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Fix casinh, casin inaccuracy from cancellation (bug 14994).

This commit is contained in:
Joseph Myers 2013-01-04 13:25:17 +00:00
parent 6420d207bb
commit cdc1c96fba
8 changed files with 171 additions and 19 deletions
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12
ChangeLog
View File

@ -1,3 +1,15 @@
2013-01-04 Joseph Myers <joseph@codesourcery.com>
[BZ #14994]
* math/s_casinh.c (__casinh): Reduce finite argument to first
quadrant then set signs of results at the end.
* math/s_casinhf.c (__casinhf): Likewise.
* math/s_casinhl.c (__casinhl): Likewise.
* math/libm-test.inc (casin_test): Add more tests.
(casinh_test): Likewise.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
2013-01-04 Siddhesh Poyarekar <siddhesh@redhat.com>
* sysdeps/ieee754/dbl-64/mpa.h: Fix code formatting.

2
NEWS
View File

@ -9,7 +9,7 @@ Version 2.18
* The following bugs are resolved with this release:
13951, 14317, 14981, 14982.
13951, 14317, 14981, 14982, 14994.
Version 2.17

58
math/libm-test.inc
View File

@ -1698,6 +1698,35 @@ casin_test (void)
TEST_c_c (casin, 1.5L, plus_zero, M_PI_2l, 0.9624236501192068949955178268487368462704L);
TEST_c_c (casin, 1.5L, minus_zero, M_PI_2l, -0.9624236501192068949955178268487368462704L);
TEST_c_c (casin, 0x1p50L, 1.0L, 1.570796326794895731052901991514519103193L, 3.535050620855721078027883819436720218708e1L);
TEST_c_c (casin, 0x1p50L, -1.0L, 1.570796326794895731052901991514519103193L, -3.535050620855721078027883819436720218708e1L);
TEST_c_c (casin, -0x1p50L, 1.0L, -1.570796326794895731052901991514519103193L, 3.535050620855721078027883819436720218708e1L);
TEST_c_c (casin, -0x1p50L, -1.0L, -1.570796326794895731052901991514519103193L, -3.535050620855721078027883819436720218708e1L);
TEST_c_c (casin, 1.0L, 0x1p50L, 8.881784197001252323389053344720723756399e-16L, 3.535050620855721078027883819436759661753e1L);
TEST_c_c (casin, -1.0L, 0x1p50L, -8.881784197001252323389053344720723756399e-16L, 3.535050620855721078027883819436759661753e1L);
TEST_c_c (casin, 1.0L, -0x1p50L, 8.881784197001252323389053344720723756399e-16L, -3.535050620855721078027883819436759661753e1L);
TEST_c_c (casin, -1.0L, -0x1p50L, -8.881784197001252323389053344720723756399e-16L, -3.535050620855721078027883819436759661753e1L);
#ifndef TEST_FLOAT
TEST_c_c (casin, 0x1p500L, 1.0L, 1.570796326794896619231321691639751442099L, 3.472667374605326000180332928505464606058e2L);
TEST_c_c (casin, 0x1p500L, -1.0L, 1.570796326794896619231321691639751442099L, -3.472667374605326000180332928505464606058e2L);
TEST_c_c (casin, -0x1p500L, 1.0L, -1.570796326794896619231321691639751442099L, 3.472667374605326000180332928505464606058e2L);
TEST_c_c (casin, -0x1p500L, -1.0L, -1.570796326794896619231321691639751442099L, -3.472667374605326000180332928505464606058e2L);
