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Fix casinh spurious underflows away from [-i,i] (bug 15062)
- From: "Joseph S. Myers" <joseph at codesourcery dot com>
- To: <libc-alpha at sourceware dot org>
- Date: Thu, 24 Jan 2013 21:48:52 +0000
- Subject: Fix casinh spurious underflows away from [-i,i] (bug 15062)
Bug 15062 is casinh (and thereby casin and cacos) producing spurious
underflow exceptions when the final result does not underflow, because
of underflow in computing csqrt (1 + z*z).
This patch fixes this, for the case of z not too close to the line
from -i to i (which I restricted the bug to since cases close to that
line will need fixing separately along with other accuracy bugs
there), by using simpler expressions for the real and imaginary parts
separately that have negligible error when the relevant part of the
argument is sufficiently small. With this logic, any underflow
exception that is correct for the final result will be generated by
atan2 while other calculations avoid such exceptions.
Tested x86_64 and x86 and ulps updated accordingly.
(For arguments in the regions fixed by this patch, I don't believe the
underflows could have caused any inaccurate results from scaling up an
underflowed value. But such inaccuracy may occur for cases of
underflow close to the line from -i to i, in addition to the inherent
inaccuracy of a real part of a result computed by clog of something
close to |z|=1.)
2013-01-24 Joseph Myers <joseph@codesourcery.com>
[BZ #15062]
* math/k_casinh.c (__kernel_casinh): Compute real and imaginary
parts of result separately when argument is not close to line from
-i to i and one part of argument is small.
* math/k_casinhf.c (__kernel_casinhf): Likewise.
* math/k_casinhl.c (__kernel_casinhl): Likewise.
* math/libm-test.inc (cacos_test): Add more tests.
(casin_test): Likewise.
(casinh_test): Likewise.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
diff --git a/math/k_casinh.c b/math/k_casinh.c
index 7f98f24..41cd5ec 100644
--- a/math/k_casinh.c
+++ b/math/k_casinh.c
@@ -57,6 +57,26 @@ __kernel_casinh (__complex__ double x, int adj)
res = __clog (y);
__real__ res += M_LN2;
}
+ else if (rx >= 0.5 && ix < DBL_EPSILON / 8.0)
+ {
+ double s = __ieee754_hypot (1.0, rx);
+
+ __real__ res = __ieee754_log (rx + s);
+ if (adj)
+ __imag__ res = __ieee754_atan2 (s, __imag__ x);
+ else
+ __imag__ res = __ieee754_atan2 (ix, s);
+ }
+ else if (rx < DBL_EPSILON / 8.0 && ix >= 1.5)
+ {
+ double s = __ieee754_sqrt ((ix + 1.0) * (ix - 1.0));
+
+ __real__ res = __ieee754_log (ix + s);
+ if (adj)
+ __imag__ res = __ieee754_atan2 (rx, __copysign (s, __imag__ x));
+ else
+ __imag__ res = __ieee754_atan2 (s, rx);
+ }
else
{
__real__ y = (rx - ix) * (rx + ix) + 1.0;
diff --git a/math/k_casinhf.c b/math/k_casinhf.c
index 9401636..3152ea2 100644
--- a/math/k_casinhf.c
+++ b/math/k_casinhf.c
@@ -57,6 +57,26 @@ __kernel_casinhf (__complex__ float x, int adj)
res = __clogf (y);
__real__ res += (float) M_LN2;
}
+ else if (rx >= 0.5f && ix < FLT_EPSILON / 8.0f)
+ {
+ float s = __ieee754_hypotf (1.0f, rx);
+
+ __real__ res = __ieee754_logf (rx + s);
+ if (adj)
+ __imag__ res = __ieee754_atan2f (s, __imag__ x);
+ else
+ __imag__ res = __ieee754_atan2f (ix, s);
+ }
+ else if (rx < FLT_EPSILON / 8.0f && ix >= 1.5f)
+ {
+ float s = __ieee754_sqrtf ((ix + 1.0f) * (ix - 1.0f));
+
+ __real__ res = __ieee754_logf (ix + s);
+ if (adj)
+ __imag__ res = __ieee754_atan2f (rx, __copysignf (s, __imag__ x));
+ else
+ __imag__ res = __ieee754_atan2f (s, rx);
+ }
else
{
__real__ y = (rx - ix) * (rx + ix) + 1.0;
diff --git a/math/k_casinhl.c b/math/k_casinhl.c
index 6412979..110ae33 100644
--- a/math/k_casinhl.c
+++ b/math/k_casinhl.c
@@ -64,6 +64,26 @@ __kernel_casinhl (__complex__ long double x, int adj)
res = __clogl (y);
__real__ res += M_LN2l;
}
+ else if (rx >= 0.5L && ix < LDBL_EPSILON / 8.0L)
+ {
+ long double s = __ieee754_hypotl (1.0L, rx);
+
+ __real__ res = __ieee754_logl (rx + s);
+ if (adj)
+ __imag__ res = __ieee754_atan2l (s, __imag__ x);
+ else
+ __imag__ res = __ieee754_atan2l (ix, s);
+ }
+ else if (rx < LDBL_EPSILON / 8.0L && ix >= 1.5L)
+ {
+ long double s = __ieee754_sqrtl ((ix + 1.0L) * (ix - 1.0L));
+
+ __real__ res = __ieee754_logl (ix + s);
+ if (adj)
+ __imag__ res = __ieee754_atan2l (rx, __copysignl (s, __imag__ x));
+ else
+ __imag__ res = __ieee754_atan2l (s, rx);
+ }
else
{
__real__ y = (rx - ix) * (rx + ix) + 1.0;
diff --git a/math/libm-test.inc b/math/libm-test.inc
index 1c2970f..6ac3cd2 100644
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -1490,6 +1490,35 @@ cacos_test (void)
TEST_c_c (cacos, 0x1.fp16383L, 0x1.fp16383L, 7.853981633974483096156608458198757210493e-1L, -1.135753137836666928715489992987020363057e4L);
#endif
+ TEST_c_c (cacos, 0x1.fp-129L, 1.5L, 1.570796326794896619231321691639751442097L, -1.194763217287109304111930828519090523536L);
+ TEST_c_c (cacos, 0x1.fp-129L, -1.5L, 1.570796326794896619231321691639751442097L, 1.194763217287109304111930828519090523536L);
