Abstract

This PEP describes an extension to the built-in divmod() function, allowing it to take multiple divisors, chaining several calls to divmod() into one.

Pronouncement

This PEP is rejected. Most uses for chained divmod() involve a constant modulus (in radix conversions for example) and are more properly coded as a loop. The example of splitting seconds into days/hours/minutes/seconds does not generalize to months and years; rather, the whole use case is handled more flexibly and robustly by date and time modules. The other use cases mentioned in the PEP are somewhat rare in real code. The proposal is also problematic in terms of clarity and obviousness. In the examples, it is not immediately clear that the argument order is correct or that the target tuple is of the right length. Users from other languages are more likely to understand the standard two argument form without having to re-read the documentation. See python-dev discussion on 17 June 2005 [1].

Specification

The built-in divmod() function would be changed to accept multiple divisors, changing its signature from divmod(dividend, divisor) to divmod(dividend, *divisors). The dividend is divided by the last divisor, giving a quotient and a remainder. The quotient is then divided by the second to last divisor, giving a new quotient and remainder. This is repeated until all divisors have been used, and divmod() then returns a tuple consisting of the quotient from the last step, and the remainders from all the steps.

A Python implementation of the new divmod() behaviour could look like:

def divmod(dividend, *divisors):
    modulos = ()
    q = dividend
    while divisors:
        q, r = q.__divmod__(divisors[-1])
        modulos = (r,) + modulos
        divisors = divisors[:-1]
    return (q,) + modulos

Motivation

Occasionally one wants to perform a chain of divmod() operations, calling divmod() on the quotient from the previous step, with varying divisors. The most common case is probably converting a number of seconds into weeks, days, hours, minutes and seconds. This would today be written as:

def secs_to_wdhms(seconds):
    m, s = divmod(seconds, 60)
    h, m = divmod(m, 60)
    d, h = divmod(h, 24)
    w, d = divmod(d, 7)
    return (w, d, h, m, s)

This is tedious and easy to get wrong each time you need it.

If instead the divmod() built-in is changed according the proposal, the code for converting seconds to weeks, days, hours, minutes and seconds then become

def secs_to_wdhms(seconds):
    w, d, h, m, s = divmod(seconds, 7, 24, 60, 60)
    return (w, d, h, m, s)

which is easier to type, easier to type correctly, and easier to read.

Other applications are:

• Astronomical angles (declination is measured in degrees, minutes and seconds, right ascension is measured in hours, minutes and seconds).
• Old British currency (1 pound = 20 shilling, 1 shilling = 12 pence).
• Anglo-Saxon length units: 1 mile = 1760 yards, 1 yard = 3 feet, 1 foot = 12 inches.
• Anglo-Saxon weight units: 1 long ton = 160 stone, 1 stone = 14 pounds, 1 pound = 16 ounce, 1 ounce = 16 dram.
• British volumes: 1 gallon = 4 quart, 1 quart = 2 pint, 1 pint = 20 fluid ounces.

Rationale

The idea comes from APL, which has an operator that does this. (I don’t remember what the operator looks like, and it would probably be impossible to render in ASCII anyway.)

The APL operator takes a list as its second operand, while this PEP proposes that each divisor should be a separate argument to the divmod() function. This is mainly because it is expected that the most common uses will have the divisors as constants right in the call (as the 7, 24, 60, 60 above), and adding a set of parentheses or brackets would just clutter the call.

Requiring an explicit sequence as the second argument to divmod() would seriously break backwards compatibility. Making divmod() check its second argument for being a sequence is deemed to be too ugly to contemplate. And in the case where one does have a sequence that is computed other-where, it is easy enough to write divmod(x, *divs) instead.

Requiring at least one divisor, i.e rejecting divmod(x), has been considered, but no good reason to do so has come to mind, and is thus allowed in the name of generality.

Calling divmod() with no divisors should still return a tuple (of one element). Code that calls divmod() with a varying number of divisors, and thus gets a return value with an “unknown” number of elements, would otherwise have to special case that case. Code that knows it is calling divmod() with no divisors is considered to be too silly to warrant a special case.

Processing the divisors in the other direction, i.e dividing with the first divisor first, instead of dividing with the last divisor first, has been considered. However, the result comes with the most significant part first and the least significant part last (think of the chained divmod as a way of splitting a number into “digits”, with varying weights), and it is reasonable to specify the divisors (weights) in the same order as the result.

The inverse operation:

def inverse_divmod(seq, *factors):
    product = seq[0]
    for x, y in zip(factors, seq[1:]):
        product = product * x + y
    return product

could also be useful. However, writing

seconds = (((((w * 7) + d) * 24 + h) * 60 + m) * 60 + s)

is less cumbersome both to write and to read than the chained divmods. It is therefore deemed to be less important, and its introduction can be deferred to its own PEP. Also, such a function needs a good name, and the PEP author has not managed to come up with one yet.

Calling divmod("spam") does not raise an error, despite strings supporting neither division nor modulo. However, unless we know the other object too, we can’t determine whether divmod() would work or not, and thus it seems silly to forbid it.

Backwards Compatibility

Any module that replaces the divmod() function in the __builtin__ module, may cause other modules using the new syntax to break. It is expected that this is very uncommon.

Code that expects a TypeError exception when calling divmod() with anything but two arguments will break. This is also expected to be very uncommon.

No other issues regarding backwards compatibility are known.

Reference Implementation

Not finished yet, but it seems a rather straightforward new implementation of the function builtin_divmod() in Python/bltinmodule.c.

References

[1]

Raymond Hettinger, “Propose rejection of PEP 303 – Extend divmod() for Multiple Divisors” https://mail.python.org/pipermail/python-dev/2005-June/054283.html

Copyright

This document has been placed in the public domain.