Add CPython math/cmath tests (#150794)

Tests:
* test_math.py
* test_cmath.py

Minor changes were made to each test to run them inside Dynamo

One can reproduce the changes by downloading the tests from CPython and applying the diff:

```bash
for f in "test_math" "test_cmath"; do
	wget -O "test/dynamo/cpython/3_13/${f}.py" "https://raw.githubusercontent.com/python/cpython/refs/heads/3.13/Lib/test/${f}.py"
	git apply "test/dynamo/cpython/3_13/${f}.diff"
done
```

Pull Request resolved: https://github.com/pytorch/pytorch/pull/150794
Approved by: https://github.com/zou3519

test/dynamo/cpython/3_13/mathdata/formatfloat_testcases.txt

@@ -0,0 +1,355 @@
+-- 'f' code formatting, with explicit precision (>= 0).  Output always
+-- has the given number of places after the point;  zeros are added if
+-- necessary to make this true.
+
+-- zeros
+%.0f 0 -> 0
+%.1f 0 -> 0.0
+%.2f 0 -> 0.00
+%.3f 0 -> 0.000
+%.50f 0 -> 0.00000000000000000000000000000000000000000000000000
+
+-- precision 0;  result should never include a .
+%.0f 1.5 -> 2
+%.0f 2.5 -> 2
+%.0f 3.5 -> 4
+%.0f 0.0 -> 0
+%.0f 0.1 -> 0
+%.0f 0.001 -> 0
+%.0f 10.0 -> 10
+%.0f 10.1 -> 10
+%.0f 10.01 -> 10
+%.0f 123.456 -> 123
+%.0f 1234.56 -> 1235
+%.0f 1e49 -> 9999999999999999464902769475481793196872414789632
+%.0f 9.9999999999999987e+49 -> 99999999999999986860582406952576489172979654066176
+%.0f 1e50 -> 100000000000000007629769841091887003294964970946560
+
+-- precision 1
+%.1f 0.0001 -> 0.0
+%.1f 0.001 -> 0.0
+%.1f 0.01 -> 0.0
+%.1f 0.04 -> 0.0
+%.1f 0.06 -> 0.1
+%.1f 0.25 -> 0.2
+%.1f 0.75 -> 0.8
+%.1f 1.4 -> 1.4
+%.1f 1.5 -> 1.5
+%.1f 10.0 -> 10.0
+%.1f 1000.03 -> 1000.0
+%.1f 1234.5678 -> 1234.6
+%.1f 1234.7499 -> 1234.7
+%.1f 1234.75 -> 1234.8
+
+-- precision 2
+%.2f 0.0001 -> 0.00
+%.2f 0.001 -> 0.00
+%.2f 0.004999 -> 0.00
+%.2f 0.005001 -> 0.01
+%.2f 0.01 -> 0.01
+%.2f 0.125 -> 0.12
+%.2f 0.375 -> 0.38
+%.2f 1234500 -> 1234500.00
+%.2f 1234560 -> 1234560.00
+%.2f 1234567 -> 1234567.00
+%.2f 1234567.8 -> 1234567.80
+%.2f 1234567.89 -> 1234567.89
+%.2f 1234567.891 -> 1234567.89
+%.2f 1234567.8912 -> 1234567.89
+
+-- alternate form always includes a decimal point.  This only
+-- makes a difference when the precision is 0.
+%#.0f 0 -> 0.
+%#.1f 0 -> 0.0
+%#.0f 1.5 -> 2.
+%#.0f 2.5 -> 2.
+%#.0f 10.1 -> 10.
+%#.0f 1234.56 -> 1235.
+%#.1f 1.4 -> 1.4
+%#.2f 0.375 -> 0.38
+
+-- if precision is omitted it defaults to 6
+%f 0 -> 0.000000
+%f 1230000 -> 1230000.000000
+%f 1234567 -> 1234567.000000
+%f 123.4567 -> 123.456700
+%f 1.23456789 -> 1.234568
+%f 0.00012 -> 0.000120
+%f 0.000123 -> 0.000123
+%f 0.00012345 -> 0.000123
+%f 0.000001 -> 0.000001
+%f 0.0000005001 -> 0.000001
+%f 0.0000004999 -> 0.000000
+
+-- 'e' code formatting with explicit precision (>= 0). Output should
+-- always have exactly the number of places after the point that were
+-- requested.
+
+-- zeros
+%.0e 0 -> 0e+00
+%.1e 0 -> 0.0e+00
+%.2e 0 -> 0.00e+00
+%.10e 0 -> 0.0000000000e+00
+%.50e 0 -> 0.00000000000000000000000000000000000000000000000000e+00
+
+-- precision 0.  no decimal point in the output
+%.0e 0.01 -> 1e-02
+%.0e 0.1 -> 1e-01
+%.0e 1 -> 1e+00
+%.0e 10 -> 1e+01
+%.0e 100 -> 1e+02
+%.0e 0.012 -> 1e-02
+%.0e 0.12 -> 1e-01
+%.0e 1.2 -> 1e+00
+%.0e 12 -> 1e+01
+%.0e 120 -> 1e+02
+%.0e 123.456 -> 1e+02
+%.0e 0.000123456 -> 1e-04
+%.0e 123456000 -> 1e+08
+%.0e 0.5 -> 5e-01
+%.0e 1.4 -> 1e+00
+%.0e 1.5 -> 2e+00
+%.0e 1.6 -> 2e+00
+%.0e 2.4999999 -> 2e+00
+%.0e 2.5 -> 2e+00
+%.0e 2.5000001 -> 3e+00
+%.0e 3.499999999999 -> 3e+00
+%.0e 3.5 -> 4e+00
+%.0e 4.5 -> 4e+00
+%.0e 5.5 -> 6e+00
+%.0e 6.5 -> 6e+00
+%.0e 7.5 -> 8e+00
+%.0e 8.5 -> 8e+00
+%.0e 9.4999 -> 9e+00
+%.0e 9.5 -> 1e+01
+%.0e 10.5 -> 1e+01
+%.0e 14.999 -> 1e+01
+%.0e 15 -> 2e+01
+
+-- precision 1
+%.1e 0.0001 -> 1.0e-04
+%.1e 0.001 -> 1.0e-03
+%.1e 0.01 -> 1.0e-02
+%.1e 0.1 -> 1.0e-01
+%.1e 1 -> 1.0e+00
+%.1e 10 -> 1.0e+01
+%.1e 100 -> 1.0e+02
+%.1e 120 -> 1.2e+02
+%.1e 123 -> 1.2e+02
+%.1e 123.4 -> 1.2e+02
+
+-- precision 2
+%.2e 0.00013 -> 1.30e-04
+%.2e 0.000135 -> 1.35e-04
+%.2e 0.0001357 -> 1.36e-04
+%.2e 0.0001 -> 1.00e-04
+%.2e 0.001 -> 1.00e-03
+%.2e 0.01 -> 1.00e-02
+%.2e 0.1 -> 1.00e-01
+%.2e 1 -> 1.00e+00
+%.2e 10 -> 1.00e+01
+%.2e 100 -> 1.00e+02
+%.2e 1000 -> 1.00e+03
+%.2e 1500 -> 1.50e+03
+%.2e 1590 -> 1.59e+03
+%.2e 1598 -> 1.60e+03
+%.2e 1598.7 -> 1.60e+03
+%.2e 1598.76 -> 1.60e+03
+%.2e 9999 -> 1.00e+04
+
+-- omitted precision defaults to 6
+%e 0 -> 0.000000e+00
+%e 165 -> 1.650000e+02
+%e 1234567 -> 1.234567e+06
+%e 12345678 -> 1.234568e+07
+%e 1.1 -> 1.100000e+00
+
+-- alternate form always contains a decimal point.  This only makes
+-- a difference when precision is 0.
+
+%#.0e 0.01 -> 1.e-02
+%#.0e 0.1 -> 1.e-01
+%#.0e 1 -> 1.e+00
+%#.0e 10 -> 1.e+01
+%#.0e 100 -> 1.e+02
+%#.0e 0.012 -> 1.e-02
+%#.0e 0.12 -> 1.e-01
+%#.0e 1.2 -> 1.e+00
+%#.0e 12 -> 1.e+01
+%#.0e 120 -> 1.e+02
+%#.0e 123.456 -> 1.e+02
+%#.0e 0.000123456 -> 1.e-04
+%#.0e 123456000 -> 1.e+08
+%#.0e 0.5 -> 5.e-01
+%#.0e 1.4 -> 1.e+00
+%#.0e 1.5 -> 2.e+00
+%#.0e 1.6 -> 2.e+00
+%#.0e 2.4999999 -> 2.e+00
+%#.0e 2.5 -> 2.e+00
+%#.0e 2.5000001 -> 3.e+00
+%#.0e 3.499999999999 -> 3.e+00
+%#.0e 3.5 -> 4.e+00
+%#.0e 4.5 -> 4.e+00
+%#.0e 5.5 -> 6.e+00
+%#.0e 6.5 -> 6.e+00
+%#.0e 7.5 -> 8.e+00
+%#.0e 8.5 -> 8.e+00
+%#.0e 9.4999 -> 9.e+00
+%#.0e 9.5 -> 1.e+01
+%#.0e 10.5 -> 1.e+01
+%#.0e 14.999 -> 1.e+01
+%#.0e 15 -> 2.e+01
+%#.1e 123.4 -> 1.2e+02
+%#.2e 0.0001357 -> 1.36e-04
+
+-- 'g' code formatting.
+
+-- zeros
+%.0g 0 -> 0
+%.1g 0 -> 0
+%.2g 0 -> 0
+%.3g 0 -> 0
+%.4g 0 -> 0
+%.10g 0 -> 0
+%.50g 0 -> 0
+%.100g 0 -> 0
+
+-- precision 0 doesn't make a lot of sense for the 'g' code (what does
+-- it mean to have no significant digits?); in practice, it's interpreted
+-- as identical to precision 1
+%.0g 1000 -> 1e+03
+%.0g 100 -> 1e+02
+%.0g 10 -> 1e+01
+%.0g 1 -> 1
+%.0g 0.1 -> 0.1
+%.0g 0.01 -> 0.01
+%.0g 1e-3 -> 0.001
+%.0g 1e-4 -> 0.0001
+%.0g 1e-5 -> 1e-05
+%.0g 1e-6 -> 1e-06
+%.0g 12 -> 1e+01
+%.0g 120 -> 1e+02
+%.0g 1.2 -> 1
+%.0g 0.12 -> 0.1
+%.0g 0.012 -> 0.01
+%.0g 0.0012 -> 0.001
+%.0g 0.00012 -> 0.0001
+%.0g 0.000012 -> 1e-05
+%.0g 0.0000012 -> 1e-06
+
+-- precision 1 identical to precision 0
+%.1g 1000 -> 1e+03
+%.1g 100 -> 1e+02
+%.1g 10 -> 1e+01
+%.1g 1 -> 1
+%.1g 0.1 -> 0.1
+%.1g 0.01 -> 0.01
+%.1g 1e-3 -> 0.001
+%.1g 1e-4 -> 0.0001
+%.1g 1e-5 -> 1e-05
+%.1g 1e-6 -> 1e-06
+%.1g 12 -> 1e+01
+%.1g 120 -> 1e+02
+%.1g 1.2 -> 1
+%.1g 0.12 -> 0.1
+%.1g 0.012 -> 0.01
+%.1g 0.0012 -> 0.001
+%.1g 0.00012 -> 0.0001
+%.1g 0.000012 -> 1e-05
+%.1g 0.0000012 -> 1e-06
+
+-- precision 2
+%.2g 1000 -> 1e+03
+%.2g 100 -> 1e+02
+%.2g 10 -> 10
+%.2g 1 -> 1
+%.2g 0.1 -> 0.1
+%.2g 0.01 -> 0.01
+%.2g 0.001 -> 0.001
+%.2g 1e-4 -> 0.0001
+%.2g 1e-5 -> 1e-05
+%.2g 1e-6 -> 1e-06
+%.2g 1234 -> 1.2e+03
+%.2g 123 -> 1.2e+02
+%.2g 12.3 -> 12
+%.2g 1.23 -> 1.2
+%.2g 0.123 -> 0.12
+%.2g 0.0123 -> 0.012
+%.2g 0.00123 -> 0.0012
+%.2g 0.000123 -> 0.00012
+%.2g 0.0000123 -> 1.2e-05
+
+-- bad cases from http://bugs.python.org/issue9980
+%.12g 38210.0 -> 38210
+%.12g 37210.0 -> 37210
+%.12g 36210.0 -> 36210
+
+-- alternate g formatting:  always include decimal point and
+-- exactly <precision> significant digits.
+%#.0g 0 -> 0.
+%#.1g 0 -> 0.
+%#.2g 0 -> 0.0
+%#.3g 0 -> 0.00
+%#.4g 0 -> 0.000
+
+%#.0g 0.2 -> 0.2
+%#.1g 0.2 -> 0.2
+%#.2g 0.2 -> 0.20
+%#.3g 0.2 -> 0.200
+%#.4g 0.2 -> 0.2000
+%#.10g 0.2 -> 0.2000000000
+
+%#.0g 2 -> 2.
+%#.1g 2 -> 2.
+%#.2g 2 -> 2.0
+%#.3g 2 -> 2.00
+%#.4g 2 -> 2.000
+
+%#.0g 20 -> 2.e+01
+%#.1g 20 -> 2.e+01
+%#.2g 20 -> 20.
+%#.3g 20 -> 20.0
+%#.4g 20 -> 20.00
+
+%#.0g 234.56 -> 2.e+02
+%#.1g 234.56 -> 2.e+02
+%#.2g 234.56 -> 2.3e+02
+%#.3g 234.56 -> 235.
+%#.4g 234.56 -> 234.6
+%#.5g 234.56 -> 234.56
+%#.6g 234.56 -> 234.560
+
+-- repr formatting.  Result always includes decimal point and at
+-- least one digit after the point, or an exponent.
+%r 0 -> 0.0
+%r 1 -> 1.0
+
+%r 0.01 -> 0.01
+%r 0.02 -> 0.02
+%r 0.03 -> 0.03
+%r 0.04 -> 0.04
+%r 0.05 -> 0.05
+
+-- values >= 1e16 get an exponent
+%r 10 -> 10.0
+%r 100 -> 100.0
+%r 1e15 -> 1000000000000000.0
+%r 9.999e15 -> 9999000000000000.0
+%r 9999999999999998 -> 9999999999999998.0
+%r 9999999999999999 -> 1e+16
+%r 1e16 -> 1e+16
+%r 1e17 -> 1e+17
+
+-- as do values < 1e-4
+%r 1e-3 -> 0.001
+%r 1.001e-4 -> 0.0001001
+%r 1.0000000000000001e-4 -> 0.0001
+%r 1.000000000000001e-4 -> 0.0001000000000000001
+%r 1.00000000001e-4 -> 0.000100000000001
+%r 1.0000000001e-4 -> 0.00010000000001
+%r 1e-4 -> 0.0001
+%r 0.99999999999999999e-4 -> 0.0001
+%r 0.9999999999999999e-4 -> 9.999999999999999e-05
+%r 0.999999999999e-4 -> 9.99999999999e-05
+%r 0.999e-4 -> 9.99e-05
+%r 1e-5 -> 1e-05