+ TEST_c_c (cacos, -0x1.fp-129L, 1.5L, 1.570796326794896619231321691639751442100L, -1.194763217287109304111930828519090523536L);
+ TEST_c_c (cacos, -0x1.fp-129L, -1.5L, 1.570796326794896619231321691639751442100L, 1.194763217287109304111930828519090523536L);
+ TEST_c_c (cacos, 1.5L, 0x1.fp-129L, 2.546345110742945032959687790021055102355e-39L, -9.624236501192068949955178268487368462704e-1L, UNDERFLOW_EXCEPTION_FLOAT);
+ TEST_c_c (cacos, -1.5L, 0x1.fp-129L, 3.141592653589793238462643383279502884195L, -9.624236501192068949955178268487368462704e-1L);
+ TEST_c_c (cacos, 1.5L, -0x1.fp-129L, 2.546345110742945032959687790021055102355e-39L, 9.624236501192068949955178268487368462704e-1L, UNDERFLOW_EXCEPTION_FLOAT);
+ TEST_c_c (cacos, -1.5L, -0x1.fp-129L, 3.141592653589793238462643383279502884195L, 9.624236501192068949955178268487368462704e-1L);
+#ifndef TEST_FLOAT
+ TEST_c_c (cacos, 0x1.fp-1025L, 1.5L, 1.570796326794896619231321691639751442099L, -1.194763217287109304111930828519090523536L);
+ TEST_c_c (cacos, 0x1.fp-1025L, -1.5L, 1.570796326794896619231321691639751442099L, 1.194763217287109304111930828519090523536L);
+ TEST_c_c (cacos, -0x1.fp-1025L, 1.5L, 1.570796326794896619231321691639751442099L, -1.194763217287109304111930828519090523536L);
+ TEST_c_c (cacos, -0x1.fp-1025L, -1.5L, 1.570796326794896619231321691639751442099L, 1.194763217287109304111930828519090523536L);
+ TEST_c_c (cacos, 1.5L, 0x1.fp-1025L, 4.819934639999230680322935210539402497827e-309L, -9.624236501192068949955178268487368462704e-1L, UNDERFLOW_EXCEPTION_DOUBLE);
+ TEST_c_c (cacos, -1.5L, 0x1.fp-1025L, 3.141592653589793238462643383279502884197L, -9.624236501192068949955178268487368462704e-1L);
+ TEST_c_c (cacos, 1.5L, -0x1.fp-1025L, 4.819934639999230680322935210539402497827e-309L, 9.624236501192068949955178268487368462704e-1L, UNDERFLOW_EXCEPTION_DOUBLE);
+ TEST_c_c (cacos, -1.5L, -0x1.fp-1025L, 3.141592653589793238462643383279502884197L, 9.624236501192068949955178268487368462704e-1L);
+#endif
+#if defined TEST_LDOUBLE && LDBL_MIN_EXP <= -16381
+ TEST_c_c (cacos, 0x1.fp-16385L, 1.5L, 1.570796326794896619231321691639751442099L, -1.194763217287109304111930828519090523536L);
+ TEST_c_c (cacos, 0x1.fp-16385L, -1.5L, 1.570796326794896619231321691639751442099L, 1.194763217287109304111930828519090523536L);
+ TEST_c_c (cacos, -0x1.fp-16385L, 1.5L, 1.570796326794896619231321691639751442099L, -1.194763217287109304111930828519090523536L);
+ TEST_c_c (cacos, -0x1.fp-16385L, -1.5L, 1.570796326794896619231321691639751442099L, 1.194763217287109304111930828519090523536L);
+ TEST_c_c (cacos, 1.5L, 0x1.fp-16385L, 7.282957076134209141226696333885150260319e-4933L, -9.624236501192068949955178268487368462704e-1L, UNDERFLOW_EXCEPTION);
+ TEST_c_c (cacos, -1.5L, 0x1.fp-16385L, 3.141592653589793238462643383279502884197L, -9.624236501192068949955178268487368462704e-1L);
+ TEST_c_c (cacos, 1.5L, -0x1.fp-16385L, 7.282957076134209141226696333885150260319e-4933L, 9.624236501192068949955178268487368462704e-1L, UNDERFLOW_EXCEPTION);
+ TEST_c_c (cacos, -1.5L, -0x1.fp-16385L, 3.141592653589793238462643383279502884197L, 9.624236501192068949955178268487368462704e-1L);
+#endif
+
TEST_c_c (cacos, 0.75L, 1.25L, 1.11752014915610270578240049553777969L, -1.13239363160530819522266333696834467L);
TEST_c_c (cacos, -2, -3, 2.1414491111159960199416055713254211L, 1.9833870299165354323470769028940395L);
@@ -1772,6 +1801,35 @@ casin_test (void)
TEST_c_c (casin, 0x1.fp16383L, 0x1.fp16383L, 7.853981633974483096156608458198757210493e-1L, 1.135753137836666928715489992987020363057e4L);
#endif
+ TEST_c_c (casin, 0x1.fp-129L, 1.5L, 1.579176199917649005841160751101628985741e-39L, 1.194763217287109304111930828519090523536L, UNDERFLOW_EXCEPTION_FLOAT);
+ TEST_c_c (casin, 0x1.fp-129L, -1.5L, 1.579176199917649005841160751101628985741e-39L, -1.194763217287109304111930828519090523536L, UNDERFLOW_EXCEPTION_FLOAT);
+ TEST_c_c (casin, -0x1.fp-129L, 1.5L, -1.579176199917649005841160751101628985741e-39L, 1.194763217287109304111930828519090523536L, UNDERFLOW_EXCEPTION_FLOAT);
+ TEST_c_c (casin, -0x1.fp-129L, -1.5L, -1.579176199917649005841160751101628985741e-39L, -1.194763217287109304111930828519090523536L, UNDERFLOW_EXCEPTION_FLOAT);
+ TEST_c_c (casin, 1.5L, 0x1.fp-129L, 1.570796326794896619231321691639751442096L, 9.624236501192068949955178268487368462704e-1L);
+ TEST_c_c (casin, -1.5L, 0x1.fp-129L, -1.570796326794896619231321691639751442096L, 9.624236501192068949955178268487368462704e-1L);
+ TEST_c_c (casin, 1.5L, -0x1.fp-129L, 1.570796326794896619231321691639751442096L, -9.624236501192068949955178268487368462704e-1L);
+ TEST_c_c (casin, -1.5L, -0x1.fp-129L, -1.570796326794896619231321691639751442096L, -9.624236501192068949955178268487368462704e-1L);
+#ifndef TEST_FLOAT
+ TEST_c_c (casin, 0x1.fp-1025L, 1.5L, 2.989196569048182929051881765490354365918e-309L, 1.194763217287109304111930828519090523536L, UNDERFLOW_EXCEPTION_DOUBLE);
