
||||
ildouble: 3
|
||||
ldouble: 3
|
||||
Test "Real part of: ctan (0x1p1023 + 1 i) == -0.2254627924997545057926782581695274244229 + 0.8786063118883068695462540226219865087189 i":
|
||||
double: 1
|
||||
idouble: 1
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
Test "Imaginary part of: ctan (0x1p1023 + 1 i) == -0.2254627924997545057926782581695274244229 + 0.8786063118883068695462540226219865087189 i":
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
Test "Real part of: ctan (0x1p127 + 1 i) == 0.2446359391192790896381501310437708987204 + 0.9101334047676183761532873794426475906201 i":
|
||||
float: 1
|
||||
ifloat: 1
|
||||
Test "Real part of: ctan (0x3.243f6cp-1 + 0 i) == -2.287733242885645987394874673945769518150e7 + 0.0 i":
|
||||
float: 1
|
||||
ifloat: 1
|
||||
Test "Real part of: ctan (1 + 45 i) == 1.490158918874345552942703234806348520895e-39 + 1.000000000000000000000000000000000000001 i":
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
Test "Real part of: ctan (1 + 47 i) == 2.729321264492904590777293425576722354636e-41 + 1.0 i":
|
||||
double: 1
|
||||
idouble: 1
|
||||
ildouble: 2
|
||||
ldouble: 2
|
||||
|
||||
# ctanh
|
||||
Test "Real part of: ctanh (-2 - 3 i) == -0.965385879022133124278480269394560686 + 0.988437503832249372031403430350121098e-2 i":
|
||||
float: 1
|
||||
ifloat: 1
|
||||
ildouble: 3
|
||||
ldouble: 3
|
||||
Test "Imaginary part of: ctanh (-2 - 3 i) == -0.965385879022133124278480269394560686 + 0.988437503832249372031403430350121098e-2 i":
|
||||
@ -1019,9 +1043,14 @@ float: 1
|
||||
ifloat: 1
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
Test "Imaginary part of: ctanh (0 + 0x3.243f6cp-1 i) == 0.0 - 2.287733242885645987394874673945769518150e7 i":
|
||||
float: 1
|
||||
ifloat: 1
|
||||
Test "Imaginary part of: ctanh (0 + pi/4 i) == 0.0 + 1.0 i":
|
||||
float: 1
|
||||
ifloat: 1
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
Test "Real part of: ctanh (0.75 + 1.25 i) == 1.37260757053378320258048606571226857 + 0.385795952609750664177596760720790220 i":
|
||||
double: 1
|
||||
float: 1
|
||||
@ -1034,6 +1063,25 @@ idouble: 1
|
||||
ifloat: 1
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
Test "Real part of: ctanh (1 + 0x1p1023 i) == 0.8786063118883068695462540226219865087189 - 0.2254627924997545057926782581695274244229 i":
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
Test "Imaginary part of: ctanh (1 + 0x1p1023 i) == 0.8786063118883068695462540226219865087189 - 0.2254627924997545057926782581695274244229 i":
|
||||
double: 1
|
||||
idouble: 1
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
Test "Imaginary part of: ctanh (1 + 0x1p127 i) == 0.9101334047676183761532873794426475906201 + 0.2446359391192790896381501310437708987204 i":
|
||||
float: 1
|
||||
ifloat: 1
|
||||
Test "Imaginary part of: ctanh (45 + 1 i) == 1.000000000000000000000000000000000000001 + 1.490158918874345552942703234806348520895e-39 i":
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
Test "Imaginary part of: ctanh (47 + 1 i) == 1.0 + 2.729321264492904590777293425576722354636e-41 i":
|
||||
double: 1
|
||||
idouble: 1
|
||||
ildouble: 2
|
||||
ldouble: 2
|
||||
|
||||
# erf
|
||||
Test "erf (1.25) == 0.922900128256458230136523481197281140":
|
||||
@ -2342,33 +2390,35 @@ ldouble: 1
|
||||
|
||||
Function: Real part of "ctan":
|
||||
double: 1
|
||||
float: 1
|
||||
idouble: 1
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
ifloat: 1
|
||||
ildouble: 2
|
||||
ldouble: 2
|
||||
|
||||
Function: Imaginary part of "ctan":
|
||||
double: 1
|
||||
float: 1
|
||||
idouble: 1
|
||||
ifloat: 1
|
||||
ildouble: 3
|
||||
ldouble: 3
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: Real part of "ctanh":
|
||||
double: 1
|
||||
float: 1
|
||||
idouble: 1
|
||||
ifloat: 1
|
||||
ildouble: 3
|
||||
ldouble: 3
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: Imaginary part of "ctanh":
|
||||
double: 1
|
||||
float: 1
|
||||
idouble: 1
|
||||
ifloat: 1
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
ildouble: 2
|
||||
ldouble: 2
|
||||
|
||||
Function: "erf":
|
||||
double: 1
|
||||
|
||||
@ -1011,11 +1011,15 @@ ldouble: 1
|
||||
# ctan
|
||||
Test "Real part of: ctan (-2 - 3 i) == 0.376402564150424829275122113032269084e-2 - 1.00323862735360980144635859782192726 i":
|
||||
double: 1
|
||||
float: 1
|
||||
idouble: 1
|
||||
ifloat: 1
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
Test "Imaginary part of: ctan (-2 - 3 i) == 0.376402564150424829275122113032269084e-2 - 1.00323862735360980144635859782192726 i":
|
||||
double: 1
|
||||
float: 1
|
||||
idouble: 1
|
