## Feature #3289

### Division of negative numbers

**Description**

=begin

The documentation for Numeric (http://www.ruby-doc.org/core/classes/Numeric.html#M000179) states that integer divmod() (and, by extension, /) rounds the quotient towards negative infinity. Python and Tcl behave similarly, while C, Java, bc, and gdb round the quotient towards zero, as is taught in standard arithmetic courses.

Is this a quirk of MRI's implementation, or is it desired Ruby behavior? If so, why?

It's counterintuitive that (-x/y) ≠ -(x/y), and even moreso when (-x/y) = -(x/y) if x or y is a non-integer.

=end

### History

#### #1 Updated by Shyouhei Urabe over 5 years ago

=begin

Japanese elementary schools tend to teach their children that "x / y is z remainder w" means

x == y * z + w, where 0 <= w < y.

So we follow it.

=end

#### #2 Updated by Yusuke Endoh over 5 years ago

**Assignee**set to*Yukihiro Matsumoto***Priority**changed from*Normal*to*3*

=begin

Hi,

2010/5/14 Patrick Thomson redmine@ruby-lang.org:

The documentation for Numeric (http://www.ruby-doc.org/core/classes/Numeric.html#M000179) states that integer divmod() (and, by extension, /) rounds the quotient towards negative infinity. Python and Tcl behave similarly, while C, Java, bc, and gdb round the quotient towards zero, as is taught in standard arithmetic courses.

It is very various. According to:

"Integer modulo operators in various programming languages"

http://en.wikipedia.org/wiki/Modulo_operation

J, Lua, Mathematica, Excel, Oberon, Perl, PL/I, Python, R, Ruby,

Smalltalk, Tcl and Turing seem to behave the same.

I bet Ruby's division is taken after Perl.

Anyway, it is too late to change.

--

Yusuke Endoh mame@tsg.ne.jp

=end

#### #4 Updated by Akira Tanaka over 4 years ago

**Project**changed from*Ruby*to*Ruby trunk***Category**changed from*core*to*core*

#### #5 [ruby-core:40517] Updated by Alexey Muranov over 4 years ago

I think that division with always rounding towards 0 is not logical. Rounding towards the closest integer, going towards 0 if there are 2 integers at equal distance, sounds better to me. This would be symmetric with respect to exchanging x and -x. The current behavior/definition of '/' is also an important operation. Maybe it can be renamed to 'div' and return both the quotient and the remainder in the "integral" sense (quotient being rounded towards -\infty)?

Update: Sorry, i have not read the documentation! So divmod does exactly what one would expect it to do. The division '/' for integers is indeed questionable. I would suggest that it raise an exception or return some special value if two integers do not divide evenly. Apart from being nice in mathematical sense, this can help to avoid unexpected bugs.

-Alexey.

#### #6 [ruby-core:49679] Updated by Yusuke Endoh about 3 years ago

**Description**updated (diff)**Target version**set to*Next Major*

#### #7 [ruby-core:54600] Updated by Anonymous almost 3 years ago

Given the context, Ruby choice seems right to me. But the real core of the problem is

the minus sign. My father says, that minus simply represents an unfinished operation,

intention to subtract. Citing anonymous Wikipedia contributor:

"Negative numbers appeared for the first time in history in the Nine Chapters on

the Mathematical Art, which in its present form dates from the period of the

Chinese Han Dynasty (202 BC. - AD 220), but may well contain much older material.

Indian mathematicians developed consistent and correct rules on the use of negative

numbers, which later spread to the Middle East and then into Europe. Prior to the

concept of negative numbers, negative solutions to problems were considered "false"

and equations requiring negative solutions were described as absurd (Diophantus's

Arithmetica cited)."

My father thinks, that Greek adherence to natural numbers, inherited by medieval Europe,

was not due to their backwardness (they eg. knew that π was irrational), but because

complicated objects catering to daily needs of bookkepers were bad elementary blocks

for general-purpose applied mathematics.

I would like to see basic math rebuilt without reaching for minus (and zero) too early.

Relevant Ruby proposal would be: have true natural numbers (class Natural), have morally

sound rationals (natural/ natural), and positive-only floats. Will I try to prototype

this myself one day? Regarding zero, which has similar issues as minus and is absent

from true natural numbers. I wonder how far would one get using nil (or null?) in its

stead, like ancient Romans did...