test/dynamo/cpython/3_13/mathdata/ieee754.txt

@@ -0,0 +1,183 @@
+======================================
+Python IEEE 754 floating point support
+======================================
+
+>>> from sys import float_info as FI
+>>> from math import *
+>>> PI = pi
+>>> E = e
+
+You must never compare two floats with == because you are not going to get
+what you expect. We treat two floats as equal if the difference between them
+is small than epsilon.
+>>> EPS = 1E-15
+>>> def equal(x, y):
+...     """Almost equal helper for floats"""
+...     return abs(x - y) < EPS
+
+
+NaNs and INFs
+=============
+
+In Python 2.6 and newer NaNs (not a number) and infinity can be constructed
+from the strings 'inf' and 'nan'.
+
+>>> INF = float('inf')
+>>> NINF = float('-inf')
+>>> NAN = float('nan')
+
+>>> INF
+inf
+>>> NINF
+-inf
+>>> NAN
+nan
+
+The math module's ``isnan`` and ``isinf`` functions can be used to detect INF
+and NAN:
+>>> isinf(INF), isinf(NINF), isnan(NAN)
+(True, True, True)
+>>> INF == -NINF
+True
+
+Infinity
+--------
+
+Ambiguous operations like ``0 * inf`` or ``inf - inf`` result in NaN.
+>>> INF * 0
+nan
+>>> INF - INF
+nan
+>>> INF / INF
+nan
+
+However unambigous operations with inf return inf:
+>>> INF * INF
+inf
+>>> 1.5 * INF
+inf
+>>> 0.5 * INF
+inf
+>>> INF / 1000
+inf
+
+Not a Number
+------------
+
+NaNs are never equal to another number, even itself
+>>> NAN == NAN
+False
+>>> NAN < 0
+False
+>>> NAN >= 0
+False
+
+All operations involving a NaN return a NaN except for nan**0 and 1**nan.
+>>> 1 + NAN
+nan
+>>> 1 * NAN
+nan
+>>> 0 * NAN
+nan
+>>> 1 ** NAN
+1.0
+>>> NAN ** 0
+1.0
+>>> 0 ** NAN
+nan
+>>> (1.0 + FI.epsilon) * NAN
+nan
+
+Misc Functions
+==============
+
+The power of 1 raised to x is always 1.0, even for special values like 0,
+infinity and NaN.
+
+>>> pow(1, 0)
+1.0
+>>> pow(1, INF)
+1.0
+>>> pow(1, -INF)
+1.0
+>>> pow(1, NAN)
+1.0
+
+The power of 0 raised to x is defined as 0, if x is positive. Negative
+finite values are a domain error or zero division error and NaN result in a
+silent NaN.
+
+>>> pow(0, 0)
+1.0
+>>> pow(0, INF)
+0.0
+>>> pow(0, -INF)
+inf
+>>> 0 ** -1
+Traceback (most recent call last):
+...
+ZeroDivisionError: 0.0 cannot be raised to a negative power
+>>> pow(0, NAN)
+nan
+
+
+Trigonometric Functions
+=======================
+
+>>> sin(INF)
+Traceback (most recent call last):
+...
+ValueError: math domain error
+>>> sin(NINF)
+Traceback (most recent call last):
+...
+ValueError: math domain error
+>>> sin(NAN)
+nan
+>>> cos(INF)
+Traceback (most recent call last):
+...
+ValueError: math domain error
+>>> cos(NINF)
+Traceback (most recent call last):
+...
+ValueError: math domain error
+>>> cos(NAN)
+nan
+>>> tan(INF)
+Traceback (most recent call last):
+...
+ValueError: math domain error
+>>> tan(NINF)
+Traceback (most recent call last):
+...
+ValueError: math domain error
+>>> tan(NAN)
+nan
+
+Neither pi nor tan are exact, but you can assume that tan(pi/2) is a large value
+and tan(pi) is a very small value:
+>>> tan(PI/2) > 1E10
+True
+>>> -tan(-PI/2) > 1E10
+True
+>>> tan(PI) < 1E-15
+True
+
+>>> asin(NAN), acos(NAN), atan(NAN)
+(nan, nan, nan)
+>>> asin(INF), asin(NINF)
+Traceback (most recent call last):
+...
+ValueError: math domain error
+>>> acos(INF), acos(NINF)
+Traceback (most recent call last):
+...
+ValueError: math domain error
+>>> equal(atan(INF), PI/2), equal(atan(NINF), -PI/2)
+(True, True)
+
+
+Hyberbolic Functions
+====================
+

