[Octave-bug-tracker] [bug #43349] asin() behaves differently from Matlab for arguments larger than 1

[Rik]

Follow-up Comment #17, bug #43349 (project octave):

The phase makes a difference because


x*x


preserves the signbit on the imaginary portion of the product when it is zero.
 I tried in C++ and


2-0i * 2-0i = 4 - 0i


The sqrt function distinguishes between the two phase angles -0, +0 and so the
results come out different for asin (2-0i) and asin (-2+0i).  I had the sign
reversed in my first attempt but the attached second attempt works fine.


 Complex
 rc_asin (double x)
 {
-  return fabs (x) > 1.0 ? asin (Complex (x)) : Complex (asin (x));
+  return fabs (x) > 1.0 ? asin (Complex (x, signbit (x) ? 0.0 : -0.0))
+                        : Complex (asin (x));
 }


I used the following as a reference for expected values across the branch cut:
http://www.mathworks.com/help/symbolic/mupad_ref/arcsin.html#stdlib-invtrigfuncs-ex4

I think either patch will work.  I tried timing them and jwe's method is 2%
faster, although that is close to being noise.  I tried asin on a 3000 x 3000
element matrix with the following results.


rik Patch
---------
2.277
2.261
2.263
2.257

mean = 2.2645

jwe Patch
---------
2.211
2.213
2.217
2.234

mean = 2.2188



(file #32237)
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Additional Item Attachment:

File name: asin.patch                     Size:0 KB


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