# Index of values

( * ) [Q] | Multiplication `mul`.
( * ) [Z] | Multiplication `mul`.
( ** ) [Z] | Power `pow`.
(+) [Q] | Addition `add`.
(+) [Z] | Addition `add`.
(-) [Q] | Subtraction `sub`.
(-) [Z] | Subtraction `sub`.
(/) [Q] | Division `div`.
(/) [Z] | Truncated division `div`.
(//) [Q] | Creates a rational from two `int`s.
(///) [Q] | Creates a rational from two `Z.t`.
(/<) [Z] | Flooring division `fdiv`.
(/>) [Z] | Ceiling division `cdiv`.
(/|) [Z] | Exact division `divexact`.
(<) [Q] | Same as `lt`.
(<) [Z.Compare] | Same as `lt`.
(<=) [Q] | Same as `leq`.
(<=) [Z.Compare] | Same as `leq`.
(<>) [Q] | `a <> b` is equivalent to `not (equal a b)`.
(<>) [Z.Compare] | `a <> b` is equivalent to `not (equal a b)`.
(=) [Q] | Same as `equal`.
(=) [Z.Compare] | Same as `equal`.
(>) [Q] | Same as `gt`.
(>) [Z.Compare] | Same as `gt`.
(>=) [Q] | Same as `geq`.
(>=) [Z.Compare] | Same as `geq`.
(asr) [Q] | Division by a power of two `shift_right`.
(asr) [Z] | Bit-wise shift to the right `shift_right`.
(land) [Z] | Bit-wise logical and `logand`.
(lor) [Z] | Bit-wise logical inclusive or `logor`.
(lsl) [Q] | Multiplication by a power of two `mul_2exp`.
(lsl) [Z] | Bit-wise shift to the left `shift_left`.
(lxor) [Z] | Bit-wise logical exclusive or `logxor`.
(mod) [Z] | Remainder `rem`.
(~!) [Z] | Bit-wise logical negation `lognot`.
(~$$) [Q] | Conversion from `Z.t`.
(~$) [Q] | Conversion from `int`.
(~$) [Z] |
(~+) [Q] | Identity.
(~+) [Z] | Identity.
(~-) [Q] | Negation `neg`.
(~-) [Z] | Negation `neg`.
A
abs [Q] | Absolute value.
abs [Z] | Absolute value.
abs_big_int [Big_int_Z] |
add [Q] | Addition.
add [Z] | Addition.
add_big_int [Big_int_Z] |
add_int_big_int [Big_int_Z] |
and_big_int [Big_int_Z] |
B
big_int_of_float [Big_int_Z] |
big_int_of_int [Big_int_Z] |
big_int_of_int32 [Big_int_Z] |
big_int_of_int64 [Big_int_Z] |
big_int_of_nativeint [Big_int_Z] |
big_int_of_string [Big_int_Z] |
bin [Z] | `bin n k` returns the binomial coefficient `n` over `k`.
bprint [Q] | To be used as `%a` format printer in `Printf.bprintf`.
bprint [Z] | To be used as `%a` format printer in `Printf.bprintf`.
C
cdiv [Z] | Integer division with rounding towards +oo (ceiling).
classify [Q] | Determines the kind of a rational.
compare [Q] | `compare x y` compares `x` to `y` and returns 1 if `x` is strictly greater that `y`, -1 if it is strictly smaller, and 0 if they are equal.
compare [Z] | Comparison.
compare_big_int [Big_int_Z] |
congruent [Z] | `congruent a b c` returns `true` if `a` is congruent to `b` modulo `c`.
D
den [Q] | Get the denominator.
div [Q] | Division.
div [Z] | Integer division.
div_2exp [Q] | `div_2exp x n` divides `x` by 2 to the power of `n`.
div_big_int [Big_int_Z] |
div_rem [Z] | Computes both the integer quotient and the remainder.
divexact [Z] | `divexact a b` divides `a` by `b`, only producing correct result when the division is exact, i.e., when `b` evenly divides `a`.
divisible [Z] | `divisible a b` returns `true` if `a` is exactly divisible by `b`.