test/dynamo/cpython/3_13/mathdata/math_testcases.txt

@@ -0,0 +1,633 @@
+-- Testcases for functions in math.
+--
+-- Each line takes the form:
+--
+-- <testid> <function> <input_value> -> <output_value> <flags>
+--
+-- where:
+--
+--   <testid> is a short name identifying the test,
+--
+--   <function> is the function to be tested (exp, cos, asinh, ...),
+--
+--   <input_value> is a string representing a floating-point value
+--
+--   <output_value> is the expected (ideal) output value, again
+--     represented as a string.
+--
+--   <flags> is a list of the floating-point flags required by C99
+--
+-- The possible flags are:
+--
+--   divide-by-zero : raised when a finite input gives a
+--     mathematically infinite result.
+--
+--   overflow : raised when a finite input gives a finite result that
+--     is too large to fit in the usual range of an IEEE 754 double.
+--
+--   invalid : raised for invalid inputs (e.g., sqrt(-1))
+--
+--   ignore-sign : indicates that the sign of the result is
+--     unspecified; e.g., if the result is given as inf,
+--     then both -inf and inf should be accepted as correct.
+--
+-- Flags may appear in any order.
+--
+-- Lines beginning with '--' (like this one) start a comment, and are
+-- ignored.  Blank lines, or lines containing only whitespace, are also
+-- ignored.
+
+-- Many of the values below were computed with the help of
+-- version 2.4 of the MPFR library for multiple-precision
+-- floating-point computations with correct rounding.  All output
+-- values in this file are (modulo yet-to-be-discovered bugs)
+-- correctly rounded, provided that each input and output decimal
+-- floating-point value below is interpreted as a representation of
+-- the corresponding nearest IEEE 754 double-precision value.  See the
+-- MPFR homepage at http://www.mpfr.org for more information about the
+-- MPFR project.
+
+
+-------------------------
+-- erf: error function --
+-------------------------
+
+erf0000 erf 0.0 -> 0.0
+erf0001 erf -0.0 -> -0.0
+erf0002 erf inf -> 1.0
+erf0003 erf -inf -> -1.0
+erf0004 erf nan -> nan
+
+-- tiny values
+erf0010 erf 1e-308 -> 1.1283791670955125e-308
+erf0011 erf 5e-324 -> 4.9406564584124654e-324
+erf0012 erf 1e-10 -> 1.1283791670955126e-10
+
+-- small integers
+erf0020 erf 1 -> 0.84270079294971489
+erf0021 erf 2 -> 0.99532226501895271
+erf0022 erf 3 -> 0.99997790950300136
+erf0023 erf 4 -> 0.99999998458274209
+erf0024 erf 5 -> 0.99999999999846256
+erf0025 erf 6 -> 1.0
+
+erf0030 erf -1 -> -0.84270079294971489
+erf0031 erf -2 -> -0.99532226501895271
+erf0032 erf -3 -> -0.99997790950300136
+erf0033 erf -4 -> -0.99999998458274209
+erf0034 erf -5 -> -0.99999999999846256
+erf0035 erf -6 -> -1.0
+
+-- huge values should all go to +/-1, depending on sign
+erf0040 erf -40 -> -1.0
+erf0041 erf 1e16 -> 1.0
+erf0042 erf -1e150 -> -1.0
+erf0043 erf 1.7e308 -> 1.0
+
+-- Issue 8986: inputs x with exp(-x*x) near the underflow threshold
+-- incorrectly signalled overflow on some platforms.
+erf0100 erf 26.2 -> 1.0
+erf0101 erf 26.4 -> 1.0
+erf0102 erf 26.6 -> 1.0
+erf0103 erf 26.8 -> 1.0
+erf0104 erf 27.0 -> 1.0
+erf0105 erf 27.2 -> 1.0
+erf0106 erf 27.4 -> 1.0
+erf0107 erf 27.6 -> 1.0
+
+erf0110 erf -26.2 -> -1.0
+erf0111 erf -26.4 -> -1.0
+erf0112 erf -26.6 -> -1.0
+erf0113 erf -26.8 -> -1.0
+erf0114 erf -27.0 -> -1.0
+erf0115 erf -27.2 -> -1.0
+erf0116 erf -27.4 -> -1.0
+erf0117 erf -27.6 -> -1.0
+
+----------------------------------------
+-- erfc: complementary error function --
+----------------------------------------
+
+erfc0000 erfc 0.0 -> 1.0
+erfc0001 erfc -0.0 -> 1.0
+erfc0002 erfc inf -> 0.0
+erfc0003 erfc -inf -> 2.0
+erfc0004 erfc nan -> nan
+
+-- tiny values
+erfc0010 erfc 1e-308 -> 1.0
+erfc0011 erfc 5e-324 -> 1.0
+erfc0012 erfc 1e-10 -> 0.99999999988716204
+
+-- small integers
+erfc0020 erfc 1 -> 0.15729920705028513
+erfc0021 erfc 2 -> 0.0046777349810472662
+erfc0022 erfc 3 -> 2.2090496998585441e-05
+erfc0023 erfc 4 -> 1.541725790028002e-08
+erfc0024 erfc 5 -> 1.5374597944280349e-12
+erfc0025 erfc 6 -> 2.1519736712498913e-17
+
+erfc0030 erfc -1 -> 1.8427007929497148
+erfc0031 erfc -2 -> 1.9953222650189528
+erfc0032 erfc -3 -> 1.9999779095030015
+erfc0033 erfc -4 -> 1.9999999845827421
+erfc0034 erfc -5 -> 1.9999999999984626
+erfc0035 erfc -6 -> 2.0
+
+-- as x -> infinity, erfc(x) behaves like exp(-x*x)/x/sqrt(pi)
+erfc0040 erfc 20 -> 5.3958656116079012e-176
+erfc0041 erfc 25 -> 8.3001725711965228e-274
+erfc0042 erfc 27 -> 5.2370464393526292e-319
+erfc0043 erfc 28 -> 0.0
+
+-- huge values
+erfc0050 erfc -40 -> 2.0
+erfc0051 erfc 1e16 -> 0.0
+erfc0052 erfc -1e150 -> 2.0
+erfc0053 erfc 1.7e308 -> 0.0
+
+-- Issue 8986: inputs x with exp(-x*x) near the underflow threshold
+-- incorrectly signalled overflow on some platforms.
+erfc0100 erfc 26.2 -> 1.6432507924389461e-300
+erfc0101 erfc 26.4 -> 4.4017768588035426e-305
+erfc0102 erfc 26.6 -> 1.0885125885442269e-309
+erfc0103 erfc 26.8 -> 2.4849621571966629e-314
+erfc0104 erfc 27.0 -> 5.2370464393526292e-319
+erfc0105 erfc 27.2 -> 9.8813129168249309e-324
+erfc0106 erfc 27.4 -> 0.0
+erfc0107 erfc 27.6 -> 0.0
+
+erfc0110 erfc -26.2 -> 2.0
+erfc0111 erfc -26.4 -> 2.0
+erfc0112 erfc -26.6 -> 2.0
+erfc0113 erfc -26.8 -> 2.0
+erfc0114 erfc -27.0 -> 2.0
+erfc0115 erfc -27.2 -> 2.0
+erfc0116 erfc -27.4 -> 2.0
+erfc0117 erfc -27.6 -> 2.0
+
+---------------------------------------------------------
+-- lgamma: log of absolute value of the gamma function --
+---------------------------------------------------------
+
+-- special values
+lgam0000 lgamma 0.0 -> inf      divide-by-zero
+lgam0001 lgamma -0.0 -> inf     divide-by-zero
+lgam0002 lgamma inf -> inf
+lgam0003 lgamma -inf -> inf
+lgam0004 lgamma nan -> nan
+
+-- negative integers
+lgam0010 lgamma -1 -> inf       divide-by-zero
+lgam0011 lgamma -2 -> inf       divide-by-zero
+lgam0012 lgamma -1e16 -> inf    divide-by-zero
+lgam0013 lgamma -1e300 -> inf   divide-by-zero
+lgam0014 lgamma -1.79e308 -> inf divide-by-zero
+
+-- small positive integers give factorials
+lgam0020 lgamma 1 -> 0.0
+lgam0021 lgamma 2 -> 0.0
+lgam0022 lgamma 3 -> 0.69314718055994529
+lgam0023 lgamma 4 -> 1.791759469228055
+lgam0024 lgamma 5 -> 3.1780538303479458
+lgam0025 lgamma 6 -> 4.7874917427820458
+
+-- half integers
+lgam0030 lgamma 0.5 -> 0.57236494292470008
+lgam0031 lgamma 1.5 -> -0.12078223763524522
+lgam0032 lgamma 2.5 -> 0.28468287047291918
+lgam0033 lgamma 3.5 -> 1.2009736023470743
+lgam0034 lgamma -0.5 -> 1.2655121234846454
+lgam0035 lgamma -1.5 -> 0.86004701537648098
+lgam0036 lgamma -2.5 -> -0.056243716497674054
+lgam0037 lgamma -3.5 -> -1.309006684993042
+
+-- values near 0
+lgam0040 lgamma 0.1 -> 2.252712651734206
+lgam0041 lgamma 0.01 -> 4.5994798780420219
+lgam0042 lgamma 1e-8 -> 18.420680738180209
+lgam0043 lgamma 1e-16 -> 36.841361487904734
+lgam0044 lgamma 1e-30 -> 69.077552789821368
+lgam0045 lgamma 1e-160 -> 368.41361487904732
+lgam0046 lgamma 1e-308 -> 709.19620864216608
+lgam0047 lgamma 5.6e-309 -> 709.77602713741896
+lgam0048 lgamma 5.5e-309 -> 709.79404564292167
+lgam0049 lgamma 1e-309 -> 711.49879373516012
+lgam0050 lgamma 1e-323 -> 743.74692474082133
+lgam0051 lgamma 5e-324 -> 744.44007192138122
+lgam0060 lgamma -0.1 -> 2.3689613327287886
+lgam0061 lgamma -0.01 -> 4.6110249927528013
+lgam0062 lgamma -1e-8 -> 18.420680749724522
+lgam0063 lgamma -1e-16 -> 36.841361487904734
+lgam0064 lgamma -1e-30 -> 69.077552789821368
+lgam0065 lgamma -1e-160 -> 368.41361487904732
+lgam0066 lgamma -1e-308 -> 709.19620864216608
+lgam0067 lgamma -5.6e-309 -> 709.77602713741896
+lgam0068 lgamma -5.5e-309 -> 709.79404564292167
+lgam0069 lgamma -1e-309 -> 711.49879373516012
+lgam0070 lgamma -1e-323 -> 743.74692474082133
+lgam0071 lgamma -5e-324 -> 744.44007192138122
+
+-- values near negative integers
+lgam0080 lgamma -0.99999999999999989 -> 36.736800569677101
+lgam0081 lgamma -1.0000000000000002 -> 36.043653389117154
+lgam0082 lgamma -1.9999999999999998 -> 35.350506208557213
+lgam0083 lgamma -2.0000000000000004 -> 34.657359027997266
+lgam0084 lgamma -100.00000000000001 -> -331.85460524980607
+lgam0085 lgamma -99.999999999999986 -> -331.85460524980596
+
+-- large inputs
+lgam0100 lgamma 170 -> 701.43726380873704
+lgam0101 lgamma 171 -> 706.57306224578736
+lgam0102 lgamma 171.624 -> 709.78077443669895
+lgam0103 lgamma 171.625 -> 709.78591682948365
+lgam0104 lgamma 172 -> 711.71472580228999
+lgam0105 lgamma 2000 -> 13198.923448054265
+lgam0106 lgamma 2.55998332785163e305 -> 1.7976931348623099e+308
+lgam0107 lgamma 2.55998332785164e305 -> inf overflow
+lgam0108 lgamma 1.7e308 -> inf overflow
+
+-- inputs for which gamma(x) is tiny
+lgam0120 lgamma -100.5 -> -364.90096830942736
+lgam0121 lgamma -160.5 -> -656.88005261126432
+lgam0122 lgamma -170.5 -> -707.99843314507882
+lgam0123 lgamma -171.5 -> -713.14301641168481
+lgam0124 lgamma -176.5 -> -738.95247590846486
+lgam0125 lgamma -177.5 -> -744.13144651738037
+lgam0126 lgamma -178.5 -> -749.3160351186001
+
+lgam0130 lgamma -1000.5 -> -5914.4377011168517
+lgam0131 lgamma -30000.5 -> -279278.6629959144
+lgam0132 lgamma -4503599627370495.5 -> -1.5782258434492883e+17
+
+-- results close to 0:  positive argument ...
+lgam0150 lgamma 0.99999999999999989 -> 6.4083812134800075e-17
+lgam0151 lgamma 1.0000000000000002 -> -1.2816762426960008e-16
+lgam0152 lgamma 1.9999999999999998 -> -9.3876980655431170e-17
+lgam0153 lgamma 2.0000000000000004 -> 1.8775396131086244e-16
+
+-- ... and negative argument
+lgam0160 lgamma -2.7476826467 -> -5.2477408147689136e-11
+lgam0161 lgamma -2.457024738 -> 3.3464637541912932e-10
+
+
+---------------------------
+-- gamma: Gamma function --
+---------------------------
+
+-- special values
+gam0000 gamma 0.0 -> inf        divide-by-zero
+gam0001 gamma -0.0 -> -inf      divide-by-zero
+gam0002 gamma inf -> inf
+gam0003 gamma -inf -> nan       invalid
+gam0004 gamma nan -> nan
+
+-- negative integers inputs are invalid
+gam0010 gamma -1 -> nan         invalid
+gam0011 gamma -2 -> nan         invalid
+gam0012 gamma -1e16 -> nan      invalid
+gam0013 gamma -1e300 -> nan     invalid
+
+-- small positive integers give factorials
+gam0020 gamma 1 -> 1
+gam0021 gamma 2 -> 1
+gam0022 gamma 3 -> 2
+gam0023 gamma 4 -> 6
+gam0024 gamma 5 -> 24
+gam0025 gamma 6 -> 120
+
+-- half integers
+gam0030 gamma 0.5 -> 1.7724538509055161
+gam0031 gamma 1.5 -> 0.88622692545275805
+gam0032 gamma 2.5 -> 1.3293403881791370
+gam0033 gamma 3.5 -> 3.3233509704478426
+gam0034 gamma -0.5 -> -3.5449077018110322
+gam0035 gamma -1.5 -> 2.3632718012073548
+gam0036 gamma -2.5 -> -0.94530872048294190
+gam0037 gamma -3.5 -> 0.27008820585226911
+
+-- values near 0
+gam0040 gamma 0.1 -> 9.5135076986687306
+gam0041 gamma 0.01 -> 99.432585119150602
+gam0042 gamma 1e-8 -> 99999999.422784343
+gam0043 gamma 1e-16 -> 10000000000000000
+gam0044 gamma 1e-30 -> 9.9999999999999988e+29
+gam0045 gamma 1e-160 -> 1.0000000000000000e+160
+gam0046 gamma 1e-308 -> 1.0000000000000000e+308
+gam0047 gamma 5.6e-309 -> 1.7857142857142848e+308
+gam0048 gamma 5.5e-309 -> inf   overflow
+gam0049 gamma 1e-309 -> inf     overflow
+gam0050 gamma 1e-323 -> inf     overflow
+gam0051 gamma 5e-324 -> inf     overflow
+gam0060 gamma -0.1 -> -10.686287021193193
+gam0061 gamma -0.01 -> -100.58719796441078
+gam0062 gamma -1e-8 -> -100000000.57721567
+gam0063 gamma -1e-16 -> -10000000000000000
+gam0064 gamma -1e-30 -> -9.9999999999999988e+29
+gam0065 gamma -1e-160 -> -1.0000000000000000e+160
+gam0066 gamma -1e-308 -> -1.0000000000000000e+308
+gam0067 gamma -5.6e-309 -> -1.7857142857142848e+308
+gam0068 gamma -5.5e-309 -> -inf overflow
+gam0069 gamma -1e-309 -> -inf   overflow
+gam0070 gamma -1e-323 -> -inf   overflow
+gam0071 gamma -5e-324 -> -inf   overflow
+
+-- values near negative integers
+gam0080 gamma -0.99999999999999989 -> -9007199254740992.0
+gam0081 gamma -1.0000000000000002 -> 4503599627370495.5
+gam0082 gamma -1.9999999999999998 -> 2251799813685248.5
+gam0083 gamma -2.0000000000000004 -> -1125899906842623.5
+gam0084 gamma -100.00000000000001 -> -7.5400833348831090e-145
+gam0085 gamma -99.999999999999986 -> 7.5400833348840962e-145
+
+-- large inputs
+gam0100 gamma 170 -> 4.2690680090047051e+304
+gam0101 gamma 171 -> 7.2574156153079990e+306
