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href="../devdocs/debuggingtips.html">gdb debugging tips</a></li><li><a class="toctext" href="../devdocs/valgrind.html">Using Valgrind with Julia</a></li><li><a class="toctext" href="../devdocs/sanitizers.html">Sanitizer support</a></li></ul></li></ul></li></ul></nav><article id="docs"><header><nav><ul><li>Standard Library</li><li><a href="numbers.html">Numbers</a></li></ul><a class="edit-page" href="https://github.com/JuliaLang/julia/blob/master/doc/src/stdlib/numbers.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Numbers</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="lib-numbers-1" href="#lib-numbers-1">Numbers</a></h1><h2><a class="nav-anchor" id="Standard-Numeric-Types-1" href="#Standard-Numeric-Types-1">Standard Numeric Types</a></h2><h3><a class="nav-anchor" id="Abstract-number-types-1" href="#Abstract-number-types-1">Abstract number types</a></h3><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Core.Number" href="#Core.Number"><code>Core.Number</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Number</code></pre><p>Abstract supertype for all number types.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L2668-L2672">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Core.Real" href="#Core.Real"><code>Core.Real</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Real <: Number</code></pre><p>Abstract supertype for all real numbers.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L2675-L2679">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Core.AbstractFloat" href="#Core.AbstractFloat"><code>Core.AbstractFloat</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">AbstractFloat <: Real</code></pre><p>Abstract supertype for all floating point numbers.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L2682-L2686">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Core.Integer" href="#Core.Integer"><code>Core.Integer</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Integer <: Real</code></pre><p>Abstract supertype for all integers.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L2689-L2693">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Core.Signed" href="#Core.Signed"><code>Core.Signed</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Signed <: Integer</code></pre><p>Abstract supertype for all signed integers.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L2696-L2700">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Core.Unsigned" href="#Core.Unsigned"><code>Core.Unsigned</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Unsigned <: Integer</code></pre><p>Abstract supertype for all unsigned integers.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L2703-L2707">source</a></section><h3><a class="nav-anchor" id="Concrete-number-types-1" href="#Concrete-number-types-1">Concrete number types</a></h3><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Core.Float16" href="#Core.Float16"><code>Core.Float16</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Float16 <: AbstractFloat</code></pre><p>16-bit floating point number type.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L2719-L2723">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Core.Float32" href="#Core.Float32"><code>Core.Float32</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Float32 <: AbstractFloat</code></pre><p>32-bit floating point number type.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L2719-L2723">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Core.Float64" href="#Core.Float64"><code>Core.Float64</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Float64 <: AbstractFloat</code></pre><p>64-bit floating point number type.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L2719-L2723">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.MPFR.BigFloat" href="#Base.MPFR.BigFloat"><code>Base.MPFR.BigFloat</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">BigFloat <: AbstractFloat</code></pre><p>Arbitrary precision floating point number type.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/mpfr.jl#L43-L47">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Core.Bool" href="#Core.Bool"><code>Core.Bool</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Bool <: Integer</code></pre><p>Boolean type.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L2710-L2714">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Core.Int8" href="#Core.Int8"><code>Core.Int8</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Int8 <: Signed</code></pre><p>8-bit signed integer type.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L2730-L2734">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Core.UInt8" href="#Core.UInt8"><code>Core.UInt8</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">UInt8 <: Unsigned</code></pre><p>8-bit unsigned integer type.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L2737-L2741">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Core.Int16" href="#Core.Int16"><code>Core.Int16</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Int16 <: Signed</code></pre><p>16-bit signed integer type.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L2730-L2734">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Core.UInt16" href="#Core.UInt16"><code>Core.UInt16</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">UInt16 <: Unsigned</code></pre><p>16-bit unsigned integer type.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L2737-L2741">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Core.Int32" href="#Core.Int32"><code>Core.Int32</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Int32 <: Signed</code></pre><p>32-bit signed integer type.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L2730-L2734">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Core.UInt32" href="#Core.UInt32"><code>Core.UInt32</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">UInt32 <: Unsigned</code></pre><p>32-bit unsigned integer type.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L2737-L2741">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Core.Int64" href="#Core.Int64"><code>Core.Int64</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Int64 <: Signed</code></pre><p>64-bit signed integer type.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L2730-L2734">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Core.UInt64" href="#Core.UInt64"><code>Core.UInt64</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">UInt64 <: Unsigned</code></pre><p>64-bit unsigned integer type.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L2737-L2741">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Core.Int128" href="#Core.Int128"><code>Core.Int128</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Int128 <: Signed</code></pre><p>128-bit signed integer type.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L2730-L2734">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Core.UInt128" href="#Core.UInt128"><code>Core.UInt128</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">UInt128 <: Unsigned</code></pre><p>128-bit unsigned integer type.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L2737-L2741">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.GMP.BigInt" href="#Base.GMP.BigInt"><code>Base.GMP.BigInt</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">BigInt <: Integer</code></pre><p>Arbitrary precision integer type.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/gmp.jl#L40-L44">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.Complex" href="#Base.Complex"><code>Base.Complex</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Complex{T<:Real} <: Number</code></pre><p>Complex number type with real and imaginary part of type <code>T</code>.</p><p><code>Complex32</code>, <code>Complex64</code> and <code>Complex128</code> are aliases for <code>Complex{Float16}</code>, <code>Complex{Float32}</code> and <code>Complex{Float64}</code> respectively.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/complex.jl#L3-L10">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.Rational" href="#Base.Rational"><code>Base.Rational</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Rational{T<:Integer} <: Real</code></pre><p>Rational number type, with numerator and denominator of type <code>T</code>.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/rational.jl#L3-L7">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.Irrational" href="#Base.Irrational"><code>Base.Irrational</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">Irrational <: Real</code></pre><p>Irrational number type.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/irrationals.jl#L5-L9">source</a></section><h2><a class="nav-anchor" id="Data-Formats-1" href="#Data-Formats-1">Data Formats</a></h2><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.bin" href="#Base.bin"><code>Base.bin</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">bin(n, pad::Int=1)</code></pre><p>Convert an integer to a binary string, optionally specifying a number of digits to pad to.</p><pre><code class="language-julia-repl">julia> bin(10,2)
