module Int32:`sig`

..`end`

32-bit integers.

This module provides operations on the type `int32`

of signed 32-bit integers. Unlike the built-in `int`

type,
the type `int32`

is guaranteed to be exactly 32-bit wide on all
platforms. All arithmetic operations over `int32`

are taken
modulo 2^{32}.

Performance notice: values of type `int32`

occupy more memory
space than values of type `int`

, and arithmetic operations on
`int32`

are generally slower than those on `int`

. Use `int32`

only when the application requires exact 32-bit arithmetic.

Literals for 32-bit integers are suffixed by l:

```
let zero: int32 = 0l
let one: int32 = 1l
let m_one: int32 = -1l
```

`val zero : ``int32`

The 32-bit integer 0.

`val one : ``int32`

The 32-bit integer 1.

`val minus_one : ``int32`

The 32-bit integer -1.

`val neg : ``int32 -> int32`

Unary negation.

`val add : ``int32 -> int32 -> int32`

Addition.

`val sub : ``int32 -> int32 -> int32`

Subtraction.

`val mul : ``int32 -> int32 -> int32`

Multiplication.

`val div : ``int32 -> int32 -> int32`

Integer division. This division rounds the real quotient of
its arguments towards zero, as specified for `(/)`

.

**Raises**`Division_by_zero`

if the second argument is zero.

`val unsigned_div : ``int32 -> int32 -> int32`

Same as `Int32.div`

, except that arguments and result are interpreted as * unsigned* 32-bit integers.

**Since**4.08.0

`val rem : ``int32 -> int32 -> int32`

Integer remainder. If `y`

is not zero, the result
of `Int32.rem x y`

satisfies the following property:
`x = Int32.add (Int32.mul (Int32.div x y) y) (Int32.rem x y)`

.
If `y = 0`

, `Int32.rem x y`

raises `Division_by_zero`

.

`val unsigned_rem : ``int32 -> int32 -> int32`

Same as `Int32.rem`

, except that arguments and result are interpreted as * unsigned* 32-bit integers.

**Since**4.08.0

`val succ : ``int32 -> int32`

Successor. `Int32.succ x`

is `Int32.add x Int32.one`

.

`val pred : ``int32 -> int32`

Predecessor. `Int32.pred x`

is `Int32.sub x Int32.one`

.

`val abs : ``int32 -> int32`

`abs x`

is the absolute value of `x`

. On `min_int`

this
is `min_int`

itself and thus remains negative.

`val max_int : ``int32`

The greatest representable 32-bit integer, 2^{31} - 1.

`val min_int : ``int32`

The smallest representable 32-bit integer, -2^{31}.

`val logand : ``int32 -> int32 -> int32`

Bitwise logical and.

`val logor : ``int32 -> int32 -> int32`

Bitwise logical or.

`val logxor : ``int32 -> int32 -> int32`

Bitwise logical exclusive or.

`val lognot : ``int32 -> int32`

Bitwise logical negation.

`val shift_left : ``int32 -> int -> int32`

`Int32.shift_left x y`

shifts `x`

to the left by `y`

bits.
The result is unspecified if `y < 0`

or `y >= 32`

.

`val shift_right : ``int32 -> int -> int32`

`Int32.shift_right x y`

shifts `x`

to the right by `y`

bits.
This is an arithmetic shift: the sign bit of `x`

is replicated
and inserted in the vacated bits.
The result is unspecified if `y < 0`

or `y >= 32`

.

`val shift_right_logical : ``int32 -> int -> int32`

`Int32.shift_right_logical x y`

shifts `x`

to the right by `y`

bits.
This is a logical shift: zeroes are inserted in the vacated bits
regardless of the sign of `x`

.
The result is unspecified if `y < 0`

or `y >= 32`

.

`val of_int : ``int -> int32`

Convert the given integer (type `int`

) to a 32-bit integer
(type `int32`

). On 64-bit platforms, the argument is taken
modulo 2^{32}.

`val to_int : ``int32 -> int`

Convert the given 32-bit integer (type `int32`

) to an
integer (type `int`

). On 32-bit platforms, the 32-bit integer
is taken modulo 2^{31}, i.e. the high-order bit is lost
during the conversion. On 64-bit platforms, the conversion
is exact.

`val unsigned_to_int : ``int32 -> int option`

Same as `Int32.to_int`

, but interprets the argument as an *unsigned* integer.
Returns `None`

if the unsigned value of the argument cannot fit into an
`int`

.

**Since**4.08.0

`val of_float : ``float -> int32`

Convert the given floating-point number to a 32-bit integer,
discarding the fractional part (truncate towards 0).
If the truncated floating-point number is outside the range
[`Int32.min_int`

, `Int32.max_int`

], no exception is raised, and
an unspecified, platform-dependent integer is returned.

`val to_float : ``int32 -> float`

Convert the given 32-bit integer to a floating-point number.

`val of_string : ``string -> int32`

Convert the given string to a 32-bit integer.
The string is read in decimal (by default, or if the string
begins with `0u`

) or in hexadecimal, octal or binary if the
string begins with `0x`

, `0o`

or `0b`

respectively.

The `0u`

prefix reads the input as an unsigned integer in the range
`[0, 2*Int32.max_int+1]`

. If the input exceeds `Int32.max_int`

it is converted to the signed integer
`Int32.min_int + input - Int32.max_int - 1`

.

The `_`

(underscore) character can appear anywhere in the string
and is ignored.

**Raises**`Failure`

if the given string is not a valid representation of an integer, or if the integer represented exceeds the range of integers representable in type`int32`

.

`val of_string_opt : ``string -> int32 option`

Same as `of_string`

, but return `None`

instead of raising.

**Since**4.05

`val to_string : ``int32 -> string`

Return the string representation of its argument, in signed decimal.

`val bits_of_float : ``float -> int32`

Return the internal representation of the given float according to the IEEE 754 floating-point 'single format' bit layout. Bit 31 of the result represents the sign of the float; bits 30 to 23 represent the (biased) exponent; bits 22 to 0 represent the mantissa.

`val float_of_bits : ``int32 -> float`

Return the floating-point number whose internal representation,
according to the IEEE 754 floating-point 'single format' bit layout,
is the given `int32`

.

type`t =`

`int32`

An alias for the type of 32-bit integers.

`val compare : ``t -> t -> int`

`val unsigned_compare : ``t -> t -> int`

Same as `Int32.compare`

, except that arguments are interpreted as *unsigned*
32-bit integers.

**Since**4.08.0

`val equal : ``t -> t -> bool`

The equal function for int32s.

**Since**4.03.0

`val min : ``t -> t -> t`

Return the smaller of the two arguments.

**Since**4.13.0

`val max : ``t -> t -> t`

Return the greater of the two arguments.

**Since**4.13.0