+gam0102 gamma 171.624 -> 1.7942117599248104e+308
+gam0103 gamma 171.625 -> inf    overflow
+gam0104 gamma 172 -> inf        overflow
+gam0105 gamma 2000 -> inf       overflow
+gam0106 gamma 1.7e308 -> inf    overflow
+
+-- inputs for which gamma(x) is tiny
+gam0120 gamma -100.5 -> -3.3536908198076787e-159
+gam0121 gamma -160.5 -> -5.2555464470078293e-286
+gam0122 gamma -170.5 -> -3.3127395215386074e-308
+gam0123 gamma -171.5 -> 1.9316265431711902e-310
+gam0124 gamma -176.5 -> -1.1956388629358166e-321
+gam0125 gamma -177.5 -> 4.9406564584124654e-324
+gam0126 gamma -178.5 -> -0.0
+gam0127 gamma -179.5 -> 0.0
+gam0128 gamma -201.0001 -> 0.0
+gam0129 gamma -202.9999 -> -0.0
+gam0130 gamma -1000.5 -> -0.0
+gam0131 gamma -1000000000.3 -> -0.0
+gam0132 gamma -4503599627370495.5 -> 0.0
+
+-- inputs that cause problems for the standard reflection formula,
+-- thanks to loss of accuracy in 1-x
+gam0140 gamma -63.349078729022985 -> 4.1777971677761880e-88
+gam0141 gamma -127.45117632943295 -> 1.1831110896236810e-214
+
+
+-----------------------------------------------------------
+-- log1p: log(1 + x), without precision loss for small x --
+-----------------------------------------------------------
+
+-- special values
+log1p0000 log1p 0.0 -> 0.0
+log1p0001 log1p -0.0 -> -0.0
+log1p0002 log1p inf -> inf
+log1p0003 log1p -inf -> nan             invalid
+log1p0004 log1p nan -> nan
+
+-- singularity at -1.0
+log1p0010 log1p -1.0 -> -inf            divide-by-zero
+log1p0011 log1p -0.9999999999999999 -> -36.736800569677101
+
+-- finite values < 1.0 are invalid
+log1p0020 log1p -1.0000000000000002 -> nan invalid
+log1p0021 log1p -1.1 -> nan invalid
+log1p0022 log1p -2.0 -> nan invalid
+log1p0023 log1p -1e300 -> nan invalid
+
+-- tiny x: log1p(x) ~ x
+log1p0110 log1p 5e-324 -> 5e-324
+log1p0111 log1p 1e-320 -> 1e-320
+log1p0112 log1p 1e-300 -> 1e-300
+log1p0113 log1p 1e-150 -> 1e-150
+log1p0114 log1p 1e-20 -> 1e-20
+
+log1p0120 log1p -5e-324 -> -5e-324
+log1p0121 log1p -1e-320 -> -1e-320
+log1p0122 log1p -1e-300 -> -1e-300
+log1p0123 log1p -1e-150 -> -1e-150
+log1p0124 log1p -1e-20 -> -1e-20
+
+-- some (mostly) random small and moderate-sized values
+log1p0200 log1p -0.89156889782277482 -> -2.2216403106762863
+log1p0201 log1p -0.23858496047770464 -> -0.27257668276980057
+log1p0202 log1p -0.011641726191307515 -> -0.011710021654495657
+log1p0203 log1p -0.0090126398571693817 -> -0.0090534993825007650
+log1p0204 log1p -0.00023442805985712781 -> -0.00023445554240995693
+log1p0205 log1p -1.5672870980936349e-5 -> -1.5672993801662046e-5
+log1p0206 log1p -7.9650013274825295e-6 -> -7.9650330482740401e-6
+log1p0207 log1p -2.5202948343227410e-7 -> -2.5202951519170971e-7
+log1p0208 log1p -8.2446372820745855e-11 -> -8.2446372824144559e-11
+log1p0209 log1p -8.1663670046490789e-12 -> -8.1663670046824230e-12
+log1p0210 log1p 7.0351735084656292e-18 -> 7.0351735084656292e-18
+log1p0211 log1p 5.2732161907375226e-12 -> 5.2732161907236188e-12
+log1p0212 log1p 1.0000000000000000e-10 -> 9.9999999995000007e-11
+log1p0213 log1p 2.1401273266000197e-9 -> 2.1401273243099470e-9
+log1p0214 log1p 1.2668914653979560e-8 -> 1.2668914573728861e-8
+log1p0215 log1p 1.6250007816299069e-6 -> 1.6249994613175672e-6
+log1p0216 log1p 8.3740495645839399e-6 -> 8.3740145024266269e-6
+log1p0217 log1p 3.0000000000000001e-5 -> 2.9999550008999799e-5
+log1p0218 log1p 0.0070000000000000001 -> 0.0069756137364252423
+log1p0219 log1p 0.013026235315053002 -> 0.012942123564008787
+log1p0220 log1p 0.013497160797236184 -> 0.013406885521915038
+log1p0221 log1p 0.027625599078135284 -> 0.027250897463483054
+log1p0222 log1p 0.14179687245544870 -> 0.13260322540908789
+
+-- large values
+log1p0300 log1p 1.7976931348623157e+308 -> 709.78271289338397
+log1p0301 log1p 1.0000000000000001e+300 -> 690.77552789821368
+log1p0302 log1p 1.0000000000000001e+70 -> 161.18095650958321
+log1p0303 log1p 10000000000.000000 -> 23.025850930040455
+
+-- other values transferred from testLog1p in test_math
+log1p0400 log1p -0.63212055882855767 -> -1.0000000000000000
+log1p0401 log1p 1.7182818284590451 -> 1.0000000000000000
+log1p0402 log1p 1.0000000000000000 -> 0.69314718055994529
+log1p0403 log1p 1.2379400392853803e+27 -> 62.383246250395075
+
+
+-----------------------------------------------------------
+-- expm1: exp(x) - 1, without precision loss for small x --
+-----------------------------------------------------------
+
+-- special values
+expm10000 expm1 0.0 -> 0.0
+expm10001 expm1 -0.0 -> -0.0
+expm10002 expm1 inf -> inf
+expm10003 expm1 -inf -> -1.0
+expm10004 expm1 nan -> nan
+
+-- expm1(x) ~ x for tiny x
+expm10010 expm1 5e-324 -> 5e-324
+expm10011 expm1 1e-320 -> 1e-320
+expm10012 expm1 1e-300 -> 1e-300
+expm10013 expm1 1e-150 -> 1e-150
+expm10014 expm1 1e-20 -> 1e-20
+
+expm10020 expm1 -5e-324 -> -5e-324
+expm10021 expm1 -1e-320 -> -1e-320
+expm10022 expm1 -1e-300 -> -1e-300
+expm10023 expm1 -1e-150 -> -1e-150
+expm10024 expm1 -1e-20 -> -1e-20
+
+-- moderate sized values, where direct evaluation runs into trouble
+expm10100 expm1 1e-10 -> 1.0000000000500000e-10
+expm10101 expm1 -9.9999999999999995e-08 -> -9.9999995000000163e-8
+expm10102 expm1 3.0000000000000001e-05 -> 3.0000450004500034e-5
+expm10103 expm1 -0.0070000000000000001 -> -0.0069755570667648951
+expm10104 expm1 -0.071499208740094633 -> -0.069002985744820250
+expm10105 expm1 -0.063296004180116799 -> -0.061334416373633009
+expm10106 expm1 0.02390954035597756 -> 0.024197665143819942
+expm10107 expm1 0.085637352649044901 -> 0.089411184580357767
+expm10108 expm1 0.5966174947411006 -> 0.81596588596501485
+expm10109 expm1 0.30247206212075139 -> 0.35319987035848677
+expm10110 expm1 0.74574727375889516 -> 1.1080161116737459
+expm10111 expm1 0.97767512926555711 -> 1.6582689207372185
+expm10112 expm1 0.8450154566787712 -> 1.3280137976535897
+expm10113 expm1 -0.13979260323125264 -> -0.13046144381396060
+expm10114 expm1 -0.52899322039643271 -> -0.41080213643695923
+expm10115 expm1 -0.74083261478900631 -> -0.52328317124797097
+expm10116 expm1 -0.93847766984546055 -> -0.60877704724085946
+expm10117 expm1 10.0 -> 22025.465794806718
+expm10118 expm1 27.0 -> 532048240600.79865
+expm10119 expm1 123 -> 2.6195173187490626e+53
+expm10120 expm1 -12.0 -> -0.99999385578764666
+expm10121 expm1 -35.100000000000001 -> -0.99999999999999944
+
+-- extreme negative values
+expm10201 expm1 -37.0 -> -0.99999999999999989
+expm10200 expm1 -38.0 -> -1.0
+expm10210 expm1 -710.0 -> -1.0
+-- the formula expm1(x) = 2 * sinh(x/2) * exp(x/2) doesn't work so
+-- well when exp(x/2) is subnormal or underflows to zero; check we're
+-- not using it!
+expm10211 expm1 -1420.0 -> -1.0
+expm10212 expm1 -1450.0 -> -1.0
+expm10213 expm1 -1500.0 -> -1.0
+expm10214 expm1 -1e50 -> -1.0
+expm10215 expm1 -1.79e308 -> -1.0
+
+-- extreme positive values
+expm10300 expm1 300 -> 1.9424263952412558e+130
+expm10301 expm1 700 -> 1.0142320547350045e+304
+-- the next test (expm10302) is disabled because it causes failure on
+-- OS X 10.4/Intel: apparently all values over 709.78 produce an
+-- overflow on that platform.  See issue #7575.
+-- expm10302 expm1 709.78271289328393 -> 1.7976931346824240e+308
+expm10303 expm1 709.78271289348402 -> inf overflow
+expm10304 expm1 1000 -> inf overflow
+expm10305 expm1 1e50 -> inf overflow
+expm10306 expm1 1.79e308 -> inf overflow
+
+-- weaker version of expm10302
+expm10307 expm1 709.5 -> 1.3549863193146328e+308
+
+-------------------------
+-- log2: log to base 2 --
+-------------------------
+
+-- special values
+log20000 log2 0.0 -> -inf               divide-by-zero
+log20001 log2 -0.0 -> -inf              divide-by-zero
+log20002 log2 inf -> inf
+log20003 log2 -inf -> nan               invalid
+log20004 log2 nan -> nan
+
+-- exact value at 1.0
+log20010 log2 1.0 -> 0.0
+
+-- negatives
+log20020 log2 -5e-324 -> nan            invalid
+log20021 log2 -1.0 -> nan               invalid
+log20022 log2 -1.7e-308 -> nan          invalid
+
+-- exact values at powers of 2
+log20100 log2 2.0 -> 1.0
+log20101 log2 4.0 -> 2.0
+log20102 log2 8.0 -> 3.0
+log20103 log2 16.0 -> 4.0
+log20104 log2 32.0 -> 5.0
+log20105 log2 64.0 -> 6.0
+log20106 log2 128.0 -> 7.0
+log20107 log2 256.0 -> 8.0
+log20108 log2 512.0 -> 9.0
+log20109 log2 1024.0 -> 10.0
+log20110 log2 2048.0 -> 11.0
+
+log20200 log2 0.5 -> -1.0
+log20201 log2 0.25 -> -2.0
+log20202 log2 0.125 -> -3.0
+log20203 log2 0.0625 -> -4.0
+
+-- values close to 1.0
+log20300 log2 1.0000000000000002 -> 3.2034265038149171e-16
+log20301 log2 1.0000000001 -> 1.4426951601859516e-10
+log20302 log2 1.00001 -> 1.4426878274712997e-5
+
+log20310 log2 0.9999999999999999 -> -1.6017132519074588e-16
+log20311 log2 0.9999999999 -> -1.4426951603302210e-10
+log20312 log2 0.99999 -> -1.4427022544056922e-5
+
+-- tiny values
+log20400 log2 5e-324 -> -1074.0
+log20401 log2 1e-323 -> -1073.0
+log20402 log2 1.5e-323 -> -1072.4150374992789
+log20403 log2 2e-323 -> -1072.0
+
+log20410 log2 1e-308 -> -1023.1538532253076
+log20411 log2 2.2250738585072014e-308 -> -1022.0
+log20412 log2 4.4501477170144028e-308 -> -1021.0
+log20413 log2 1e-307 -> -1019.8319251304202
+
+-- huge values
+log20500 log2 1.7976931348623157e+308 -> 1024.0
+log20501 log2 1.7e+308 -> 1023.9193879716706
+log20502 log2 8.9884656743115795e+307 -> 1023.0
+
+-- selection of random values
+log20600 log2 -7.2174324841039838e+289 -> nan   invalid
+log20601 log2 -2.861319734089617e+265 -> nan    invalid
+log20602 log2 -4.3507646894008962e+257 -> nan   invalid
+log20603 log2 -6.6717265307520224e+234 -> nan   invalid
+log20604 log2 -3.9118023786619294e+229 -> nan   invalid
+log20605 log2 -1.5478221302505161e+206 -> nan   invalid
+log20606 log2 -1.4380485131364602e+200 -> nan   invalid
+log20607 log2 -3.7235198730382645e+185 -> nan   invalid
+log20608 log2 -1.0472242235095724e+184 -> nan   invalid
+log20609 log2 -5.0141781956163884e+160 -> nan   invalid
+log20610 log2 -2.1157958031160324e+124 -> nan   invalid
+log20611 log2 -7.9677558612567718e+90 -> nan    invalid
+log20612 log2 -5.5553906194063732e+45 -> nan    invalid
+log20613 log2 -16573900952607.953 -> nan        invalid
+log20614 log2 -37198371019.888618 -> nan        invalid
+log20615 log2 -6.0727115121422674e-32 -> nan    invalid
+log20616 log2 -2.5406841656526057e-38 -> nan    invalid
+log20617 log2 -4.9056766703267657e-43 -> nan    invalid
+log20618 log2 -2.1646786075228305e-71 -> nan    invalid
+log20619 log2 -2.470826790488573e-78 -> nan     invalid
+log20620 log2 -3.8661709303489064e-165 -> nan   invalid
+log20621 log2 -1.0516496976649986e-182 -> nan   invalid
+log20622 log2 -1.5935458614317996e-255 -> nan   invalid
+log20623 log2 -2.8750977267336654e-293 -> nan   invalid
+log20624 log2 -7.6079466794732585e-296 -> nan   invalid
+log20625 log2 3.2073253539988545e-307 -> -1018.1505544209213
+log20626 log2 1.674937885472249e-244 -> -809.80634755783126
+log20627 log2 1.0911259044931283e-214 -> -710.76679472274213
+log20628 log2 2.0275372624809709e-154 -> -510.55719818383272
+log20629 log2 7.3926087369631841e-115 -> -379.13564735312292
+log20630 log2 1.3480198206342423e-86 -> -285.25497445094436
+log20631 log2 8.9927384655719947e-83 -> -272.55127136401637
+log20632 log2 3.1452398713597487e-60 -> -197.66251564496875
+log20633 log2 7.0706573215457351e-55 -> -179.88420087782217
+log20634 log2 3.1258285390731669e-49 -> -161.13023800505653
+log20635 log2 8.2253046627829942e-41 -> -133.15898277355879
+log20636 log2 7.8691367397519897e+49 -> 165.75068202732419
+log20637 log2 2.9920561983925013e+64 -> 214.18453534573757
+log20638 log2 4.7827254553946841e+77 -> 258.04629628445673
+log20639 log2 3.1903566496481868e+105 -> 350.47616767491166
+log20640 log2 5.6195082449502419e+113 -> 377.86831861008250
+log20641 log2 9.9625658250651047e+125 -> 418.55752921228753
+log20642 log2 2.7358945220961532e+145 -> 483.13158636923413
+log20643 log2 2.785842387926931e+174 -> 579.49360214860280
+log20644 log2 2.4169172507252751e+193 -> 642.40529039289652
+log20645 log2 3.1689091206395632e+205 -> 682.65924573798395
+log20646 log2 2.535995592365391e+208 -> 692.30359597460460
+log20647 log2 6.2011236566089916e+233 -> 776.64177576730913
+log20648 log2 2.1843274820677632e+253 -> 841.57499717289647
+log20649 log2 8.7493931063474791e+297 -> 989.74182713073981

