[newlib-cygwin] casinh: Use approximation for large input.
Corinna Vinschen
corinna@sourceware.org
Thu Aug 4 10:56:42 GMT 2022
https://sourceware.org/git/gitweb.cgi?p=newlib-cygwin.git;h=d939b16adc9d05d225970de1281684fa097565eb
commit d939b16adc9d05d225970de1281684fa097565eb
Author: Markus Mützel <markus.muetzel@gmx.de>
Date: Thu Aug 4 12:55:17 2022 +0200
casinh: Use approximation for large input.
Signed-off-by: Martin Storsjö <martin@martin.st>
Signed-off-by: Corinna Vinschen <corinna@vinschen.de>
Diff:
---
winsup/cygwin/math/casinh.def.h | 21 +++++++++++++++++++++
1 file changed, 21 insertions(+)
diff --git a/winsup/cygwin/math/casinh.def.h b/winsup/cygwin/math/casinh.def.h
index 0cf46980d..3d04d483b 100644
--- a/winsup/cygwin/math/casinh.def.h
+++ b/winsup/cygwin/math/casinh.def.h
@@ -87,6 +87,27 @@ __FLT_ABI(casinh) (__FLT_TYPE __complex__ z)
if (r_class == FP_ZERO && i_class == FP_ZERO)
return z;
+ /* casinh(z) = log(z + sqrt(z*z + 1)) */
+
+ if (__FLT_ABI(fabs) (__real__ z) >= __FLT_CST(1.0)/__FLT_EPSILON
+ || __FLT_ABI(fabs) (__imag__ z) >= __FLT_CST(1.0)/__FLT_EPSILON)
+ {
+ /* For large z, z + sqrt(z*z + 1) is approximately 2*z.
+ Use that approximation to avoid overflow when squaring.
+ Additionally, use symmetries to perform the calculation in the first
+ quadrant. */
+ __real__ x = __FLT_ABI(fabs) (__real__ z);
+ __imag__ x = __FLT_ABI(fabs) (__imag__ z);
+ x = __FLT_ABI(clog) (x);
+ __real__ x += M_LN2;
+
+ /* adjust signs for input quadrant */
+ __real__ ret = __FLT_ABI(copysign) (__real__ x, __real__ z);
+ __imag__ ret = __FLT_ABI(copysign) (__imag__ x, __imag__ z);
+
+ return ret;
+ }
+
__real__ x = (__real__ z - __imag__ z) * (__real__ z + __imag__ z) + __FLT_CST(1.0);
__imag__ x = __FLT_CST(2.0) * __real__ z * __imag__ z;
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