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_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 `b`.
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 a regular `int`.
fits_int32 [Z]	Whether the argument fits in an `int32`.
fits_int64 [Z]	Whether the argument fits in an `int64`.
fits_nativeint [Z]	Whether the argument fits in a `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 integer.
of_int64 [Q]
of_int64 [Z]	Converts from a 64-bit 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 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
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
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 base integer.
to_int32 [Q]
to_int32 [Z]	Converts to a 32-bit integer.
to_int64 [Q]
to_int64 [Z]	Converts to a 64-bit integer.
to_nativeint [Q]	Convert to integer by truncation.
to_nativeint [Z]	Converts to a native 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]