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-rw-r--r--math/libm-test.inc60
-rw-r--r--math/s_ctan.c44
-rw-r--r--math/s_ctanf.c44
-rw-r--r--math/s_ctanh.c43
-rw-r--r--math/s_ctanhf.c43
-rw-r--r--math/s_ctanhl.c43
-rw-r--r--math/s_ctanl.c45
7 files changed, 252 insertions, 70 deletions
diff --git a/math/libm-test.inc b/math/libm-test.inc
index 0533483749..a551b9f3f4 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 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;
}
}
diff --git a/math/s_ctanf.c b/math/s_ctanf.c
index 5f7f28ad07..4cba559a44 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 9cecb8bdb7..201871e7ec 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 fce5aaf290..e505155774 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 d22e13a975..e5d677903f 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 112dd723d8..12d700cad9 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;
}
}
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