This is the mail archive of the
libc-alpha@sourceware.org
mailing list for the glibc project.
Fix cacos real-part inaccuracy for result real part near 0 (bug15023)
- From: "Joseph S. Myers" <joseph at codesourcery dot com>
- To: <libc-alpha at sourceware dot org>
- Date: Thu, 17 Jan 2013 00:57:44 +0000
- Subject: Fix cacos real-part inaccuracy for result real part near 0 (bug15023)
cacos is implemented in terms of casin (which in turn is implemented
in terms of casinh) using the formula cacos = pi/2 - casin.
This results in inaccuracy of the real part, through cancellation,
when the real part of the result of cacos is close to zero; this is
bug 15023. The real part of the result of casin comes from the
imaginary part of the result of clog in the calculation of casinh
(which in turn comes from a call to atan2); avoiding the cancellation
is simply a matter of adjusting the number passed to clog so that its
argument is the desired real part of the result of cacos, so avoiding
cancellation from subtraction.
This patch duly implements this fix, putting the relevant code in a
new __kernel_casinh function that takes an extra argument to say what
exactly it should be calculating (like other functions such as
__kernel_tanf, for example). cacos calls this function directly when
it receives a finite nonzero argument (for zero arguments and argument
involving infinities or NaNs, the present logic is kept). Testcases
for cacos are added corresponding to those recently added for casinh
and casin; some of those illustrate the bug this patch fixes, and the
bugs recently fixed for casinh and casin equally applied to cacos (and
were fixed by those casinh patches) so should be tested for cacos as
well.
I intend to make cacosh use __kernel_casinh as well for better
accuracy in various cases and avoiding spurious underflows and
overflows, but that will need to wait until the remaining spurious
underflows and inaccuracy in __kernel_casinh are fixed. (The
different branch cut used for cacosh makes the adjustments a little
more complicated than those for cacos, but still certainly better than
repeating for cacosh near the line from -1 to 1 all the logic that
will be needed to get casinh accurate near the line from -i to i.)
Tested x86_64 and x86 and ulps updated accordingly.
2013-01-17 Joseph Myers <joseph@codesourcery.com>
[BZ #15023]
* include/complex.h: Condition contents on [!_COMPLEX_H].
(__kernel_casinhf): New prototype.
(__kernel_casinh): Likewise.
(__kernel_casinhl): Likewise.
* math/Makefile (libm_calls): Add k_casinh.
* math/k_casinh.c: New file.
* math/k_casinhf.c: Likewise.
* math/k_casinhl.c: Likewise.
* math/s_cacos.c (__cacos): Implement using __kernel_casinh for
finite nonzero arguments.
* math/s_cacosf.c (__cacosf): Implement using __kernel_casinhf for
finite nonzero arguments.
* math/s_cacosl.c (__cacosl): Implement using __kernel_casinhl for
finite nonzero arguments.
* math/s_casinh.c: Do not include <float.h>.
(__casinh): Move code for finite nonzero arguments to k_casinh.c.
* math/s_casinhf.c: Do not include <float.h>.
(__casinhf): Move code for finite nonzero arguments to
k_casinhf.c.
* math/s_casinhl.c: Do not include <float.h>.
[LDBL_MANT_DIG == 106] (LDBL_EPSILON): Do not undefine and
redefine.
(__casinhl): Move code for finite nonzero arguments to
k_casinhl.c.
