Fix ctan, ctanh of subnormals in round-upwards mode (bug 14328).

IBM long double fixes and POWER ulps update.
This commit is contained in:
Adhemerval Zanella 2012-07-11 09:19:27 -03:00
parent 6b90f98178
commit 28cfe84316
4 changed files with 331 additions and 23 deletions

View File

@ -1,3 +1,10 @@
2012-07-11 Adhemerval Zanella <azanella@linux.vnet.ibm.com>
* sysdeps/ieee754/ldbl-128ibm/s_ctanhl.c: Do not call sinh and cosh
for subnormals or multiply small sinh result by itself.
* sysdeps/ieee754/ldbl-128ibm/s_ctanl.c: Likewise.
* sysdeps/powerpc/fpu/libm-test-ulps: Update.
2012-07-11 David S. Miller <davem@davemloft.net>
* sysdeps/sparc/fpu/libm-test-ulps: Update.

View File

@ -25,6 +25,8 @@
#include <math_private.h>
/* IBM long double GCC builtin sets LDBL_EPSILON == LDBL_DENORM_MIN */
static const long double ldbl_eps = 0x1p-106L;
__complex__ long double
__ctanhl (__complex__ long double x)
@ -35,8 +37,8 @@ __ctanhl (__complex__ long double x)
{
if (__isinfl (__real__ x))
{
__real__ res = __copysignl (1.0, __real__ x);
__imag__ res = __copysignl (0.0, __imag__ x);
__real__ res = __copysignl (1.0L, __real__ x);
__imag__ res = __copysignl (0.0L, __imag__ x);
}
else if (__imag__ x == 0.0)
{
@ -57,7 +59,7 @@ __ctanhl (__complex__ long double x)
{
long double sinix, cosix;
long double den;
const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2);
const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2.0L);
/* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
= (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */
@ -71,7 +73,7 @@ __ctanhl (__complex__ long double x)
the real part is +/- 1, the imaginary part is
sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */
long double exp_2t = __ieee754_expl (2 * t);
__real__ res = __copysignl (1.0, __real__ x);
__real__ res = __copysignl (1.0L, __real__ x);
__imag__ res = 4 * sinix * cosix;
__real__ x = fabsl (__real__ x);
__real__ x -= t;
@ -83,22 +85,34 @@ __ctanhl (__complex__ long double x)
__imag__ res /= exp_2t;
}
else
__imag__ res /= __ieee754_expl (2 * __real__ x);
__imag__ res /= __ieee754_expl (2.0L * __real__ x);
}
else
{
long double sinhrx = __ieee754_sinhl (__real__ x);
long double coshrx = __ieee754_coshl (__real__ x);
long double sinhrx, coshrx;
if (fabs (__real__ x) > LDBL_MIN)
{
sinhrx = __ieee754_sinhl (__real__ x);
coshrx = __ieee754_coshl (__real__ x);
}
else
{
sinhrx = __real__ x;
coshrx = 1.0L;
}
den = sinhrx * sinhrx + cosix * cosix;
__real__ res = sinhrx * coshrx / den;
__imag__ res = sinix * cosix / den;
if (fabsl (sinhrx) > fabsl (cosix) * ldbl_eps)
den = sinhrx * sinhrx + cosix * cosix;
else
den = cosix * cosix;
__real__ res = sinhrx * (coshrx / den);
__imag__ res = sinix * (cosix / den);
}
/* __gcc_qmul does not respect -0.0 so we need the following fixup. */
if ((__real__ res == 0.0) && (__real__ x == 0.0))
if ((__real__ res == 0.0L) && (__real__ x == 0.0L))
__real__ res = __real__ x;
if ((__real__ res == 0.0) && (__imag__ x == 0.0))
if ((__real__ res == 0.0L) && (__imag__ x == 0.0L))
__imag__ res = __imag__ x;
}

