Docs formatting (#50049)

doc/src/manual/functions.md

@@ -5,7 +5,7 @@ functions are not pure mathematical functions, because they can alter and be aff
 by the global state of the program. The basic syntax for defining functions in Julia is:
 
 ```jldoctest
-julia> function f(x,y)
+julia> function f(x, y)
            x + y
        end
 f (generic function with 1 method)
@@ -18,7 +18,7 @@ There is a second, more terse syntax for defining a function in Julia. The tradi
 declaration syntax demonstrated above is equivalent to the following compact "assignment form":
 
 ```jldoctest fofxy
-julia> f(x,y) = x + y
+julia> f(x, y) = x + y
 f (generic function with 1 method)
 ```
 
@@ -30,7 +30,7 @@ both typing and visual noise.
 A function is called using the traditional parenthesis syntax:
 
 ```jldoctest fofxy
-julia> f(2,3)
+julia> f(2, 3)
 5
 ```
 
@@ -40,14 +40,14 @@ like any other value:
 ```jldoctest fofxy
 julia> g = f;
 
-julia> g(2,3)
+julia> g(2, 3)
 5
 ```
 
 As with variables, Unicode can also be used for function names:
 
 ```jldoctest
-julia> ∑(x,y) = x + y
+julia> ∑(x, y) = x + y
 ∑ (generic function with 1 method)
 
 julia> ∑(2, 3)
@@ -77,7 +77,7 @@ by the caller for this argument.   On the other hand, the assignment `y = 7 + y`
 `y` to refer to a new value `7 + y`, rather than mutating the *original* object referred to by `y`,
 and hence does *not* change the corresponding argument passed by the caller.   This can be seen if we call `f(x, y)`:
 ```julia-repl
-julia> a = [4,5,6]
+julia> a = [4, 5, 6]
 3-element Vector{Int64}:
  4
  5
@@ -130,7 +130,7 @@ the `return` keyword causes a function to return immediately, providing
 an expression whose value is returned:
 
 ```julia
-function g(x,y)
+function g(x, y)
     return x * y
     x + y
 end
@@ -140,19 +140,19 @@ Since function definitions can be entered into interactive sessions, it is easy
 definitions:
 
 ```jldoctest
-julia> f(x,y) = x + y
+julia> f(x, y) = x + y
 f (generic function with 1 method)
 
-julia> function g(x,y)
+julia> function g(x, y)
            return x * y
            x + y
        end
 g (generic function with 1 method)
 
-julia> f(2,3)
+julia> f(2, 3)
 5
 
-julia> g(2,3)
+julia> g(2, 3)
 6
 ```
 
@@ -163,18 +163,18 @@ is of real use. Here, for example, is a function that computes the hypotenuse le
 triangle with sides of length `x` and `y`, avoiding overflow:
 
 ```jldoctest
-julia> function hypot(x,y)
+julia> function hypot(x, y)
            x = abs(x)
            y = abs(y)
            if x > y
                r = y/x
-               return x*sqrt(1+r*r)
+               return x*sqrt(1 + r*r)
            end
            if y == 0
                return zero(x)
            end
            r = x/y
-           return y*sqrt(1+r*r)
+           return y*sqrt(1 + r*r)
        end
 hypot (generic function with 1 method)
 
@@ -243,7 +243,7 @@ as you would any other function:
 julia> 1 + 2 + 3
 6
 
-julia> +(1,2,3)
+julia> +(1, 2, 3)
 6
 ```
 
@@ -254,7 +254,7 @@ operators such as [`+`](@ref) and [`*`](@ref) just like you would with other fun
 ```jldoctest
 julia> f = +;
 
-julia> f(1,2,3)
+julia> f(1, 2, 3)
 6
 ```
 
@@ -402,7 +402,7 @@ left side of an assignment: the value on the right side is _destructured_ by ite
 over and assigning to each variable in turn:
 
 ```jldoctest
-julia> (a,b,c) = 1:3
+julia> (a, b, c) = 1:3
 1:3
 
 julia> b
@@ -417,7 +417,7 @@ This can be used to return multiple values from functions by returning a tuple o
 other iterable value. For example, the following function returns two values:
 
 ```jldoctest foofunc
-julia> function foo(a,b)
+julia> function foo(a, b)
            a+b, a*b
        end
 foo (generic function with 1 method)
@@ -427,14 +427,14 @@ If you call it in an interactive session without assigning the return value anyw
 see the tuple returned:
 
 ```jldoctest foofunc
-julia> foo(2,3)
+julia> foo(2, 3)
 (5, 6)
 ```
 
 Destructuring assignment extracts each value into a variable:
 
 ```jldoctest foofunc
-julia> x, y = foo(2,3)
+julia> x, y = foo(2, 3)
 (5, 6)
 
 julia> x
@@ -473,7 +473,7 @@ Other valid left-hand side expressions can be used as elements of the assignment
 ```jldoctest
 julia> X = zeros(3);
 