* math/libm-test.inc (cacos_test): Add more tests.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
diff --git a/include/complex.h b/include/complex.h
index acf8cf1..e173f1f 100644
--- a/include/complex.h
+++ b/include/complex.h
@@ -1 +1,11 @@
-#include <math/complex.h>
+#ifndef _COMPLEX_H
+# include <math/complex.h>
+
+/* Return the complex inverse hyperbolic sine of finite nonzero Z,
+ with the imaginary part of the result subtracted from pi/2 if ADJ
+ is nonzero. */
+extern complex float __kernel_casinhf (complex float z, int adj);
+extern complex double __kernel_casinh (complex double z, int adj);
+extern complex long double __kernel_casinhl (complex long double z, int adj);
+
+#endif
diff --git a/math/Makefile b/math/Makefile
index b9519cf..da18b56 100644
--- a/math/Makefile
+++ b/math/Makefile
@@ -58,7 +58,7 @@ libm-calls = e_acos e_acosh e_asin e_atan2 e_atanh e_cosh e_exp e_fmod \
s_catan s_casin s_ccos s_csin s_ctan s_ctanh s_cacos \
s_casinh s_cacosh s_catanh s_csqrt s_cpow s_cproj s_clog10 \
s_fma s_lrint s_llrint s_lround s_llround e_exp10 w_log2 \
- s_isinf_ns $(calls:s_%=m_%) x2y2m1
+ s_isinf_ns $(calls:s_%=m_%) x2y2m1 k_casinh
include ../Makeconfig
diff --git a/math/k_casinh.c b/math/k_casinh.c
new file mode 100644
index 0000000..7f98f24
--- /dev/null
+++ b/math/k_casinh.c
@@ -0,0 +1,85 @@
+/* Return arc hyperbole sine for double value, with the imaginary part
+ of the result possibly adjusted for use in computing other
+ functions.
+ Copyright (C) 1997-2013 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
+
+#include <complex.h>
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+
+/* Return the complex inverse hyperbolic sine of finite nonzero Z,
+ with the imaginary part of the result subtracted from pi/2 if ADJ
+ is nonzero. */
+
+__complex__ double
+__kernel_casinh (__complex__ double x, int adj)
+{
+ __complex__ double res;
+ double rx, ix;
+ __complex__ double y;
+
+ /* Avoid cancellation by reducing to the first quadrant. */
+ rx = fabs (__real__ x);
+ ix = fabs (__imag__ x);
+
+ if (rx >= 1.0 / DBL_EPSILON || ix >= 1.0 / DBL_EPSILON)
+ {
+ /* For large x in the first quadrant, x + csqrt (1 + x * x)
+ is sufficiently close to 2 * x to make no significant
+ difference to the result; avoid possible overflow from
+ the squaring and addition. */
+ __real__ y = rx;
+ __imag__ y = ix;
+
+ if (adj)
+ {
+ double t = __real__ y;
+ __real__ y = __copysign (__imag__ y, __imag__ x);
+ __imag__ y = t;
+ }
+
+ res = __clog (y);
+ __real__ res += M_LN2;
+ }
+ else
+ {
+ __real__ y = (rx - ix) * (rx + ix) + 1.0;
+ __imag__ y = 2.0 * rx * ix;
+
+ y = __csqrt (y);
+
+ __real__ y += rx;
+ __imag__ y += ix;
+
+ if (adj)
+ {
+ double t = __real__ y;
+ __real__ y = copysign (__imag__ y, __imag__ x);
+ __imag__ y = t;
+ }
+
+ res = __clog (y);
+ }
+
+ /* Give results the correct sign for the original argument. */
+ __real__ res = __copysign (__real__ res, __real__ x);
+ __imag__ res = __copysign (__imag__ res, (adj ? 1.0 : __imag__ x));
+
+ return res;
+}
diff --git a/math/k_casinhf.c b/math/k_casinhf.c
new file mode 100644
index 0000000..9401636
--- /dev/null
+++ b/math/k_casinhf.c
@@ -0,0 +1,85 @@
+/* Return arc hyperbole sine for float value, with the imaginary part
+ of the result possibly adjusted for use in computing other
+ functions.