+ TEST_c_c (casin, 0x1.fp-1025L, -1.5L, 2.989196569048182929051881765490354365918e-309L, -1.194763217287109304111930828519090523536L, UNDERFLOW_EXCEPTION_DOUBLE);
+ TEST_c_c (casin, -0x1.fp-1025L, 1.5L, -2.989196569048182929051881765490354365918e-309L, 1.194763217287109304111930828519090523536L, UNDERFLOW_EXCEPTION_DOUBLE);
+ TEST_c_c (casin, -0x1.fp-1025L, -1.5L, -2.989196569048182929051881765490354365918e-309L, -1.194763217287109304111930828519090523536L, UNDERFLOW_EXCEPTION_DOUBLE);
+ TEST_c_c (casin, 1.5L, 0x1.fp-1025L, 1.570796326794896619231321691639751442099L, 9.624236501192068949955178268487368462704e-1L);
+ TEST_c_c (casin, -1.5L, 0x1.fp-1025L, -1.570796326794896619231321691639751442099L, 9.624236501192068949955178268487368462704e-1L);
+ TEST_c_c (casin, 1.5L, -0x1.fp-1025L, 1.570796326794896619231321691639751442099L, -9.624236501192068949955178268487368462704e-1L);
+ TEST_c_c (casin, -1.5L, -0x1.fp-1025L, -1.570796326794896619231321691639751442099L, -9.624236501192068949955178268487368462704e-1L);
+#endif
+#if defined TEST_LDOUBLE && LDBL_MIN_EXP <= -16381
+ TEST_c_c (casin, 0x1.fp-16385L, 1.5L, 4.516698239814521372306784062043266700598e-4933L, 1.194763217287109304111930828519090523536L, UNDERFLOW_EXCEPTION);
+ TEST_c_c (casin, 0x1.fp-16385L, -1.5L, 4.516698239814521372306784062043266700598e-4933L, -1.194763217287109304111930828519090523536L, UNDERFLOW_EXCEPTION);
+ TEST_c_c (casin, -0x1.fp-16385L, 1.5L, -4.516698239814521372306784062043266700598e-4933L, 1.194763217287109304111930828519090523536L, UNDERFLOW_EXCEPTION);
+ TEST_c_c (casin, -0x1.fp-16385L, -1.5L, -4.516698239814521372306784062043266700598e-4933L, -1.194763217287109304111930828519090523536L, UNDERFLOW_EXCEPTION);
+ TEST_c_c (casin, 1.5L, 0x1.fp-16385L, 1.570796326794896619231321691639751442099L, 9.624236501192068949955178268487368462704e-1L);
+ TEST_c_c (casin, -1.5L, 0x1.fp-16385L, -1.570796326794896619231321691639751442099L, 9.624236501192068949955178268487368462704e-1L);
+ TEST_c_c (casin, 1.5L, -0x1.fp-16385L, 1.570796326794896619231321691639751442099L, -9.624236501192068949955178268487368462704e-1L);
+ TEST_c_c (casin, -1.5L, -0x1.fp-16385L, -1.570796326794896619231321691639751442099L, -9.624236501192068949955178268487368462704e-1L);
+#endif
+
TEST_c_c (casin, 0.75L, 1.25L, 0.453276177638793913448921196101971749L, 1.13239363160530819522266333696834467L);
TEST_c_c (casin, -2, -3, -0.57065278432109940071028387968566963L, -1.9833870299165354323470769028940395L);
@@ -1899,6 +1957,35 @@ casinh_test (void)
TEST_c_c (casinh, 0x1.fp16383L, 0x1.fp16383L, 1.135753137836666928715489992987020363057e4L, 7.853981633974483096156608458198757210493e-1L);
#endif
+ TEST_c_c (casinh, 0x1.fp-129L, 1.5L, 9.624236501192068949955178268487368462704e-1L, 1.570796326794896619231321691639751442096L);
+ TEST_c_c (casinh, 0x1.fp-129L, -1.5L, 9.624236501192068949955178268487368462704e-1L, -1.570796326794896619231321691639751442096L);
+ TEST_c_c (casinh, -0x1.fp-129L, 1.5L, -9.624236501192068949955178268487368462704e-1L, 1.570796326794896619231321691639751442096L);
+ TEST_c_c (casinh, -0x1.fp-129L, -1.5L, -9.624236501192068949955178268487368462704e-1L, -1.570796326794896619231321691639751442096L);
+ TEST_c_c (casinh, 1.5L, 0x1.fp-129L, 1.194763217287109304111930828519090523536L, 1.579176199917649005841160751101628985741e-39L, UNDERFLOW_EXCEPTION_FLOAT);
+ TEST_c_c (casinh, -1.5L, 0x1.fp-129L, -1.194763217287109304111930828519090523536L, 1.579176199917649005841160751101628985741e-39L, UNDERFLOW_EXCEPTION_FLOAT);
+ TEST_c_c (casinh, 1.5L, -0x1.fp-129L, 1.194763217287109304111930828519090523536L, -1.579176199917649005841160751101628985741e-39L, UNDERFLOW_EXCEPTION_FLOAT);
+ TEST_c_c (casinh, -1.5L, -0x1.fp-129L, -1.194763217287109304111930828519090523536L, -1.579176199917649005841160751101628985741e-39L, UNDERFLOW_EXCEPTION_FLOAT);
+#ifndef TEST_FLOAT
+ TEST_c_c (casinh, 0x1.fp-1025L, 1.5L, 9.624236501192068949955178268487368462704e-1L, 1.570796326794896619231321691639751442099L);
+ TEST_c_c (casinh, 0x1.fp-1025L, -1.5L, 9.624236501192068949955178268487368462704e-1L, -1.570796326794896619231321691639751442099L);
+ TEST_c_c (casinh, -0x1.fp-1025L, 1.5L, -9.624236501192068949955178268487368462704e-1L, 1.570796326794896619231321691639751442099L);
+ TEST_c_c (casinh, -0x1.fp-1025L, -1.5L, -9.624236501192068949955178268487368462704e-1L, -1.570796326794896619231321691639751442099L);
+ TEST_c_c (casinh, 1.5L, 0x1.fp-1025L, 1.194763217287109304111930828519090523536L, 2.989196569048182929051881765490354365918e-309L, UNDERFLOW_EXCEPTION_DOUBLE);
+ TEST_c_c (casinh, -1.5L, 0x1.fp-1025L, -1.194763217287109304111930828519090523536L, 2.989196569048182929051881765490354365918e-309L, UNDERFLOW_EXCEPTION_DOUBLE);
+ TEST_c_c (casinh, 1.5L, -0x1.fp-1025L, 1.194763217287109304111930828519090523536L, -2.989196569048182929051881765490354365918e-309L, UNDERFLOW_EXCEPTION_DOUBLE);
+ TEST_c_c (casinh, -1.5L, -0x1.fp-1025L, -1.194763217287109304111930828519090523536L, -2.989196569048182929051881765490354365918e-309L, UNDERFLOW_EXCEPTION_DOUBLE);
