Module Stdlib.Int

The type for integer values.

zero is the integer 0.

one is the integer 1.

minus_one is the integer -1.

neg x is ~-x.

add x y is the addition x + y.

sub x y is the subtraction x - y.

mul x y is the multiplication x * y.

Rounding division. div x y is the real quotient x / y rounded towards zero to an integer. See Stdlib.(/) for details.

• raises Division_by_zero

  if the second argument is 0.

rem x y is the remainder of the rounding division div x y. We have rem x y = x - div x y * y. See Stdlib.(mod) for details.

• raises Division_by_zero

  if the second argument is 0.

Floor division. fdiv x y is the real quotient x / y rounded down to an integer. We have fdiv x y <= div x y <= cdiv x y and cdiv x y - fdiv x y <= 1.

• raises Division_by_zero

  if the second argument is 0.

• since 5.5

Ceil division. cdiv x y is the real quotient x / y rounded up to an integer. We have fdiv x y <= div x y <= cdiv x y and cdiv x y - fdiv x y <= 1.

• raises Division_by_zero

  if the second argument is 0.

• since 5.5

Euclidean division. ediv x y is the real quotient x / y rounded down to an integer if y > 0 and rounded up to an integer if y < 0. The remainder erem x y = x - ediv x y * y is always non-negative. Moreover, ediv x (-y) = - ediv x y.

• raises Division_by_zero

  if the second argument is 0.

• since 5.5

Euclidean remainder. If y is not zero, we have x = ediv x y * y + erem x y and 0 <= erem x y <= abs y - 1. The result of erem x y is always non-negative, unlike the result of rem x y, which has the sign of x.

• raises Division_by_zero

  if the second argument is 0.

• since 5.5

succ x is add x 1.

pred x is sub x 1.

abs x is the absolute value of x. That is x if x is positive and neg x if x is negative. Warning. This may be negative if the argument is min_int.

max_int is the greatest representable integer, 2Sys.int_size - 1-1.

min_int is the smallest representable integer, -2Sys.int_size - 1.

logand x y is the bitwise logical and of x and y.

logor x y is the bitwise logical or of x and y.

logxor x y is the bitwise logical exclusive or of x and y.

lognot x is the bitwise logical negation of x.

shift_left x n shifts x to the left by n bits. The result is unspecified if n < 0 or n > Sys.int_size.

shift_right x n shifts x to the right by n bits. This is an arithmetic shift: the sign bit of x is replicated and inserted in the vacated bits. The result is unspecified if n < 0 or n > Sys.int_size.

shift_right_logical x n shifts x to the right by n bits. This is a logical shift: zeroes are inserted in the vacated bits regardless of the sign of x. The result is unspecified if n < 0 or n > Sys.int_size.

equal x y is true if and only if x = y.

compare x y is Stdlib.compare x y but more efficient.

Return the smaller of the two arguments.

• since 4.13

Return the greater of the two arguments.

• since 4.13

Population count, also known as Hamming weight. popcount n is the number of 1 bits in the binary representation of n. Negative n are represented in two's complement.

• since 5.5

unsigned_bitsize n is the minimal number of bits needed to represent n as an unsigned binary number. It is the smallest integer i between 0 and Sys.int_size inclusive such that 0 <= n < 2{^i} (unsigned).

• since 5.5

signed_bitsize n is the minimal number of bits needed to represent n as a signed, two's complement binary number. It is the smallest integer i between 1 and Sys.int_size inclusive such that -2{^i-1} <= n < 2{^i-1} (signed).

• since 5.5

leading_zeros n is the number of leading (most significant) 0 bits in the binary representation of n. It is an integer between 0 and Sys.int_size inclusive. If n is negative, leading_zeros n = 0 since the most significant bit of n is 1. leading_zeros n = {!Sys.int_size} if and only if n = zero. Note that leading_zeros n + unsigned_bitsize n = {!Sys.int_size}.

• since 5.5

leading_sign_bits n is the number of leading (most significant) sign bits in the binary representation of n, excluding the sign bit itself. It is an integer between 0 and {!Sys.int_size} - 1 inclusive. For positive n, it is the number of leading zero bits minus one. For negative n, it is the number of leading one bits minus one. Note that leading_sign_bits n + signed_bitsize n = {!Sys.int_size}.

• since 5.5

trailing_zeros n is the number of trailing (least significant) 0 bits in the binary representation of n. It is an integer between 0 and Sys.int_size inclusive. It is the largest integer i <= {!Sys.int_size} such that 2{^i} divides n evenly. For example, trailing_zeros n = 0 if and only if n is odd, and trailing_zeros n = {!Sys.int_size} if and only if n = zero.

• since 5.5

to_float x is x as a floating point number.

of_float x truncates x to an integer. The result is unspecified if the argument is nan or falls outside the range of representable integers.

to_string x is the written representation of x in decimal.

A seeded hash function for ints, with the same output value as Hashtbl.seeded_hash. This function allows this module to be passed as argument to the functor Hashtbl.MakeSeeded.

• since 5.1

An unseeded hash function for ints, with the same output value as Hashtbl.hash. This function allows this module to be passed as argument to the functor Hashtbl.Make.

• since 5.1