+ Copyright (C) 1997-2013 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
+
+#include <complex.h>
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+
+/* Return the complex inverse hyperbolic sine of finite nonzero Z,
+ with the imaginary part of the result subtracted from pi/2 if ADJ
+ is nonzero. */
+
+__complex__ float
+__kernel_casinhf (__complex__ float x, int adj)
+{
+ __complex__ float res;
+ float rx, ix;
+ __complex__ float y;
+
+ /* Avoid cancellation by reducing to the first quadrant. */
+ rx = fabsf (__real__ x);
+ ix = fabsf (__imag__ x);
+
+ if (rx >= 1.0f / FLT_EPSILON || ix >= 1.0f / FLT_EPSILON)
+ {
+ /* For large x in the first quadrant, x + csqrt (1 + x * x)
+ is sufficiently close to 2 * x to make no significant
+ difference to the result; avoid possible overflow from
+ the squaring and addition. */
+ __real__ y = rx;
+ __imag__ y = ix;
+
+ if (adj)
+ {
+ float t = __real__ y;
+ __real__ y = __copysignf (__imag__ y, __imag__ x);
+ __imag__ y = t;
+ }
+
+ res = __clogf (y);
+ __real__ res += (float) M_LN2;
+ }
+ else
+ {
+ __real__ y = (rx - ix) * (rx + ix) + 1.0;
+ __imag__ y = 2.0 * rx * ix;
+
+ y = __csqrtf (y);
+
+ __real__ y += rx;
+ __imag__ y += ix;
+
+ if (adj)
+ {
+ float t = __real__ y;
+ __real__ y = __copysignf (__imag__ y, __imag__ x);
+ __imag__ y = t;
+ }
+
+ res = __clogf (y);
+ }
+
+ /* Give results the correct sign for the original argument. */
+ __real__ res = __copysignf (__real__ res, __real__ x);
+ __imag__ res = __copysignf (__imag__ res, (adj ? 1.0f : __imag__ x));
+
+ return res;
+}
diff --git a/math/k_casinhl.c b/math/k_casinhl.c
new file mode 100644
index 0000000..6412979
--- /dev/null
+++ b/math/k_casinhl.c
@@ -0,0 +1,92 @@
+/* Return arc hyperbole sine for long double value, with the imaginary
+ part of the result possibly adjusted for use in computing other
+ functions.
+ Copyright (C) 1997-2013 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
+
+#include <complex.h>
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+
+/* To avoid spurious overflows, use this definition to treat IBM long
+ double as approximating an IEEE-style format. */
+#if LDBL_MANT_DIG == 106
+# undef LDBL_EPSILON
+# define LDBL_EPSILON 0x1p-106L
+#endif
+
+/* Return the complex inverse hyperbolic sine of finite nonzero Z,
+ with the imaginary part of the result subtracted from pi/2 if ADJ
+ is nonzero. */
+
+__complex__ long double
+__kernel_casinhl (__complex__ long double x, int adj)
+{
+ __complex__ long double res;
+ long double rx, ix;
+ __complex__ long double y;
+
+ /* Avoid cancellation by reducing to the first quadrant. */
+ rx = fabsl (__real__ x);
+ ix = fabsl (__imag__ x);
+
+ if (rx >= 1.0L / LDBL_EPSILON || ix >= 1.0L / LDBL_EPSILON)
+ {
+ /* For large x in the first quadrant, x + csqrt (1 + x * x)
+ is sufficiently close to 2 * x to make no significant
+ difference to the result; avoid possible overflow from
+ the squaring and addition. */
+ __real__ y = rx;
+ __imag__ y = ix;
+
+ if (adj)
+ {
+ long double t = __real__ y;
+ __real__ y = __copysignl (__imag__ y, __imag__ x);
+ __imag__ y = t;
+ }
+
+ res = __clogl (y);
+ __real__ res += M_LN2l;
+ }
+ else
+ {
+ __real__ y = (rx - ix) * (rx + ix) + 1.0;
+ __imag__ y = 2.0 * rx * ix;
+
+ y = __csqrtl (y);
+
+ __real__ y += rx;
+ __imag__ y += ix;
+
+ if (adj)
+ {
