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Fix cacos real-part inaccuracy for result real part near 0 (bug 15023).

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This commit is contained in:
Joseph Myers 2013-01-17 20:25:51 +00:00
parent 2a26ef3a01
commit 728d7b43fc
16 changed files with 424 additions and 124 deletions
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31
ChangeLog
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@ -1,3 +1,34 @@
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.
2013-01-17 Pino Toscano <toscano.pino@tiscali.it>
* sysdeps/unix/sysv/linux/malloc-sysdep.h (HAVE_MREMAP): New define.

2
NEWS
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@ -10,7 +10,7 @@ Version 2.18
* The following bugs are resolved with this release:
13951, 14200, 14317, 14327, 14964, 14981, 14982, 14985, 14994, 14996,
15003.
15003, 15023.
Version 2.17

12
include/complex.h
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@ -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

2
math/Makefile
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@ -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

85
math/k_casinh.c Normal file
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@ -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;
}

85
math/k_casinhf.c Normal file
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@ -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;
}

92
math/k_casinhl.c Normal file
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@ -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;
}

37
math/libm-test.inc
View File

@ -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);

22
math/s_cacos.c
View File

@ -25,11 +25,27 @@ __cacos (__complex__ double x)
{
__complex__ double y;
__complex__ double res;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
y = __casin (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;
__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;
}

22
math/s_cacosf.c
View File

@ -25,11 +25,27 @@ __cacosf (__complex__ float x)
{
__complex__ float y;
__complex__ float res;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
y = __casinf (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;
__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;
}

22
math/s_cacosl.c
View File

@ -25,11 +25,27 @@ __cacosl (__complex__ long double x)
{
__complex__ long double y;
__complex__ long double res;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
y = __casinl (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;
__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;
}

36
math/s_casinh.c
View File

@ -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;

36
math/s_casinhf.c
View File

@ -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;

43
math/s_casinhl.c
View File

@ -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;

6
sysdeps/i386/fpu/libm-test-ulps
View File

@ -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

15
sysdeps/x86_64/fpu/libm-test-ulps
View File

@ -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