|
||
"1010"
|
||
|
||
julia> bin(10,8)
|
||
"00001010"</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/intfuncs.jl#L601-L613">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.hex" href="#Base.hex"><code>Base.hex</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">hex(n, pad::Int=1)</code></pre><p>Convert an integer to a hexadecimal string, optionally specifying a number of digits to pad to.</p><pre><code class="language-julia-repl">julia> hex(20)
|
||
"14"
|
||
|
||
julia> hex(20, 3)
|
||
"014"</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/intfuncs.jl#L616-L629">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.dec" href="#Base.dec"><code>Base.dec</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">dec(n, pad::Int=1)</code></pre><p>Convert an integer to a decimal string, optionally specifying a number of digits to pad to.</p><p><strong>Examples</strong></p><pre><code class="language-julia-repl">julia> dec(20)
|
||
"20"
|
||
|
||
julia> dec(20, 3)
|
||
"020"</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/intfuncs.jl#L648-L662">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.oct" href="#Base.oct"><code>Base.oct</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">oct(n, pad::Int=1)</code></pre><p>Convert an integer to an octal string, optionally specifying a number of digits to pad to.</p><pre><code class="language-julia-repl">julia> oct(20)
|
||
"24"
|
||
|
||
julia> oct(20, 3)
|
||
"024"</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/intfuncs.jl#L632-L645">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.base" href="#Base.base"><code>Base.base</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">base(base::Integer, n::Integer, pad::Integer=1)</code></pre><p>Convert an integer <code>n</code> to a string in the given <code>base</code>, optionally specifying a number of digits to pad to.</p><pre><code class="language-julia-repl">julia> base(13,5,4)
|
||
"0005"
|
||
|
||
julia> base(5,13,4)
|
||
"0023"</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/intfuncs.jl#L574-L587">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.digits" href="#Base.digits"><code>Base.digits</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">digits([T<:Integer], n::Integer, base::T=10, pad::Integer=1)</code></pre><p>Returns an array with element type <code>T</code> (default <code>Int</code>) of the digits of <code>n</code> in the given base, optionally padded with zeros to a specified size. More significant digits are at higher indexes, such that <code>n == sum([digits[k]*base^(k-1) for k=1:length(digits)])</code>.</p><p><strong>Examples</strong></p><pre><code class="language-julia-repl">julia> digits(10, 10)
|
||
2-element Array{Int64,1}:
|
||
0
|
||
1
|
||
|
||
julia> digits(10, 2)
|
||
4-element Array{Int64,1}:
|
||
0
|
||
1
|
||
0
|
||
1
|
||
|
||
julia> digits(10, 2, 6)
|
||
6-element Array{Int64,1}:
|
||
0
|
||
1
|
||
0
|
||
1
|
||
0
|
||
0</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/intfuncs.jl#L671-L701">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.digits!" href="#Base.digits!"><code>Base.digits!</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">digits!(array, n::Integer, base::Integer=10)</code></pre><p>Fills an array of the digits of <code>n</code> in the given base. More significant digits are at higher indexes. If the array length is insufficient, the least significant digits are filled up to the array length. If the array length is excessive, the excess portion is filled with zeros.</p><p><strong>Examples</strong></p><pre><code class="language-julia-repl">julia> digits!([2,2,2,2], 10, 2)
|
||
4-element Array{Int64,1}:
|
||
0
|
||
1
|
||
0
|
||
1
|
||
|
||
julia> digits!([2,2,2,2,2,2], 10, 2)
|
||
6-element Array{Int64,1}:
|
||
0
|
||
1
|
||
0
|
||
1
|
||
0
|
||
0</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/intfuncs.jl#L709-L734">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.bits" href="#Base.bits"><code>Base.bits</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">bits(n)</code></pre><p>A string giving the literal bit representation of a number.</p><p><strong>Example</strong></p><pre><code class="language-julia-repl">julia> bits(4)
|
||
"0000000000000000000000000000000000000000000000000000000000000100"
|
||
|
||
julia> bits(2.2)
|
||
"0100000000000001100110011001100110011001100110011001100110011010"</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L80-L93">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.parse-Tuple{Type,Any,Any}" href="#Base.parse-Tuple{Type,Any,Any}"><code>Base.parse</code></a> — <span class="docstring-category">Method</span>.</div><div><pre><code class="language-none">parse(type, str, [base])</code></pre><p>Parse a string as a number. If the type is an integer type, then a base can be specified (the default is 10). If the type is a floating point type, the string is parsed as a decimal floating point number. If the string does not contain a valid number, an error is raised.</p><pre><code class="language-julia-repl">julia> parse(Int, "1234")
|
||
1234
|
||
|
||
julia> parse(Int, "1234", 5)
|
||
194
|
||
|
||
julia> parse(Int, "afc", 16)
|
||
2812
|
||
|
||
julia> parse(Float64, "1.2e-3")
|
||
0.0012</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L1201-L1221">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.tryparse" href="#Base.tryparse"><code>Base.tryparse</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">tryparse(type, str, [base])</code></pre><p>Like <a href="numbers.html#Base.parse-Tuple{Type,Any,Any}"><code>parse</code></a>, but returns a <a href="base.html#Base.Nullable"><code>Nullable</code></a> of the requested type. The result will be null if the string does not contain a valid number.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L2478-L2483">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.big" href="#Base.big"><code>Base.big</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">big(x)</code></pre><p>Convert a number to a maximum precision representation (typically <a href="numbers.html#Base.GMP.BigInt"><code>BigInt</code></a> or <code>BigFloat</code>). See <a href="numbers.html#Base.MPFR.BigFloat"><code>BigFloat</code></a> for information about some pitfalls with floating-point numbers.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L1373-L1378">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.signed" href="#Base.signed"><code>Base.signed</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">signed(x)</code></pre><p>Convert a number to a signed integer. If the argument is unsigned, it is reinterpreted as signed without checking for overflow.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L2566-L2571">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.unsigned" href="#Base.unsigned"><code>Base.unsigned</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">unsigned(x) -> Unsigned</code></pre><p>Convert a number to an unsigned integer. If the argument is signed, it is reinterpreted as unsigned without checking for negative values.</p><p><strong>Examples</strong></p><pre><code class="language-julia-repl">julia> unsigned(-2)