test/dynamo/cpython/3_13/test_cmath.diff

@@ -0,0 +1,116 @@
+diff --git a/test/dynamo/cpython/3_13/test_cmath.py b/test/dynamo/cpython/3_13/test_cmath.py
+index a96a5780b31..883e87a0733 100644
+--- a/test/dynamo/cpython/3_13/test_cmath.py
++++ b/test/dynamo/cpython/3_13/test_cmath.py
+@@ -1,5 +1,55 @@
++# ======= BEGIN Dynamo patch =======
++# Owner(s): ["module: dynamo"]
++
++# ruff: noqa
++# flake8: noqa
++
++import sys
++import torch
++import torch._dynamo.test_case
++import unittest
++from torch._dynamo.test_case import CPythonTestCase
++from torch.testing._internal.common_utils import run_tests
++
++__TestCase = CPythonTestCase
++
++
++# redirect import statements
++import sys
++import importlib.abc
++
++redirect_imports = (
++    "test.mapping_tests",
++    "test.typinganndata",
++    "test.test_grammar",
++    "test.test_math",
++    "test.test_iter",
++    "test.typinganndata.ann_module",
++)
++
++class RedirectImportFinder(importlib.abc.MetaPathFinder):
++    def find_spec(self, fullname, path, target=None):
++        # Check if the import is the problematic one
++        if fullname in redirect_imports:
++            try:
++                # Attempt to import the standalone module
++                name = fullname.removeprefix("test.")
++                r = importlib.import_module(name)
++                # Redirect the module in sys.modules
++                sys.modules[fullname] = r
++                # Return a module spec from the found module
++                return importlib.util.find_spec(name)
++            except ImportError:
++                return None
++        return None
++
++# Add the custom finder to sys.meta_path
++sys.meta_path.insert(0, RedirectImportFinder())
++
++
++# ======= END DYNAMO PATCH =======
++
+ from test.support import requires_IEEE_754, cpython_only, import_helper
+-from test.support.testcase import ComplexesAreIdenticalMixin
+ from test.test_math import parse_testfile, test_file
+ import test.test_math as test_math
+ import unittest
+@@ -50,7 +100,7 @@ complex_nans = [complex(x, y) for x, y in [
+         (INF, NAN)
+         ]]
+ 
+-class CMathTests(ComplexesAreIdenticalMixin, unittest.TestCase):
++class CMathTests(__TestCase):
+     # list of all functions in cmath
+     test_functions = [getattr(cmath, fname) for fname in [
+             'acos', 'acosh', 'asin', 'asinh', 'atan', 'atanh',
+@@ -66,6 +116,39 @@ class CMathTests(ComplexesAreIdenticalMixin, unittest.TestCase):
+     def tearDown(self):
+         self.test_values.close()
+ 
++    def assertFloatIdentical(self, x, y):
++        """Fail unless floats x and y are identical, in the sense that:
++        (1) both x and y are nans, or
++        (2) both x and y are infinities, with the same sign, or
++        (3) both x and y are zeros, with the same sign, or
++        (4) x and y are both finite and nonzero, and x == y
++
++        """
++        msg = 'floats {!r} and {!r} are not identical'
++
++        if math.isnan(x) or math.isnan(y):
++            if math.isnan(x) and math.isnan(y):
++                return
++        elif x == y:
++            if x != 0.0:
++                return
++            # both zero; check that signs match
++            elif math.copysign(1.0, x) == math.copysign(1.0, y):
++                return
++            else:
++                msg += ': zeros have different signs'
++        self.fail(msg.format(x, y))
++
++    def assertComplexesAreIdentical(self, x, y):
++        """Fail unless complex numbers x and y have equal values and signs.
++
++        In particular, if x and y both have real (or imaginary) part
++        zero, but the zeros have different signs, this test will fail.
++
++        """
++        self.assertFloatIdentical(x.real, y.real)
++        self.assertFloatIdentical(x.imag, y.imag)
++
+     def rAssertAlmostEqual(self, a, b, rel_err = 2e-15, abs_err = 5e-323,
+                            msg=None):
+         """Fail if the two floating-point numbers are not almost equal.
+@@ -590,4 +673,4 @@ class IsCloseTests(test_math.IsCloseTests):
+ 
+ 
+ if __name__ == "__main__":
+-    unittest.main()
++    run_tests()