TEST_c_c (casin, 1.0L, 0x1p500L, 3.054936363499604682051979393213617699789e-151L, 3.472667374605326000180332928505464606058e2L);
TEST_c_c (casin, -1.0L, 0x1p500L, -3.054936363499604682051979393213617699789e-151L, 3.472667374605326000180332928505464606058e2L);
TEST_c_c (casin, 1.0L, -0x1p500L, 3.054936363499604682051979393213617699789e-151L, -3.472667374605326000180332928505464606058e2L);
TEST_c_c (casin, -1.0L, -0x1p500L, -3.054936363499604682051979393213617699789e-151L, -3.472667374605326000180332928505464606058e2L);
#endif
#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
TEST_c_c (casin, 0x1p5000L, 1.0L, 1.570796326794896619231321691639751442099L, 3.466429049980286492395577839412341016946e3L);
TEST_c_c (casin, 0x1p5000L, -1.0L, 1.570796326794896619231321691639751442099L, -3.466429049980286492395577839412341016946e3L);
TEST_c_c (casin, -0x1p5000L, 1.0L, -1.570796326794896619231321691639751442099L, 3.466429049980286492395577839412341016946e3L);
TEST_c_c (casin, -0x1p5000L, -1.0L, -1.570796326794896619231321691639751442099L, -3.466429049980286492395577839412341016946e3L);
TEST_c_c (casin, 1.0L, 0x1p5000L, 7.079811261048172892385615158694057552948e-1506L, 3.466429049980286492395577839412341016946e3L);
TEST_c_c (casin, -1.0L, 0x1p5000L, -7.079811261048172892385615158694057552948e-1506L, 3.466429049980286492395577839412341016946e3L);
TEST_c_c (casin, 1.0L, -0x1p5000L, 7.079811261048172892385615158694057552948e-1506L, -3.466429049980286492395577839412341016946e3L);
TEST_c_c (casin, -1.0L, -0x1p5000L, -7.079811261048172892385615158694057552948e-1506L, -3.466429049980286492395577839412341016946e3L);
#endif
TEST_c_c (casin, 0.75L, 1.25L, 0.453276177638793913448921196101971749L, 1.13239363160530819522266333696834467L);
TEST_c_c (casin, -2, -3, -0.57065278432109940071028387968566963L, -1.9833870299165354323470769028940395L);
@ -1788,6 +1817,35 @@ casinh_test (void)
TEST_c_c (casinh, 1.5L, plus_zero, 1.194763217287109304111930828519090523536L, plus_zero);
TEST_c_c (casinh, 1.5L, minus_zero, 1.194763217287109304111930828519090523536L, minus_zero);
TEST_c_c (casinh, 0x1p50L, 1.0L, 3.535050620855721078027883819436759661753e1L, 8.881784197001252323389053344720723756399e-16L);
TEST_c_c (casinh, 0x1p50L, -1.0L, 3.535050620855721078027883819436759661753e1L, -8.881784197001252323389053344720723756399e-16L);
TEST_c_c (casinh, -0x1p50L, 1.0L, -3.535050620855721078027883819436759661753e1L, 8.881784197001252323389053344720723756399e-16L);
TEST_c_c (casinh, -0x1p50L, -1.0L, -3.535050620855721078027883819436759661753e1L, -8.881784197001252323389053344720723756399e-16L);
TEST_c_c (casinh, 1.0L, 0x1p50L, 3.535050620855721078027883819436720218708e1L, 1.570796326794895731052901991514519103193L);
