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[3.13] gh-113841: fix possible undefined division by 0 in _Py_c_pow() (GH-127211) (#127216)
Note, that transformed expression is not an equivalent for original one (1/exp(-x) != exp(x) in general for floating-point numbers). Though, the difference seems to be ~1ULP for good libm implementations.
It's more interesting why division was used from beginning. Closest algorithm I've found (no error checks, of course;)) - it's Algorithm 190 from ACM: https://dl.acm.org/doi/10.1145/366663.366679. It uses subtraction in the exponent.
(cherry picked from commit f7bb658124
)
Co-authored-by: Sergey B Kirpichev <skirpichev@gmail.com>
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3 changed files with 8 additions and 1 deletions
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@ -147,7 +147,7 @@ _Py_c_pow(Py_complex a, Py_complex b)
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at = atan2(a.imag, a.real);
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phase = at*b.real;
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if (b.imag != 0.0) {
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len /= exp(at*b.imag);
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len *= exp(-at*b.imag);
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phase += b.imag*log(vabs);
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}
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r.real = len*cos(phase);
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