test/dynamo/cpython/3_13/test_cmath.py

@@ -0,0 +1,676 @@
+# ======= BEGIN Dynamo patch =======
+# Owner(s): ["module: dynamo"]
+
+# ruff: noqa
+# flake8: noqa
+
+import sys
+import torch
+import torch._dynamo.test_case
+import unittest
+from torch._dynamo.test_case import CPythonTestCase
+from torch.testing._internal.common_utils import run_tests
+
+__TestCase = CPythonTestCase
+
+
+# redirect import statements
+import sys
+import importlib.abc
+
+redirect_imports = (
+    "test.mapping_tests",
+    "test.typinganndata",
+    "test.test_grammar",
+    "test.test_math",
+    "test.test_iter",
+    "test.typinganndata.ann_module",
+)
+
+class RedirectImportFinder(importlib.abc.MetaPathFinder):
+    def find_spec(self, fullname, path, target=None):
+        # Check if the import is the problematic one
+        if fullname in redirect_imports:
+            try:
+                # Attempt to import the standalone module
+                name = fullname.removeprefix("test.")
+                r = importlib.import_module(name)
+                # Redirect the module in sys.modules
+                sys.modules[fullname] = r
+                # Return a module spec from the found module
+                return importlib.util.find_spec(name)
+            except ImportError:
+                return None
+        return None
+
+# Add the custom finder to sys.meta_path
+sys.meta_path.insert(0, RedirectImportFinder())
+
+
+# ======= END DYNAMO PATCH =======
+
+from test.support import requires_IEEE_754, cpython_only, import_helper
+from test.test_math import parse_testfile, test_file
+import test.test_math as test_math
+import unittest
+import cmath, math
+from cmath import phase, polar, rect, pi
+import platform
+import sys
+
+
+INF = float('inf')
+NAN = float('nan')
+
+complex_zeros = [complex(x, y) for x in [0.0, -0.0] for y in [0.0, -0.0]]
+complex_infinities = [complex(x, y) for x, y in [
+        (INF, 0.0),  # 1st quadrant
+        (INF, 2.3),
+        (INF, INF),
+        (2.3, INF),
+        (0.0, INF),
+        (-0.0, INF), # 2nd quadrant
+        (-2.3, INF),
+        (-INF, INF),
+        (-INF, 2.3),
+        (-INF, 0.0),
+        (-INF, -0.0), # 3rd quadrant
+        (-INF, -2.3),
+        (-INF, -INF),
+        (-2.3, -INF),
+        (-0.0, -INF),
+        (0.0, -INF), # 4th quadrant
+        (2.3, -INF),
+        (INF, -INF),
+        (INF, -2.3),
+        (INF, -0.0)
+        ]]
+complex_nans = [complex(x, y) for x, y in [
+        (NAN, -INF),
+        (NAN, -2.3),
+        (NAN, -0.0),
+        (NAN, 0.0),
+        (NAN, 2.3),
+        (NAN, INF),
+        (-INF, NAN),
+        (-2.3, NAN),
+        (-0.0, NAN),
+        (0.0, NAN),
+        (2.3, NAN),
+        (INF, NAN)
+        ]]
+
+class CMathTests(__TestCase):
+    # list of all functions in cmath
+    test_functions = [getattr(cmath, fname) for fname in [
+            'acos', 'acosh', 'asin', 'asinh', 'atan', 'atanh',
+            'cos', 'cosh', 'exp', 'log', 'log10', 'sin', 'sinh',
+            'sqrt', 'tan', 'tanh']]
+    # test first and second arguments independently for 2-argument log
+    test_functions.append(lambda x : cmath.log(x, 1729. + 0j))
+    test_functions.append(lambda x : cmath.log(14.-27j, x))
+
+    def setUp(self):
+        self.test_values = open(test_file, encoding="utf-8")
+
+    def tearDown(self):
+        self.test_values.close()
+
+    def assertFloatIdentical(self, x, y):
+        """Fail unless floats x and y are identical, in the sense that:
+        (1) both x and y are nans, or
+        (2) both x and y are infinities, with the same sign, or
+        (3) both x and y are zeros, with the same sign, or
+        (4) x and y are both finite and nonzero, and x == y
+
+        """
+        msg = 'floats {!r} and {!r} are not identical'
+
+        if math.isnan(x) or math.isnan(y):
+            if math.isnan(x) and math.isnan(y):
+                return
+        elif x == y:
+            if x != 0.0:
+                return
+            # both zero; check that signs match
+            elif math.copysign(1.0, x) == math.copysign(1.0, y):
+                return
+            else:
+                msg += ': zeros have different signs'
+        self.fail(msg.format(x, y))
+
+    def assertComplexesAreIdentical(self, x, y):
+        """Fail unless complex numbers x and y have equal values and signs.
+
+        In particular, if x and y both have real (or imaginary) part
+        zero, but the zeros have different signs, this test will fail.
+
+        """
+        self.assertFloatIdentical(x.real, y.real)
+        self.assertFloatIdentical(x.imag, y.imag)
+
+    def rAssertAlmostEqual(self, a, b, rel_err = 2e-15, abs_err = 5e-323,
+                           msg=None):
+        """Fail if the two floating-point numbers are not almost equal.
+
+        Determine whether floating-point values a and b are equal to within
+        a (small) rounding error.  The default values for rel_err and
+        abs_err are chosen to be suitable for platforms where a float is
+        represented by an IEEE 754 double.  They allow an error of between
+        9 and 19 ulps.
+        """
+
+        # special values testing
+        if math.isnan(a):
+            if math.isnan(b):
+                return
+            self.fail(msg or '{!r} should be nan'.format(b))
+
+        if math.isinf(a):
+            if a == b:
+                return
+            self.fail(msg or 'finite result where infinity expected: '
+                      'expected {!r}, got {!r}'.format(a, b))
+
+        # if both a and b are zero, check whether they have the same sign
+        # (in theory there are examples where it would be legitimate for a
+        # and b to have opposite signs; in practice these hardly ever
+        # occur).
+        if not a and not b:
+            if math.copysign(1., a) != math.copysign(1., b):
+                self.fail(msg or 'zero has wrong sign: expected {!r}, '
+                          'got {!r}'.format(a, b))
+
+        # if a-b overflows, or b is infinite, return False.  Again, in
+        # theory there are examples where a is within a few ulps of the
+        # max representable float, and then b could legitimately be
+        # infinite.  In practice these examples are rare.
+        try:
+            absolute_error = abs(b-a)
+        except OverflowError:
+            pass
+        else:
+            # test passes if either the absolute error or the relative
+            # error is sufficiently small.  The defaults amount to an
+            # error of between 9 ulps and 19 ulps on an IEEE-754 compliant
+            # machine.
+            if absolute_error <= max(abs_err, rel_err * abs(a)):
+                return
+        self.fail(msg or
+                  '{!r} and {!r} are not sufficiently close'.format(a, b))
+
+    def test_constants(self):
+        e_expected = 2.71828182845904523536
+        pi_expected = 3.14159265358979323846
+        self.assertAlmostEqual(cmath.pi, pi_expected, places=9,
+            msg="cmath.pi is {}; should be {}".format(cmath.pi, pi_expected))
+        self.assertAlmostEqual(cmath.e, e_expected, places=9,
+            msg="cmath.e is {}; should be {}".format(cmath.e, e_expected))
+
+    def test_infinity_and_nan_constants(self):
+        self.assertEqual(cmath.inf.real, math.inf)
+        self.assertEqual(cmath.inf.imag, 0.0)
+        self.assertEqual(cmath.infj.real, 0.0)
+        self.assertEqual(cmath.infj.imag, math.inf)
+
+        self.assertTrue(math.isnan(cmath.nan.real))
+        self.assertEqual(cmath.nan.imag, 0.0)
+        self.assertEqual(cmath.nanj.real, 0.0)
+        self.assertTrue(math.isnan(cmath.nanj.imag))
+        # Also check that the sign of all of these is positive:
+        self.assertEqual(math.copysign(1., cmath.nan.real), 1.)
+        self.assertEqual(math.copysign(1., cmath.nan.imag), 1.)
+        self.assertEqual(math.copysign(1., cmath.nanj.real), 1.)
+        self.assertEqual(math.copysign(1., cmath.nanj.imag), 1.)
+
+        # Check consistency with reprs.
+        self.assertEqual(repr(cmath.inf), "inf")
+        self.assertEqual(repr(cmath.infj), "infj")
+        self.assertEqual(repr(cmath.nan), "nan")
+        self.assertEqual(repr(cmath.nanj), "nanj")
+
+    def test_user_object(self):
+        # Test automatic calling of __complex__ and __float__ by cmath
+        # functions
+
+        # some random values to use as test values; we avoid values
+        # for which any of the functions in cmath is undefined
+        # (i.e. 0., 1., -1., 1j, -1j) or would cause overflow
+        cx_arg = 4.419414439 + 1.497100113j
+        flt_arg = -6.131677725
+
+        # a variety of non-complex numbers, used to check that
+        # non-complex return values from __complex__ give an error
+        non_complexes = ["not complex", 1, 5, 2., None,
+                         object(), NotImplemented]
+
+        # Now we introduce a variety of classes whose instances might
+        # end up being passed to the cmath functions
+
+        # usual case: new-style class implementing __complex__
+        class MyComplex:
+            def __init__(self, value):
+                self.value = value
+            def __complex__(self):
+                return self.value
+
+        # classes for which __complex__ raises an exception
+        class SomeException(Exception):
+            pass
+        class MyComplexException:
+            def __complex__(self):
+                raise SomeException
+
+        # some classes not providing __float__ or __complex__
+        class NeitherComplexNorFloat(object):
+            pass
+        class Index:
+            def __int__(self): return 2
+            def __index__(self): return 2
+        class MyInt:
+            def __int__(self): return 2
+
+        # other possible combinations of __float__ and __complex__
+        # that should work
+        class FloatAndComplex:
+            def __float__(self):
+                return flt_arg
+            def __complex__(self):
+                return cx_arg
+        class JustFloat:
+            def __float__(self):
+                return flt_arg
+
+        for f in self.test_functions:
+            # usual usage
+            self.assertEqual(f(MyComplex(cx_arg)), f(cx_arg))
+            # other combinations of __float__ and __complex__
+            self.assertEqual(f(FloatAndComplex()), f(cx_arg))
+            self.assertEqual(f(JustFloat()), f(flt_arg))
+            self.assertEqual(f(Index()), f(int(Index())))
+            # TypeError should be raised for classes not providing
+            # either __complex__ or __float__, even if they provide
+            # __int__ or __index__:
+            self.assertRaises(TypeError, f, NeitherComplexNorFloat())
+            self.assertRaises(TypeError, f, MyInt())
+            # non-complex return value from __complex__ -> TypeError
+            for bad_complex in non_complexes:
+                self.assertRaises(TypeError, f, MyComplex(bad_complex))
+            # exceptions in __complex__ should be propagated correctly
+            self.assertRaises(SomeException, f, MyComplexException())
+
+    def test_input_type(self):
+        # ints should be acceptable inputs to all cmath
+        # functions, by virtue of providing a __float__ method
+        for f in self.test_functions:
+            for arg in [2, 2.]:
+                self.assertEqual(f(arg), f(arg.__float__()))
+
+        # but strings should give a TypeError
+        for f in self.test_functions:
+            for arg in ["a", "long_string", "0", "1j", ""]:
+                self.assertRaises(TypeError, f, arg)
+
+    def test_cmath_matches_math(self):
+        # check that corresponding cmath and math functions are equal
+        # for floats in the appropriate range
+
+        # test_values in (0, 1)
+        test_values = [0.01, 0.1, 0.2, 0.5, 0.9, 0.99]
+
+        # test_values for functions defined on [-1., 1.]
+        unit_interval = test_values + [-x for x in test_values] + \
+            [0., 1., -1.]
+
+        # test_values for log, log10, sqrt
+        positive = test_values + [1.] + [1./x for x in test_values]
+        nonnegative = [0.] + positive
+
+        # test_values for functions defined on the whole real line
+        real_line = [0.] + positive + [-x for x in positive]
+
+        test_functions = {
+            'acos' : unit_interval,
+            'asin' : unit_interval,
+            'atan' : real_line,
+            'cos' : real_line,
+            'cosh' : real_line,
+            'exp' : real_line,
+            'log' : positive,
+            'log10' : positive,
+            'sin' : real_line,
+            'sinh' : real_line,
+            'sqrt' : nonnegative,
+            'tan' : real_line,
+            'tanh' : real_line}
+
+        for fn, values in test_functions.items():
+            float_fn = getattr(math, fn)
+            complex_fn = getattr(cmath, fn)
+            for v in values:
+                z = complex_fn(v)
+                self.rAssertAlmostEqual(float_fn(v), z.real)
+                self.assertEqual(0., z.imag)
