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From: "andreas_roever at web dot de" <gcc-bugzilla@gcc.gnu.org>
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Subject: [Bug libstdc++/103005] experimental simd sin and cos with big
 arguments returns values bigger than 1
Date: Sat, 06 Nov 2021 16:51:28 +0000
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https://gcc.gnu.org/bugzilla/show_bug.cgi?id=3D103005

--- Comment #2 from Andreas R=C3=B6ver <andreas_roever at web dot de> ---
I think the source of the problem is function

__fold_input(const simd<double, _Abi>& __x)

in simd_math.h

this function should return values between -pi/4 and pi/4 but doesn't for t=
he
big argument. E.g for=20

2985064393126969344

it returns

27.678747

according to wolfram alpha it should return=20

0.189812

This "big" value throws off the calculation of the power series that is
performed after this


the 27.678646 is the result of a rounding error

2985064393126969344 / (pi/2) is (according to wolfram alpha again)=20

1900351014455063569.620838

but the CPU gets

1900351014455063552

This seems to be the closest value that the CPU can get to the real value.

the difference between those 2 times pi/2 is the above mentioned 27.67...

... now my numerics skills are not good enough to find a cure for that prob=
lem.=