Issue #19543: Implementation of isclose as per PEP 485

For details, see:
PEP 0485 -- A Function for testing approximate equality

Functions added: math.isclose() and cmath.isclose().

Original code by Chris Barker. Patch by Tal Einat.
diff --git a/Modules/clinic/cmathmodule.c.h b/Modules/clinic/cmathmodule.c.h
index e8fa6cb..7d61649 100644
--- a/Modules/clinic/cmathmodule.c.h
+++ b/Modules/clinic/cmathmodule.c.h
@@ -806,4 +806,55 @@
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=274f59792cf4f418 input=a9049054013a1b77]*/
+
+PyDoc_STRVAR(cmath_isclose__doc__,
+"isclose($module, /, a, b, *, rel_tol=1e-09, abs_tol=0.0)\n"
+"--\n"
+"\n"
+"Determine whether two complex numbers are close in value.\n"
+"\n"
+"  rel_tol\n"
+"    maximum difference for being considered \"close\", relative to the\n"
+"    magnitude of the input values\n"
+"  abs_tol\n"
+"    maximum difference for being considered \"close\", regardless of the\n"
+"    magnitude of the input values\n"
+"\n"
+"Return True if a is close in value to b, and False otherwise.\n"
+"\n"
+"For the values to be considered close, the difference between them must be\n"
+"smaller than at least one of the tolerances.\n"
+"\n"
+"-inf, inf and NaN behave similarly to the IEEE 754 Standard. That is, NaN is\n"
+"not close to anything, even itself. inf and -inf are only close to themselves.");
+
+#define CMATH_ISCLOSE_METHODDEF    \
+    {"isclose", (PyCFunction)cmath_isclose, METH_VARARGS|METH_KEYWORDS, cmath_isclose__doc__},
+
+static int
+cmath_isclose_impl(PyModuleDef *module, Py_complex a, Py_complex b,
+                   double rel_tol, double abs_tol);
+
+static PyObject *
+cmath_isclose(PyModuleDef *module, PyObject *args, PyObject *kwargs)
+{
+    PyObject *return_value = NULL;
+    static char *_keywords[] = {"a", "b", "rel_tol", "abs_tol", NULL};
+    Py_complex a;
+    Py_complex b;
+    double rel_tol = 1e-09;
+    double abs_tol = 0.0;
+    int _return_value;
+
+    if (!PyArg_ParseTupleAndKeywords(args, kwargs, "DD|$dd:isclose", _keywords,
+        &a, &b, &rel_tol, &abs_tol))
+        goto exit;
+    _return_value = cmath_isclose_impl(module, a, b, rel_tol, abs_tol);
+    if ((_return_value == -1) && PyErr_Occurred())
+        goto exit;
+    return_value = PyBool_FromLong((long)_return_value);
+
+exit:
+    return return_value;
+}
+/*[clinic end generated code: output=229e9c48c9d27362 input=a9049054013a1b77]*/
diff --git a/Modules/cmathmodule.c b/Modules/cmathmodule.c
index 921eaaa..d12e4c5 100644
--- a/Modules/cmathmodule.c
+++ b/Modules/cmathmodule.c
@@ -1114,6 +1114,73 @@
                            Py_IS_INFINITY(z.imag));
 }
 
+/*[clinic input]
+cmath.isclose -> bool
+
+    a: Py_complex
+    b: Py_complex
+    *
+    rel_tol: double = 1e-09
+        maximum difference for being considered "close", relative to the
+        magnitude of the input values
+    abs_tol: double = 0.0
+        maximum difference for being considered "close", regardless of the
+        magnitude of the input values
+
+Determine whether two complex numbers are close in value.
+
+Return True if a is close in value to b, and False otherwise.
+
+For the values to be considered close, the difference between them must be
+smaller than at least one of the tolerances.
+
+-inf, inf and NaN behave similarly to the IEEE 754 Standard. That is, NaN is
+not close to anything, even itself. inf and -inf are only close to themselves.
+[clinic start generated code]*/
+
+static int
+cmath_isclose_impl(PyModuleDef *module, Py_complex a, Py_complex b,
+                   double rel_tol, double abs_tol)
+/*[clinic end generated code: output=da0c535fb54e2310 input=df9636d7de1d4ac3]*/
+{
+    double diff;
+
+    /* sanity check on the inputs */
+    if (rel_tol < 0.0 || abs_tol < 0.0 ) {
+        PyErr_SetString(PyExc_ValueError,
+                        "tolerances must be non-negative");
+        return -1;
+    }
+
+    if ( (a.real == b.real) && (a.imag == b.imag) ) {
+        /* short circuit exact equality -- needed to catch two infinities of
+           the same sign. And perhaps speeds things up a bit sometimes.
+        */
+        return 1;
+    }
+
+    /* This catches the case of two infinities of opposite sign, or
+       one infinity and one finite number. Two infinities of opposite
+       sign would otherwise have an infinite relative tolerance.
+       Two infinities of the same sign are caught by the equality check
+       above.
+    */
+
+    if (Py_IS_INFINITY(a.real) || Py_IS_INFINITY(a.imag) ||
+        Py_IS_INFINITY(b.real) || Py_IS_INFINITY(b.imag)) {
+        return 0;
+    }
+
+    /* now do the regular computation
+       this is essentially the "weak" test from the Boost library
+    */
+
+    diff = _Py_c_abs(_Py_c_diff(a, b));
+
+    return (((diff <= rel_tol * _Py_c_abs(b)) ||
+             (diff <= rel_tol * _Py_c_abs(a))) ||
+            (diff <= abs_tol));
+}
 