||||
ifloat: 1
|
||||
ildouble: 2
|
||||
ldouble: 2
|
||||
@ -1029,6 +1033,26 @@ idouble: 1
|
||||
ifloat: 1
|
||||
ildouble: 3
|
||||
ldouble: 3
|
||||
Test "Real part of: ctan (0x1p1023 + 1 i) == -0.2254627924997545057926782581695274244229 + 0.8786063118883068695462540226219865087189 i":
|
||||
double: 1
|
||||
idouble: 1
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
Test "Imaginary part of: ctan (0x1p1023 + 1 i) == -0.2254627924997545057926782581695274244229 + 0.8786063118883068695462540226219865087189 i":
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
Test "Imaginary part of: ctan (0x1p127 + 1 i) == 0.2446359391192790896381501310437708987204 + 0.9101334047676183761532873794426475906201 i":
|
||||
double: 1
|
||||
idouble: 1
|
||||
Test "Real part of: ctan (0x3.243f6cp-1 + 0 i) == -2.287733242885645987394874673945769518150e7 + 0.0 i":
|
||||
float: 1
|
||||
ifloat: 1
|
||||
Test "Real part of: ctan (1 + 45 i) == 1.490158918874345552942703234806348520895e-39 + 1.000000000000000000000000000000000000001 i":
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
Test "Real part of: ctan (1 + 47 i) == 2.729321264492904590777293425576722354636e-41 + 1.0 i":
|
||||
ildouble: 2
|
||||
ldouble: 2
|
||||
|
||||
# ctanh
|
||||
Test "Real part of: ctanh (-2 - 3 i) == -0.965385879022133124278480269394560686 + 0.988437503832249372031403430350121098e-2 i":
|
||||
@ -1039,19 +1063,51 @@ ifloat: 2
|
||||
ildouble: 3
|
||||
ldouble: 3
|
||||
Test "Imaginary part of: ctanh (-2 - 3 i) == -0.965385879022133124278480269394560686 + 0.988437503832249372031403430350121098e-2 i":
|
||||
double: 1
|
||||
float: 1
|
||||
idouble: 1
|
||||
ifloat: 1
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
Test "Imaginary part of: ctanh (0 + pi/4 i) == 0.0 + 1.0 i":
|
||||
Test "Imaginary part of: ctanh (0 + 0x3.243f6cp-1 i) == 0.0 - 2.287733242885645987394874673945769518150e7 i":
|
||||
float: 1
|
||||
ifloat: 1
|
||||
Test "Imaginary part of: ctanh (0 + pi/4 i) == 0.0 + 1.0 i":
|
||||
double: 1
|
||||
float: 1
|
||||
idouble: 1
|
||||
ifloat: 1
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
Test "Real part of: ctanh (0.75 + 1.25 i) == 1.37260757053378320258048606571226857 + 0.385795952609750664177596760720790220 i":
|
||||
double: 1
|
||||
float: 1
|
||||
idouble: 1
|
||||
ifloat: 1
|
||||
Test "Imaginary part of: ctanh (0.75 + 1.25 i) == 1.37260757053378320258048606571226857 + 0.385795952609750664177596760720790220 i":
|
||||
double: 1
|
||||
float: 2
|
||||
idouble: 1
|
||||
ifloat: 2
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
Test "Real part of: ctanh (1 + 0x1p1023 i) == 0.8786063118883068695462540226219865087189 - 0.2254627924997545057926782581695274244229 i":
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
Test "Imaginary part of: ctanh (1 + 0x1p1023 i) == 0.8786063118883068695462540226219865087189 - 0.2254627924997545057926782581695274244229 i":
|
||||
double: 1
|
||||
idouble: 1
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
Test "Real part of: ctanh (1 + 0x1p127 i) == 0.9101334047676183761532873794426475906201 + 0.2446359391192790896381501310437708987204 i":
|
||||
double: 1
|
||||
idouble: 1
|
||||
Test "Imaginary part of: ctanh (45 + 1 i) == 1.000000000000000000000000000000000000001 + 1.490158918874345552942703234806348520895e-39 i":
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
Test "Imaginary part of: ctanh (47 + 1 i) == 1.0 + 2.729321264492904590777293425576722354636e-41 i":
|
||||
ildouble: 2
|
||||
ldouble: 2
|
||||
|
||||
# erf
|
||||
Test "erf (1.25) == 0.922900128256458230136523481197281140":
|
||||
@ -2300,34 +2356,36 @@ ldouble: 1
|
||||
|
||||
Function: Real part of "ctan":
|
||||
double: 1
|
||||
float: 1
|
||||
idouble: 1
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
ifloat: 1
|
||||
ildouble: 2
|
||||
ldouble: 2
|
||||
|
||||
Function: Imaginary part of "ctan":
|
||||
double: 1
|
||||
float: 1
|
||||
idouble: 1
|
||||
ifloat: 1
|
||||
ildouble: 3
|
||||
ldouble: 3
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: Real part of "ctanh":
|
||||
double: 1
|
||||
float: 2
|
||||
idouble: 1
|
||||
ifloat: 2
|
||||
ildouble: 3
|
||||
ldouble: 3
|
||||
|
||||
Function: Imaginary part of "ctanh":
|
||||
double: 1
|
||||
float: 1
|
||||
idouble: 1
|
||||
ifloat: 1
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: Imaginary part of "ctanh":
|
||||
double: 1
|
||||
float: 2
|
||||
idouble: 1
|
||||
ifloat: 2
|
||||
ildouble: 2
|
||||
ldouble: 2
|
||||
|
||||
Function: "erf":
|
||||
double: 1
|
||||
idouble: 1
|
||||
|
||||
Loading…
Reference in New Issue
Block a user