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Julia provides a set of efficient, portable standard mathematical functions. * * * ## Numeric Comparison The following table lists the functions used for numeric comparison: | Function | Tests whether the following property is satisfied | | --- | --- | | `isequal(x, y)` | whether x and y are identical in value and type | | `isfinite(x)` | whether x is a finite number | | `isinf(x)` | whether x is (positive/negative) infinity | | `isnan(x)` | whether x is NaN | isequal considers NaN values to be equal: ## Example julia>isequal(NaN, NaN) true julia>isequal(, ) true julia>isequal(NaN, NaN32) true isequal can also be used to distinguish signed zeros: ## Example julia> -0.0 == 0.0 true julia>isequal(-0.0, 0.0) false Other function examples: ## Example julia> isfinite(5) true julia> isfinite(NaN32) false * * * ## Rounding Functions The following table lists the rounding functions supported by Julia: | Function | Description | Return Type | | --- | --- | --- | | `round(x)` | round x to the nearest integer | `typeof(x)` | | `round(T, x)` | round x to the nearest integer | `T` | | `floor(x)` | round x towards `-Inf` | `typeof(x)` | | `floor(T, x)` | round x towards `-Inf` | `T` | | `ceil(x)` | round x towards `+Inf` | `typeof(x)` | | `ceil(T, x)` | round x towards `+Inf` | `T` | | `trunc(x)` | round x towards 0 | `typeof(x)` | | `trunc(T, x)` | round x towards 0 | `T` | ## Example julia>round(3.8) 4.0 julia>round(Int, 3.8) 4 julia> floor(3.8) 3.0 julia> floor(Int, 3.8) 3 julia> ceil(3.8) 4.0 julia> ceil(Int, 3.8) 4 julia> trunc(3.8) 3.0 julia> trunc(Int, 3.8) 3 * * * ## Division Functions The following table lists the division functions supported by Julia: | Function | Description | | --- | --- | | `div(x,y)`, `x÷y` | truncated division; for any type of division, the result truncates the decimal portion, leaving only the integer part, with the quotient rounded towards zero | | `fld(x,y)` | floor division; quotient rounded towards `-Inf` | | `cld(x,y)` | ceiling division; quotient rounded towards `+Inf` | | `rem(x,y)` | remainder; satisfies `x == div(x,y)*y + rem(x,y)`; sign matches x | | `mod(x,y)` | modulo; satisfies `x == fld(x,y)*y + mod(x,y)`; sign matches y | | `mod1(x,y)` | offset-1 mod; if y>0, returns r∈(0,y]; if y<0, r∈[y,0) and satisfies `mod(r, y) == mod(x, y)` | | `mod2pi(x)` | modulo 2pi; `0 <= mod2pi(x) div(11, 4) 2 julia> div(7, 4) 1 julia> fld(11, 4) 2 julia> fld(-5,3) -2 julia> fld(7.5,3.3) 2.0 julia> cld(7.5,3.3) 3.0 julia> mod(5, 0:2) 2 julia> mod(3, 0:2) 0 julia> mod(8.9,2) 0.9000000000000004 julia> rem(8,4) 0 julia> rem(9,4) 1 julia> mod2pi(7*pi/5) 4.39822971502571 julia>divrem(8,3) (2, 2) julia> fldmod(12,4) (3, 0) julia> fldmod(13,4) (3, 1) julia> mod1(5,4) 1 julia> gcd(6,0) 6 julia> gcd(1//3,2//3) 1//3 julia> lcm(1//3,2//3) 2//3 * * * ## Sign and Absolute Value Functions The following table lists the sign and absolute value functions supported by Julia: | Function | Description | | --- | --- | | `abs(x)` | absolute value of x | | `abs2(x)` | squared absolute value of x | | `sign(x)` | sign of x, returns -1, 0, or +1 | | `signbit(x)` | sign bit, returns true or false | | `copys