. . 28 基础知识与参考文献 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 5.3 任意精度算术 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 5.4 着相邻的二进制整数表示。 舍入模式 一个数如果没有精确的浮点表示，就必须被舍入到一个合适的可表示的值。然而，如果想的话，可 以根据舍入模式改变舍入的方式，如 IEEE 754 标准 所述。 5.3. 任意精度算术 29 Julia 所使用的默认模式总是 RoundNearest，指舍入到最接近的可表示的值，这个被舍入的值会使用 尽量少的有效位数。 基础知识与参考文献 浮点算术带来了很多 以参见 William Kahan 的写作集。他以“浮点数之父”闻名。特别感兴趣的话可以看 An Interview with the Old Man of Floating-Point。 5.3 任意精度算术 为了允许使用任意精度的整数与浮点数，Julia 分别包装了 GNU Multiple Precision Arithmetic Library (GMP) 以及 GNU MPFR

26 5.2 Boolean Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.3 Bitwise Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.4 Updating an integer type and all the usual promotion rules and numeric operators are also defined on it. 5.3 Bitwise Operators The following bitwise operators are supported on all primitive integer types: Here complex number: 3.0 * exp(4.0im) julia> [Polar(3, 4.0), Polar(4.0,5.3)] 2-element Vector{Polar{Float64}}: 3.0 * exp(4.0im) 4.0 * exp(5.3im) where the single-line show(io, z) form is still used for an

26 5.2 Boolean Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.3 Bitwise Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.4 Updating an integer type and all the usual promotion rules and numeric operators are also defined on it. 5.3 Bitwise Operators The following bitwise operators are supported on all primitive integer types: Here complex number: 3.0 * exp(4.0im) julia> [Polar(3, 4.0), Polar(4.0,5.3)] 2-element Vector{Polar{Float64}}: 3.0 * exp(4.0im) 4.0 * exp(5.3im) where the single-line show(io, z) form is still used for an

Bitwise Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 5.3 Updating operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . julia> 123 ⊻ 234 145 julia> xor(123, 234) 145 julia> ~UInt32(123) 5.3. UPDATING OPERATORS 29 0xffffff84 julia> ~UInt8(123) 0x84 5.3 Updating operators Every binary arithmetic and bitwise operator also complex number: 3.0 * exp(4.0im) julia> [Polar(3, 4.0), Polar(4.0,5.3)] 2-element Array{Polar{Float64},1}: 3.0 * exp(4.0im) 4.0 * exp(5.3im) where the single-line show(io, z) form is still used for an

Bitwise Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 5.3 Updating operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . julia> 123 ⊻ 234 145 julia> xor(123, 234) 145 julia> ~UInt32(123) 5.3. UPDATING OPERATORS 29 0xffffff84 julia> ~UInt8(123) 0x84 5.3 Updating operators Every binary arithmetic and bitwise operator also complex number: 3.0 * exp(4.0im) julia> [Polar(3, 4.0), Polar(4.0,5.3)] 2-element Array{Polar{Float64},1}: 3.0 * exp(4.0im) 4.0 * exp(5.3im) where the single-line show(io, z) form is still used for an

Bitwise Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 5.3 Updating operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . julia> 123 ⊻ 234 145 julia> xor(123, 234) 145 julia> ~UInt32(123) 5.3. UPDATING OPERATORS 29 0xffffff84 julia> ~UInt8(123) 0x84 5.3 Updating operators Every binary arithmetic and bitwise operator also complex number: 3.0 * exp(4.0im) julia> [Polar(3, 4.0), Polar(4.0,5.3)] 2-element Array{Polar{Float64},1}: 3.0 * exp(4.0im) 4.0 * exp(5.3im) where the single-line show(io, z) form is still used for an

Bitwise Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 5.3 Updating operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . julia> 123 ⊻ 234 145 julia> xor(123, 234) 145 julia> ~UInt32(123) 5.3. UPDATING OPERATORS 29 0xffffff84 julia> ~UInt8(123) 0x84 5.3 Updating operators Every binary arithmetic and bitwise operator also complex number: 3.0 * exp(4.0im) julia> [Polar(3, 4.0), Polar(4.0,5.3)] 2-element Array{Polar{Float64},1}: 3.0 * exp(4.0im) 4.0 * exp(5.3im) where the single-line show(io, z) form is still used for an

Bitwise Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 5.3 Updating operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . julia> 123 ⊻ 234 145 julia> xor(123, 234) 145 julia> ~UInt32(123) 5.3. UPDATING OPERATORS 29 0xffffff84 julia> ~UInt8(123) 0x84 5.3 Updating operators Every binary arithmetic and bitwise operator also complex number: 3.0 * exp(4.0im) julia> [Polar(3, 4.0), Polar(4.0,5.3)] 2-element Array{Polar{Float64},1}: 3.0 * exp(4.0im) 4.0 * exp(5.3im) where the single-line show(io, z) form is still used for an

5.2 Floating-Point Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 5.3 Arbitrary Precision Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 5.4 Numeric Floating-Point". Of particular interest may be An Interview with the Old Man of Floating-Point. 5.3 Arbitrary Precision Arithmetic To allow computations with arbitrary-precision integers and floating complex number: 3.0 * exp(4.0im) julia> [Polar(3, 4.0), Polar(4.0,5.3)] 2-element Vector{Polar{Float64}}: 3.0 * exp(4.0im) 4.0 * exp(5.3im) where the single-line show(io, z) form is still used for an

5.2 Floating-Point Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 5.3 Arbitrary Precision Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 5.4 Numeric Floating-Point". Of particular interest may be An Interview with the Old Man of Floating-Point. 5.3 Arbitrary Precision Arithmetic To allow computations with arbitrary-precision integers and floating complex number: 3.0 * exp(4.0im) julia> [Polar(3, 4.0), Polar(4.0,5.3)] 2-element Vector{Polar{Float64}}: 3.0 * exp(4.0im) 4.0 * exp(5.3im) where the single-line show(io, z) form is still used for an