5 ms·

Careful what you wish for. What should -7 / 2 return? -3 kind of makes sense, because 7/2 is 3. It also desirable to have the remainder consistent with the res

Careful what you wish for. What should -7 / 2 return? -3 kind of makes sense, because 7/2 is 3. It also desirable to have the remainder consistent with the result of division, such that x = d*r + mod, where r is the result of division. Combine that with the above requires negative mods.

masklinn 5y ago
> Careful what you wish for. What should -7 / 2 return? -3 kind of makes sense, because 7/2 is 3. -4 also makes sense. > It also desirable to have the remainder consistent with the result of division, such that x = d*r + mod, where r is the result of division. Combine that with the above requires negative mods. Python's behaviour is consistent with that definition: >>> divmod(-7, 2) (-4, 1) -7 = -4 * 2 + 1
naniwaduni 5y ago
It's highly desirable for -7/2 to equal -4, since this lets integer division by powers of two be exactly equivalent to a two's complement arithmetic right shift. In a C mindset, rounding toward zero is pretty much an objectively wrong holdover from before we knew better.
Laremere 5y ago
Moving past the intuition for how division and remainders work for real numbers, there are other ways to look at "obvious" answers that suggests -7/2=4. Consider x/3=y. For real numbers, it's trivial to manipulate this equation into (x-3)/3=y-1. However, this only works when integer division rounds down. 5/3 = 1 rem 2 or 1 rem 2 4/3 = 1 rem 1 or 1 rem 1 3/3 = 1 rem 0 or 1 rem 0 2/3 = 0 rem 2 or 0 rem 2 1/3 = 0 rem 1 or 0 rem 1 0/3 = 0 rem 0 or 0 rem 0 -1/3 = -1 rem 2 or 0 rem -1 -2/3 = -1 rem 1 or 0 rem -2 -3/3 = -1 rem 0 or -1 rem 0 One of these has a consistent pattern, the other doesn't. All of this is a fairly moot point: The answer is it should do what the algorithm using it needs it to do.
- superjan 5y ago
  It is not so much my intuition but the intuition of the language designers. I would prefer euclidian division personally.
- strenholme 5y ago
  True, but both Python’s “int()” operation and the C99 and C11 standard for division operators truncate towards 0. [1] [1] e.g. http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1256.pdf http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1256.pdf PDF page 94/physical page 82
  - housecarpenter 5y ago
    Python's int() truncates towards 0, but (at least in Python 3, I don't know if it was always the same in older versions) its division operator always floors, so -7 // 2 gives -4 even though int(-3.5) is 3. (The int() function is best thought of as just "make this float into an integer, I don't really care how"; if you want to be more specific, you have math.floor(), math.ceil() and math.trunc(), and you also have round(), which rounds towards the closest integer; if the float is evenly between the two integers, it goes towards 0 when the integer part is even and away from 0 when the integer part is odd.)
strenholme 5y ago
In my experience, when looking at how division should operate for a given well-established language, it doesn’t matter what you and I think should be the result of the operation; it matters what the standard says on it. From PDF page 94 (physical page 82) of the draft C99 standard: [1] The result of the / operator is the quotient from the division of the first operand by the second This is a little vague; it would be better if they called it the “quotient from Euclidean division” (EDIT: This was incorrect. Actually, it’s the quotient from algebraic division, with the fraction truncated, also called “truncation towards zero”. See discussion below.), which is well defined as being -3 in the above example; see https://en.wikipedia.org/wiki/Euclidean_division https://en.wikipedia.org/wiki/Euclidean_division (EDIT: Euclidean is -4; truncation towards 0 is -3) [1] http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1256.pdf http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1256.pdf
- naniwaduni 5y ago
  Euclidian division actually gives -7 = -4*2 + 1
  - strenholme 5y ago
    It’s -3 in GCC 11.2.0 main() { printf("%d\n",-7/2);} Let’s look at, oh, C11: http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1570.pdf http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1570.pdf PDF page 110, physical page 92: When integers are divided, the result of the / operator is the algebraic quotient with any fractional part discarded. with a footnote: This is often called ‘‘truncation toward zero’’ -7/2 is -3.5, so discarding the fractional part gives us -3
    - naniwaduni 5y ago
      Yes, and this is not Euclidean division in the usual sense.
      - strenholme 5y ago
        Indeed. The C99 and C11 standards define integer division as the “algebraic quotient with any fractional part discarded”, not as Euclidean division.