-julia> X[1], (a,b) = (1, (2, 3))
+julia> X[1], (a, b) = (1, (2, 3))
 (1, (2, 3))
 
 julia> X
@@ -625,7 +625,7 @@ julia> foo(A(3, 4))
 For anonymous functions, destructuring a single argument requires an extra comma:
 
 ```
-julia> map(((x,y),) -> x + y, [(1,2), (3,4)])
+julia> map(((x, y),) -> x + y, [(1, 2), (3, 4)])
 2-element Array{Int64,1}:
  3
  7
@@ -638,7 +638,7 @@ Such functions are traditionally known as "varargs" functions, which is short fo
 of arguments". You can define a varargs function by following the last positional argument with an ellipsis:
 
 ```jldoctest barfunc
-julia> bar(a,b,x...) = (a,b,x)
+julia> bar(a, b, x...) = (a, b, x)
 bar (generic function with 1 method)
 ```
 
@@ -647,16 +647,16 @@ The variables `a` and `b` are bound to the first two argument values as usual, a
 two arguments:
 
 ```jldoctest barfunc
-julia> bar(1,2)
+julia> bar(1, 2)
 (1, 2, ())
 
-julia> bar(1,2,3)
+julia> bar(1, 2, 3)
 (1, 2, (3,))
 
 julia> bar(1, 2, 3, 4)
 (1, 2, (3, 4))
 
-julia> bar(1,2,3,4,5,6)
+julia> bar(1, 2, 3, 4, 5, 6)
 (1, 2, (3, 4, 5, 6))
 ```
 
@@ -673,7 +673,7 @@ call instead:
 julia> x = (3, 4)
 (3, 4)
 
-julia> bar(1,2,x...)
+julia> bar(1, 2, x...)
 (1, 2, (3, 4))
 ```
 
@@ -684,7 +684,7 @@ of arguments go. This need not be the case, however:
 julia> x = (2, 3, 4)
 (2, 3, 4)
 
-julia> bar(1,x...)
+julia> bar(1, x...)
 (1, 2, (3, 4))
 
 julia> x = (1, 2, 3, 4)
@@ -697,15 +697,15 @@ julia> bar(x...)
 Furthermore, the iterable object splatted into a function call need not be a tuple:
 
 ```jldoctest barfunc
-julia> x = [3,4]
+julia> x = [3, 4]
 2-element Vector{Int64}:
  3
  4
 
-julia> bar(1,2,x...)
+julia> bar(1, 2, x...)
 (1, 2, (3, 4))
 
-julia> x = [1,2,3,4]
+julia> x = [1, 2, 3, 4]
 4-element Vector{Int64}:
  1
  2
@@ -720,17 +720,17 @@ Also, the function that arguments are splatted into need not be a varargs functi
 often is):
 
 ```jldoctest
-julia> baz(a,b) = a + b;
+julia> baz(a, b) = a + b;
 
-julia> args = [1,2]
+julia> args = [1, 2]
 2-element Vector{Int64}:
  1
  2
 
 julia> baz(args...)
 3
 
-julia> args = [1,2,3]
+julia> args = [1, 2, 3]
 3-element Vector{Int64}:
  1
  2
@@ -831,7 +831,7 @@ prior keyword arguments.
 The types of keyword arguments can be made explicit as follows:
 
 ```julia
-function f(;x::Int=1)
+function f(; x::Int=1)
     ###
 end
 ```
@@ -1077,13 +1077,13 @@ in advance by the library writer.
 