+
+        # test two-argument version of log with various bases
+        for base in [0.5, 2., 10.]:
+            for v in positive:
+                z = cmath.log(v, base)
+                self.rAssertAlmostEqual(math.log(v, base), z.real)
+                self.assertEqual(0., z.imag)
+
+    @requires_IEEE_754
+    def test_specific_values(self):
+        # Some tests need to be skipped on ancient OS X versions.
+        # See issue #27953.
+        SKIP_ON_TIGER = {'tan0064'}
+
+        osx_version = None
+        if sys.platform == 'darwin':
+            version_txt = platform.mac_ver()[0]
+            try:
+                osx_version = tuple(map(int, version_txt.split('.')))
+            except ValueError:
+                pass
+
+        def rect_complex(z):
+            """Wrapped version of rect that accepts a complex number instead of
+            two float arguments."""
+            return cmath.rect(z.real, z.imag)
+
+        def polar_complex(z):
+            """Wrapped version of polar that returns a complex number instead of
+            two floats."""
+            return complex(*polar(z))
+
+        for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file):
+            arg = complex(ar, ai)
+            expected = complex(er, ei)
+
+            # Skip certain tests on OS X 10.4.
+            if osx_version is not None and osx_version < (10, 5):
+                if id in SKIP_ON_TIGER:
+                    continue
+
+            if fn == 'rect':
+                function = rect_complex
+            elif fn == 'polar':
+                function = polar_complex
+            else:
+                function = getattr(cmath, fn)
+            if 'divide-by-zero' in flags or 'invalid' in flags:
+                try:
+                    actual = function(arg)
+                except ValueError:
+                    continue
+                else:
+                    self.fail('ValueError not raised in test '
+                          '{}: {}(complex({!r}, {!r}))'.format(id, fn, ar, ai))
+
+            if 'overflow' in flags:
+                try:
+                    actual = function(arg)
+                except OverflowError:
+                    continue
+                else:
+                    self.fail('OverflowError not raised in test '
+                          '{}: {}(complex({!r}, {!r}))'.format(id, fn, ar, ai))
+
+            actual = function(arg)
+
+            if 'ignore-real-sign' in flags:
+                actual = complex(abs(actual.real), actual.imag)
+                expected = complex(abs(expected.real), expected.imag)
+            if 'ignore-imag-sign' in flags:
+                actual = complex(actual.real, abs(actual.imag))
+                expected = complex(expected.real, abs(expected.imag))
+
+            # for the real part of the log function, we allow an
+            # absolute error of up to 2e-15.
+            if fn in ('log', 'log10'):
+                real_abs_err = 2e-15
+            else:
+                real_abs_err = 5e-323
+
+            error_message = (
+                '{}: {}(complex({!r}, {!r}))\n'
+                'Expected: complex({!r}, {!r})\n'
+                'Received: complex({!r}, {!r})\n'
+                'Received value insufficiently close to expected value.'
+                ).format(id, fn, ar, ai,
+                     expected.real, expected.imag,
+                     actual.real, actual.imag)
+            self.rAssertAlmostEqual(expected.real, actual.real,
+                                        abs_err=real_abs_err,
+                                        msg=error_message)
+            self.rAssertAlmostEqual(expected.imag, actual.imag,
+                                        msg=error_message)
+
+    def check_polar(self, func):
+        def check(arg, expected):
+            got = func(arg)
+            for e, g in zip(expected, got):
+                self.rAssertAlmostEqual(e, g)
+        check(0, (0., 0.))
+        check(1, (1., 0.))
+        check(-1, (1., pi))
+        check(1j, (1., pi / 2))
+        check(-3j, (3., -pi / 2))
+        inf = float('inf')
+        check(complex(inf, 0), (inf, 0.))
+        check(complex(-inf, 0), (inf, pi))
+        check(complex(3, inf), (inf, pi / 2))
+        check(complex(5, -inf), (inf, -pi / 2))
+        check(complex(inf, inf), (inf, pi / 4))
+        check(complex(inf, -inf), (inf, -pi / 4))
+        check(complex(-inf, inf), (inf, 3 * pi / 4))
+        check(complex(-inf, -inf), (inf, -3 * pi / 4))
+        nan = float('nan')
+        check(complex(nan, 0), (nan, nan))
+        check(complex(0, nan), (nan, nan))
+        check(complex(nan, nan), (nan, nan))
+        check(complex(inf, nan), (inf, nan))
+        check(complex(-inf, nan), (inf, nan))
+        check(complex(nan, inf), (inf, nan))
+        check(complex(nan, -inf), (inf, nan))
+
+    def test_polar(self):
+        self.check_polar(polar)
+
+    @cpython_only
+    def test_polar_errno(self):
+        # Issue #24489: check a previously set C errno doesn't disturb polar()
+        _testcapi = import_helper.import_module('_testcapi')
+        def polar_with_errno_set(z):
+            _testcapi.set_errno(11)
+            try:
+                return polar(z)
+            finally:
+                _testcapi.set_errno(0)
+        self.check_polar(polar_with_errno_set)
+
+    def test_phase(self):
+        self.assertAlmostEqual(phase(0), 0.)
+        self.assertAlmostEqual(phase(1.), 0.)
+        self.assertAlmostEqual(phase(-1.), pi)
+        self.assertAlmostEqual(phase(-1.+1E-300j), pi)
+        self.assertAlmostEqual(phase(-1.-1E-300j), -pi)
+        self.assertAlmostEqual(phase(1j), pi/2)
+        self.assertAlmostEqual(phase(-1j), -pi/2)
+
+        # zeros
+        self.assertEqual(phase(complex(0.0, 0.0)), 0.0)
+        self.assertEqual(phase(complex(0.0, -0.0)), -0.0)
+        self.assertEqual(phase(complex(-0.0, 0.0)), pi)
+        self.assertEqual(phase(complex(-0.0, -0.0)), -pi)
+
+        # infinities
+        self.assertAlmostEqual(phase(complex(-INF, -0.0)), -pi)
+        self.assertAlmostEqual(phase(complex(-INF, -2.3)), -pi)
+        self.assertAlmostEqual(phase(complex(-INF, -INF)), -0.75*pi)
+        self.assertAlmostEqual(phase(complex(-2.3, -INF)), -pi/2)
+        self.assertAlmostEqual(phase(complex(-0.0, -INF)), -pi/2)
+        self.assertAlmostEqual(phase(complex(0.0, -INF)), -pi/2)
+        self.assertAlmostEqual(phase(complex(2.3, -INF)), -pi/2)
+        self.assertAlmostEqual(phase(complex(INF, -INF)), -pi/4)
+        self.assertEqual(phase(complex(INF, -2.3)), -0.0)
+        self.assertEqual(phase(complex(INF, -0.0)), -0.0)
+        self.assertEqual(phase(complex(INF, 0.0)), 0.0)
+        self.assertEqual(phase(complex(INF, 2.3)), 0.0)
+        self.assertAlmostEqual(phase(complex(INF, INF)), pi/4)
+        self.assertAlmostEqual(phase(complex(2.3, INF)), pi/2)
+        self.assertAlmostEqual(phase(complex(0.0, INF)), pi/2)
+        self.assertAlmostEqual(phase(complex(-0.0, INF)), pi/2)
+        self.assertAlmostEqual(phase(complex(-2.3, INF)), pi/2)
+        self.assertAlmostEqual(phase(complex(-INF, INF)), 0.75*pi)
+        self.assertAlmostEqual(phase(complex(-INF, 2.3)), pi)
+        self.assertAlmostEqual(phase(complex(-INF, 0.0)), pi)
+
+        # real or imaginary part NaN
+        for z in complex_nans:
+            self.assertTrue(math.isnan(phase(z)))
+
+    def test_abs(self):
+        # zeros
+        for z in complex_zeros:
+            self.assertEqual(abs(z), 0.0)
+
+        # infinities
+        for z in complex_infinities:
+            self.assertEqual(abs(z), INF)
+
+        # real or imaginary part NaN
+        self.assertEqual(abs(complex(NAN, -INF)), INF)
+        self.assertTrue(math.isnan(abs(complex(NAN, -2.3))))
+        self.assertTrue(math.isnan(abs(complex(NAN, -0.0))))
+        self.assertTrue(math.isnan(abs(complex(NAN, 0.0))))
+        self.assertTrue(math.isnan(abs(complex(NAN, 2.3))))
+        self.assertEqual(abs(complex(NAN, INF)), INF)
+        self.assertEqual(abs(complex(-INF, NAN)), INF)
+        self.assertTrue(math.isnan(abs(complex(-2.3, NAN))))
+        self.assertTrue(math.isnan(abs(complex(-0.0, NAN))))
+        self.assertTrue(math.isnan(abs(complex(0.0, NAN))))
+        self.assertTrue(math.isnan(abs(complex(2.3, NAN))))
+        self.assertEqual(abs(complex(INF, NAN)), INF)
+        self.assertTrue(math.isnan(abs(complex(NAN, NAN))))
+
+
+    @requires_IEEE_754
+    def test_abs_overflows(self):
+        # result overflows
+        self.assertRaises(OverflowError, abs, complex(1.4e308, 1.4e308))
+
+    def assertCEqual(self, a, b):
+        eps = 1E-7
+        if abs(a.real - b[0]) > eps or abs(a.imag - b[1]) > eps:
+            self.fail((a ,b))
+
+    def test_rect(self):
+        self.assertCEqual(rect(0, 0), (0, 0))
+        self.assertCEqual(rect(1, 0), (1., 0))
+        self.assertCEqual(rect(1, -pi), (-1., 0))
+        self.assertCEqual(rect(1, pi/2), (0, 1.))
+        self.assertCEqual(rect(1, -pi/2), (0, -1.))
+
+    def test_isfinite(self):
+        real_vals = [float('-inf'), -2.3, -0.0,
+                     0.0, 2.3, float('inf'), float('nan')]
+        for x in real_vals:
+            for y in real_vals:
+                z = complex(x, y)
+                self.assertEqual(cmath.isfinite(z),
+                                  math.isfinite(x) and math.isfinite(y))
+
+    def test_isnan(self):
+        self.assertFalse(cmath.isnan(1))
+        self.assertFalse(cmath.isnan(1j))
+        self.assertFalse(cmath.isnan(INF))
+        self.assertTrue(cmath.isnan(NAN))
+        self.assertTrue(cmath.isnan(complex(NAN, 0)))
+        self.assertTrue(cmath.isnan(complex(0, NAN)))
+        self.assertTrue(cmath.isnan(complex(NAN, NAN)))
+        self.assertTrue(cmath.isnan(complex(NAN, INF)))
+        self.assertTrue(cmath.isnan(complex(INF, NAN)))
+
+    def test_isinf(self):
+        self.assertFalse(cmath.isinf(1))
+        self.assertFalse(cmath.isinf(1j))
+        self.assertFalse(cmath.isinf(NAN))
+        self.assertTrue(cmath.isinf(INF))
+        self.assertTrue(cmath.isinf(complex(INF, 0)))
+        self.assertTrue(cmath.isinf(complex(0, INF)))
+        self.assertTrue(cmath.isinf(complex(INF, INF)))
+        self.assertTrue(cmath.isinf(complex(NAN, INF)))
+        self.assertTrue(cmath.isinf(complex(INF, NAN)))
+
+    @requires_IEEE_754
+    def testTanhSign(self):
+        for z in complex_zeros:
+            self.assertComplexesAreIdentical(cmath.tanh(z), z)
+
+    # The algorithm used for atan and atanh makes use of the system
+    # log1p function; If that system function doesn't respect the sign
+    # of zero, then atan and atanh will also have difficulties with
+    # the sign of complex zeros.
+    @requires_IEEE_754
+    def testAtanSign(self):
+        for z in complex_zeros:
+            self.assertComplexesAreIdentical(cmath.atan(z), z)
+
+    @requires_IEEE_754
+    def testAtanhSign(self):
+        for z in complex_zeros:
+            self.assertComplexesAreIdentical(cmath.atanh(z), z)
+
+
+class IsCloseTests(test_math.IsCloseTests):
+    isclose = cmath.isclose
+
+    def test_reject_complex_tolerances(self):
+        with self.assertRaises(TypeError):
+            self.isclose(1j, 1j, rel_tol=1j)
+
+        with self.assertRaises(TypeError):
+            self.isclose(1j, 1j, abs_tol=1j)
+
+        with self.assertRaises(TypeError):
+            self.isclose(1j, 1j, rel_tol=1j, abs_tol=1j)
+
+    def test_complex_values(self):
+        # test complex values that are close to within 12 decimal places
+        complex_examples = [(1.0+1.0j, 1.000000000001+1.0j),
+                            (1.0+1.0j, 1.0+1.000000000001j),
+                            (-1.0+1.0j, -1.000000000001+1.0j),
+                            (1.0-1.0j, 1.0-0.999999999999j),
+                            ]
+
+        self.assertAllClose(complex_examples, rel_tol=1e-12)
+        self.assertAllNotClose(complex_examples, rel_tol=1e-13)
+
+    def test_complex_near_zero(self):
+        # test values near zero that are near to within three decimal places
+        near_zero_examples = [(0.001j, 0),
+                              (0.001, 0),
+                              (0.001+0.001j, 0),
+                              (-0.001+0.001j, 0),
+                              (0.001-0.001j, 0),
+                              (-0.001-0.001j, 0),
+                              ]
+
+        self.assertAllClose(near_zero_examples, abs_tol=1.5e-03)
+        self.assertAllNotClose(near_zero_examples, abs_tol=0.5e-03)
+
+        self.assertIsClose(0.001-0.001j, 0.001+0.001j, abs_tol=2e-03)
+        self.assertIsNotClose(0.001-0.001j, 0.001+0.001j, abs_tol=1e-03)
+
+    def test_complex_special(self):
+        self.assertIsNotClose(INF, INF*1j)
+        self.assertIsNotClose(INF*1j, INF)
+        self.assertIsNotClose(INF, -INF)
+        self.assertIsNotClose(-INF, INF)
+        self.assertIsNotClose(0, INF)
+        self.assertIsNotClose(0, INF*1j)
+
+
+if __name__ == "__main__":
+    run_tests()