TEST_c_c (casinh, -1.0L, 0x1p50L, -3.535050620855721078027883819436720218708e1L, 1.570796326794895731052901991514519103193L);
TEST_c_c (casinh, 1.0L, -0x1p50L, 3.535050620855721078027883819436720218708e1L, -1.570796326794895731052901991514519103193L);
TEST_c_c (casinh, -1.0L, -0x1p50L, -3.535050620855721078027883819436720218708e1L, -1.570796326794895731052901991514519103193L);
#ifndef TEST_FLOAT
TEST_c_c (casinh, 0x1p500L, 1.0L, 3.472667374605326000180332928505464606058e2L, 3.054936363499604682051979393213617699789e-151L);
TEST_c_c (casinh, 0x1p500L, -1.0L, 3.472667374605326000180332928505464606058e2L, -3.054936363499604682051979393213617699789e-151L);
TEST_c_c (casinh, -0x1p500L, 1.0L, -3.472667374605326000180332928505464606058e2L, 3.054936363499604682051979393213617699789e-151L);
TEST_c_c (casinh, -0x1p500L, -1.0L, -3.472667374605326000180332928505464606058e2L, -3.054936363499604682051979393213617699789e-151L);
TEST_c_c (casinh, 1.0L, 0x1p500L, 3.472667374605326000180332928505464606058e2L, 1.570796326794896619231321691639751442099L);
TEST_c_c (casinh, -1.0L, 0x1p500L, -3.472667374605326000180332928505464606058e2L, 1.570796326794896619231321691639751442099L);
TEST_c_c (casinh, 1.0L, -0x1p500L, 3.472667374605326000180332928505464606058e2L, -1.570796326794896619231321691639751442099L);
TEST_c_c (casinh, -1.0L, -0x1p500L, -3.472667374605326000180332928505464606058e2L, -1.570796326794896619231321691639751442099L);
#endif
#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
TEST_c_c (casinh, 0x1p5000L, 1.0L, 3.466429049980286492395577839412341016946e3L, 7.079811261048172892385615158694057552948e-1506L);
TEST_c_c (casinh, 0x1p5000L, -1.0L, 3.466429049980286492395577839412341016946e3L, -7.079811261048172892385615158694057552948e-1506L);
TEST_c_c (casinh, -0x1p5000L, 1.0L, -3.466429049980286492395577839412341016946e3L, 7.079811261048172892385615158694057552948e-1506L);
TEST_c_c (casinh, -0x1p5000L, -1.0L, -3.466429049980286492395577839412341016946e3L, -7.079811261048172892385615158694057552948e-1506L);
TEST_c_c (casinh, 1.0L, 0x1p5000L, 3.466429049980286492395577839412341016946e3L, 1.570796326794896619231321691639751442099L);
TEST_c_c (casinh, -1.0L, 0x1p5000L, -3.466429049980286492395577839412341016946e3L, 1.570796326794896619231321691639751442099L);
TEST_c_c (casinh, 1.0L, -0x1p5000L, 3.466429049980286492395577839412341016946e3L, -1.570796326794896619231321691639751442099L);
TEST_c_c (casinh, -1.0L, -0x1p5000L, -3.466429049980286492395577839412341016946e3L, -1.570796326794896619231321691639751442099L);
#endif
TEST_c_c (casinh, 0.75L, 1.25L, 1.03171853444778027336364058631006594L, 0.911738290968487636358489564316731207L);
TEST_c_c (casinh, -2, -3, -1.9686379257930962917886650952454982L, -0.96465850440760279204541105949953237L);

