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Use Kahan's formula in cacosh

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Ulrich Drepper
2011-12-21 22:08:12 -05:00
parent b27e24b874
commit e3a851a21b
4 changed files with 24 additions and 0 deletions
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7
ChangeLog
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@ -1,3 +1,10 @@
2011-12-21 Ulrich Drepper <drepper@gmail.com>
* math/s_cacosh.c: Use Kahan's formula if the subtraction could lead
to large cancellation.
* math/s_cacoshf.c: Likewise.
* math/s_cacoshl.c: Likewise.
2011-11-18 Richard B. Kreckel <kreckel@ginac.de> 2011-11-18 Richard B. Kreckel <kreckel@ginac.de>
[BZ #13305] [BZ #13305]

5
math/s_cacosh.c
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@ -65,6 +65,11 @@ __cacosh (__complex__ double x)
__real__ res = 0.0; __real__ res = 0.0;
__imag__ res = __copysign (M_PI_2, __imag__ x); __imag__ res = __copysign (M_PI_2, __imag__ x);
} }
/* The factor 16 is just a guess. */
else if (16.0 * fabs (__imag__ x) < fabs (__real__ x))
/* Kahan's formula which avoid cancellation through subtraction in
some cases. */
res = 2.0 * __clog (__csqrt ((x + 1.0) / 2.0) + __csqrt ((x - 1.0) / 2.0));
else else
{ {
__complex__ double y; __complex__ double y;

6
math/s_cacoshf.c
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@ -65,6 +65,12 @@ __cacoshf (__complex__ float x)
__real__ res = 0.0; __real__ res = 0.0;
__imag__ res = __copysignf (M_PI_2, __imag__ x); __imag__ res = __copysignf (M_PI_2, __imag__ x);
} }
/* The factor 16 is just a guess. */
else if (16.0 * fabsf (__imag__ x) < fabsf (__real__ x))
/* Kahan's formula which avoid cancellation through subtraction in
some cases. */
res = 2.0 * __clogf (__csqrtf ((x + 1.0) / 2.0)
+ __csqrtf ((x - 1.0) / 2.0));
else else
{ {
__complex__ float y; __complex__ float y;

6
math/s_cacoshl.c
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@ -65,6 +65,12 @@ __cacoshl (__complex__ long double x)
__real__ res = 0.0; __real__ res = 0.0;
__imag__ res = __copysignl (M_PI_2l, __imag__ x); __imag__ res = __copysignl (M_PI_2l, __imag__ x);
} }
/* The factor 16 is just a guess. */
else if (16.0L * fabsl (__imag__ x) < fabsl (__real__ x))
/* Kahan's formula which avoid cancellation through subtraction in
some cases. */
res = 2.0L * __clogl (__csqrtl ((x + 1.0L) / 2.0L)
+ __csqrtl ((x - 1.0L) / 2.0L));
else else
{ {
__complex__ long double y; __complex__ long double y;