+#endif
+#if defined TEST_LDOUBLE && LDBL_MIN_EXP <= -16381
+ TEST_c_c (casinh, 0x1.fp-16385L, 1.5L, 9.624236501192068949955178268487368462704e-1L, 1.570796326794896619231321691639751442099L);
+ TEST_c_c (casinh, 0x1.fp-16385L, -1.5L, 9.624236501192068949955178268487368462704e-1L, -1.570796326794896619231321691639751442099L);
+ TEST_c_c (casinh, -0x1.fp-16385L, 1.5L, -9.624236501192068949955178268487368462704e-1L, 1.570796326794896619231321691639751442099L);
+ TEST_c_c (casinh, -0x1.fp-16385L, -1.5L, -9.624236501192068949955178268487368462704e-1L, -1.570796326794896619231321691639751442099L);
+ TEST_c_c (casinh, 1.5L, 0x1.fp-16385L, 1.194763217287109304111930828519090523536L, 4.516698239814521372306784062043266700598e-4933L, UNDERFLOW_EXCEPTION);
+ TEST_c_c (casinh, -1.5L, 0x1.fp-16385L, -1.194763217287109304111930828519090523536L, 4.516698239814521372306784062043266700598e-4933L, UNDERFLOW_EXCEPTION);
+ TEST_c_c (casinh, 1.5L, -0x1.fp-16385L, 1.194763217287109304111930828519090523536L, -4.516698239814521372306784062043266700598e-4933L, UNDERFLOW_EXCEPTION);
+ TEST_c_c (casinh, -1.5L, -0x1.fp-16385L, -1.194763217287109304111930828519090523536L, -4.516698239814521372306784062043266700598e-4933L, UNDERFLOW_EXCEPTION);
+#endif
+
TEST_c_c (casinh, 0.75L, 1.25L, 1.03171853444778027336364058631006594L, 0.911738290968487636358489564316731207L);
TEST_c_c (casinh, -2, -3, -1.9686379257930962917886650952454982L, -0.96465850440760279204541105949953237L);
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index 1525b16..fd0180f 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -275,6 +275,18 @@ ifloat: 1
Test "Imaginary part of: cacos (-0 - 1.5 i) == pi/2 + 1.194763217287109304111930828519090523536 i":
double: 1
idouble: 1
+Test "Imaginary part of: cacos (-0x1.fp-1025 + 1.5 i) == 1.570796326794896619231321691639751442099 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (-0x1.fp-1025 - 1.5 i) == 1.570796326794896619231321691639751442099 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (-0x1.fp-129 + 1.5 i) == 1.570796326794896619231321691639751442100 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (-0x1.fp-129 - 1.5 i) == 1.570796326794896619231321691639751442100 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
Test "Imaginary part of: cacos (-1.5 + +0 i) == pi - 0.9624236501192068949955178268487368462704 i":
double: 1
float: 1
@@ -282,9 +294,27 @@ idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
+Test "Imaginary part of: cacos (-1.5 + 0x1.fp-1025 i) == 3.141592653589793238462643383279502884197 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (-1.5 + 0x1.fp-129 i) == 3.141592653589793238462643383279502884195 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (-1.5 + 0x1.fp-16385 i) == 3.141592653589793238462643383279502884197 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
Test "Imaginary part of: cacos (-1.5 - 0 i) == pi + 0.9624236501192068949955178268487368462704 i":
ildouble: 1
ldouble: 1
+Test "Imaginary part of: cacos (-1.5 - 0x1.fp-1025 i) == 3.141592653589793238462643383279502884197 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (-1.5 - 0x1.fp-129 i) == 3.141592653589793238462643383279502884195 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (-1.5 - 0x1.fp-16385 i) == 3.141592653589793238462643383279502884197 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
Test "Real part of: cacos (0.5 + +0 i) == 1.047197551196597746154214461093167628066 - 0 i":
double: 1
idouble: 1
@@ -303,6 +333,18 @@ float: 1
ifloat: 1
ildouble: 2
ldouble: 2
+Test "Imaginary part of: cacos (0x1.fp-1025 + 1.5 i) == 1.570796326794896619231321691639751442099 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (0x1.fp-1025 - 1.5 i) == 1.570796326794896619231321691639751442099 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (0x1.fp-129 + 1.5 i) == 1.570796326794896619231321691639751442097 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (0x1.fp-129 - 1.5 i) == 1.570796326794896619231321691639751442097 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
Test "Imaginary part of: cacos (0x1.fp1023 + 0x1.fp1023 i) == 7.853981633974483096156608458198757210493e-1 - 7.107906849659093345062145442726115449315e2 i":
double: 1
idouble: 1
@@ -316,9 +358,27 @@ idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
+Test "Imaginary part of: cacos (1.5 + 0x1.fp-1025 i) == 4.819934639999230680322935210539402497827e-309 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (1.5 + 0x1.fp-129 i) == 2.546345110742945032959687790021055102355e-39 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (1.5 + 0x1.fp-16385 i) == 7.282957076134209141226696333885150260319e-4933 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
Test "Imaginary part of: cacos (1.5 - 0 i) == +0 + 0.9624236501192068949955178268487368462704 i":
ildouble: 1
ldouble: 1