|
||
0xfffffffffffffffe
|
||
|
||
julia> unsigned(2)
|
||
0x0000000000000002
|
||
|
||
julia> signed(unsigned(-2))
|
||
-2</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L2420-L2437">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.float-Tuple{Any}" href="#Base.float-Tuple{Any}"><code>Base.float</code></a> — <span class="docstring-category">Method</span>.</div><div><pre><code class="language-none">float(x)</code></pre><p>Convert a number or array to a floating point data type. When passed a string, this function is equivalent to <code>parse(Float64, x)</code>.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/float.jl#L252-L257">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.Math.significand" href="#Base.Math.significand"><code>Base.Math.significand</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">significand(x)</code></pre><p>Extract the <code>significand(s)</code> (a.k.a. mantissa), in binary representation, of a floating-point number. If <code>x</code> is a non-zero finite number, then the result will be a number of the same type on the interval <span>$[1,2)$</span>. Otherwise <code>x</code> is returned.</p><p><strong>Examples</strong></p><pre><code class="language-julia-repl">julia> significand(15.2)/15.2
|
||
0.125
|
||
|
||
julia> significand(15.2)*8
|
||
15.2</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/math.jl#L584-L599">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.Math.exponent" href="#Base.Math.exponent"><code>Base.Math.exponent</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">exponent(x) -> Int</code></pre><p>Get the exponent of a normalized floating-point number.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/math.jl#L567-L571">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.complex-Tuple{Complex}" href="#Base.complex-Tuple{Complex}"><code>Base.complex</code></a> — <span class="docstring-category">Method</span>.</div><div><pre><code class="language-none">complex(r, [i])</code></pre><p>Convert real numbers or arrays to complex. <code>i</code> defaults to zero.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/complex.jl#L122-L126">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.bswap" href="#Base.bswap"><code>Base.bswap</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">bswap(n)</code></pre><p>Byte-swap an integer. Flip the bits of its binary representation.</p><p><strong>Examples</strong></p><pre><code class="language-julia-repl">julia> a = bswap(4)
|
||
288230376151711744
|
||
|
||
julia> bswap(a)
|
||
4
|
||
|
||
julia> bin(1)
|
||
"1"
|
||
|
||
julia> bin(bswap(1))
|
||
"100000000000000000000000000000000000000000000000000000000"</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L1294-L1313">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.num2hex" href="#Base.num2hex"><code>Base.num2hex</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">num2hex(f)</code></pre><p>Get a hexadecimal string of the binary representation of a floating point number.</p><p><strong>Example</strong></p><pre><code class="language-julia-repl">julia> num2hex(2.2)
|
||
"400199999999999a"</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L602-L612">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.hex2num" href="#Base.hex2num"><code>Base.hex2num</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">hex2num(str)</code></pre><p>Convert a hexadecimal string to the floating point number it represents.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L1602-L1606">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.hex2bytes" href="#Base.hex2bytes"><code>Base.hex2bytes</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">hex2bytes(s::AbstractString)</code></pre><p>Convert an arbitrarily long hexadecimal string to its binary representation. Returns an <code>Array{UInt8,1}</code>, i.e. an array of bytes.</p><pre><code class="language-julia-repl">julia> a = hex(12345)
|
||
"3039"
|
||
|
||
julia> hex2bytes(a)
|
||
2-element Array{UInt8,1}:
|
||
0x30
|
||
0x39</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/strings/util.jl#L408-L423">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.bytes2hex" href="#Base.bytes2hex"><code>Base.bytes2hex</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">bytes2hex(bin_arr::Array{UInt8, 1}) -> String</code></pre><p>Convert an array of bytes to its hexadecimal representation. All characters are in lower-case.</p><pre><code class="language-julia-repl">julia> a = hex(12345)
|
||
"3039"
|
||
|
||
julia> b = hex2bytes(a)
|
||
2-element Array{UInt8,1}:
|
||
0x30
|
||
0x39
|
||
|
||
julia> bytes2hex(b)
|
||
"3039"</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/strings/util.jl#L446-L464">source</a></section><h2><a class="nav-anchor" id="General-Number-Functions-and-Constants-1" href="#General-Number-Functions-and-Constants-1">General Number Functions and Constants</a></h2><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.one" href="#Base.one"><code>Base.one</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">one(x)
|
||
one(T::type)</code></pre><p>Return a multiplicative identity for <code>x</code>: a value such that <code>one(x)*x == x*one(x) == x</code>. Alternatively <code>one(T)</code> can take a type <code>T</code>, in which case <code>one</code> returns a multiplicative identity for any <code>x</code> of type <code>T</code>.</p><p>If possible, <code>one(x)</code> returns a value of the same type as <code>x</code>, and <code>one(T)</code> returns a value of type <code>T</code>. However, this may not be the case for types representing dimensionful quantities (e.g. time in days), since the multiplicative identity must be dimensionless. In that case, <code>one(x)</code> should return an identity value of the same precision (and shape, for matrices) as <code>x</code>.</p><p>If you want a quantity that is of the same type as <code>x</code>, or of type <code>T</code>, even if <code>x</code> is dimensionful, use <a href="numbers.html#Base.oneunit"><code>oneunit</code></a> instead.</p><pre><code class="language-julia-repl">julia> one(3.7)
|
||
1.0
|
||
|
||
julia> one(Int)
|
||
1
|
||
|
||
julia> one(Dates.Day(1))
|
||
1</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/number.jl#L159-L188">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.oneunit" href="#Base.oneunit"><code>Base.oneunit</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">oneunit(x::T)
|
||
oneunit(T::Type)</code></pre><p>Returns <code>T(one(x))</code>, where <code>T</code> is either the type of the argument or (if a type is passed) the argument. This differs from <a href="numbers.html#Base.one"><code>one</code></a> for dimensionful quantities: <code>one</code> is dimensionless (a multiplicative identity) while <code>oneunit</code> is dimensionful (of the same type as <code>x</code>, or of type <code>T</code>).</p><pre><code class="language-julia-repl">julia> oneunit(3.7)
|
||
1.0
|
||
|
||
julia> oneunit(Dates.Day)
|
||
1 day</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/number.jl#L194-L210">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.zero" href="#Base.zero"><code>Base.zero</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">zero(x)</code></pre><p>Get the additive identity element for the type of <code>x</code> (<code>x</code> can also specify the type itself).</p><pre><code class="language-julia-repl">julia> zero(1)
|
||
0
|
||
|
||
julia> zero(big"2.0")
|
||
0.000000000000000000000000000000000000000000000000000000000000000000000000000000
|
||
|
||
julia> zero(rand(2,2))
|
||
2×2 Array{Float64,2}:
|
||
0.0 0.0
|
||
0.0 0.0</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/number.jl#L138-L155">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.pi" href="#Base.pi"><code>Base.pi</code></a> — <span class="docstring-category">Constant</span>.</div><div><pre><code class="language-none">pi
|
||
π</code></pre><p>The constant pi.</p><pre><code class="language-julia-repl">julia> pi
|
||