test/dynamo/cpython/3_13/test_math.diff

@@ -0,0 +1,169 @@
+diff --git a/test/dynamo/cpython/3_13/test_math.py b/test/dynamo/cpython/3_13/test_math.py
+index d309e8c1c41..8d95b65ac9d 100644
+--- a/test/dynamo/cpython/3_13/test_math.py
++++ b/test/dynamo/cpython/3_13/test_math.py
+@@ -1,3 +1,59 @@
++# ======= BEGIN Dynamo patch =======
++# Owner(s): ["module: dynamo"]
++
++# ruff: noqa
++# flake8: noqa
++
++import sys
++import torch
++import torch._dynamo.test_case
++import unittest
++from torch._dynamo.test_case import CPythonTestCase
++from torch.testing._internal.common_utils import (
++    TEST_WITH_TORCHDYNAMO,
++    run_tests,
++    xfailIfTorchDynamo,
++    skipIfTorchDynamo,
++)
++
++__TestCase = CPythonTestCase
++
++
++# redirect import statements
++import sys
++import importlib.abc
++
++redirect_imports = (
++    "test.mapping_tests",
++    "test.typinganndata",
++    "test.test_grammar",
++    "test.test_math",
++    "test.test_iter",
++    "test.typinganndata.ann_module",
++)
++
++class RedirectImportFinder(importlib.abc.MetaPathFinder):
++    def find_spec(self, fullname, path, target=None):
++        # Check if the import is the problematic one
++        if fullname in redirect_imports:
++            try:
++                # Attempt to import the standalone module
++                name = fullname.removeprefix("test.")
++                r = importlib.import_module(name)
++                # Redirect the module in sys.modules
++                sys.modules[fullname] = r
++                # Return a module spec from the found module
++                return importlib.util.find_spec(name)
++            except ImportError:
++                return None
++        return None
++
++# Add the custom finder to sys.meta_path
++sys.meta_path.insert(0, RedirectImportFinder())
++
++
++# ======= END DYNAMO PATCH =======
++
+ # Python test set -- math module
+ # XXXX Should not do tests around zero only
+ 
+@@ -242,7 +298,7 @@ class BadDescr:
+     def __get__(self, obj, objtype=None):
+         raise ValueError
+ 
+-class MathTests(unittest.TestCase):
++class MathTests(__TestCase):
+ 
+     def ftest(self, name, got, expected, ulp_tol=5, abs_tol=0.0):
+         """Compare arguments expected and got, as floats, if either
+@@ -533,6 +589,7 @@ class MathTests(unittest.TestCase):
+         self.ftest('fabs(0)', math.fabs(0), 0)
+         self.ftest('fabs(1)', math.fabs(1), 1)
+ 
++    @skipIfTorchDynamo("infinite loop")
+     def testFactorial(self):
+         self.assertEqual(math.factorial(0), 1)
+         total = 1
+@@ -1227,6 +1284,7 @@ class MathTests(unittest.TestCase):
+         self.assertRaises(ValueError, math.log1p, -1)
+         self.assertEqual(math.log1p(INF), INF)
+ 
++    @skipIfTorchDynamo("Infinite loop")
+     @requires_IEEE_754
+     def testLog2(self):
+         self.assertRaises(TypeError, math.log2)
+@@ -1245,6 +1303,7 @@ class MathTests(unittest.TestCase):
+         self.assertRaises(ValueError, math.log2, NINF)
+         self.assertTrue(math.isnan(math.log2(NAN)))
+ 
++    @skipIfTorchDynamo("Infinite loop")
+     @requires_IEEE_754
+     # log2() is not accurate enough on Mac OS X Tiger (10.4)
+     @support.requires_mac_ver(10, 5)
+@@ -1326,7 +1385,7 @@ class MathTests(unittest.TestCase):
+         with self.assertRaises(RuntimeError):
+             sumprod(raise_after(5), range(10))
+ 
+-        from test.test_iter import BasicIterClass
++        from test_iter import BasicIterClass
+ 
+         self.assertEqual(sumprod(BasicIterClass(1), [1]), 0)
+         self.assertEqual(sumprod([1], BasicIterClass(1)), 0)
+@@ -2246,6 +2305,7 @@ class MathTests(unittest.TestCase):
+         self.assertEqual(type(prod([1, decimal.Decimal(2.0), 3, 4, 5, 6])),
+                          decimal.Decimal)
+ 
++    @skipIfTorchDynamo("Infinite loop")
+     def testPerm(self):
+         perm = math.perm
+         factorial = math.factorial
+@@ -2310,6 +2370,7 @@ class MathTests(unittest.TestCase):
+             self.assertIs(type(perm(IntSubclass(5), IntSubclass(k))), int)
+             self.assertIs(type(perm(MyIndexable(5), MyIndexable(k))), int)
+ 
++    @skipIfTorchDynamo("infinite loop")
+     def testComb(self):
+         comb = math.comb
+         factorial = math.factorial
+@@ -2502,7 +2563,7 @@ class MathTests(unittest.TestCase):
+         self.assertEqual(math.copysign(1.0, x), math.copysign(1.0, y))
+ 
+ 
+-class IsCloseTests(unittest.TestCase):
++class IsCloseTests(__TestCase):
+     isclose = math.isclose  # subclasses should override this
+ 
+     def assertIsClose(self, a, b, *args, **kwargs):
+@@ -2625,7 +2686,7 @@ class IsCloseTests(unittest.TestCase):
+         self.assertAllNotClose(fraction_examples, rel_tol=1e-9)
+ 
+ 
+-class FMATests(unittest.TestCase):
++class FMATests(__TestCase):
+     """ Tests for math.fma. """
+ 
+     def test_fma_nan_results(self):
+@@ -2713,8 +2774,7 @@ class FMATests(unittest.TestCase):
+     # properly: it doesn't use the right sign when the result is zero.
+     @unittest.skipIf(
+         sys.platform.startswith(("freebsd", "wasi", "netbsd", "emscripten"))
+-        or (sys.platform == "android" and platform.machine() == "x86_64")
+-        or support.linked_to_musl(),  # gh-131032
++        or (sys.platform == "android" and platform.machine() == "x86_64"),
+         f"this platform doesn't implement IEE 754-2008 properly")
+     def test_fma_zero_result(self):
+         nonnegative_finites = [0.0, 1e-300, 2.3, 1e300]
+@@ -2875,8 +2935,15 @@ class FMATests(unittest.TestCase):
+ 
+ def load_tests(loader, tests, pattern):
+     from doctest import DocFileSuite
+-    tests.addTest(DocFileSuite(os.path.join("mathdata", "ieee754.txt")))
++    suite = DocFileSuite(os.path.join("mathdata", "ieee754.txt"))
++    # ======= BEGIN Dynamo patch =======
++    for test in suite:
++        # Dynamically change base class
++        test.__class__ = type(test.__class__.__name__, (__TestCase, test.__class__), {})
++    # ======== END Dynamo patch ========
++    tests.addTests(suite)
+     return tests
+ 
+-if __name__ == '__main__':
+-    unittest.main()
++
++if __name__ == "__main__":
++    run_tests()