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GNU C Library master sources branch, master, updated. glibc-2.15-585-gbcc8d66
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- Date: 9 Apr 2012 22:31:46 -0000
- Subject: GNU C Library master sources branch, master, updated. glibc-2.15-585-gbcc8d66
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http://sources.redhat.com/git/gitweb.cgi?p=glibc.git;a=commitdiff;h=bcc8d6617ba029c288fff9680a02b9a3b1caa9c0
commit bcc8d6617ba029c288fff9680a02b9a3b1caa9c0
Author: Joseph Myers <joseph@codesourcery.com>
Date: Mon Apr 9 22:31:35 2012 +0000
Fix ctan, ctanh overflow (bug 11521).
diff --git a/ChangeLog b/ChangeLog
index 109b6a1..3686491 100644
--- a/ChangeLog
+++ b/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]
diff --git a/NEWS b/NEWS
index 2636c22..bb303f8 100644
--- a/NEWS
+++ b/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:
diff --git a/math/libm-test.inc b/math/libm-test.inc
index 0533483..a551b9f 100644
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -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);
}
diff --git a/math/s_ctan.c b/math/s_ctan.c
index c838fad..78117b3 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;
}
}
diff --git a/math/s_ctanf.c b/math/s_ctanf.c
index 5f7f28a..4cba559 100644
--- a/math/s_ctanf.c
+++ b/math/s_ctanf.c
@@ -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);
-
- den = cos2rx + __ieee754_coshf (2.0 * __imag__ x);
+ /* 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). */
+ __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;
}
}
diff --git a/math/s_ctanh.c b/math/s_ctanh.c
index 9cecb8b..201871e 100644
--- a/math/s_ctanh.c
+++ b/math/s_ctanh.c
@@ -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;
}
}
diff --git a/math/s_ctanhf.c b/math/s_ctanhf.c
index fce5aaf..e505155 100644
--- a/math/s_ctanhf.c
+++ b/math/s_ctanhf.c
@@ -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;
}
}
diff --git a/math/s_ctanhl.c b/math/s_ctanhl.c
index d22e13a..e5d6779 100644
--- a/math/s_ctanhl.c
+++ b/math/s_ctanhl.c
@@ -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;
}
}
diff --git a/math/s_ctanl.c b/math/s_ctanl.c
index 112dd72..12d700c 100644
--- a/math/s_ctanl.c
+++ b/math/s_ctanl.c
@@ -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);
-
- den = cos2rx + __ieee754_coshl (2.0 * __imag__ x);
+ /* 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). */
+ __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;
}
}
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index 1c79140..c3a3ce0 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -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
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index dce60cf..46d858f 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -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 + 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
-----------------------------------------------------------------------
Summary of changes:
ChangeLog | 16 +++++++
NEWS | 14 +++---
math/libm-test.inc | 60 +++++++++++++++++++++++++++
math/s_ctan.c | 44 ++++++++++++++-----
math/s_ctanf.c | 44 ++++++++++++++-----
math/s_ctanh.c | 43 ++++++++++++++-----
math/s_ctanhf.c | 43 ++++++++++++++-----
math/s_ctanhl.c | 43 ++++++++++++++-----
math/s_ctanl.c | 45 ++++++++++++++------
sysdeps/i386/fpu/libm-test-ulps | 66 ++++++++++++++++++++++++++----
sysdeps/x86_64/fpu/libm-test-ulps | 82 +++++++++++++++++++++++++++++++-----
11 files changed, 403 insertions(+), 97 deletions(-)
hooks/post-receive
--
GNU C Library master sources