π = 3.1415926535897...</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/irrationals.jl#L149-L159">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.im" href="#Base.im"><code>Base.im</code></a> — <span class="docstring-category">Constant</span>.</div><div><pre><code class="language-none">im</code></pre><p>The imaginary unit.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/complex.jl#L18-L22">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.eu" href="#Base.eu"><code>Base.eu</code></a> — <span class="docstring-category">Constant</span>.</div><div><pre><code class="language-none">e
|
||
eu</code></pre><p>The constant e.</p><pre><code class="language-julia-repl">julia> e
|
||
e = 2.7182818284590...</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/irrationals.jl#L162-L172">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.catalan" href="#Base.catalan"><code>Base.catalan</code></a> — <span class="docstring-category">Constant</span>.</div><div><pre><code class="language-none">catalan</code></pre><p>Catalan's constant.</p><pre><code class="language-julia-repl">julia> catalan
|
||
catalan = 0.9159655941772...</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/irrationals.jl#L201-L210">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.eulergamma" href="#Base.eulergamma"><code>Base.eulergamma</code></a> — <span class="docstring-category">Constant</span>.</div><div><pre><code class="language-none">γ
|
||
eulergamma</code></pre><p>Euler's constant.</p><pre><code class="language-julia-repl">julia> eulergamma
|
||
γ = 0.5772156649015...</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/irrationals.jl#L175-L185">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.golden" href="#Base.golden"><code>Base.golden</code></a> — <span class="docstring-category">Constant</span>.</div><div><pre><code class="language-none">φ
|
||
golden</code></pre><p>The golden ratio.</p><pre><code class="language-julia-repl">julia> golden
|
||
φ = 1.6180339887498...</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/irrationals.jl#L188-L198">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.Inf" href="#Base.Inf"><code>Base.Inf</code></a> — <span class="docstring-category">Constant</span>.</div><div><pre><code class="language-none">Inf</code></pre><p>Positive infinity of type <a href="numbers.html#Core.Float64"><code>Float64</code></a>.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/float.jl#L32-L36">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.Inf32" href="#Base.Inf32"><code>Base.Inf32</code></a> — <span class="docstring-category">Constant</span>.</div><div><pre><code class="language-none">Inf32</code></pre><p>Positive infinity of type <a href="numbers.html#Core.Float32"><code>Float32</code></a>.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/float.jl#L17-L21">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.Inf16" href="#Base.Inf16"><code>Base.Inf16</code></a> — <span class="docstring-category">Constant</span>.</div><div><pre><code class="language-none">Inf16</code></pre><p>Positive infinity of type <a href="numbers.html#Core.Float16"><code>Float16</code></a>.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/float.jl#L5-L9">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.NaN" href="#Base.NaN"><code>Base.NaN</code></a> — <span class="docstring-category">Constant</span>.</div><div><pre><code class="language-none">NaN</code></pre><p>A not-a-number value of type <a href="numbers.html#Core.Float64"><code>Float64</code></a>.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/float.jl#L38-L42">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.NaN32" href="#Base.NaN32"><code>Base.NaN32</code></a> — <span class="docstring-category">Constant</span>.</div><div><pre><code class="language-none">NaN32</code></pre><p>A not-a-number value of type <a href="numbers.html#Core.Float32"><code>Float32</code></a>.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/float.jl#L23-L27">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.NaN16" href="#Base.NaN16"><code>Base.NaN16</code></a> — <span class="docstring-category">Constant</span>.</div><div><pre><code class="language-none">NaN16</code></pre><p>A not-a-number value of type <a href="numbers.html#Core.Float16"><code>Float16</code></a>.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/float.jl#L11-L15">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.issubnormal" href="#Base.issubnormal"><code>Base.issubnormal</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">issubnormal(f) -> Bool</code></pre><p>Test whether a floating point number is subnormal.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L2055-L2059">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.isfinite" href="#Base.isfinite"><code>Base.isfinite</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">isfinite(f) -> Bool</code></pre><p>Test whether a number is finite.</p><pre><code class="language-julia-repl">julia> isfinite(5)
|
||
true
|
||
|
||
julia> isfinite(NaN32)
|
||
false</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/float.jl#L525-L537">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.isinf" href="#Base.isinf"><code>Base.isinf</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">isinf(f) -> Bool</code></pre><p>Test whether a number is infinite.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/float.jl#L543-L547">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.isnan" href="#Base.isnan"><code>Base.isnan</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">isnan(f) -> Bool</code></pre><p>Test whether a floating point number is not a number (NaN).</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/float.jl#L516-L520">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.iszero" href="#Base.iszero"><code>Base.iszero</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">iszero(x)</code></pre><p>Return <code>true</code> if <code>x == zero(x)</code>; if <code>x</code> is an array, this checks whether all of the elements of <code>x</code> are zero.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/number.jl#L16-L21">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.nextfloat" href="#Base.nextfloat"><code>Base.nextfloat</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">nextfloat(x::AbstractFloat, n::Integer)</code></pre><p>The result of <code>n</code> iterative applications of <code>nextfloat</code> to <code>x</code> if <code>n >= 0</code>, or <code>-n</code> applications of <code>prevfloat</code> if <code>n < 0</code>.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/float.jl#L580-L585">source</a><div><pre><code class="language-none">nextfloat(x::AbstractFloat)</code></pre><p>Returns the smallest floating point number <code>y</code> of the same type as <code>x</code> such <code>x < y</code>. If no such <code>y</code> exists (e.g. if <code>x</code> is <code>Inf</code> or <code>NaN</code>), then returns <code>x</code>.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/float.jl#L624-L629">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.prevfloat" href="#Base.prevfloat"><code>Base.prevfloat</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">prevfloat(x::AbstractFloat)</code></pre><p>Returns the largest floating point number <code>y</code> of the same type as <code>x</code> such <code>y < x</code>. If no such <code>y</code> exists (e.g. if <code>x</code> is <code>-Inf</code> or <code>NaN</code>), then returns <code>x</code>.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/float.jl#L632-L637">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.isinteger" href="#Base.isinteger"><code>Base.isinteger</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">isinteger(x) -> Bool</code></pre><p>Test whether <code>x</code> is numerically equal to some integer.</p><pre><code class="language-julia-repl">julia> isinteger(4.0)
|
||
true</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/number.jl#L4-L13">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.isreal" href="#Base.isreal"><code>Base.isreal</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">isreal(x) -> Bool</code></pre><p>Test whether <code>x</code> or all its elements are numerically equal to some real number.</p><pre><code class="language-julia-repl">julia> isreal(5.)