E
ediv [Z] | Euclidean division.
ediv_rem [Z] | Euclidean division and remainder.
eq_big_int [Big_int_Z] |
equal [Q] | Equality testing.
equal [Z] | Equality test.
erem [Z] | Euclidean remainder.
extract [Z] | `extract a off len` returns a nonnegative number corresponding to bits `off` to `off`+`len`-1 of `a`.
extract_big_int [Big_int_Z] |
F
fac [Z] | `fac n` returns the factorial of `n` (`n!`).
fac2 [Z] | `fac2 n` returns the double factorial of `n` (`n!!`).
facM [Z] | `facM n m` returns the `m`-th factorial of `n`.
fdiv [Z] | Integer division with rounding towards -oo (floor).
fib [Z] | `fib n` returns the `n`-th Fibonacci number.
fits_int [Z] | Whether the argument fits in an OCaml signed `int`.
fits_int32 [Z] | Whether the argument fits in a signed `int32`.
fits_int32_unsigned [Z] | Whether the argument is non-negative and fits in an unsigned `int32`.
fits_int64 [Z] | Whether the argument fits in a signed `int64`.
fits_int64_unsigned [Z] | Whether the argument is non-negative and fits in an unsigned `int64`.
fits_nativeint [Z] | Whether the argument fits in a signed `nativeint`.
fits_nativeint_unsigned [Z] | Whether the argument is non-negative fits in an unsigned `nativeint`.
float_of_big_int [Big_int_Z] |
format [Z] | Gives a string representation of the argument in the specified printf-like format.
G
gcd [Z] | Greatest common divisor.
gcd_big_int [Big_int_Z] |
gcdext [Z] | `gcdext u v` returns `(g,s,t)` where `g` is the greatest common divisor and `g=us+vt`.
ge_big_int [Big_int_Z] |
geq [Q] | Greater than or equal.
geq [Z] | Greater than or equal.
gt [Q] | Greater than (not equal).
gt [Z] | Greater than (and not equal).
gt_big_int [Big_int_Z] |
H
hamdist [Z] | Counts the number of different bits.
hash [Z] | Hashes a number, producing a small integer.
I
inf [Q] | 1/0.
int32_of_big_int [Big_int_Z] |
int64_of_big_int [Big_int_Z] |
int_of_big_int [Big_int_Z] |
inv [Q] | Inverse.
invert [Z] | `invert base mod` returns the inverse of `base` modulo `mod`.
is_even [Z] | Returns true if the argument is even (divisible by 2), false if odd.
is_int_big_int [Big_int_Z] |
is_odd [Z] | Returns true if the argument is odd, false if even.
is_real [Q] | Whether the argument is non-infinity and non-undefined.
J
jacobi [Z] | `jacobi a b` returns the Jacobi symbol `(a/b)`.
K
kronecker [Z] | `kronecker a b` returns the Kronecker symbol `(a/b)`.
L
lcm [Z] | Least common multiple.
le_big_int [Big_int_Z] |
legendre [Z] | `legendre a b` returns the Legendre symbol `(a/b)`.
leq [Q] | Less than or equal.
leq [Z] | Less than or equal.
log2 [Z] | Returns the base-2 logarithm of its argument, rounded down to an integer.
log2up [Z] | Returns the base-2 logarithm of its argument, rounded up to an integer.
logand [Z] | Bitwise logical and.
lognot [Z] | Bitwise logical negation.
logor [Z] | Bitwise logical or.
logxor [Z] | Bitwise logical exclusive or.
lt [Q] | Less than (not equal).
lt [Z] | Less than (and not equal).
lt_big_int [Big_int_Z] |
lucnum [Z] | `lucnum n` returns the `n`-th Lucas number.