+ long double t = __real__ y;
+ __real__ y = __copysignl (__imag__ y, __imag__ x);
+ __imag__ y = t;
+ }
+
+ res = __clogl (y);
+ }
+
+ /* Give results the correct sign for the original argument. */
+ __real__ res = __copysignl (__real__ res, __real__ x);
+ __imag__ res = __copysignl (__imag__ res, (adj ? 1.0L : __imag__ x));
+
+ return res;
+}
diff --git a/math/libm-test.inc b/math/libm-test.inc
index 56e3217..1c2970f 100644
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -1453,6 +1453,43 @@ cacos_test (void)
TEST_c_c (cacos, 1.5L, plus_zero, plus_zero, -0.9624236501192068949955178268487368462704L);
TEST_c_c (cacos, 1.5L, minus_zero, plus_zero, 0.9624236501192068949955178268487368462704L);
+ TEST_c_c (cacos, 0x1p50L, 1.0L, 8.881784197001252323389053344727730248720e-16L, -3.535050620855721078027883819436720218708e1L);
+ TEST_c_c (cacos, 0x1p50L, -1.0L, 8.881784197001252323389053344727730248720e-16L, 3.535050620855721078027883819436720218708e1L);
+ TEST_c_c (cacos, -0x1p50L, 1.0L, 3.141592653589792350284223683154270545292L, -3.535050620855721078027883819436720218708e1L);
+ TEST_c_c (cacos, -0x1p50L, -1.0L, 3.141592653589792350284223683154270545292L, 3.535050620855721078027883819436720218708e1L);
+ TEST_c_c (cacos, 1.0L, 0x1p50L, 1.570796326794895731052901991514519103193L, -3.535050620855721078027883819436759661753e1L);
+ TEST_c_c (cacos, -1.0L, 0x1p50L, 1.570796326794897507409741391764983781004L, -3.535050620855721078027883819436759661753e1L);
+ TEST_c_c (cacos, 1.0L, -0x1p50L, 1.570796326794895731052901991514519103193L, 3.535050620855721078027883819436759661753e1L);
+ TEST_c_c (cacos, -1.0L, -0x1p50L, 1.570796326794897507409741391764983781004L, 3.535050620855721078027883819436759661753e1L);
+#ifndef TEST_FLOAT
+ TEST_c_c (cacos, 0x1p500L, 1.0L, 3.054936363499604682051979393213617699789e-151L, -3.472667374605326000180332928505464606058e2L);
+ TEST_c_c (cacos, 0x1p500L, -1.0L, 3.054936363499604682051979393213617699789e-151L, 3.472667374605326000180332928505464606058e2L);
+ TEST_c_c (cacos, -0x1p500L, 1.0L, 3.141592653589793238462643383279502884197L, -3.472667374605326000180332928505464606058e2L);
+ TEST_c_c (cacos, -0x1p500L, -1.0L, 3.141592653589793238462643383279502884197L, 3.472667374605326000180332928505464606058e2L);
+ TEST_c_c (cacos, 1.0L, 0x1p500L, 1.570796326794896619231321691639751442099L, -3.472667374605326000180332928505464606058e2L);
+ TEST_c_c (cacos, -1.0L, 0x1p500L, 1.570796326794896619231321691639751442099L, -3.472667374605326000180332928505464606058e2L);
+ TEST_c_c (cacos, 1.0L, -0x1p500L, 1.570796326794896619231321691639751442099L, 3.472667374605326000180332928505464606058e2L);
+ TEST_c_c (cacos, -1.0L, -0x1p500L, 1.570796326794896619231321691639751442099L, 3.472667374605326000180332928505464606058e2L);
+#endif
+#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
+ TEST_c_c (cacos, 0x1p5000L, 1.0L, 7.079811261048172892385615158694057552948e-1506L, -3.466429049980286492395577839412341016946e3L);
+ TEST_c_c (cacos, 0x1p5000L, -1.0L, 7.079811261048172892385615158694057552948e-1506L, 3.466429049980286492395577839412341016946e3L);
+ TEST_c_c (cacos, -0x1p5000L, 1.0L, 3.141592653589793238462643383279502884197L, -3.466429049980286492395577839412341016946e3L);
+ TEST_c_c (cacos, -0x1p5000L, -1.0L, 3.141592653589793238462643383279502884197L, 3.466429049980286492395577839412341016946e3L);
