[ruby-core:109276] [Ruby master Feature#18809] Add Numeric#ceildiv

Issue #18809 has been updated by mame (Yusuke Endoh).


Additional information.

* We do introduce only `Integer#ceildiv`.
* We do not introduce `Numeric#ceildiv` until we see the need. There is already `Numeric#div`, but a consistency with it is not a sufficient reason to introduce it.
* We do not introduce `Numeric#floordiv`.
* `3.ceildiv(-2)` should return -1, which is ceil(-(3/2)). Note that the naive implementation of `(a + b - 1) / b`, which returns (3 + (-2) - 1) / (-2) = 0. (As far as we glanced at the PR, it is implemented correctly.)

----------------------------------------
Feature #18809: Add Numeric#ceildiv
https://bugs.ruby-lang.org/issues/18809#change-98408

* Author: kyanagi (Kouhei Yanagita)
* Status: Open
* Priority: Normal
----------------------------------------
pull request: https://github.com/ruby/ruby/pull/5965

I have needed to implement "rounding up division" several times.

("rounding up division" means getting a quotient of division which is rounded up to the nearest integer.)

Typically, this is implemented as follows:

``` ruby
# notice that b > 0 is assumed
def rounding_up_division(a, b)
  (a + b - 1) / b
end
```

But for me, this is difficult to write without careful consideration.
Every time I implement this, I need to think for a few minutes on paper.

So I propose to add a new method `Numeric#ceildiv`.

Typical examples where this is necessary are counting groups and pagination.

e.g. There are 123 items. If you display 10 items on each page, how many pages are there?

``` ruby
123.ceildiv(10) # => 13
```

We can find several examples of this division also in the Ruby's source code. (Try `grep -r -E -e '([^ ]+) *- *1\) */ *\1' .`)


```
./internal.h:#define roomof(x, y) (((x) + (y) - 1) / (y))
./array.c:    len = (len + ustep - 1) / ustep;
./include/ruby/internal/memory.h:    const size_t cnt = (total_size + sizeof(VALUE) - 1) / sizeof(VALUE);
./ext/bigdecimal/missing/dtoa.c:#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
./ext/bigdecimal/bigdecimal.c:  nc += (nc + mc - 1) / mc + 1;
./ext/bigdecimal/bigdecimal.c:    mx = (mx + BASE_FIG - 1) / BASE_FIG;    /* Determine allocation unit. */
./ext/bigdecimal/bigdecimal.c:                mf = (mf + BASE_FIG - 1) / BASE_FIG + 2; /* Needs 1 more for div */
./ext/bigdecimal/bigdecimal.c:    nalloc = (ni + nf + BASE_FIG - 1) / BASE_FIG + 1;    /* set effective allocation  */
./ext/bigdecimal/bigdecimal.c:    size_t const round_limit = (VpGetPrecLimit() + BASE_FIG - 1) / BASE_FIG;
./ext/bigdecimal/bigdecimal.c:    if ((ix + BASE_FIG - 1) / BASE_FIG > ixDigit + 1) return 0;
./ext/bigdecimal/bits.h:#define roomof(x, y) (((x) + (y) - 1) / (y))
./internal/numeric.h:    VALUE values[(SIZEOF_DOUBLE + SIZEOF_VALUE - 1) / SIZEOF_VALUE];
./regcomp.c:  OnigDistance str_len = (byte_len + mb_len - 1) / mb_len;
./bignum.c:    size_t num_bdigits = (num_bits + BITSPERDIG - 1) / BITSPERDIG;
./missing/dtoa.c:#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
./numeric.c:    char buf[float_dig + (decimal_mant + CHAR_BIT - 1) / CHAR_BIT + 10];
./gc.c:#define CEILDIV(i, mod) (((i) + (mod) - 1)/(mod))
```

Naming:

I was not sure whether to name it `ceildiv` or `divceil` because there are both `divmod` and `fdiv`.
Since `divmod` is a method that returns two elements, the quotient and the remainder,
while `fdiv` is a method that performs Float division, I decided to follow `fdiv`.




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