|
||
true
|
||
|
||
julia> isreal([4.; complex(0,1)])
|
||
false</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/complex.jl#L101-L113">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Core.Float32-Tuple{Any}" href="#Core.Float32-Tuple{Any}"><code>Core.Float32</code></a> — <span class="docstring-category">Method</span>.</div><div><pre><code class="language-none">Float32(x [, mode::RoundingMode])</code></pre><p>Create a Float32 from <code>x</code>. If <code>x</code> is not exactly representable then <code>mode</code> determines how <code>x</code> is rounded.</p><p><strong>Examples</strong></p><pre><code class="language-julia-repl">julia> Float32(1/3, RoundDown)
|
||
0.3333333f0
|
||
|
||
julia> Float32(1/3, RoundUp)
|
||
0.33333334f0</code></pre><p>See <a href="math.html#Base.Rounding.RoundingMode"><code>RoundingMode</code></a> for available rounding modes.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L221-L237">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Core.Float64-Tuple{Any}" href="#Core.Float64-Tuple{Any}"><code>Core.Float64</code></a> — <span class="docstring-category">Method</span>.</div><div><pre><code class="language-none">Float64(x [, mode::RoundingMode])</code></pre><p>Create a Float64 from <code>x</code>. If <code>x</code> is not exactly representable then <code>mode</code> determines how <code>x</code> is rounded.</p><p><strong>Examples</strong></p><pre><code class="language-julia-repl">julia> Float64(pi, RoundDown)
|
||
3.141592653589793
|
||
|
||
julia> Float64(pi, RoundUp)
|
||
3.1415926535897936</code></pre><p>See <a href="math.html#Base.Rounding.RoundingMode"><code>RoundingMode</code></a> for available rounding modes.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L925-L941">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.GMP.BigInt-Tuple{Any}" href="#Base.GMP.BigInt-Tuple{Any}"><code>Base.GMP.BigInt</code></a> — <span class="docstring-category">Method</span>.</div><div><pre><code class="language-none">BigInt(x)</code></pre><p>Create an arbitrary precision integer. <code>x</code> may be an <code>Int</code> (or anything that can be converted to an <code>Int</code>). The usual mathematical operators are defined for this type, and results are promoted to a <a href="numbers.html#Base.GMP.BigInt"><code>BigInt</code></a>.</p><p>Instances can be constructed from strings via <a href="numbers.html#Base.parse-Tuple{Type,Any,Any}"><code>parse</code></a>, or using the <code>big</code> string literal.</p><pre><code class="language-julia-repl">julia> parse(BigInt, "42")
|
||
42
|
||
|
||
julia> big"313"
|
||
313</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/gmp.jl#L61-L78">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.MPFR.BigFloat-Tuple{Any}" href="#Base.MPFR.BigFloat-Tuple{Any}"><code>Base.MPFR.BigFloat</code></a> — <span class="docstring-category">Method</span>.</div><div><pre><code class="language-none">BigFloat(x)</code></pre><p>Create an arbitrary precision floating point number. <code>x</code> may be an <a href="numbers.html#Core.Integer"><code>Integer</code></a>, a <a href="numbers.html#Core.Float64"><code>Float64</code></a> or a <a href="numbers.html#Base.GMP.BigInt"><code>BigInt</code></a>. The usual mathematical operators are defined for this type, and results are promoted to a <a href="numbers.html#Base.MPFR.BigFloat"><code>BigFloat</code></a>.</p><p>Note that because decimal literals are converted to floating point numbers when parsed, <code>BigFloat(2.1)</code> may not yield what you expect. You may instead prefer to initialize constants from strings via <a href="numbers.html#Base.parse-Tuple{Type,Any,Any}"><code>parse</code></a>, or using the <code>big</code> string literal.</p><pre><code class="language-julia-repl">julia> BigFloat(2.1)
|
||
2.100000000000000088817841970012523233890533447265625000000000000000000000000000
|
||
|
||
julia> big"2.1"
|
||
2.099999999999999999999999999999999999999999999999999999999999999999999999999986</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/mpfr.jl#L68-L86">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.Rounding.rounding" href="#Base.Rounding.rounding"><code>Base.Rounding.rounding</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">rounding(T)</code></pre><p>Get the current floating point rounding mode for type <code>T</code>, controlling the rounding of basic arithmetic functions (<a href="math.html#Base.:+"><code>+</code></a>, <a href="math.html#Base.:--Tuple{Any}"><code>-</code></a>, <a href="strings.html#Base.:*-Tuple{AbstractString,Vararg{Any,N} where N}"><code>*</code></a>, <a href="math.html#Base.:/"><code>/</code></a> and <a href="math.html#Base.sqrt"><code>sqrt</code></a>) and type conversion.</p><p>See <a href="math.html#Base.Rounding.RoundingMode"><code>RoundingMode</code></a> for available modes.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/rounding.jl#L131-L139">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.Rounding.setrounding-Tuple{Type,Any}" href="#Base.Rounding.setrounding-Tuple{Type,Any}"><code>Base.Rounding.setrounding</code></a> — <span class="docstring-category">Method</span>.</div><div><pre><code class="language-none">setrounding(T, mode)</code></pre><p>Set the rounding mode of floating point type <code>T</code>, controlling the rounding of basic arithmetic functions (<a href="math.html#Base.:+"><code>+</code></a>, <a href="math.html#Base.:--Tuple{Any}"><code>-</code></a>, <a href="strings.html#Base.:*-Tuple{AbstractString,Vararg{Any,N} where N}"><code>*</code></a>, <a href="math.html#Base.:/"><code>/</code></a> and <a href="math.html#Base.sqrt"><code>sqrt</code></a>) and type conversion. Other numerical functions may give incorrect or invalid values when using rounding modes other than the default <code>RoundNearest</code>.</p><p>Note that this may affect other types, for instance changing the rounding mode of <a href="numbers.html#Core.Float64"><code>Float64</code></a> will change the rounding mode of <a href="numbers.html#Core.Float32"><code>Float32</code></a>. See <a href="math.html#Base.Rounding.RoundingMode"><code>RoundingMode</code></a> for available modes.</p><div class="admonition warning"><div class="admonition-title">Warning</div><div class="admonition-text"><p>This feature is still experimental, and may give unexpected or incorrect values.</p></div></div></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/rounding.jl#L112-L128">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.Rounding.setrounding-Tuple{Function,Type,RoundingMode}" href="#Base.Rounding.setrounding-Tuple{Function,Type,RoundingMode}"><code>Base.Rounding.setrounding</code></a> — <span class="docstring-category">Method</span>.</div><div><pre><code class="language-none">setrounding(f::Function, T, mode)</code></pre><p>Change the rounding mode of floating point type <code>T</code> for the duration of <code>f</code>. It is logically equivalent to:</p><pre><code class="language-none">old = rounding(T)
|
||
setrounding(T, mode)
|
||
f()
|
||
setrounding(T, old)</code></pre><p>See <a href="math.html#Base.Rounding.RoundingMode"><code>RoundingMode</code></a> for available rounding modes.</p><div class="admonition warning"><div class="admonition-title">Warning</div><div class="admonition-text"><p>This feature is still experimental, and may give unexpected or incorrect values. A known problem is the interaction with compiler optimisations, e.g.</p><pre><code class="language-none">julia> setrounding(Float64,RoundDown) do