+ TEST_c_c (cacos, 1.0L, 0x1p5000L, 1.570796326794896619231321691639751442099L, -3.466429049980286492395577839412341016946e3L);
+ TEST_c_c (cacos, -1.0L, 0x1p5000L, 1.570796326794896619231321691639751442099L, -3.466429049980286492395577839412341016946e3L);
+ TEST_c_c (cacos, 1.0L, -0x1p5000L, 1.570796326794896619231321691639751442099L, 3.466429049980286492395577839412341016946e3L);
+ TEST_c_c (cacos, -1.0L, -0x1p5000L, 1.570796326794896619231321691639751442099L, 3.466429049980286492395577839412341016946e3L);
+#endif
+
+ TEST_c_c (cacos, 0x1.fp127L, 0x1.fp127L, 7.853981633974483096156608458198757210493e-1L, -8.973081118419833726837456344608533993585e1L);
+#ifndef TEST_FLOAT
+ TEST_c_c (cacos, 0x1.fp1023L, 0x1.fp1023L, 7.853981633974483096156608458198757210493e-1L, -7.107906849659093345062145442726115449315e2L);
+#endif
+#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
+ TEST_c_c (cacos, 0x1.fp16383L, 0x1.fp16383L, 7.853981633974483096156608458198757210493e-1L, -1.135753137836666928715489992987020363057e4L);
+#endif
+
TEST_c_c (cacos, 0.75L, 1.25L, 1.11752014915610270578240049553777969L, -1.13239363160530819522266333696834467L);
TEST_c_c (cacos, -2, -3, 2.1414491111159960199416055713254211L, 1.9833870299165354323470769028940395L);
diff --git a/math/s_cacos.c b/math/s_cacos.c
index 6604b5a..acd9b24 100644
--- a/math/s_cacos.c
+++ b/math/s_cacos.c
@@ -25,11 +25,27 @@ __cacos (__complex__ double x)
{
__complex__ double y;
__complex__ double res;
-
- y = __casin (x);
-
- __real__ res = (double) M_PI_2 - __real__ y;
- __imag__ res = -__imag__ y;
+ int rcls = fpclassify (__real__ x);
+ int icls = fpclassify (__imag__ x);
+
+ if (rcls <= FP_INFINITE || icls <= FP_INFINITE
+ || (rcls == FP_ZERO && icls == FP_ZERO))
+ {
+ y = __casin (x);
+
+ __real__ res = (double) M_PI_2 - __real__ y;
+ __imag__ res = -__imag__ y;
+ }
+ else
+ {
+ __real__ y = -__imag__ x;
+ __imag__ y = __real__ x;
+
+ y = __kernel_casinh (y, 1);
+
+ __real__ res = __imag__ y;
+ __imag__ res = __real__ y;
+ }
return res;
}
diff --git a/math/s_cacosf.c b/math/s_cacosf.c
index 04c13e4..df2bf21 100644
--- a/math/s_cacosf.c
+++ b/math/s_cacosf.c
@@ -25,11 +25,27 @@ __cacosf (__complex__ float x)
{
__complex__ float y;
__complex__ float res;
-
- y = __casinf (x);
-
- __real__ res = (float) M_PI_2 - __real__ y;
- __imag__ res = -__imag__ y;
+ int rcls = fpclassify (__real__ x);
+ int icls = fpclassify (__imag__ x);
+
+ if (rcls <= FP_INFINITE || icls <= FP_INFINITE
+ || (rcls == FP_ZERO && icls == FP_ZERO))
+ {
+ y = __casinf (x);
+
+ __real__ res = (float) M_PI_2 - __real__ y;
+ __imag__ res = -__imag__ y;
+ }
+ else
+ {
+ __real__ y = -__imag__ x;
+ __imag__ y = __real__ x;
+
+ y = __kernel_casinhf (y, 1);
+
+ __real__ res = __imag__ y;
+ __imag__ res = __real__ y;
+ }
return res;
}
diff --git a/math/s_cacosl.c b/math/s_cacosl.c
index 304076d..8eab1f0 100644
--- a/math/s_cacosl.c
+++ b/math/s_cacosl.c
@@ -25,11 +25,27 @@ __cacosl (__complex__ long double x)
{
__complex__ long double y;
__complex__ long double res;
-
- y = __casinl (x);
-
- __real__ res = M_PI_2l - __real__ y;
- __imag__ res = -__imag__ y;
+ int rcls = fpclassify (__real__ x);
+ int icls = fpclassify (__imag__ x);
+
+ if (rcls <= FP_INFINITE || icls <= FP_INFINITE
+ || (rcls == FP_ZERO && icls == FP_ZERO))
+ {