masklinn 5y ago

> Careful what you wish for. What should -7 / 2 return? -3 kind of makes sense, because 7/2 is 3. -4 also makes sense. > It also desirable to have the remainder consistent with the result of division, such that x = d*r + mod, where r is the result of division. Combine that with the above requires negative mods. Python's behaviour is consistent with that definition: >>> divmod(-7, 2) (-4, 1) -7 = -4 * 2 + 1

naniwaduni 5y ago

It's highly desirable for -7/2 to equal -4, since this lets integer division by powers of two be exactly equivalent to a two's complement arithmetic right shift. In a C mindset, rounding toward zero is pretty much an objectively wrong holdover from before we knew better.

Laremere 5y ago

Moving past the intuition for how division and remainders work for real numbers, there are other ways to look at "obvious" answers that suggests -7/2=4. Consider x/3=y. For real numbers, it's trivial to manipulate this equation into (x-3)/3=y-1. However, this only works when integer division rounds down. 5/3 = 1 rem 2 or 1 rem 2 4/3 = 1 rem 1 or 1 rem 1 3/3 = 1 rem 0 or 1 rem 0 2/3 = 0 rem 2 or 0 rem 2 1/3 = 0 rem 1 or 0 rem 1 0/3 = 0 rem 0 or 0 rem 0 -1/3 = -1 rem 2 or 0 rem -1 -2/3 = -1 rem 1 or 0 rem -2 -3/3 = -1 rem 0 or -1 rem 0 One of these has a consistent pattern, the other doesn't. All of this is a fairly moot point: The answer is it should do what the algorithm using it needs it to do.

superjan 5y ago
It is not so much my intuition but the intuition of the language designers. I would prefer euclidian division personally.
strenholme 5y ago
True, but both Python’s “int()” operation and the C99 and C11 standard for division operators truncate towards 0. [1] [1] e.g. http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1256.pdf http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1256.pdf PDF page 94/physical page 82
- housecarpenter 5y ago
  Python's int() truncates towards 0, but (at least in Python 3, I don't know if it was always the same in older versions) its division operator always floors, so -7 // 2 gives -4 even though int(-3.5) is 3. (The int() function is best thought of as just "make this float into an integer, I don't really care how"; if you want to be more specific, you have math.floor(), math.ceil() and math.trunc(), and you also have round(), which rounds towards the closest integer; if the float is evenly between the two integers, it goes towards 0 when the integer part is even and away from 0 when the integer part is odd.)

strenholme 5y ago

In my experience, when looking at how division should operate for a given well-established language, it doesn’t matter what you and I think should be the result of the operation; it matters what the standard says on it. From PDF page 94 (physical page 82) of the draft C99 standard: [1] The result of the / operator is the quotient from the division of the first operand by the second This is a little vague; it would be better if they called it the “quotient from Euclidean division” (EDIT: This was incorrect. Actually, it’s the quotient from algebraic division, with the fraction truncated, also called “truncation towards zero”. See discussion below.), which is well defined as being -3 in the above example; see https://en.wikipedia.org/wiki/Euclidean_division https://en.wikipedia.org/wiki/Euclidean_division (EDIT: Euclidean is -4; truncation towards 0 is -3) [1] http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1256.pdf http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1256.pdf

naniwaduni 5y ago
Euclidian division actually gives -7 = -4*2 + 1
- strenholme 5y ago
  It’s -3 in GCC 11.2.0 main() { printf("%d\n",-7/2);} Let’s look at, oh, C11: http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1570.pdf http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1570.pdf PDF page 110, physical page 92: When integers are divided, the result of the / operator is the algebraic quotient with any fractional part discarded. with a footnote: This is often called ‘‘truncation toward zero’’ -7/2 is -3.5, so discarding the fractional part gives us -3
  - naniwaduni 5y ago
    Yes, and this is not Euclidean division in the usual sense.
    - strenholme 5y ago
      Indeed. The C99 and C11 standards define integer division as the “algebraic quotient with any fractional part discarded”, not as Euclidean division.