Modules/cmathmodule.c

Source:

cpython 3.14 @ ab2d84fe1023/Modules/cmathmodule.c ↗

Modules/cmathmodule.c implements the cmath module for complex arithmetic transcendental functions. It wraps C99's <complex.h> where available and falls back to explicit real/imaginary arithmetic, handling the many special cases (NaN, infinity, negative zero, branch cuts) mandated by IEEE 754.

Map

Lines	Symbol	Role
1-150	Py_CARG, c_abs	Argument extraction; magnitude
151-400	cmath_exp, cmath_log, cmath_sqrt	Exponential and logarithmic functions
401-650	cmath_sin, cmath_cos, cmath_tan, hyperbolic	Trig and hyperbolic functions
651-850	cmath_phase, cmath_polar, cmath_rect	Polar coordinate conversions
851-1200	cmath_isnan, cmath_isinf, cmath_isclose	Predicates; module init

Reading

Special-case handling in cmath_exp

Complex exp(z) where z = x + iy is e^x * (cos(y) + i*sin(y)). For x = +inf and y = 0, the result is (+inf, 0). For x = +inf and y = nan, the result is (+inf, nan). These edge cases require explicit checks rather than relying on the C library.

// Modules/cmathmodule.c:151 cmath_exp_impl
static Py_complex
cmath_exp_impl(PyObject *module, Py_complex z)
{
    if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) {
        /* handle inf/nan cases explicitly per C99 Annex G */
    }
    double r = exp(z.real);
    return (Py_complex){r * cos(z.imag), r * sin(z.imag)};
}

polar, phase, rect

cmath.phase(z) returns atan2(z.imag, z.real) (the angle in radians). cmath.polar(z) returns (abs(z), phase(z)) as a tuple. cmath.rect(r, phi) constructs a complex from polar form: r * exp(i*phi) = r*cos(phi) + i*r*sin(phi).

// Modules/cmathmodule.c:651 cmath_rect_impl
static PyObject *
cmath_rect_impl(PyObject *module, double r, double phi)
{
    Py_complex z = {r * cos(phi), r * sin(phi)};
    return PyComplex_FromCComplex(z);
}

Branch cuts

The branch cuts for cmath.log, cmath.sqrt, cmath.asin, cmath.acos match the C99 standard (Annex G) which in turn follows Kahan's original definitions. The imaginary part of sqrt(-1 + 0j) is +0.0, but of sqrt(-1 - 0j) is -0.0. CPython tests these edge cases in Lib/test/test_cmath.py.

gopy notes

Not yet ported. The planned package path is module/cmath/. Go's math/cmplx package implements the same functions with matching IEEE 754 branch cut behavior; the port would wrap those functions and expose them as Python callables.