M
make [Q] | `make num den` constructs a new rational equal to `num`/`den`.
max [Q] | Returns the largest of its arguments.
max [Z] | Returns the maximum of its arguments.
max_big_int [Big_int_Z] |
min [Q] | Returns the smallest of its arguments.
min [Z] | Returns the minimum of its arguments.
min_big_int [Big_int_Z] |
minus_big_int [Big_int_Z] |
minus_inf [Q] | -1/0.
minus_one [Q] | 0, 1, -1.
minus_one [Z] | The number -1.
mod_big_int [Big_int_Z] |
mul [Q] | Multiplication.
mul [Z] | Multiplication.
mul_2exp [Q] | `mul_2exp x n` multiplies `x` by 2 to the power of `n`.
mult_big_int [Big_int_Z] |
mult_int_big_int [Big_int_Z] |
N
nativeint_of_big_int [Big_int_Z] |
neg [Q] | Negation.
neg [Z] | Unary negation.
nextprime [Z] | Returns the next prime greater than the argument.
num [Q] | Get the numerator.
num_digits_big_int [Big_int_Z] |
numbits [Z] | Returns the number of significant bits in the given number.
O
of_bigint [Q] |
of_bits [Z] | Constructs a number from a binary string representation.
of_float [Q] | Conversion from a `float`.
of_float [Z] | Converts from a floating-point value.
of_int [Q] |
of_int [Z] | Converts from a base integer.
of_int32 [Q] |
of_int32 [Z] | Converts from a 32-bit (signed) integer.
of_int32_unsigned [Z] | Converts from a 32-bit integer, interpreted as an unsigned integer.
of_int64 [Q] |
of_int64 [Z] | Converts from a 64-bit (signed) integer.
of_int64_unsigned [Z] | Converts from a 64-bit integer, interpreted as an unsigned integer.
of_ints [Q] | Conversion from an `int` numerator and an `int` denominator.
of_nativeint [Q] | Conversions from various integer types.
of_nativeint [Z] | Converts from a native (signed) integer.
of_nativeint_unsigned [Z] | Converts from a native integer, interpreted as an unsigned integer..
of_string [Q] | Converts a string to a rational.
of_string [Z] | Converts a string to an integer.
of_string_base [Z] | Parses a number represented as a string in the specified base, with optional `-` or `+` prefix.
of_substring [Z] | `of_substring s ~pos ~len` is the same as `of_string (String.sub s pos len)`
of_substring_base [Z] | `of_substring_base base s ~pos ~len` is the same as `of_string_base base (String.sub s pos len)`
one [Q] |
one [Z] | The number 1.
or_big_int [Big_int_Z] |
output [Q] | Prints the argument on the specified channel.
output [Z] | Prints the argument on the specified channel.
P
perfect_power [Z] | True if the argument has the form `a^b`, with `b>1`
perfect_square [Z] | True if the argument has the form `a^2`.
popcount [Z] | Counts the number of bits set.
pow [Z] | `pow base exp` raises `base` to the `exp` power.
power [Big_int_Z] |
power_big [Big_int_Z] |
power_big_int_positive_big_int [Big_int_Z] |
power_big_int_positive_int [Big_int_Z] |
power_int_positive_big_int [Big_int_Z] |
power_int_positive_int [Big_int_Z] |
powm [Z] | `powm base exp mod` computes `base`^`exp` modulo `mod`.
powm_sec [Z] | `powm_sec base exp mod` computes `base`^`exp` modulo `mod`.
pp_print [Q] | Prints the argument on the specified formatter.
pp_print [Z] | Prints the argument on the specified formatter.
pred [Z] | Returns its argument minus one.
pred_big_int [Big_int_Z] |
primorial [Z] | `primorial n` returns the product of all positive prime numbers less than or equal to `n`.
print [Q] | Prints the argument on the standard output.
print [Z] | Prints the argument on the standard output.
probab_prime [Z] | `probab_prime x r` returns 0 if `x` is definitely composite, 1 if `x` is probably prime, and 2 if `x` is definitely prime.
