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Maths: fundamental and advanced mathematical functions.

Basic functions
val add : float -> float -> float

``add x y``

val sub : float -> float -> float

``sub x y``

val mul : float -> float -> float

``mul x y``

val div : float -> float -> float

``div x y``

val fmod : float -> float -> float

``fmod x y``

val atan2 : float -> float -> float

``atan2 x y``

val hypot : float -> float -> float

``hypot x y``

val abs : float -> float

``abs x``

val neg : float -> float

``neg x``

val reci : float -> float

``reci x``

val floor : float -> float

``floor x``

val ceil : float -> float

``ceil x``

val round : float -> float

``round x``

val trunc : float -> float

``trunc x``

val fix : float -> float

``fix x``

val sqr : float -> float

``sqr x``

val sqrt : float -> float

``sqrt x``

val cbrt : float -> float

``cbrt x``

val pow : float -> float -> float

``pow x``

val exp : float -> float

``exp x``

val exp2 : float -> float

``exp2 x``

val exp10 : float -> float

``exp10 x``

val expm1 : float -> float

``expm1 x``

val log : float -> float

``log x``

val log2 : float -> float

``log2 x``

val log10 : float -> float

``log10 x``

val log1p : float -> float

``log1p x``

val sigmoid : float -> float

``sigmod x``

val signum : float -> float

``signum x``

val softsign : float -> float

``softsign x``

val softplus : float -> float

``softplus x``

val relu : float -> float

``relu x``

val dawsn : float -> float

``dawsn x``

val sin : float -> float

``sin x``

val cos : float -> float

``cos x``

val tan : float -> float

``tan x``

val cot : float -> float

``cot x``

val sec : float -> float

``sec x``

val csc : float -> float

``csc x``

val asin : float -> float

``asin x``

val acos : float -> float

``acos x``

val atan : float -> float

``atan x``

val acot : float -> float

``cot x``

val asec : float -> float

``sec x``

val acsc : float -> float

``csc x``

val sinh : float -> float

``sinh x``

val cosh : float -> float

``cosh x``

val tanh : float -> float

``tanh x``

val asinh : float -> float

``asinh x``

val acosh : float -> float

``acosh x``

val atanh : float -> float

``atanh x``

val acoth : float -> float

``coth x``

val asech : float -> float

``sech x``

val acsch : float -> float

``csch x``

val xlogy : float -> float -> float

``xlogy(x, y)``

val xlog1py : float -> float -> float

``xlog1py(x, y)``

val logit : float -> float

``logit(x)``

val expit : float -> float

``expit(x)``

val log1mexp : float -> float

``log1mexp(x)``

val log1pexp : float -> float

``log1pexp(x)``

Error functions
val erf : float -> float

``erf(x)``

val erfc : float -> float

``erfc(x)``

val erfcx : float -> float

``erfcx(x)``

Helper functions
val is_nan : float -> bool

``is_nan x`` returns ``true`` if ``x`` is ``nan``.

val is_inf : float -> bool

``is_inf x`` returns ``true`` if ``x`` is ``infinity`` or ``neg_infinity``.

val is_normal : float -> bool

``is_normal x`` returns ``true`` if ``x`` is a normal float number.

val is_subnormal : float -> bool

``is_nan x`` returns ``true`` if ``x`` is subnormal float number.

val is_odd : int -> bool

``is_odd x`` returns ``true`` if ``x`` is odd.

val is_even : int -> bool

``is_even x`` returns ``true`` if ``x`` is even.

val is_pow2 : int -> bool

``is_pow2 x`` return ``true`` if ``x`` is integer power of 2, e.g. 32, 64, etc.

val same_sign : float -> float -> bool

``same_sign x y`` returns ``true`` if ``x`` and ``y`` have the same sign, otherwise it returns ``false``. Positive and negative zeros are special cases and always returns ``true``.

val is_simplex : float array -> bool

``is_simplex x`` checks whether ``x`` is simplex. In other words, :math:`\sum_i^K x_i = 1` and :math:`x_i \ge 0, \forall x_i \in 1,K`.

val is_int : float -> bool
val is_sqr : int -> bool

``is_sqr x`` checks if ``x`` is the square of an integer.

val mulmod : int -> int -> int -> int

``mulmod a b m`` computes (a*b) mod m.

val powmod : int -> int -> int -> int

``powmod a b m`` computes (a^b) mod m.

val is_prime : int -> bool

``is_prime x`` returns ``true`` if ``x`` is a prime number. The function is deterministic for all numbers representable by an int. The function uses the Rabin–Miller primality test.

val fermat_fact : int -> int * int

``fermat_fact x`` performs Fermat factorisation over ``x``, i.e. into two roughly equal factors. ``x`` must be an odd number.

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