+Test "Imaginary part of: cacos (1.5 - 0x1.fp-1025 i) == 4.819934639999230680322935210539402497827e-309 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (1.5 - 0x1.fp-129 i) == 2.546345110742945032959687790021055102355e-39 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (1.5 - 0x1.fp-16385 i) == 7.282957076134209141226696333885150260319e-4933 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
# cacosh
Test "Real part of: cacosh (+0 + 0.5 i) == 0.4812118250596034474977589134243684231352 + pi/2 i":
@@ -502,6 +562,18 @@ ifloat: 1
Test "Imaginary part of: casin (-0 - 1.5 i) == -0 - 1.194763217287109304111930828519090523536 i":
double: 1
idouble: 1
+Test "Imaginary part of: casin (-0x1.fp-1025 + 1.5 i) == -2.989196569048182929051881765490354365918e-309 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (-0x1.fp-1025 - 1.5 i) == -2.989196569048182929051881765490354365918e-309 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (-0x1.fp-129 + 1.5 i) == -1.579176199917649005841160751101628985741e-39 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (-0x1.fp-129 - 1.5 i) == -1.579176199917649005841160751101628985741e-39 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
Test "Imaginary part of: casin (-1.5 + +0 i) == -pi/2 + 0.9624236501192068949955178268487368462704 i":
double: 1
float: 1
@@ -509,9 +581,27 @@ idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
+Test "Imaginary part of: casin (-1.5 + 0x1.fp-1025 i) == -1.570796326794896619231321691639751442099 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (-1.5 + 0x1.fp-129 i) == -1.570796326794896619231321691639751442096 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (-1.5 + 0x1.fp-16385 i) == -1.570796326794896619231321691639751442099 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
Test "Imaginary part of: casin (-1.5 - 0 i) == -pi/2 - 0.9624236501192068949955178268487368462704 i":
ildouble: 1
ldouble: 1
+Test "Imaginary part of: casin (-1.5 - 0x1.fp-1025 i) == -1.570796326794896619231321691639751442099 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (-1.5 - 0x1.fp-129 i) == -1.570796326794896619231321691639751442096 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (-1.5 - 0x1.fp-16385 i) == -1.570796326794896619231321691639751442099 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
Test "Real part of: casin (0.75 + 1.25 i) == 0.453276177638793913448921196101971749 + 1.13239363160530819522266333696834467 i":
double: 1
float: 1
@@ -524,6 +614,18 @@ float: 1
ifloat: 1
ildouble: 2
ldouble: 2
+Test "Imaginary part of: casin (0x1.fp-1025 + 1.5 i) == 2.989196569048182929051881765490354365918e-309 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (0x1.fp-1025 - 1.5 i) == 2.989196569048182929051881765490354365918e-309 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (0x1.fp-129 + 1.5 i) == 1.579176199917649005841160751101628985741e-39 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (0x1.fp-129 - 1.5 i) == 1.579176199917649005841160751101628985741e-39 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
Test "Imaginary part of: casin (0x1.fp1023 + 0x1.fp1023 i) == 7.853981633974483096156608458198757210493e-1 + 7.107906849659093345062145442726115449315e2 i":
double: 1
idouble: 1
@@ -537,9 +639,27 @@ idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
+Test "Imaginary part of: casin (1.5 + 0x1.fp-1025 i) == 1.570796326794896619231321691639751442099 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (1.5 + 0x1.fp-129 i) == 1.570796326794896619231321691639751442096 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (1.5 + 0x1.fp-16385 i) == 1.570796326794896619231321691639751442099 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
Test "Imaginary part of: casin (1.5 - 0 i) == pi/2 - 0.9624236501192068949955178268487368462704 i":
ildouble: 1
ldouble: 1
+Test "Imaginary part of: casin (1.5 - 0x1.fp-1025 i) == 1.570796326794896619231321691639751442099 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (1.5 - 0x1.fp-129 i) == 1.570796326794896619231321691639751442096 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (1.5 - 0x1.fp-16385 i) == 1.570796326794896619231321691639751442099 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
# casinh
Test "Real part of: casinh (+0 + 1.5 i) == 0.9624236501192068949955178268487368462704 + pi/2 i":
@@ -576,6 +696,24 @@ idouble: 2
ifloat: 1
ildouble: 1
ldouble: 1
+Test "Real part of: casinh (-0x1.fp-1025 + 1.5 i) == -9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (-0x1.fp-1025 - 1.5 i) == -9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (-0x1.fp-129 + 1.5 i) == -9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442096 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (-0x1.fp-129 - 1.5 i) == -9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442096 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (-0x1.fp-16385 + 1.5 i) == -9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (-0x1.fp-16385 - 1.5 i) == -9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