|
||
1.1 + 0.1
|
||
end
|
||
1.2000000000000002</code></pre><p>Here the compiler is <em>constant folding</em>, that is evaluating a known constant expression at compile time, however the rounding mode is only changed at runtime, so this is not reflected in the function result. This can be avoided by moving constants outside the expression, e.g.</p><pre><code class="language-none">julia> x = 1.1; y = 0.1;
|
||
|
||
julia> setrounding(Float64,RoundDown) do
|
||
x + y
|
||
end
|
||
1.2</code></pre></div></div></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/rounding.jl#L148-L182">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.Rounding.get_zero_subnormals" href="#Base.Rounding.get_zero_subnormals"><code>Base.Rounding.get_zero_subnormals</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">get_zero_subnormals() -> Bool</code></pre><p>Returns <code>false</code> if operations on subnormal floating-point values ("denormals") obey rules for IEEE arithmetic, and <code>true</code> if they might be converted to zeros.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/rounding.jl#L235-L240">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.Rounding.set_zero_subnormals" href="#Base.Rounding.set_zero_subnormals"><code>Base.Rounding.set_zero_subnormals</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">set_zero_subnormals(yes::Bool) -> Bool</code></pre><p>If <code>yes</code> is <code>false</code>, subsequent floating-point operations follow rules for IEEE arithmetic on subnormal values ("denormals"). Otherwise, floating-point operations are permitted (but not required) to convert subnormal inputs or outputs to zero. Returns <code>true</code> unless <code>yes==true</code> but the hardware does not support zeroing of subnormal numbers.</p><p><code>set_zero_subnormals(true)</code> can speed up some computations on some hardware. However, it can break identities such as <code>(x-y==0) == (x==y)</code>.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/rounding.jl#L222-L232">source</a></section><h3><a class="nav-anchor" id="Integers-1" href="#Integers-1">Integers</a></h3><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.count_ones" href="#Base.count_ones"><code>Base.count_ones</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">count_ones(x::Integer) -> Integer</code></pre><p>Number of ones in the binary representation of <code>x</code>.</p><pre><code class="language-julia-repl">julia> count_ones(7)
|
||
3</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/int.jl#L216-L225">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.count_zeros" href="#Base.count_zeros"><code>Base.count_zeros</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">count_zeros(x::Integer) -> Integer</code></pre><p>Number of zeros in the binary representation of <code>x</code>.</p><pre><code class="language-julia-repl">julia> count_zeros(Int32(2 ^ 16 - 1))
|
||
16</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/int.jl#L252-L261">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.leading_zeros" href="#Base.leading_zeros"><code>Base.leading_zeros</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">leading_zeros(x::Integer) -> Integer</code></pre><p>Number of zeros leading the binary representation of <code>x</code>.</p><pre><code class="language-julia-repl">julia> leading_zeros(Int32(1))
|
||
31</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/int.jl#L228-L237">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.leading_ones" href="#Base.leading_ones"><code>Base.leading_ones</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">leading_ones(x::Integer) -> Integer</code></pre><p>Number of ones leading the binary representation of <code>x</code>.</p><pre><code class="language-julia-repl">julia> leading_ones(UInt32(2 ^ 32 - 2))
|
||
31</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/int.jl#L264-L273">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.trailing_zeros" href="#Base.trailing_zeros"><code>Base.trailing_zeros</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">trailing_zeros(x::Integer) -> Integer</code></pre><p>Number of zeros trailing the binary representation of <code>x</code>.</p><pre><code class="language-julia-repl">julia> trailing_zeros(2)
|
||
1</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/int.jl#L240-L249">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.trailing_ones" href="#Base.trailing_ones"><code>Base.trailing_ones</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">trailing_ones(x::Integer) -> Integer</code></pre><p>Number of ones trailing the binary representation of <code>x</code>.</p><pre><code class="language-julia-repl">julia> trailing_ones(3)
|
||
2</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/int.jl#L276-L285">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.isodd" href="#Base.isodd"><code>Base.isodd</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">isodd(x::Integer) -> Bool</code></pre><p>Returns <code>true</code> if <code>x</code> is odd (that is, not divisible by 2), and <code>false</code> otherwise.</p><pre><code class="language-julia-repl">julia> isodd(9)
|
||
true
|
||
|
||
julia> isodd(10)
|
||
false</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/int.jl#L40-L52">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.iseven" href="#Base.iseven"><code>Base.iseven</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">iseven(x::Integer) -> Bool</code></pre><p>Returns <code>true</code> is <code>x</code> is even (that is, divisible by 2), and <code>false</code> otherwise.</p><pre><code class="language-julia-repl">julia> iseven(9)
|
||
false
|
||
|
||
julia> iseven(10)
|
||
true</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/int.jl#L55-L67">source</a></section><h2><a class="nav-anchor" id="BigFloats-1" href="#BigFloats-1">BigFloats</a></h2><p>The <a href="numbers.html#Base.MPFR.BigFloat"><code>BigFloat</code></a> type implements arbitrary-precision floating-point arithmetic using the <a href="http://www.mpfr.org/">GNU MPFR library</a>.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.precision" href="#Base.precision"><code>Base.precision</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">precision(num::AbstractFloat)</code></pre><p>Get the precision of a floating point number, as defined by the effective number of bits in the mantissa.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/docs/helpdb/Base.jl#L58-L63">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.precision-Tuple{Type{BigFloat}}" href="#Base.precision-Tuple{Type{BigFloat}}"><code>Base.precision</code></a> — <span class="docstring-category">Method</span>.</div><div><pre><code class="language-none">precision(BigFloat)</code></pre><p>Get the precision (in bits) currently used for <a href="numbers.html#Base.MPFR.BigFloat"><code>BigFloat</code></a> arithmetic.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/mpfr.jl#L715-L719">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.MPFR.setprecision" href="#Base.MPFR.setprecision"><code>Base.MPFR.setprecision</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">setprecision([T=BigFloat,] precision::Int)</code></pre><p>Set the precision (in bits) to be used for <code>T</code> arithmetic.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/mpfr.jl#L722-L726">source</a><div><pre><code class="language-none">setprecision(f::Function, [T=BigFloat,] precision::Integer)</code></pre><p>Change the <code>T</code> arithmetic precision (in bits) for the duration of <code>f</code>. It is logically equivalent to:</p><pre><code class="language-none">old = precision(BigFloat)