16
math/s_casinh.c
View File

@ -62,20 +62,24 @@ __casinh (__complex__ double x)
}
else
{
double rx, ix;
__complex__ double y;
__real__ y = (__real__ x - __imag__ x) * (__real__ x + __imag__ x) + 1.0;
__imag__ y = 2.0 * __real__ x * __imag__ x;
/* Avoid cancellation by reducing to the first quadrant. */
rx = fabs (__real__ x);
ix = fabs (__imag__ x);
__real__ y = (rx - ix) * (rx + ix) + 1.0;
__imag__ y = 2.0 * rx * ix;
y = __csqrt (y);
__real__ y += __real__ x;
__imag__ y += __imag__ x;
__real__ y += rx;
__imag__ y += ix;
res = __clog (y);
/* Ensure zeros have correct sign and results are correct if
very close to branch cuts. */
/* Give results the correct sign for the original argument. */
__real__ res = __copysign (__real__ res, __real__ x);
__imag__ res = __copysign (__imag__ res, __imag__ x);
}

16
math/s_casinhf.c
View File

@ -62,20 +62,24 @@ __casinhf (__complex__ float x)
}
else
{
float rx, ix;
__complex__ float y;
__real__ y = (__real__ x - __imag__ x) * (__real__ x + __imag__ x) + 1.0;
__imag__ y = 2.0 * __real__ x * __imag__ x;
/* Avoid cancellation by reducing to the first quadrant. */
rx = fabsf (__real__ x);
ix = fabsf (__imag__ x);
__real__ y = (rx - ix) * (rx + ix) + 1.0;
__imag__ y = 2.0 * rx * ix;
y = __csqrtf (y);
__real__ y += __real__ x;
__imag__ y += __imag__ x;
__real__ y += rx;
__imag__ y += ix;
res = __clogf (y);
/* Ensure zeros have correct sign and results are correct if
very close to branch cuts. */
/* Give results the correct sign for the original argument. */
__real__ res = __copysignf (__real__ res, __real__ x);
__imag__ res = __copysignf (__imag__ res, __imag__ x);
}

16
math/s_casinhl.c
View File

@ -62,20 +62,24 @@ __casinhl (__complex__ long double x)
}
else
{
long double rx, ix;
__complex__ long double y;
__real__ y = (__real__ x - __imag__ x) * (__real__ x + __imag__ x) + 1.0;
__imag__ y = 2.0 * __real__ x * __imag__ x;
/* Avoid cancellation by reducing to the first quadrant. */
rx = fabsl (__real__ x);
ix = fabsl (__imag__ x);
__real__ y = (rx - ix) * (rx + ix) + 1.0;
__imag__ y = 2.0 * rx * ix;
y = __csqrtl (y);
__real__ y += __real__ x;
__imag__ y += __imag__ x;
__real__ y += rx;
__imag__ y += ix;
res = __clogl (y);
/* Ensure zeros have correct sign and results are correct if
very close to branch cuts. */
/* Give results the correct sign for the original argument. */
__real__ res = __copysignl (__real__ res, __real__ x);
__imag__ res = __copysignl (__imag__ res, __imag__ x);
}

41
sysdeps/i386/fpu/libm-test-ulps
View File

@ -209,7 +209,11 @@ ldouble: 1
# cacos
Test "Imaginary part of: cacos (+0 + 0.5 i) == pi/2 - 0.4812118250596034474977589134243684231352 i":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: cacos (+0 + 1.0 i) == pi/2 - 0.8813735870195430252326093249797923090282 i":
double: 2
float: 1
@ -239,7 +243,11 @@ double: 1
idouble: 1
Test "Imaginary part of: cacos (-0 + 0.5 i) == pi/2 - 0.4812118250596034474977589134243684231352 i":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: cacos (-0 + 1.0 i) == pi/2 - 0.8813735870195430252326093249797923090282 i":
double: 2
float: 1
@ -272,6 +280,8 @@ double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: cacos (-1.5 - 0 i) == pi + 0.9624236501192068949955178268487368462704 i":
ildouble: 1
ldouble: 1
@ -285,6 +295,9 @@ double: 1
idouble: 1
ildouble: 1
ldouble: 1
Test "Real part of: cacos (0.75 + 1.25 i) == 1.11752014915610270578240049553777969 - 1.13239363160530819522266333696834467 i":
float: 1
ifloat: 1
Test "Imaginary part of: cacos (0.75 + 1.25 i) == 1.11752014915610270578240049553777969 - 1.13239363160530819522266333696834467 i":
float: 1
ifloat: 1
@ -295,6 +308,8 @@ double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: cacos (1.5 - 0 i) == +0 + 0.9624236501192068949955178268487368462704 i":
ildouble: 1
ldouble: 1
@ -415,7 +430,11 @@ ldouble: 1
# casin
Test "Imaginary part of: casin (+0 + 0.5 i) == +0 + 0.4812118250596034474977589134243684231352 i":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: casin (+0 + 1.0 i) == +0 + 0.8813735870195430252326093249797923090282 i":
double: 2
float: 1
@ -445,7 +464,11 @@ double: 1
idouble: 1
Test "Imaginary part of: casin (-0 + 0.5 i) == -0 + 0.4812118250596034474977589134243684231352 i":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: casin (-0 + 1.0 i) == -0 + 0.8813735870195430252326093249797923090282 i":
double: 2
float: 1
@ -478,6 +501,8 @@ double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: casin (-1.5 - 0 i) == -pi/2 - 0.9624236501192068949955178268487368462704 i":
ildouble: 1
ldouble: 1
@ -498,6 +523,8 @@ double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: casin (1.5 - 0 i) == pi/2 - 0.9624236501192068949955178268487368462704 i":
ildouble: 1
ldouble: 1
@ -514,17 +541,29 @@ double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Test "Real part of: casinh (-0 - 1.5 i) == -0.9624236501192068949955178268487368462704 - pi/2 i":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Test "Real part of: casinh (-0.5 + +0 i) == -0.4812118250596034474977589134243684231352 + +0 i":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 1
ldouble: 1
Test "Real part of: casinh (-0.5 - 0 i) == -0.4812118250596034474977589134243684231352 - 0 i":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 1
ldouble: 1
Test "Real part of: casinh (-1.0 + +0 i) == -0.8813735870195430252326093249797923090282 + +0 i":
double: 2
float: 1
@ -3288,7 +3327,9 @@ ldouble: 1
Function: Real part of "cacos":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1