Test "Real part of: casinh (-1.0 + +0 i) == -0.8813735870195430252326093249797923090282 + +0 i":
double: 2
float: 1
@@ -595,11 +733,23 @@ double: 2
float: 1
idouble: 2
ifloat: 1
+Test "Real part of: casinh (-1.5 + 0x1.fp-1025 i) == -1.194763217287109304111930828519090523536 + 2.989196569048182929051881765490354365918e-309 i":
+double: 1
+idouble: 1
+Test "Real part of: casinh (-1.5 + 0x1.fp-129 i) == -1.194763217287109304111930828519090523536 + 1.579176199917649005841160751101628985741e-39 i":
+double: 1
+idouble: 1
Test "Real part of: casinh (-1.5 - 0 i) == -1.194763217287109304111930828519090523536 - 0 i":
double: 2
float: 1
idouble: 2
ifloat: 1
+Test "Real part of: casinh (-1.5 - 0x1.fp-1025 i) == -1.194763217287109304111930828519090523536 - 2.989196569048182929051881765490354365918e-309 i":
+double: 1
+idouble: 1
+Test "Real part of: casinh (-1.5 - 0x1.fp-129 i) == -1.194763217287109304111930828519090523536 - 1.579176199917649005841160751101628985741e-39 i":
+double: 1
+idouble: 1
Test "Real part of: casinh (-2 - 3 i) == -1.9686379257930962917886650952454982 - 0.96465850440760279204541105949953237 i":
double: 5
float: 1
@@ -638,6 +788,24 @@ idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
+Test "Real part of: casinh (0x1.fp-1025 + 1.5 i) == 9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (0x1.fp-1025 - 1.5 i) == 9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (0x1.fp-129 + 1.5 i) == 9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442096 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (0x1.fp-129 - 1.5 i) == 9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442096 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (0x1.fp-16385 + 1.5 i) == 9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (0x1.fp-16385 - 1.5 i) == 9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
Test "Real part of: casinh (0x1.fp1023 + 0x1.fp1023 i) == 7.107906849659093345062145442726115449315e2 + 7.853981633974483096156608458198757210493e-1 i":
double: 1
idouble: 1
@@ -657,9 +825,21 @@ ifloat: 1
Test "Real part of: casinh (1.5 + +0 i) == 1.194763217287109304111930828519090523536 + +0 i":
double: 1
idouble: 1
+Test "Real part of: casinh (1.5 + 0x1.fp-1025 i) == 1.194763217287109304111930828519090523536 + 2.989196569048182929051881765490354365918e-309 i":
+double: 1
+idouble: 1
+Test "Real part of: casinh (1.5 + 0x1.fp-129 i) == 1.194763217287109304111930828519090523536 + 1.579176199917649005841160751101628985741e-39 i":
+double: 1
+idouble: 1
Test "Real part of: casinh (1.5 - 0 i) == 1.194763217287109304111930828519090523536 - 0 i":
double: 1
idouble: 1
+Test "Real part of: casinh (1.5 - 0x1.fp-1025 i) == 1.194763217287109304111930828519090523536 - 2.989196569048182929051881765490354365918e-309 i":
+double: 1
+idouble: 1
+Test "Real part of: casinh (1.5 - 0x1.fp-129 i) == 1.194763217287109304111930828519090523536 - 1.579176199917649005841160751101628985741e-39 i":
+double: 1
+idouble: 1
# catan
Test "Imaginary part of: catan (-2 - 3 i) == -1.4099210495965755225306193844604208 - 0.22907268296853876629588180294200276 i":
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index 63c6aed..b828774 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -244,6 +244,24 @@ ifloat: 1
Test "Imaginary part of: cacos (-0 - 1.5 i) == pi/2 + 1.194763217287109304111930828519090523536 i":
double: 1
idouble: 1
+Test "Imaginary part of: cacos (-0x1.fp-1025 + 1.5 i) == 1.570796326794896619231321691639751442099 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (-0x1.fp-1025 - 1.5 i) == 1.570796326794896619231321691639751442099 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Real part of: cacos (-0x1.fp-129 + 1.5 i) == 1.570796326794896619231321691639751442100 - 1.194763217287109304111930828519090523536 i":
+float: 1
+ifloat: 1
+Test "Imaginary part of: cacos (-0x1.fp-129 + 1.5 i) == 1.570796326794896619231321691639751442100 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Real part of: cacos (-0x1.fp-129 - 1.5 i) == 1.570796326794896619231321691639751442100 + 1.194763217287109304111930828519090523536 i":
+float: 1
+ifloat: 1
+Test "Imaginary part of: cacos (-0x1.fp-129 - 1.5 i) == 1.570796326794896619231321691639751442100 + 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
@@ -257,9 +275,27 @@ idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
+Test "Imaginary part of: cacos (-1.5 + 0x1.fp-1025 i) == 3.141592653589793238462643383279502884197 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (-1.5 + 0x1.fp-129 i) == 3.141592653589793238462643383279502884195 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (-1.5 + 0x1.fp-16385 i) == 3.141592653589793238462643383279502884197 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
Test "Imaginary part of: cacos (-1.5 - 0 i) == pi + 0.9624236501192068949955178268487368462704 i":
ildouble: 1
ldouble: 1