 PyDoc_STRVAR(module_doc,
 "This module is always available. It provides access to mathematical\n"
@@ -1129,6 +1196,7 @@
     CMATH_COS_METHODDEF
     CMATH_COSH_METHODDEF
     CMATH_EXP_METHODDEF
+    CMATH_ISCLOSE_METHODDEF
     CMATH_ISFINITE_METHODDEF
     CMATH_ISINF_METHODDEF
     CMATH_ISNAN_METHODDEF
diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index a65de47..9359eb2 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -1990,6 +1990,83 @@
 "isinf(x) -> bool\n\n\
 Return True if x is a positive or negative infinity, and False otherwise.");
 
+static PyObject *
+math_isclose(PyObject *self, PyObject *args, PyObject *kwargs)
+{
+    double a, b;
+    double rel_tol = 1e-9;
+    double abs_tol = 0.0;
+    double diff = 0.0;
+    long result = 0;
+
+    static char *keywords[] = {"a", "b", "rel_tol", "abs_tol", NULL};
+
+
+    if (!PyArg_ParseTupleAndKeywords(args, kwargs, "dd|$dd:isclose",
+                                     keywords,
+                                     &a, &b, &rel_tol, &abs_tol
+                                     ))
+        return NULL;
+
+    /* sanity check on the inputs */
+    if (rel_tol < 0.0 || abs_tol < 0.0 ) {
+        PyErr_SetString(PyExc_ValueError,
+                        "tolerances must be non-negative");
+        return NULL;
+    }
+
+    if ( a == b ) {
+        /* short circuit exact equality -- needed to catch two infinities of
+           the same sign. And perhaps speeds things up a bit sometimes.
+        */
+        Py_RETURN_TRUE;
+    }
+
+    /* This catches the case of two infinities of opposite sign, or
+       one infinity and one finite number. Two infinities of opposite
+       sign would otherwise have an infinite relative tolerance.
+       Two infinities of the same sign are caught by the equality check
+       above.
+    */
+
+    if (Py_IS_INFINITY(a) || Py_IS_INFINITY(b)) {
+        Py_RETURN_FALSE;
+    }
+
+    /* now do the regular computation
+       this is essentially the "weak" test from the Boost library
+    */
+
+    diff = fabs(b - a);
+
+    result = (((diff <= fabs(rel_tol * b)) ||
+               (diff <= fabs(rel_tol * a))) ||
+              (diff <= abs_tol));
+
+    return PyBool_FromLong(result);
+}
+
+PyDoc_STRVAR(math_isclose_doc,
+"is_close(a, b, *, rel_tol=1e-09, abs_tol=0.0) -> bool\n"
+"\n"
+"Determine whether two floating point numbers are close in value.\n"
+"\n"
+"   rel_tol\n"
+"       maximum difference for being considered \"close\", relative to the\n"
+"       magnitude of the input values\n"
+"    abs_tol\n"
+"       maximum difference for being considered \"close\", regardless of the\n"
+"       magnitude of the input values\n"
+"\n"
+"Return True if a is close in value to b, and False otherwise.\n"
+"\n"
+"For the values to be considered close, the difference between them\n"
+"must be smaller than at least one of the tolerances.\n"
+"\n"
+"-inf, inf and NaN behave similarly to the IEEE 754 Standard.  That\n"
+"is, NaN is not close to anything, even itself.  inf and -inf are\n"
+"only close to themselves.");
+
 static PyMethodDef math_methods[] = {
     {"acos",            math_acos,      METH_O,         math_acos_doc},
     {"acosh",           math_acosh,     METH_O,         math_acosh_doc},
@@ -2016,6 +2093,8 @@
     {"gamma",           math_gamma,     METH_O,         math_gamma_doc},
     {"gcd",             math_gcd,       METH_VARARGS,   math_gcd_doc},
     {"hypot",           math_hypot,     METH_VARARGS,   math_hypot_doc},
+    {"isclose", (PyCFunction) math_isclose, METH_VARARGS | METH_KEYWORDS,
+    math_isclose_doc},
     {"isfinite",        math_isfinite,  METH_O,         math_isfinite_doc},
     {"isinf",           math_isinf,     METH_O,         math_isinf_doc},
     {"isnan",           math_isnan,     METH_O,         math_isnan_doc},