complex: Fix ln1p precision loss for small arguments#1635
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complex: Fix ln1p precision loss for small arguments#1635
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Use the identity ln(1+z) = 2*atanh(z/(z+2)) which avoids catastrophic cancellation when |z| is small. The previous formula ln(1+z) = ln(|1+z|) + i*arg(1+z) lost nearly all significant digits for small z because 1+z ≈ 1. Also wrap with SaveSetAngleUnits to ensure atan2 uses radians internally, preventing wrong results when the calculator is in degrees mode. Add 9 tests covering zero, real axis, purely imaginary, small values, negative real, high precision, and round-trip ln1p/expm1 identity. Restore precision settings after the identity test to avoid affecting subsequent tests.
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Summary
ln1pfor small arguments by using the identityln(1+z) = 2*atanh(z/(z+2))instead ofln(|1+z|) + i*arg(1+z)SaveSetAngleUnitsto ensureatan2uses radians internally regardless of calculator angle modeTest plan
integer::make()allocation overhead is negligible (<0.3%)