+ y = __casinl (x);
+
+ __real__ res = M_PI_2l - __real__ y;
+ __imag__ res = -__imag__ y;
+ }
+ else
+ {
+ __real__ y = -__imag__ x;
+ __imag__ y = __real__ x;
+
+ y = __kernel_casinhl (y, 1);
+
+ __real__ res = __imag__ y;
+ __imag__ res = __real__ y;
+ }
return res;
}
diff --git a/math/s_casinh.c b/math/s_casinh.c
index b493982..657e269 100644
--- a/math/s_casinh.c
+++ b/math/s_casinh.c
@@ -20,7 +20,6 @@
#include <complex.h>
#include <math.h>
#include <math_private.h>
-#include <float.h>
__complex__ double
__casinh (__complex__ double x)
@@ -62,40 +61,7 @@ __casinh (__complex__ double x)
}
else
{
- double rx, ix;
- __complex__ double y;
-
- /* Avoid cancellation by reducing to the first quadrant. */
- rx = fabs (__real__ x);
- ix = fabs (__imag__ x);
-
- if (rx >= 1.0 / DBL_EPSILON || ix >= 1.0 / DBL_EPSILON)
- {
- /* For large x in the first quadrant, x + csqrt (1 + x * x)
- is sufficiently close to 2 * x to make no significant
- difference to the result; avoid possible overflow from
- the squaring and addition. */
- __real__ y = rx;
- __imag__ y = ix;
- res = __clog (y);
- __real__ res += M_LN2;
- }
- else
- {
- __real__ y = (rx - ix) * (rx + ix) + 1.0;
- __imag__ y = 2.0 * rx * ix;
-
- y = __csqrt (y);
-
- __real__ y += rx;
- __imag__ y += ix;
-
- res = __clog (y);
- }
-
- /* Give results the correct sign for the original argument. */
- __real__ res = __copysign (__real__ res, __real__ x);
- __imag__ res = __copysign (__imag__ res, __imag__ x);
+ res = __kernel_casinh (x, 0);
}
return res;
diff --git a/math/s_casinhf.c b/math/s_casinhf.c
index f865e14..8663c2e 100644
--- a/math/s_casinhf.c
+++ b/math/s_casinhf.c
@@ -20,7 +20,6 @@
#include <complex.h>
#include <math.h>
#include <math_private.h>
-#include <float.h>
__complex__ float
__casinhf (__complex__ float x)
@@ -62,40 +61,7 @@ __casinhf (__complex__ float x)
}
else
{
- float rx, ix;
- __complex__ float y;
-
- /* Avoid cancellation by reducing to the first quadrant. */
- rx = fabsf (__real__ x);
- ix = fabsf (__imag__ x);
-
- if (rx >= 1.0f / FLT_EPSILON || ix >= 1.0f / FLT_EPSILON)
- {
- /* For large x in the first quadrant, x + csqrt (1 + x * x)
- is sufficiently close to 2 * x to make no significant
- difference to the result; avoid possible overflow from
- the squaring and addition. */
- __real__ y = rx;
- __imag__ y = ix;
- res = __clogf (y);
- __real__ res += (float) M_LN2;
- }
- else
- {
- __real__ y = (rx - ix) * (rx + ix) + 1.0;
- __imag__ y = 2.0 * rx * ix;
-
- y = __csqrtf (y);
-
- __real__ y += rx;
- __imag__ y += ix;
-
- res = __clogf (y);
- }
-
- /* Give results the correct sign for the original argument. */
- __real__ res = __copysignf (__real__ res, __real__ x);
- __imag__ res = __copysignf (__imag__ res, __imag__ x);
+ res = __kernel_casinhf (x, 0);
}
return res;
diff --git a/math/s_casinhl.c b/math/s_casinhl.c
index d7c7459..2afc527 100644
--- a/math/s_casinhl.c
+++ b/math/s_casinhl.c
@@ -20,14 +20,6 @@
#include <complex.h>
#include <math.h>
#include <math_private.h>
-#include <float.h>
-
-/* To avoid spurious overflows, use this definition to treat IBM long
- double as approximating an IEEE-style format. */
-#if LDBL_MANT_DIG == 106
-# undef LDBL_EPSILON
-# define LDBL_EPSILON 0x1p-106L
-#endif
__complex__ long double
__casinhl (__complex__ long double x)
@@ -69,40 +61,7 @@ __casinhl (__complex__ long double x)
