Why doesn't Python have a sign function?

Question

EDIT:

Indeed there was a patch which included sign() in math, but it wasn't accepted, because they didn't agree on what it should return in all the edge cases (+/-0, +/-nan, etc)

So they decided to implement only copysign, which (although more verbose) can be used to delegate to the end user the desired behavior for edge cases - which sometimes might require the call to cmp(x,0).

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I don't know why it's not a built-in, but I have some thoughts.

copysign(x,y):
Return x with the sign of y.

Most importantly, copysign is a superset of sign! Calling copysign with x=1 is the same as a sign function. So you could just use copysign and forget about it.

>>> math.copysign(1, -4)
-1.0
>>> math.copysign(1, 3)
1.0

If you get sick of passing two whole arguments, you can implement sign this way, and it will still be compatible with the IEEE stuff mentioned by others:

>>> sign = functools.partial(math.copysign, 1) # either of these
>>> sign = lambda x: math.copysign(1, x) # two will work
>>> sign(-4)
-1.0
>>> sign(3)
1.0
>>> sign(0)
1.0
>>> sign(-0.0)
-1.0
>>> sign(float('nan'))
-1.0

Secondly, usually when you want the sign of something, you just end up multiplying it with another value. And of course that's basically what copysign does.

So, instead of:

s = sign(a)
b = b * s

You can just do:

b = copysign(b, a)

And yes, I'm surprised you've been using Python for 7 years and think cmp could be so easily removed and replaced by sign! Have you never implemented a class with a __cmp__ method? Have you never called cmp and specified a custom comparator function?

In summary, I've found myself wanting a sign function too, but copysign with the first argument being 1 will work just fine. I disagree that sign would be more useful than copysign, as I've shown that it's merely a subset of the same functionality.

"copysign" is defined by IEEE 754, and part of the C99 specification. That's why it's in Python. The function cannot be implemented in full by abs(x) * sign(y) because of how it's supposed to handle NaN values.

>>> import math
>>> math.copysign(1, float("nan"))
1.0
>>> math.copysign(1, float("-nan"))
-1.0
>>> math.copysign(float("nan"), 1)
nan
>>> math.copysign(float("nan"), -1)
nan
>>> float("nan") * -1
nan
>>> float("nan") * 1
nan
>>> 

That makes copysign() a more useful function than sign().

As to specific reasons why IEEE's signbit(x) is not available in standard Python, I don't know. I can make assumptions, but it would be guessing.

The math module itself uses copysign(1, x) as a way to check if x is negative or non-negative. For most cases dealing with mathematical functions that seems more useful than having a sign(x) which returns 1, 0, or -1 because there's one less case to consider. For example, the following is from Python's math module:

static double
m_atan2(double y, double x)
{
        if (Py_IS_NAN(x) || Py_IS_NAN(y))
                return Py_NAN;
        if (Py_IS_INFINITY(y)) {
                if (Py_IS_INFINITY(x)) {
                        if (copysign(1., x) == 1.)
                                /* atan2(+-inf, +inf) == +-pi/4 */
                                return copysign(0.25*Py_MATH_PI, y);
                        else
                                /* atan2(+-inf, -inf) == +-pi*3/4 */
                                return copysign(0.75*Py_MATH_PI, y);
                }
                /* atan2(+-inf, x) == +-pi/2 for finite x */
                return copysign(0.5*Py_MATH_PI, y);

There you can clearly see that copysign() is a more effective function than a three-valued sign() function.

You wrote:

If I were a python designer, I would been the other way around: no cmp() builtin, but a sign()

That means you don't know that cmp() is used for things besides numbers. cmp("This", "That") cannot be implemented with a sign() function.

Edit to collate my additional answers elsewhere:

You base your justifications on how abs() and sign() are often seen together. As the C standard library does not contain a 'sign(x)' function of any sort, I don't know how you justify your views. There's an abs(int) and fabs(double) and fabsf(float) and fabsl(long) but no mention of sign. There is "copysign()" and "signbit()" but those only apply to IEEE 754 numbers.

With complex numbers, what would sign(-3+4j) return in Python, were it to be implemented? abs(-3+4j) return 5.0. That's a clear example of how abs() can be used in places where sign() makes no sense.

Suppose sign(x) were added to Python, as a complement to abs(x). If 'x' is an instance of a user-defined class which implements the __abs__(self) method then abs(x) will call x.__abs__(). In order to work correctly, to handle abs(x) in the same way then Python will have to gain a sign(x) slot.

This is excessive for a relatively unneeded function. Besides, why should sign(x) exist and nonnegative(x) and nonpositive(x) not exist? My snippet from Python's math module implementation shows how copybit(x, y) can be used to implement nonnegative(), which a simple sign(x) cannot do.

Python should support have better support for IEEE 754/C99 math function. That would add a signbit(x) function, which would do what you want in the case of floats. It would not work for integers or complex numbers, much less strings, and it wouldn't have the name you are looking for.

You ask "why", and the answer is "sign(x) isn't useful." You assert that it is useful. Yet your comments show that you do not know enough to be able to make that assertion, which means you would have to show convincing evidence of its need. Saying that NumPy implements it is not convincing enough. You would need to show cases of how existing code would be improved with a sign function.

And that it outside the scope of StackOverflow. Take it instead to one of the Python lists.

Another one liner for sign()

sign = lambda x: (1, -1)[x<0]

If you want it to return 0 for x = 0:

sign = lambda x: x and (1, -1)[x<0]

Since cmp has been removed, you can get the same functionality with

def cmp(a, b):
    return (a > b) - (a < b)

def sign(a):
    return (a > 0) - (a < 0)

It works for float, int and even Fraction. In the case of float, notice sign(float("nan")) is zero.

Python doesn't require that comparisons return a boolean, and so coercing the comparisons to bool() protects against allowable, but uncommon implementation:

def sign(a):
    return bool(a > 0) - bool(a < 0)