29
sysdeps/x86_64/fpu/libm-test-ulps
View File

@ -185,6 +185,8 @@ double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: cacos (+0 + 1.0 i) == pi/2 - 0.8813735870195430252326093249797923090282 i":
double: 2
float: 1
@ -215,6 +217,8 @@ double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: cacos (-0 + 1.0 i) == pi/2 - 0.8813735870195430252326093249797923090282 i":
double: 2
float: 1
@ -245,6 +249,8 @@ double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: cacos (-1.5 - 0 i) == pi + 0.9624236501192068949955178268487368462704 i":
ildouble: 1
ldouble: 1
@ -258,6 +264,9 @@ double: 1
idouble: 1
ildouble: 1
ldouble: 1
Test "Real part of: cacos (0.75 + 1.25 i) == 1.11752014915610270578240049553777969 - 1.13239363160530819522266333696834467 i":
float: 1
ifloat: 1
Test "Imaginary part of: cacos (0.75 + 1.25 i) == 1.11752014915610270578240049553777969 - 1.13239363160530819522266333696834467 i":
float: 1
ifloat: 1
@ -268,6 +277,8 @@ double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: cacos (1.5 - 0 i) == +0 + 0.9624236501192068949955178268487368462704 i":
ildouble: 1
ldouble: 1
@ -375,6 +386,8 @@ double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: casin (+0 + 1.0 i) == +0 + 0.8813735870195430252326093249797923090282 i":
double: 2
float: 1
@ -405,6 +418,8 @@ double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: casin (-0 + 1.0 i) == -0 + 0.8813735870195430252326093249797923090282 i":
double: 2
float: 1
@ -435,6 +450,8 @@ double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: casin (-1.5 - 0 i) == -pi/2 - 0.9624236501192068949955178268487368462704 i":
ildouble: 1
ldouble: 1
@ -455,6 +472,8 @@ double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: casin (1.5 - 0 i) == pi/2 - 0.9624236501192068949955178268487368462704 i":
ildouble: 1
ldouble: 1
@ -471,21 +490,29 @@ double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Test "Real part of: casinh (-0 - 1.5 i) == -0.9624236501192068949955178268487368462704 - pi/2 i":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
Test "Real part of: casinh (-0.5 + +0 i) == -0.4812118250596034474977589134243684231352 + +0 i":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 1
ldouble: 1
Test "Real part of: casinh (-0.5 - 0 i) == -0.4812118250596034474977589134243684231352 - 0 i":
double: 2
float: 1
idouble: 2
ifloat: 1
ildouble: 1
ldouble: 1
Test "Real part of: casinh (-1.0 + +0 i) == -0.8813735870195430252326093249797923090282 + +0 i":
double: 2
float: 1
@ -3066,7 +3093,9 @@ ldouble: 1
Function: Real part of "cacos":
double: 1
float: 1
idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1