}
else
{
- long double rx, ix;
- __complex__ long double y;
-
- /* Avoid cancellation by reducing to the first quadrant. */
- rx = fabsl (__real__ x);
- ix = fabsl (__imag__ x);
-
- if (rx >= 1.0L / LDBL_EPSILON || ix >= 1.0L / LDBL_EPSILON)
- {
- /* For large x in the first quadrant, x + csqrt (1 + x * x)
- is sufficiently close to 2 * x to make no significant
- difference to the result; avoid possible overflow from
- the squaring and addition. */
- __real__ y = rx;
- __imag__ y = ix;
- res = __clogl (y);
- __real__ res += M_LN2l;
- }
- else
- {
- __real__ y = (rx - ix) * (rx + ix) + 1.0;
- __imag__ y = 2.0 * rx * ix;
-
- y = __csqrtl (y);
-
- __real__ y += rx;
- __imag__ y += ix;
-
- res = __clogl (y);
- }
-
- /* Give results the correct sign for the original argument. */
- __real__ res = __copysignl (__real__ res, __real__ x);
- __imag__ res = __copysignl (__imag__ res, __imag__ x);
+ res = __kernel_casinhl (x, 0);
}
return res;
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index 3fc30de..1525b16 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -303,6 +303,12 @@ float: 1
ifloat: 1
ildouble: 2
ldouble: 2
+Test "Imaginary part of: cacos (0x1.fp1023 + 0x1.fp1023 i) == 7.853981633974483096156608458198757210493e-1 - 7.107906849659093345062145442726115449315e2 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (0x1.fp127 + 0x1.fp127 i) == 7.853981633974483096156608458198757210493e-1 - 8.973081118419833726837456344608533993585e1 i":
+double: 1
+idouble: 1
Test "Imaginary part of: cacos (1.5 + +0 i) == +0 - 0.9624236501192068949955178268487368462704 i":
double: 1
float: 1
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index 95b6aec..63c6aed 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -244,6 +244,12 @@ ifloat: 1
Test "Imaginary part of: cacos (-0 - 1.5 i) == pi/2 + 1.194763217287109304111930828519090523536 i":
double: 1
idouble: 1
+Test "Real part of: cacos (-1.0 + 0x1p50 i) == 1.570796326794897507409741391764983781004 - 3.535050620855721078027883819436759661753e1 i":
+float: 1
+ifloat: 1
+Test "Real part of: cacos (-1.0 - 0x1p50 i) == 1.570796326794897507409741391764983781004 + 3.535050620855721078027883819436759661753e1 i":
+float: 1
+ifloat: 1
Test "Imaginary part of: cacos (-1.5 + +0 i) == pi - 0.9624236501192068949955178268487368462704 i":
double: 1
float: 1
@@ -254,6 +260,9 @@ ldouble: 1
Test "Imaginary part of: cacos (-1.5 - 0 i) == pi + 0.9624236501192068949955178268487368462704 i":
ildouble: 1
ldouble: 1
+Test "Real part of: cacos (-2 - 3 i) == 2.1414491111159960199416055713254211 + 1.9833870299165354323470769028940395 i":
+float: 1
+ifloat: 1
Test "Real part of: cacos (0.5 + +0 i) == 1.047197551196597746154214461093167628066 - 0 i":
double: 1
idouble: 1
@@ -272,6 +281,12 @@ float: 1
ifloat: 1
ildouble: 2
ldouble: 2
+Test "Imaginary part of: cacos (0x1.fp1023 + 0x1.fp1023 i) == 7.853981633974483096156608458198757210493e-1 - 7.107906849659093345062145442726115449315e2 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (0x1.fp127 + 0x1.fp127 i) == 7.853981633974483096156608458198757210493e-1 - 8.973081118419833726837456344608533993585e1 i":
+double: 1
+idouble: 1
Test "Imaginary part of: cacos (1.5 + +0 i) == +0 - 0.9624236501192068949955178268487368462704 i":
double: 1
float: 1
--
Joseph S. Myers
joseph@codesourcery.com