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gh-157859: Fix cmath.atanh() returning inf at ±1 ± sqrt(DBL_MIN)*1j #157860

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gh-157859: Fix cmath.atanh() returning inf at ±1 ± sqrt(DBL_MIN)*1j #157860

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15 changes: 15 additions & 0 deletions Lib/test/mathdata/cmath_testcases.txt
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Original file line number Diff line number Diff line change
Expand Up @@ -853,6 +853,13 @@ atan0301 atan 1e-155 1.0 -> 0.78539816339744828 178.79691829731851
atan0302 atan 9.9999999999999999e-161 -1.0 -> 0.78539816339744828 -184.55338102980363
atan0303 atan -1e-165 1.0 -> -0.78539816339744828 190.30984376228875
atan0304 atan -9.9998886718268301e-321 -1.0 -> -0.78539816339744828 -368.76019403576692
-- gh-157859: real part at and next to sqrt(DBL_MIN) = 2**-511 (see atanh0305-0310)
atan0305 atan 1.4916681462400412e-154 1.0 -> 0.78539816339744828 177.445678223346
atan0306 atan 1.4916681462400413e-154 1.0 -> 0.78539816339744828 177.445678223346
atan0307 atan 1.4916681462400417e-154 1.0 -> 0.78539816339744828 177.445678223346
atan0308 atan -1.4916681462400413e-154 1.0 -> -0.78539816339744828 177.445678223346
atan0309 atan 1.4916681462400413e-154 -1.0 -> 0.78539816339744828 -177.445678223346
atan0310 atan -1.4916681462400413e-154 -1.0 -> -0.78539816339744828 -177.445678223346

-- Additional real values (mpmath)
atan0400 atan 1.7976931348623157e+308 0.0 -> 1.5707963267948966192 0.0
Expand Down Expand Up @@ -1043,6 +1050,14 @@ atanh0301 atanh 1.0 9.9999999999999997e-155 -> 177.64562575082149 0.785398163397
atanh0302 atanh -1.0 1e-161 -> -185.70467357630065 0.78539816339744828
atanh0303 atanh 1.0 -1e-165 -> 190.30984376228875 -0.78539816339744828
atanh0304 atanh -1.0 -9.8813129168249309e-324 -> -372.22003596069061 -0.78539816339744828
-- gh-157859: imaginary part at and next to sqrt(DBL_MIN) = 2**-511, where
-- the near-pole and general formulas meet; the boundary value overflowed.
atanh0305 atanh 1.0 1.4916681462400412e-154 -> 177.445678223346 0.78539816339744828
atanh0306 atanh 1.0 1.4916681462400413e-154 -> 177.445678223346 0.78539816339744828
atanh0307 atanh 1.0 1.4916681462400417e-154 -> 177.445678223346 0.78539816339744828
atanh0308 atanh 1.0 -1.4916681462400413e-154 -> 177.445678223346 -0.78539816339744828
atanh0309 atanh -1.0 1.4916681462400413e-154 -> -177.445678223346 0.78539816339744828
atanh0310 atanh -1.0 -1.4916681462400413e-154 -> -177.445678223346 -0.78539816339744828

-- special values
atanh1000 atanh 0.0 0.0 -> 0.0 0.0
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2 changes: 2 additions & 0 deletions Misc/NEWS.d/next/Library/2026-09-20-12-53-29.gh-issue-157859.wMR0YM0E.rst
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@@ -0,0 +1,2 @@
Fix :func:`cmath.atanh` and :func:`cmath.atan` returning an infinite
component instead of a finite result for certain inputs near their poles.
2 changes: 1 addition & 1 deletion Modules/cmathmodule.c
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Expand Up @@ -382,7 +382,7 @@ cmath_atanh_impl(PyObject *module, Py_complex z)
r.real = z.real/4./h/h;
r.imag = copysign(Py_MATH_PI/2., z.imag);
errno = 0;
} else if (z.real == 1. && ay < CM_SQRT_DBL_MIN) {
} else if (z.real == 1. && ay <= CM_SQRT_DBL_MIN) {
/* C99 standard says: atanh(1+/-0.) should be inf +/- 0i */
if (ay == 0.) {
r.real = INF;
Expand Down
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