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gh-156695: Improve accuracy of complex powers with small negative integer exponents #156757

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gh-156695: Improve accuracy of complex powers with small negative integer exponents #156757

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2a6a7cb
gh-156695: Improve accuracy of complex powers with small negative int…
Aniketsy Sep 1, 2026
7c611a9
📜🤖 Added by blurb_it.
blurb-it[bot] Sep 1, 2026
48e9342
fix-lint
Aniketsy Sep 1, 2026
c0eeaee
gh-156695: Improve accuracy of complex powers with small negative int…
Aniketsy Sep 1, 2026
cdf6a07
Avoid unnecessary complex power recomputation
Aniketsy Sep 2, 2026
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16 changes: 15 additions & 1 deletion Lib/test/test_complex.py
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Original file line number Diff line number Diff line change
Expand Up @@ -8,7 +8,7 @@
)

from random import random
from math import isnan, copysign
from math import isnan, copysign, ulp
import operator

INF = float("inf")
Expand Down Expand Up @@ -446,6 +446,20 @@ def test_pow_with_small_integer_exponents(self):
self.assertEqual(str(float_pow), str(int_pow))
self.assertEqual(str(complex_pow), str(int_pow))

@support.requires_IEEE_754
def test_pow_small_negative_integer_exponents(self):
z = complex(float.fromhex('0x1.47e9c711723f5p+81'),
float.fromhex('0x1.38afd1168e49fp+85'))
expected = complex(float.fromhex('0x0.4000000000000p-1022'),
float.fromhex('0x0.3ffffffffffffp-1022'))
for exponent in (-12, -12.0, complex(-12.0, 0.0)):
with self.subTest(exponent=exponent):
result = z ** exponent
self.assertLessEqual(abs(result.real - expected.real),
4 * ulp(expected.real))
self.assertLessEqual(abs(result.imag - expected.imag),
4 * ulp(expected.imag))

def test_boolcontext(self):
for i in range(100):
self.assertTrue(complex(random() + 1e-6, random() + 1e-6))
Expand Down
4 changes: 4 additions & 0 deletions Misc/NEWS.d/next/Core_and_Builtins/2026-09-01-09-09-13.gh-issue-156695.-Gih-8.rst
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Original file line number Diff line number Diff line change
@@ -0,0 +1,4 @@
Improve accuracy of :class:`complex` powers with small negative integer
exponents. Previously ``z**-n`` was computed as ``1/(z**n)``; the
intermediate ``z**n`` can overflow even when the result is representable,
in which case all precision was lost.
24 changes: 22 additions & 2 deletions Objects/complexobject.c
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Original file line number Diff line number Diff line change
Expand Up @@ -359,9 +359,29 @@ c_powi(Py_complex x, long n)
{
if (n > 0)
return c_powu(x,n);
else
return _Py_c_quot(c_1, c_powu(x,-n));

Py_complex r = _Py_c_quot(c_1, c_powu(x, -n));

/* gh-156695: x**|n| needs roughly twice the exponent range of the
result, so it can leave the range even when the result itself is
representable, leaving the quotient degenerate. Only then redo the
computation with x scaled to exponent zero; both the scaling and its
undoing are exact. The common path above is untouched. */
if (!(isfinite(r.real) && isfinite(r.imag)
&& (r.real != 0.0 || r.imag != 0.0))
&& errno != EDOM)
{
double m = fabs(x.real) > fabs(x.imag) ? fabs(x.real) : fabs(x.imag);
if (m != 0.0 && isfinite(m)) {
int e;
frexp(m, &e);
Py_complex w = {ldexp(x.real, -e), ldexp(x.imag, -e)};
r = _Py_c_quot(c_1, c_powu(w, -n));
r.real = ldexp(r.real, (int)(e * n));
r.imag = ldexp(r.imag, (int)(e * n));
}
}
return r;
}

double
Expand Down
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