View File

@ -25,6 +25,8 @@
#include <math_private.h>
/* IBM long double GCC builtin sets LDBL_EPSILON == LDBL_DENORM_MIN */
static const long double ldbl_eps = 0x1p-106L;
__complex__ long double
__ctanl (__complex__ long double x)
@ -55,7 +57,7 @@ __ctanl (__complex__ long double x)
{
long double sinrx, cosrx;
long double den;
const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2);
const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2.0L);
/* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
= (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
@ -70,7 +72,7 @@ __ctanl (__complex__ long double x)
sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */
long double exp_2t = __ieee754_expl (2 * t);
__imag__ res = __copysignl (1.0, __imag__ x);
__imag__ res = __copysignl (1.0L, __imag__ x);
__real__ res = 4 * sinrx * cosrx;
__imag__ x = fabsl (__imag__ x);
__imag__ x -= t;
@ -82,23 +84,35 @@ __ctanl (__complex__ long double x)
__real__ res /= exp_2t;
}
else
__real__ res /= __ieee754_expl (2 * __imag__ x);
__real__ res /= __ieee754_expl (2.0L * __imag__ x);
}
else
{
long double sinhix = __ieee754_sinhl (__imag__ x);
long double coshix = __ieee754_coshl (__imag__ x);
long double sinhix, coshix;
if (fabsl (__imag__ x) > LDBL_MIN)
{
sinhix = __ieee754_sinhl (__imag__ x);
coshix = __ieee754_coshl (__imag__ x);
}
else
{
sinhix = __imag__ x;
coshix = 1.0L;
}
den = cosrx * cosrx + sinhix * sinhix;
__real__ res = sinrx * cosrx / den;
__imag__ res = sinhix * coshix / den;
if (fabsl (sinhix) > fabsl (cosrx) * ldbl_eps)
den = cosrx * cosrx + sinhix * sinhix;
else
den = cosrx * cosrx;
__real__ res = sinrx * (cosrx / den);
__imag__ res = sinhix * (coshix / den);
}
/* __gcc_qmul does not respect -0.0 so we need the following fixup. */
if ((__real__ res == 0.0) && (__real__ x == 0.0))
if ((__real__ res == 0.0L) && (__real__ x == 0.0L))
__real__ res = __real__ x;
if ((__real__ res == 0.0) && (__imag__ x == 0.0))
if ((__real__ res == 0.0L) && (__imag__ x == 0.0L))
__imag__ res = __imag__ x;
}