 More generally, `f.(args...)` is actually equivalent to `broadcast(f, args...)`, which allows
 you to operate on multiple arrays (even of different shapes), or a mix of arrays and scalars (see
-[Broadcasting](@ref)). For example, if you have `f(x,y) = 3x + 4y`, then `f.(pi,A)` will return
-a new array consisting of `f(pi,a)` for each `a` in `A`, and `f.(vector1,vector2)` will return
-a new vector consisting of `f(vector1[i],vector2[i])` for each index `i` (throwing an exception
+[Broadcasting](@ref)). For example, if you have `f(x, y) = 3x + 4y`, then `f.(pi, A)` will return
+a new array consisting of `f(pi,a)` for each `a` in `A`, and `f.(vector1, vector2)` will return
+a new vector consisting of `f(vector1[i], vector2[i])` for each index `i` (throwing an exception
 if the vectors have different length).
 
 ```jldoctest
-julia> f(x,y) = 3x + 4y;
+julia> f(x, y) = 3x + 4y;
 
 julia> A = [1.0, 2.0, 3.0];
 

doc/src/manual/mathematical-operations.md

@@ -22,7 +22,7 @@ are supported on all primitive numeric types:
 | `x ^ y`    | power          | raises `x` to the `y`th power           |
 | `x % y`    | remainder      | equivalent to `rem(x, y)`               |
 
-A numeric literal placed directly before an identifier or parentheses, e.g. `2x` or `2(x+y)`, is treated as a multiplication, except with higher precedence than other binary operations.  See [Numeric Literal Coefficients](@ref man-numeric-literal-coefficients) for details.
+A numeric literal placed directly before an identifier or parentheses, e.g. `2x` or `2(x + y)`, is treated as a multiplication, except with higher precedence than other binary operations.  See [Numeric Literal Coefficients](@ref man-numeric-literal-coefficients) for details.
 
 Julia's promotion system makes arithmetic operations on mixtures of argument types "just work"
 naturally and automatically. See [Conversion and Promotion](@ref conversion-and-promotion) for details of the promotion
@@ -204,9 +204,9 @@ as `a .= a .+ b`, where `.=` is a fused *in-place* assignment operation
 (see the [dot syntax documentation](@ref man-vectorized)).
 
 Note the dot syntax is also applicable to user-defined operators.
-For example, if you define `⊗(A,B) = kron(A,B)` to give a convenient
+For example, if you define `⊗(A, B) = kron(A, B)` to give a convenient
 infix syntax `A ⊗ B` for Kronecker products ([`kron`](@ref)), then
-`[A,B] .⊗ [C,D]` will compute `[A⊗C, B⊗D]` with no additional coding.
+`[A, B] .⊗ [C, D]` will compute `[A⊗C, B⊗D]` with no additional coding.
 
 Combining dot operators with numeric literals can be ambiguous.
 For example, it is not clear whether `1.+x` means `1. + x` or `1 .+ x`.
@@ -457,7 +457,7 @@ Juxtaposition parses like a unary operator, which has the same natural asymmetry
 Julia supports three forms of numerical conversion, which differ in their handling of inexact
 conversions.
 
-  * The notation `T(x)` or `convert(T,x)` converts `x` to a value of type `T`.
+  * The notation `T(x)` or `convert(T, x)` converts `x` to a value of type `T`.
 
       * If `T` is a floating-point type, the result is the nearest representable value, which could be
         positive or negative infinity.
@@ -534,7 +534,7 @@ See [Conversion and Promotion](@ref conversion-and-promotion) for how to define
 | [`mod1(x, y)`](@ref)       | `mod` with offset 1; returns `r∈(0, y]` for `y>0` or `r∈[y, 0)` for `y<0`, where `mod(r, y) == mod(x, y)` |
 | [`mod2pi(x)`](@ref)        | modulus with respect to 2pi;  `0 <= mod2pi(x) < 2pi`                                                      |
 | [`divrem(x, y)`](@ref)     | returns `(div(x, y),rem(x, y))`                                                                           |
-| [`fldmod(x, y)`](@ref)     | returns `(fld(x, y),mod(x, y ))`                                                                          |
+| [`fldmod(x, y)`](@ref)     | returns `(fld(x, y), mod(x, y))`                                                                          |
 | [`gcd(x, y...)`](@ref)     | greatest positive common divisor of `x`, `y`,...                                                          |
 | [`lcm(x, y...)`](@ref)     | least positive common multiple of `x`, `y`,...                                                            |
 
@@ -557,13 +557,13 @@ See [Conversion and Promotion](@ref conversion-and-promotion) for how to define
 | [`cbrt(x)`](@ref), `∛x`  | cube root of `x`                                                           |
 | [`hypot(x, y)`](@ref)    | hypotenuse of right-angled triangle with other sides of length `x` and `y` |
 | [`exp(x)`](@ref)         | natural exponential function at `x`                                        |
-| [`expm1(x)`](@ref)       | accurate `exp(x)-1` for `x` near zero                                      |
-| [`ldexp(x, n)`](@ref)    | `x*2^n` computed efficiently for integer values of `n`                     |
+| [`expm1(x)`](@ref)       | accurate `exp(x) - 1` for `x` near zero                                    |
+| [`ldexp(x, n)`](@ref)    | `x * 2^n` computed efficiently for integer values of `n`                   |
 | [`log(x)`](@ref)         | natural logarithm of `x`                                                   |
 | [`log(b, x)`](@ref)      | base `b` logarithm of `x`                                                  |
 | [`log2(x)`](@ref)        | base 2 logarithm of `x`                                                    |
 | [`log10(x)`](@ref)       | base 10 logarithm of `x`                                                   |
-| [`log1p(x)`](@ref)       | accurate `log(1+x)` for `x` near zero                                      |
+| [`log1p(x)`](@ref)       | accurate `log(1 + x)` for `x` near zero                                    |
 | [`exponent(x)`](@ref)    | binary exponent of `x`                                                     |
 | [`significand(x)`](@ref) | binary significand (a.k.a. mantissa) of a floating-point number `x`        |
 
@@ -587,7 +587,7 @@ These are all single-argument functions, with [`atan`](@ref) also accepting two
 corresponding to a traditional [`atan2`](https://en.wikipedia.org/wiki/Atan2) function.
 
 Additionally, [`sinpi(x)`](@ref) and [`cospi(x)`](@ref) are provided for more accurate computations
-of [`sin(pi*x)`](@ref) and [`cos(pi*x)`](@ref) respectively.
+of [`sin(pi * x)`](@ref) and [`cos(pi * x)`](@ref) respectively.
 
 In order to compute trigonometric functions with degrees instead of radians, suffix the function
 with `d`. For example, [`sind(x)`](@ref) computes the sine of `x` where `x` is specified in degrees.