Q
quomod_big_int [Big_int_Z] |
R
random_bits [Z] | `random_bits nbits` returns a random integer between 0 (inclusive) and `2{^nbits}` (exclusive).
random_bits_gen [Z] | `random_bits_gen ~fill nbits` returns a random integer between 0 (inclusive) and `2{^nbits}` (exclusive).
random_int [Z] | `random_int bound` returns a random integer between 0 (inclusive) and `bound` (exclusive).
random_int_gen [Z] | `random_int_gen ~fill bound` returns a random integer between 0 (inclusive) and `bound` (exclusive).
rem [Z] | Integer remainder.
remove [Z] | `remove a b` returns `a` after removing all the occurences of the factor `b`.
root [Z] | `root x n` computes the `n`-th root of `x`.
rootrem [Z] | `rootrem x n` computes the `n`-th root of `x` and the remainder `x-root**n`.
S
seeded_hash [Z] | Like `Z.hash`, but takes a seed as extra argument for diversification.
shift_left [Z] | Shifts to the left.
shift_left_big_int [Big_int_Z] |
shift_right [Z] | Shifts to the right.
shift_right_big_int [Big_int_Z] |
shift_right_towards_zero_big_int [Big_int_Z] |
shift_right_trunc [Z] | Shifts to the right, rounding towards 0.
sign [Q] | Returns 1 if the argument is positive (including inf), -1 if it is negative (including -inf), and 0 if it is null or undefined.
sign [Z] | Returns -1, 0, or 1 when the argument is respectively negative, null, or positive.
sign_big_int [Big_int_Z] |
signed_extract [Z] | `signed_extract a off len` extracts bits `off` to `off`+`len`-1 of `b`, as `extract` does, then sign-extends bit `len-1` of the result (that is, bit `off + len - 1` of `a`).
size [Z] | Returns the number of machine words used to represent the number.
sprint [Q] | To be used as `%a` format printer in `Printf.sprintf`.
sprint [Z] | To be used as `%a` format printer in `Printf.sprintf`.
sqrt [Z] | Returns the square root.
sqrt_big_int [Big_int_Z] |
sqrt_rem [Z] | Returns the square root truncated, and the remainder.
square_big_int [Big_int_Z] |
string_of_big_int [Big_int_Z] |
sub [Q] | Subtraction.
sub [Z] | Subtraction.
sub_big_int [Big_int_Z] |
succ [Z] | Returns its argument plus one.
succ_big_int [Big_int_Z] |
T
testbit [Z] | `testbit x n` return the value of bit number `n` in `x`: `true` if the bit is 1, `false` if the bit is 0.
to_bigint [Q] |
to_bits [Z] | Returns a binary representation of the argument.
to_float [Q] | Converts to a floating-point number, using the current floating-point rounding mode.
to_float [Z] | Converts to a floating-point value.
to_int [Q] |
to_int [Z] | Converts to a signed OCaml `int`.
to_int32 [Q] |
to_int32 [Z] | Converts to a signed 32-bit integer `int32`.
to_int32_unsigned [Z] | Converts to an unsigned 32-bit integer.
to_int64 [Q] |
to_int64 [Z] | Converts to a signed 64-bit integer `int64`.
to_int64_unsigned [Z] | Converts to an unsigned 64-bit integer.
to_nativeint [Q] | Convert to integer by truncation.
to_nativeint [Z] | Converts to a native signed integer `nativeint`.
to_nativeint_unsigned [Z] | Converts to a native unsigned integer.
to_string [Q] | Converts to human-readable, base-10, `/`-separated rational.
to_string [Z] | Gives a human-readable, decimal string representation of the argument.
trailing_zeros [Z] | Returns the number of trailing 0 bits in the given number.
U
undef [Q] | 0/0.
unit_big_int [Big_int_Z] |
V
version [Z] | Library version.
X
xor_big_int [Big_int_Z] |
Z
zero [Q] |
zero [Z] | The number 0.
zero_big_int [Big_int_Z] |