View File

@ -1336,33 +1336,120 @@ ldouble: 1
Test "Real part of: ctan (0x1p1023 + 1 i) == -0.2254627924997545057926782581695274244229 + 0.8786063118883068695462540226219865087189 i":
double: 1
idouble: 1
Test "Imaginary part of: ctan (0x1p1023 + 1 i) == -0.2254627924997545057926782581695274244229 + 0.8786063118883068695462540226219865087189 i":
ildouble: 1
ldouble: 1
Test "Real part of: ctan (0x1p127 + 1 i) == 0.2446359391192790896381501310437708987204 + 0.9101334047676183761532873794426475906201 i":
float: 1
ifloat: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: ctan (0x1p127 + 1 i) == 0.2446359391192790896381501310437708987204 + 0.9101334047676183761532873794426475906201 i":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Test "Real part of: ctan (0x3.243f6cp-1 + 0 i) == -2.287733242885645987394874673945769518150e7 + 0.0 i":
float: 1
ifloat: 1
ildouble: 2
ldouble: 2
Test "Real part of: ctan (1 + 47 i) == 2.729321264492904590777293425576722354636e-41 + 1.0 i":
ildouble: 2
ldouble: 2
# ctan_downward
Test "Real part of: ctan_downward (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i":
ildouble: 3
ldouble: 3
Test "Real part of: ctan_downward (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 4
ldouble: 4
Test "Imaginary part of: ctan_downward (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
float: 1
ifloat: 1
ildouble: 10
ldouble: 10
# ctan_tonearest
Test "Real part of: ctan_tonearest (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
float: 1
ifloat: 1
ildouble: 2
ldouble: 2
Test "Imaginary part of: ctan_tonearest (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
float: 1
ifloat: 1
ildouble: 1
ldouble: 1
# ctan_towardzero
Test "Real part of: ctan_towardzero (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i":
ldouble: 4
ildouble: 4
Test "Imaginary part of: ctan_towardzero (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i":
ildouble: 13
ldouble: 13
Test "Real part of: ctan_towardzero (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
float: 1
ifloat: 1
ildouble: 2
ldouble: 2
Test "Imaginary part of: ctan_towardzero (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
float: 1
ifloat: 1
ildouble: 10
ldouble: 10
# ctan_upward
Test "Real part of: ctan_upward (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i":
double: 1
idouble: 1
ildouble: 6
ldouble: 6
Test "Imaginary part of: ctan_upward (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i":
ildouble: 10
ldouble: 10
Test "Real part of: ctan_upward (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 6
ldouble: 6
Test "Imaginary part of: ctan_upward (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
double: 1
float: 2
idouble: 1
ifloat: 2
ildouble: 1
ldouble: 1
# ctanh
Test "Real part of: ctanh (-2 - 3 i) == -0.965385879022133124278480269394560686 + 0.988437503832249372031403430350121098e-2 i":
double: 1
float: 2
idouble: 1
ifloat: 2
idouble: 2
ildouble: 2
ldouble: 2
Test "Imaginary part of: ctanh (-2 - 3 i) == -0.965385879022133124278480269394560686 + 0.988437503832249372031403430350121098e-2 i":
double: 1
idouble: 1
ildouble: 2
ldouble: 2
Test "Imaginary part of: ctanh (0 + 0x3.243f6cp-1 i) == 0.0 - 2.287733242885645987394874673945769518150e7 i":
float: 1
ifloat: 1
ildouble: 2
ldouble: 2
Test "Imaginary part of: ctanh (0 + pi/4 i) == 0.0 + 1.0 i":
double: 1
float: 1
@ -1378,22 +1465,100 @@ float: 1
ifloat: 1
ildouble: 2
ldouble: 2
Test "Real part of: ctanh (1 + 0x1p1023 i) == 0.8786063118883068695462540226219865087189 - 0.2254627924997545057926782581695274244229 i":
ildouble: 1
ldouble: 1
Test "Imaginary part of: ctanh (1 + 0x1p1023 i) == 0.8786063118883068695462540226219865087189 - 0.2254627924997545057926782581695274244229 i":
double: 1
idouble: 1
double: 1
Test "Real part of: ctanh (1 + 0x1p127 i) == 0.9101334047676183761532873794426475906201 + 0.2446359391192790896381501310437708987204 i":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Test "Imaginary part of: ctanh (1 + 0x1p127 i) == 0.9101334047676183761532873794426475906201 + 0.2446359391192790896381501310437708987204 i":
double: 1
float: 1
ifloat: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: ctanh (47 + 1 i) == 1.0 + 2.729321264492904590777293425576722354636e-41 i":
ildouble: 2
ldouble: 2
# ctanh_downward
Test "Imaginary part of: ctanh_downward (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
ildouble: 3
ldouble: 3
Test "Real part of: ctanh_downward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
float: 1
ifloat: 1
ildouble: 10
ldouble: 10
Test "Imaginary part of: ctanh_downward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 4
ldouble: 4
# ctanh_tonearest
Test "Real part of: ctanh_tonearest (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
float: 1
ifloat: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: ctanh_tonearest (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
float: 1
ifloat: 1
ildouble: 2
ldouble: 2
# ctanh_towardzero
Test "Real part of: ctanh_towardzero (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
ildouble: 13
ldouble: 13
Test "Imaginary part of: ctanh_towardzero (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
ildouble: 4
ldouble: 4
Test "Real part of: ctanh_towardzero (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
float: 1
ifloat: 1
ildouble: 10
ldouble: 10
Test "Imaginary part of: ctanh_towardzero (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
float: 1
ifloat: 1
ildouble: 2
ldouble: 2
# ctanh_upward
Test "Real part of: ctanh_upward (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
ildouble: 10
ldouble: 10
Test "Imaginary part of: ctanh_upward (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
double: 1
idouble: 1
ildouble: 6
ldouble: 6
Test "Real part of: ctanh_upward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
double: 1
float: 2
idouble: 1
ifloat: 2
ildouble: 1
ldouble: 1
Test "Imaginary part of: ctanh_upward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 3
ldouble: 3
# erf
Test "erf (1.25) == 0.922900128256458230136523481197281140":
double: 1
@ -2714,9 +2879,63 @@ double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: Real part of "ctan_downward":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 4
ldouble: 4
Function: Imaginary part of "ctan_downward":
float: 1
ifloat: 1
ildouble: 10
ldouble: 10
Function: Real part of "ctan_tonearest":
float: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: Imaginary part of "ctan_tonearest":
float: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Real part of "ctan_towardzero":
float: 1
ifloat: 1
ildouble: 4
ldouble: 4
Function: Imaginary part of "ctan_towardzero":
float: 1
ifloat: 1
ildouble: 13
ldouble: 13
Function: Real part of "ctan_upward":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 6
ldouble: 6
Function: Imaginary part of "ctan_upward":
double: 1
float: 2
idouble: 1
ifloat: 2
ildouble: 10
ldouble: 10
Function: Real part of "ctanh":
double: 1
float: 2
@ -2733,6 +2952,60 @@ ifloat: 1
ildouble: 2
ldouble: 2
Function: Real part of "ctanh_downward":
float: 1
ifloat: 1
ildouble: 10
ldouble: 10
Function: Imaginary part of "ctanh_downward":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 4
ldouble: 4
Function: Real part of "ctanh_tonearest":
float: 1
ifloat: 1
ildouble: 1
ldouble: 1
Function: Imaginary part of "ctanh_tonearest":
float: 1
ifloat: 1
ildouble: 2
ldouble: 2
Function: Real part of "ctanh_towardzero":
float: 1
ifloat: 1
ildouble: 13
ldouble: 13
Function: Imaginary part of "ctanh_towardzero":
float: 1
ifloat: 1
ildouble: 4
ldouble: 4
Function: Real part of "ctanh_upward":
double: 1
float: 2
idouble: 1
ifloat: 2
ildouble: 10
ldouble: 10
Function: Imaginary part of "ctanh_upward":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 6
ldouble: 6
Function: "erf":
double: 1
idouble: 1