+Test "Imaginary part of: cacos (-1.5 - 0x1.fp-1025 i) == 3.141592653589793238462643383279502884197 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (-1.5 - 0x1.fp-129 i) == 3.141592653589793238462643383279502884195 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (-1.5 - 0x1.fp-16385 i) == 3.141592653589793238462643383279502884197 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
Test "Real part of: cacos (-2 - 3 i) == 2.1414491111159960199416055713254211 + 1.9833870299165354323470769028940395 i":
float: 1
ifloat: 1
@@ -281,6 +317,18 @@ float: 1
ifloat: 1
ildouble: 2
ldouble: 2
+Test "Imaginary part of: cacos (0x1.fp-1025 + 1.5 i) == 1.570796326794896619231321691639751442099 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (0x1.fp-1025 - 1.5 i) == 1.570796326794896619231321691639751442099 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (0x1.fp-129 + 1.5 i) == 1.570796326794896619231321691639751442097 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (0x1.fp-129 - 1.5 i) == 1.570796326794896619231321691639751442097 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
Test "Imaginary part of: cacos (0x1.fp1023 + 0x1.fp1023 i) == 7.853981633974483096156608458198757210493e-1 - 7.107906849659093345062145442726115449315e2 i":
double: 1
idouble: 1
@@ -294,9 +342,27 @@ idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
+Test "Imaginary part of: cacos (1.5 + 0x1.fp-1025 i) == 4.819934639999230680322935210539402497827e-309 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (1.5 + 0x1.fp-129 i) == 2.546345110742945032959687790021055102355e-39 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (1.5 + 0x1.fp-16385 i) == 7.282957076134209141226696333885150260319e-4933 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
Test "Imaginary part of: cacos (1.5 - 0 i) == +0 + 0.9624236501192068949955178268487368462704 i":
ildouble: 1
ldouble: 1
+Test "Imaginary part of: cacos (1.5 - 0x1.fp-1025 i) == 4.819934639999230680322935210539402497827e-309 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (1.5 - 0x1.fp-129 i) == 2.546345110742945032959687790021055102355e-39 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (1.5 - 0x1.fp-16385 i) == 7.282957076134209141226696333885150260319e-4933 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
# cacosh
Test "Real part of: cacosh (+0 + 0.5 i) == 0.4812118250596034474977589134243684231352 + pi/2 i":
@@ -460,6 +526,18 @@ ifloat: 1
Test "Imaginary part of: casin (-0 - 1.5 i) == -0 - 1.194763217287109304111930828519090523536 i":
double: 1
idouble: 1
+Test "Imaginary part of: casin (-0x1.fp-1025 + 1.5 i) == -2.989196569048182929051881765490354365918e-309 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (-0x1.fp-1025 - 1.5 i) == -2.989196569048182929051881765490354365918e-309 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (-0x1.fp-129 + 1.5 i) == -1.579176199917649005841160751101628985741e-39 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (-0x1.fp-129 - 1.5 i) == -1.579176199917649005841160751101628985741e-39 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
Test "Imaginary part of: casin (-1.5 + +0 i) == -pi/2 + 0.9624236501192068949955178268487368462704 i":
double: 1
float: 1
@@ -467,9 +545,27 @@ idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
+Test "Imaginary part of: casin (-1.5 + 0x1.fp-1025 i) == -1.570796326794896619231321691639751442099 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (-1.5 + 0x1.fp-129 i) == -1.570796326794896619231321691639751442096 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (-1.5 + 0x1.fp-16385 i) == -1.570796326794896619231321691639751442099 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
Test "Imaginary part of: casin (-1.5 - 0 i) == -pi/2 - 0.9624236501192068949955178268487368462704 i":
ildouble: 1
ldouble: 1
+Test "Imaginary part of: casin (-1.5 - 0x1.fp-1025 i) == -1.570796326794896619231321691639751442099 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (-1.5 - 0x1.fp-129 i) == -1.570796326794896619231321691639751442096 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (-1.5 - 0x1.fp-16385 i) == -1.570796326794896619231321691639751442099 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
Test "Real part of: casin (0.75 + 1.25 i) == 0.453276177638793913448921196101971749 + 1.13239363160530819522266333696834467 i":
double: 1
float: 1
@@ -482,6 +578,18 @@ float: 1
ifloat: 1
ildouble: 2
ldouble: 2
+Test "Imaginary part of: casin (0x1.fp-1025 + 1.5 i) == 2.989196569048182929051881765490354365918e-309 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (0x1.fp-1025 - 1.5 i) == 2.989196569048182929051881765490354365918e-309 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (0x1.fp-129 + 1.5 i) == 1.579176199917649005841160751101628985741e-39 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (0x1.fp-129 - 1.5 i) == 1.579176199917649005841160751101628985741e-39 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
Test "Imaginary part of: casin (0x1.fp1023 + 0x1.fp1023 i) == 7.853981633974483096156608458198757210493e-1 + 7.107906849659093345062145442726115449315e2 i":