|
||
setprecision(BigFloat, precision)
|
||
f()
|
||
setprecision(BigFloat, old)</code></pre><p>Often used as <code>setprecision(T, precision) do ... end</code></p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/mpfr.jl#L859-L871">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.MPFR.BigFloat-Tuple{Any,Int64}" href="#Base.MPFR.BigFloat-Tuple{Any,Int64}"><code>Base.MPFR.BigFloat</code></a> — <span class="docstring-category">Method</span>.</div><div><pre><code class="language-none">BigFloat(x, prec::Int)</code></pre><p>Create a representation of <code>x</code> as a <a href="numbers.html#Base.MPFR.BigFloat"><code>BigFloat</code></a> with precision <code>prec</code>.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/mpfr.jl#L129-L133">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.MPFR.BigFloat-Tuple{Union{AbstractFloat, Integer, String},RoundingMode}" href="#Base.MPFR.BigFloat-Tuple{Union{AbstractFloat, Integer, String},RoundingMode}"><code>Base.MPFR.BigFloat</code></a> — <span class="docstring-category">Method</span>.</div><div><pre><code class="language-none">BigFloat(x, rounding::RoundingMode)</code></pre><p>Create a representation of <code>x</code> as a <a href="numbers.html#Base.MPFR.BigFloat"><code>BigFloat</code></a> with the current global precision and rounding mode <code>rounding</code>.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/mpfr.jl#L152-L157">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.MPFR.BigFloat-Tuple{Any,Int64,RoundingMode}" href="#Base.MPFR.BigFloat-Tuple{Any,Int64,RoundingMode}"><code>Base.MPFR.BigFloat</code></a> — <span class="docstring-category">Method</span>.</div><div><pre><code class="language-none">BigFloat(x, prec::Int, rounding::RoundingMode)</code></pre><p>Create a representation of <code>x</code> as a <a href="numbers.html#Base.MPFR.BigFloat"><code>BigFloat</code></a> with precision <code>prec</code> and rounding mode <code>rounding</code>.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/mpfr.jl#L140-L145">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.MPFR.BigFloat-Tuple{String}" href="#Base.MPFR.BigFloat-Tuple{String}"><code>Base.MPFR.BigFloat</code></a> — <span class="docstring-category">Method</span>.</div><div><pre><code class="language-none">BigFloat(x::String)</code></pre><p>Create a representation of the string <code>x</code> as a <a href="numbers.html#Base.MPFR.BigFloat"><code>BigFloat</code></a>.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/mpfr.jl#L162-L166">source</a></section><h2><a class="nav-anchor" id="Random-Numbers-1" href="#Random-Numbers-1">Random Numbers</a></h2><p>Random number generation in Julia uses the <a href="http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/SFMT/#dSFMT">Mersenne Twister library</a> via <code>MersenneTwister</code> objects. Julia has a global RNG, which is used by default. Other RNG types can be plugged in by inheriting the <code>AbstractRNG</code> type; they can then be used to have multiple streams of random numbers. Besides <code>MersenneTwister</code>, Julia also provides the <code>RandomDevice</code> RNG type, which is a wrapper over the OS provided entropy.</p><p>Most functions related to random generation accept an optional <code>AbstractRNG</code> as the first argument, <code>rng</code> , which defaults to the global one if not provided. Morever, some of them accept optionally dimension specifications <code>dims...</code> (which can be given as a tuple) to generate arrays of random values.</p><p>A <code>MersenneTwister</code> or <code>RandomDevice</code> RNG can generate random numbers of the following types: <a href="numbers.html#Core.Float16"><code>Float16</code></a>, <a href="numbers.html#Core.Float32"><code>Float32</code></a>, <a href="numbers.html#Core.Float64"><code>Float64</code></a>, <a href="numbers.html#Core.Bool"><code>Bool</code></a>, <a href="numbers.html#Core.Int8"><code>Int8</code></a>, <a href="numbers.html#Core.UInt8"><code>UInt8</code></a>, <a href="numbers.html#Core.Int16"><code>Int16</code></a>, <a href="numbers.html#Core.UInt16"><code>UInt16</code></a>, <a href="numbers.html#Core.Int32"><code>Int32</code></a>, <a href="numbers.html#Core.UInt32"><code>UInt32</code></a>, <a href="numbers.html#Core.Int64"><code>Int64</code></a>, <a href="numbers.html#Core.UInt64"><code>UInt64</code></a>, <a href="numbers.html#Core.Int128"><code>Int128</code></a>, <a href="numbers.html#Core.UInt128"><code>UInt128</code></a>, <a href="numbers.html#Base.GMP.BigInt"><code>BigInt</code></a> (or complex numbers of those types). Random floating point numbers are generated uniformly in <span>$[0, 1)$</span>. As <code>BigInt</code> represents unbounded integers, the interval must be specified (e.g. <code>rand(big(1:6))</code>).</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.Random.srand" href="#Base.Random.srand"><code>Base.Random.srand</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">srand([rng=GLOBAL_RNG], [seed]) -> rng
|
||
srand([rng=GLOBAL_RNG], filename, n=4) -> rng</code></pre><p>Reseed the random number generator. If a <code>seed</code> is provided, the RNG will give a reproducible sequence of numbers, otherwise Julia will get entropy from the system. For <code>MersenneTwister</code>, the <code>seed</code> may be a non-negative integer, a vector of <a href="numbers.html#Core.UInt32"><code>UInt32</code></a> integers or a filename, in which case the seed is read from a file (<code>4n</code> bytes are read from the file, where <code>n</code> is an optional argument). <code>RandomDevice</code> does not support seeding.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/random.jl#L227-L236">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.Random.MersenneTwister" href="#Base.Random.MersenneTwister"><code>Base.Random.MersenneTwister</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">MersenneTwister(seed)</code></pre><p>Create a <code>MersenneTwister</code> RNG object. Different RNG objects can have their own seeds, which may be useful for generating different streams of random numbers.</p><p><strong>Example</strong></p><pre><code class="language-julia-repl">julia> rng = MersenneTwister(1234);</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/random.jl#L91-L101">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.Random.RandomDevice" href="#Base.Random.RandomDevice"><code>Base.Random.RandomDevice</code></a> — <span class="docstring-category">Type</span>.</div><div><pre><code class="language-none">RandomDevice()</code></pre><p>Create a <code>RandomDevice</code> RNG object. Two such objects will always generate different streams of random numbers.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/random.jl#L58-L62">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.Random.rand" href="#Base.Random.rand"><code>Base.Random.rand</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">rand([rng=GLOBAL_RNG], [S], [dims...])