Add math.sign() function to the math module

[acolesnicov]

Feature or enhancement

Proposal:

I am proposing to add a math.sign() function to the standard math module. This function returns the sign of a number: -1 for negative values, 1 for positive values, and 0 for zero.

While this can be implemented in pure Python, a native C implementation provides better performance and, more importantly, a standardized way to handle edge cases that are often implemented inconsistently by users.

Key features of the proposed implementation:

Full IEEE 754 Support: Correctly handles NaN, signed zeros (+/-0.0), and infinities. For NaN input, it returns NaN.

Duck-typing via Rich Comparisons: The implementation is not limited to int and float. It works with any object that supports order comparisons (via > 0, < 0, and ==0 logic), including (but not restricted by) Decimal, Fraction, sympy.Rational, numpy types, and custom user classes.

Robust Error Handling: Provides informative TypeError messages when an argument doesn't support comparison, including the "Inner error" if the object's comparison protocol raises an exception.

Performance: Implemented in C as part of mathmodule.c using Argument Clinic.

Implementation status: I have a complete implementation ready and tested, including:

• C code in mathmodule.c.
• Comprehensive test suite in test_math.py covering all edge cases.
• Documentation updates for math.rst.
• Verified with regrtest -R 3:3 on a debug build (no leaks detected).

Has this already been discussed elsewhere?

I have already discussed this feature proposal on Discourse

Links to previous discussion of this feature:

https://discuss.python.org/t/include-math-sign/45404/92
The discussion was slow because the topic is set to "slow mode", and, I think, due to Christmas. I performed the full implementation quicker than we could discuss details.

Linked PRs

• gh-143132: Add math.sign() function #143133

[picnixz]

Sorry but I am against this addition. I forgot to post my answer about C99 but there is no support in that thread from a core dev for this feature and thus will close it.

[vstinner]

You can reimplement sign() on top of the existing math.signbit() function:

def sign(num):
    if num == 0:
        return 0
    return math.signbit(num) * -2 + 1

sign(float("nan")) returns 1, and sign(float("-nan")) returns -1.

[acolesnicov]

Dear Victor,   Thank you for your time and the initial feedback on the math.sign proposal.    Events have been moving faster than the forum's "slow mode" allows for updates. Over the last 17 hours, I have completely refactored the implementation. The logic is now based on a ternary state machine — there isn't a single `if-else` chain in the core comparison logic.    Core logic snippet (CPython):     /* Check for numeric NaN */     double d = PyFloat_AsDouble(x);     if (Py_IS_NAN(d)) return PyFloat_FromDouble(Py_NAN);     /* If it is something special, we will try comparisons */     if (PyErr_Occurred()) PyErr_Clear();       PyObject *zero = PyLong_FromLong(0);     if (!zero) return NULL; /* Memory Error? */       int gt = PyObject_RichCompareBool(x, zero, Py_GT) + 1; /* 2: True; 1: False; 0: Error */     int lt = PyObject_RichCompareBool(x, zero, Py_LT) + 1;     int res = gt - lt; /* Result, if nothing special */     int eq = PyObject_RichCompareBool(x, zero, Py_EQ) + 1; /* Used only to process NaN and errors */       Py_DECREF(zero); /* Not used anymore */       /* gt, lt, eq can be 0, 1, 2; let them be digits in the ternary number system */     /* code = 9*gt+3*lt+eq is the value of the number written in the ternary system        with these digits */     /* We also use 9 = 8+1, 3 = 4-1, and replace multiplication by 8 and 4 with shift */     int code = (gt << 3) + (lt << 2) + eq + res;     /* (gt<<3) = 8*gt; (lt<<2) = 4*gt; code = 8*gt + 4*lt + eq + (gt-lt) = 9*gt+3*lt+eq */          switch (code) {         case 13: { /* 111₃ ->  8+4+1+0: possible NaN     (False, False, False) */             int self_eq = PyObject_RichCompareBool(x, x, Py_EQ);             switch (self_eq) {                 case -1: return NULL; /* Error in __eq__, we keep Python error */                 case  0: return PyFloat_FromDouble(Py_NAN); /* NaN: not equal to itself */                 default: goto error; /* Not a NaN: equals to itself; not comparable to 0 */             }         }         case 14:   /* 112₃ ->  8+4+2+0: x == 0 (res= 0)  (False, False, True ) */         case 16:   /* 121₃ ->  8+8+1-1: x <  0 (res=-1)  (False, True,  False) */         case 22:   /* 211₃ -> 16+4+1+1: x >  0 (res= 1)  (True,  False, False) */             return PyLong_FromLong((long)res);         default: /* No more valid cases */             goto error;     } error:   In the meantime the PR gh-143133 was closed as unplanned. Citation from a mail:

From: Bénédikt Tran Closed #143132 as not planned.

  Then I have decided to release this as a standalone module: signum. The module is already fully functional and installed locally on my environment.   Status: I am currently finalizing the test suite and preparing the PyPI release.   For faster communication, please contact me via email.   Quick test from console: E:\signum-project>pip install . Processing e:\signum-project   Installing build dependencies ... done   Getting requirements to build wheel ... done   Preparing metadata (pyproject.toml) ... done Building wheels for collected packages: signum   Building wheel for signum (pyproject.toml) ... done   Created wheel for signum: filename=signum-1.0-cp313-cp313-win_amd64.whl size=6896 sha256=acbe96530e3b95bd207a4c1ede2f93bce10bbf569a965d1650edafbcf73b7985   Stored in directory: c:\users\pc\appdata\local\pip\cache\wheels\5b\be\e2\bcb99bf2b7f98d391fd67c036dca2dd4ef4da490b1392abc21 Successfully built signum Installing collected packages: signum Successfully installed signum-1.0   E:\signum-project>python Python 3.13.5 (tags/v3.13.5:6cb20a2, Jun 11 2025, 16:15:46) [MSC v.1943 64 bit (AMD64)] on win32 Type "help", "copyright", "credits" or "license" for more information.

>> from signum import sign >> print(sign(float('-nan')))

nan

>> print(sign(-100))

-1

>> print(sign("error"))

Traceback (most recent call last):   File "<python-input-3>", line 1, in <module>     print(sign("error"))           ~~~~^^^^^^^^^ TypeError: signum.sign: invalid argument `'error'` (type 'str'). Inner error: '<' not supported between instances of 'str' and 'int'

>> exit(0)

  Best regards, Alexandru Sent: Wednesday, December 24, 2025 at 4:57 PM From: "Victor Stinner" ***@***.***> To: "python/cpython" ***@***.***> Cc: "acolesnicov" ***@***.***>, "Author" ***@***.***> Subject: Re: [python/cpython] Add math.sign() function to the math module (Issue #143132) vstinner left a comment (python/cpython#143132) You can reimplement sign() on top of the existing math.signbit() function: def sign(num): if num == 0: return 0 return math.signbit(num) * -2 + 1 sign(float("nan")) returns 1, and sign(float("-nan")) returns -1. — Reply to this email directly, view it on GitHub, or unsubscribe. You are receiving this because you authored the thread.Message ID: ***@***.***>