double: 1
idouble: 1
@@ -495,9 +603,27 @@ idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
+Test "Imaginary part of: casin (1.5 + 0x1.fp-1025 i) == 1.570796326794896619231321691639751442099 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (1.5 + 0x1.fp-129 i) == 1.570796326794896619231321691639751442096 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (1.5 + 0x1.fp-16385 i) == 1.570796326794896619231321691639751442099 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
Test "Imaginary part of: casin (1.5 - 0 i) == pi/2 - 0.9624236501192068949955178268487368462704 i":
ildouble: 1
ldouble: 1
+Test "Imaginary part of: casin (1.5 - 0x1.fp-1025 i) == 1.570796326794896619231321691639751442099 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (1.5 - 0x1.fp-129 i) == 1.570796326794896619231321691639751442096 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (1.5 - 0x1.fp-16385 i) == 1.570796326794896619231321691639751442099 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
# casinh
Test "Real part of: casinh (+0 + 1.5 i) == 0.9624236501192068949955178268487368462704 + pi/2 i":
@@ -534,6 +660,24 @@ idouble: 2
ifloat: 1
ildouble: 1
ldouble: 1
+Test "Real part of: casinh (-0x1.fp-1025 + 1.5 i) == -9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (-0x1.fp-1025 - 1.5 i) == -9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (-0x1.fp-129 + 1.5 i) == -9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442096 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (-0x1.fp-129 - 1.5 i) == -9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442096 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (-0x1.fp-16385 + 1.5 i) == -9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (-0x1.fp-16385 - 1.5 i) == -9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
Test "Real part of: casinh (-1.0 + +0 i) == -0.8813735870195430252326093249797923090282 + +0 i":
double: 2
float: 1
@@ -553,11 +697,23 @@ double: 2
float: 1
idouble: 2
ifloat: 1
+Test "Real part of: casinh (-1.5 + 0x1.fp-1025 i) == -1.194763217287109304111930828519090523536 + 2.989196569048182929051881765490354365918e-309 i":
+double: 1
+idouble: 1
+Test "Real part of: casinh (-1.5 + 0x1.fp-129 i) == -1.194763217287109304111930828519090523536 + 1.579176199917649005841160751101628985741e-39 i":
+double: 1
+idouble: 1
Test "Real part of: casinh (-1.5 - 0 i) == -1.194763217287109304111930828519090523536 - 0 i":
double: 2
float: 1
idouble: 2
ifloat: 1
+Test "Real part of: casinh (-1.5 - 0x1.fp-1025 i) == -1.194763217287109304111930828519090523536 - 2.989196569048182929051881765490354365918e-309 i":
+double: 1
+idouble: 1
+Test "Real part of: casinh (-1.5 - 0x1.fp-129 i) == -1.194763217287109304111930828519090523536 - 1.579176199917649005841160751101628985741e-39 i":
+double: 1
+idouble: 1
Test "Real part of: casinh (-2 - 3 i) == -1.9686379257930962917886650952454982 - 0.96465850440760279204541105949953237 i":
double: 5
float: 1
@@ -592,6 +748,24 @@ idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
+Test "Real part of: casinh (0x1.fp-1025 + 1.5 i) == 9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (0x1.fp-1025 - 1.5 i) == 9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (0x1.fp-129 + 1.5 i) == 9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442096 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (0x1.fp-129 - 1.5 i) == 9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442096 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (0x1.fp-16385 + 1.5 i) == 9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (0x1.fp-16385 - 1.5 i) == 9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
Test "Real part of: casinh (0x1.fp1023 + 0x1.fp1023 i) == 7.107906849659093345062145442726115449315e2 + 7.853981633974483096156608458198757210493e-1 i":
double: 1
idouble: 1
@@ -611,9 +785,21 @@ ifloat: 1
Test "Real part of: casinh (1.5 + +0 i) == 1.194763217287109304111930828519090523536 + +0 i":
double: 1
idouble: 1
+Test "Real part of: casinh (1.5 + 0x1.fp-1025 i) == 1.194763217287109304111930828519090523536 + 2.989196569048182929051881765490354365918e-309 i":
+double: 1
+idouble: 1
+Test "Real part of: casinh (1.5 + 0x1.fp-129 i) == 1.194763217287109304111930828519090523536 + 1.579176199917649005841160751101628985741e-39 i":
+double: 1
+idouble: 1
Test "Real part of: casinh (1.5 - 0 i) == 1.194763217287109304111930828519090523536 - 0 i":
double: 1
idouble: 1
+Test "Real part of: casinh (1.5 - 0x1.fp-1025 i) == 1.194763217287109304111930828519090523536 - 2.989196569048182929051881765490354365918e-309 i":
+double: 1
+idouble: 1
+Test "Real part of: casinh (1.5 - 0x1.fp-129 i) == 1.194763217287109304111930828519090523536 - 1.579176199917649005841160751101628985741e-39 i":
+double: 1
+idouble: 1
# catan
Test "Real part of: catan (-2 - 3 i) == -1.4099210495965755225306193844604208 - 0.22907268296853876629588180294200276 i":
--
Joseph S. Myers
joseph@codesourcery.com