module Int64:`sig`

..`end`

64-bit integers.

This module provides operations on the type `int64`

of
signed 64-bit integers. Unlike the built-in `int`

type,
the type `int64`

is guaranteed to be exactly 64-bit wide on all
platforms. All arithmetic operations over `int64`

are taken
modulo 2^{64}

Performance notice: values of type `int64`

occupy more memory
space than values of type `int`

, and arithmetic operations on
`int64`

are generally slower than those on `int`

. Use `int64`

only when the application requires exact 64-bit arithmetic.

Literals for 64-bit integers are suffixed by L:

```
let zero: int64 = 0L
let one: int64 = 1L
let m_one: int64 = -1L
```

`val zero : ``int64`

The 64-bit integer 0.

`val one : ``int64`

The 64-bit integer 1.

`val minus_one : ``int64`

The 64-bit integer -1.

`val neg : ``int64 -> int64`

Unary negation.

`val add : ``int64 -> int64 -> int64`

Addition.

`val sub : ``int64 -> int64 -> int64`

Subtraction.

`val mul : ``int64 -> int64 -> int64`

Multiplication.

`val div : ``int64 -> int64 -> int64`

Integer division. Raise `Division_by_zero`

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

.

`val unsigned_div : ``int64 -> int64 -> int64`

Same as `Int64.div`

, except that arguments and result are interpreted as * unsigned* 64-bit integers.

**Since**4.08.0

`val rem : ``int64 -> int64 -> int64`

Integer remainder. If `y`

is not zero, the result
of `Int64.rem x y`

satisfies the following property:
`x = Int64.add (Int64.mul (Int64.div x y) y) (Int64.rem x y)`

.
If `y = 0`

, `Int64.rem x y`

raises `Division_by_zero`

.

`val unsigned_rem : ``int64 -> int64 -> int64`

Same as `Int64.rem`

, except that arguments and result are interpreted as * unsigned* 64-bit integers.

**Since**4.08.0

`val succ : ``int64 -> int64`

Successor. `Int64.succ x`

is `Int64.add x Int64.one`

.

`val pred : ``int64 -> int64`

Predecessor. `Int64.pred x`

is `Int64.sub x Int64.one`

.

`val abs : ``int64 -> int64`

Return the absolute value of its argument.

`val max_int : ``int64`

The greatest representable 64-bit integer, 2^{63} - 1.

`val min_int : ``int64`

The smallest representable 64-bit integer, -2^{63}.

`val logand : ``int64 -> int64 -> int64`

Bitwise logical and.

`val logor : ``int64 -> int64 -> int64`

Bitwise logical or.

`val logxor : ``int64 -> int64 -> int64`

Bitwise logical exclusive or.

`val lognot : ``int64 -> int64`

Bitwise logical negation.

`val shift_left : ``int64 -> int -> int64`

`Int64.shift_left x y`

shifts `x`

to the left by `y`

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

or `y >= 64`

.

`val shift_right : ``int64 -> int -> int64`

`Int64.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 >= 64`

.

`val shift_right_logical : ``int64 -> int -> int64`

`Int64.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 >= 64`

.

`val of_int : ``int -> int64`

Convert the given integer (type `int`

) to a 64-bit integer
(type `int64`

).

`val to_int : ``int64 -> int`

Convert the given 64-bit integer (type `int64`

) to an
integer (type `int`

). On 64-bit platforms, the 64-bit integer
is taken modulo 2^{63}, i.e. the high-order bit is lost
during the conversion. On 32-bit platforms, the 64-bit integer
is taken modulo 2^{31}, i.e. the top 33 bits are lost
during the conversion.

`val unsigned_to_int : ``int64 -> int option`

Same as `Int64.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 -> int64`

Convert the given floating-point number to a 64-bit integer,
discarding the fractional part (truncate towards 0).
The result of the conversion is undefined if, after truncation,
the number is outside the range [`Int64.min_int`

, `Int64.max_int`

].

`val to_float : ``int64 -> float`

Convert the given 64-bit integer to a floating-point number.

`val of_int32 : ``int32 -> int64`

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

)
to a 64-bit integer (type `int64`

).

`val to_int32 : ``int64 -> int32`

Convert the given 64-bit integer (type `int64`

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

). The 64-bit integer
is taken modulo 2^{32}, i.e. the top 32 bits are lost
during the conversion.

`val of_nativeint : ``nativeint -> int64`

Convert the given native integer (type `nativeint`

)
to a 64-bit integer (type `int64`

).

`val to_nativeint : ``int64 -> nativeint`

Convert the given 64-bit integer (type `int64`

) to a
native integer. On 32-bit platforms, the 64-bit integer
is taken modulo 2^{32}. On 64-bit platforms,
the conversion is exact.

`val of_string : ``string -> int64`

Convert the given string to a 64-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*Int64.max_int+1]`

. If the input exceeds `Int64.max_int`

it is converted to the signed integer
`Int64.min_int + input - Int64.max_int - 1`

.

The `_`

(underscore) character can appear anywhere in the string
and is ignored.
Raise `Failure "Int64.of_string"`

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 `int64`

.

`val of_string_opt : ``string -> int64 option`

Same as `of_string`

, but return `None`

instead of raising.

**Since**4.05

`val to_string : ``int64 -> string`

Return the string representation of its argument, in decimal.

`val bits_of_float : ``float -> int64`

Return the internal representation of the given float according to the IEEE 754 floating-point 'double format' bit layout. Bit 63 of the result represents the sign of the float; bits 62 to 52 represent the (biased) exponent; bits 51 to 0 represent the mantissa.

`val float_of_bits : ``int64 -> float`

Return the floating-point number whose internal representation,
according to the IEEE 754 floating-point 'double format' bit layout,
is the given `int64`

.

type`t =`

`int64`

An alias for the type of 64-bit integers.

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

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

Same as `Int64.compare`

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

**Since**4.08.0

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

The equal function for int64s.

**Since**4.03.0