</code></pre><p>Pick a random element or array of random elements from the set of values specified by <code>S</code>; <code>S</code> can be</p><ul><li><p>an indexable collection (for example <code>1:n</code> or <code>['x','y','z']</code>), or</p></li><li><p>a type: the set of values to pick from is then equivalent to <code>typemin(S):typemax(S)</code> for integers (this is not applicable to <a href="numbers.html#Base.GMP.BigInt"><code>BigInt</code></a>), and to <span>$[0, 1)$</span> for floating point numbers;</p></li></ul><p><code>S</code> defaults to <a href="numbers.html#Core.Float64"><code>Float64</code></a>.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/random.jl#L270-L281">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.Random.rand!" href="#Base.Random.rand!"><code>Base.Random.rand!</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">rand!([rng=GLOBAL_RNG], A, [coll])</code></pre><p>Populate the array <code>A</code> with random values. If the indexable collection <code>coll</code> is specified, the values are picked randomly from <code>coll</code>. This is equivalent to <code>copy!(A, rand(rng, coll, size(A)))</code> or <code>copy!(A, rand(rng, eltype(A), size(A)))</code> but without allocating a new array.</p><p><strong>Example</strong></p><pre><code class="language-julia-repl">julia> rng = MersenneTwister(1234);
|
||
|
||
julia> rand!(rng, zeros(5))
|
||
5-element Array{Float64,1}:
|
||
0.590845
|
||
0.766797
|
||
0.566237
|
||
0.460085
|
||
0.794026</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/random.jl#L292-L312">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.Random.bitrand" href="#Base.Random.bitrand"><code>Base.Random.bitrand</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">bitrand([rng=GLOBAL_RNG], [dims...])</code></pre><p>Generate a <code>BitArray</code> of random boolean values.</p><p><strong>Example</strong></p><pre><code class="language-julia-repl">julia> rng = MersenneTwister(1234);
|
||
|
||
julia> bitrand(rng, 10)
|
||
10-element BitArray{1}:
|
||
true
|
||
true
|
||
true
|
||
false
|
||
true
|
||
false
|
||
false
|
||
true
|
||
false
|
||
true</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/random.jl#L710-L733">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.Random.randn" href="#Base.Random.randn"><code>Base.Random.randn</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">randn([rng=GLOBAL_RNG], [T=Float64], [dims...])</code></pre><p>Generate a normally-distributed random number of type <code>T</code> with mean 0 and standard deviation 1. Optionally generate an array of normally-distributed random numbers. The <code>Base</code> module currently provides an implementation for the types <a href="numbers.html#Core.Float16"><code>Float16</code></a>, <a href="numbers.html#Core.Float32"><code>Float32</code></a>, and <a href="numbers.html#Core.Float64"><code>Float64</code></a> (the default).</p><p><strong>Examples</strong></p><pre><code class="language-julia-repl">julia> rng = MersenneTwister(1234);
|
||
|
||
julia> randn(rng, Float64)
|
||
0.8673472019512456
|
||
|
||
julia> randn(rng, Float32, (2, 4))
|
||
2×4 Array{Float32,2}:
|
||
-0.901744 -0.902914 2.21188 -0.271735
|
||
-0.494479 0.864401 0.532813 0.502334</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/random.jl#L1234-L1255">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.Random.randn!" href="#Base.Random.randn!"><code>Base.Random.randn!</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">randn!([rng=GLOBAL_RNG], A::AbstractArray) -> A</code></pre><p>Fill the array <code>A</code> with normally-distributed (mean 0, standard deviation 1) random numbers. Also see the <a href="numbers.html#Base.Random.rand"><code>rand</code></a> function.</p><p><strong>Example</strong></p><pre><code class="language-julia-repl">julia> rng = MersenneTwister(1234);
|
||
|
||
julia> randn!(rng, zeros(5))
|
||
5-element Array{Float64,1}:
|
||
0.867347
|
||
-0.901744
|
||
-0.494479
|
||
-0.902914
|
||
0.864401</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/random.jl#L1325-L1344">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.Random.randexp" href="#Base.Random.randexp"><code>Base.Random.randexp</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">randexp([rng=GLOBAL_RNG], [T=Float64], [dims...])</code></pre><p>Generate a random number of type <code>T</code> according to the exponential distribution with scale 1. Optionally generate an array of such random numbers. The <code>Base</code> module currently provides an implementation for the types <a href="numbers.html#Core.Float16"><code>Float16</code></a>, <a href="numbers.html#Core.Float32"><code>Float32</code></a>, and <a href="numbers.html#Core.Float64"><code>Float64</code></a> (the default).</p><p><strong>Examples</strong></p><pre><code class="language-julia-repl">julia> rng = MersenneTwister(1234);
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julia> randexp(rng, Float32)
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2.4835055f0
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julia> randexp(rng, 3, 3)
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3×3 Array{Float64,2}:
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1.5167 1.30652 0.344435
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0.604436 2.78029 0.418516
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0.695867 0.693292 0.643644</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/random.jl#L1282-L1304">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.Random.randexp!" href="#Base.Random.randexp!"><code>Base.Random.randexp!</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">randexp!([rng=GLOBAL_RNG], A::AbstractArray) -> A</code></pre><p>Fill the array <code>A</code> with random numbers following the exponential distribution (with scale 1).</p><p><strong>Example</strong></p><pre><code class="language-julia-repl">julia> rng = MersenneTwister(1234);
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|
||
julia> randexp!(rng, zeros(5))
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5-element Array{Float64,1}:
|
||
2.48351
|
||
1.5167
|
||
0.604436
|
||
0.695867
|
||
1.30652</code></pre></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/random.jl#L1347-L1365">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Base.Random.randjump" href="#Base.Random.randjump"><code>Base.Random.randjump</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">randjump(r::MersenneTwister, jumps::Integer, [jumppoly::AbstractString=dSFMT.JPOLY1e21]) -> Vector{MersenneTwister}</code></pre><p>Create an array of the size <code>jumps</code> of initialized <code>MersenneTwister</code> RNG objects. The first RNG object given as a parameter and following <code>MersenneTwister</code> RNGs in the array are initialized such that a state of the RNG object in the array would be moved forward (without generating numbers) from a previous RNG object array element on a particular number of steps encoded by the jump polynomial <code>jumppoly</code>.</p><p>Default jump polynomial moves forward <code>MersenneTwister</code> RNG state by <code>10^20</code> steps.</p></div><a class="source-link" target="_blank" href="https://github.com/JuliaLang/julia/blob/d55cadc350d426a95fd967121ba77494d08364c8/base/random.jl#L158-L168">source</a></section><footer><hr/><a class="previous" href="math.html"><span class="direction">Previous</span><span class="title">Mathematics</span></a><a class="next" href="strings.html"><span class="direction">Next</span><span class="title">Strings</span></a></footer></article></body></html>
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