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doc: add spaces after commas in some function calls (#50478)
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@navidcy
navidcy authored Jul 10, 2023
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56 changes: 28 additions & 28 deletions doc/src/manual/mathematical-operations.md
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Expand Up @@ -20,7 +20,7 @@ are supported on all primitive numeric types:
| `x ÷ y` | integer divide | x / y, truncated to an integer |
| `x \ y` | inverse divide | equivalent to `y / x` |
| `x ^ y` | power | raises `x` to the `y`th power |
| `x % y` | remainder | equivalent to `rem(x,y)` |
| `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.

Expand Down Expand Up @@ -171,15 +171,15 @@ The updating versions of all the binary arithmetic and bitwise operators are:
For *every* binary operation like `^`, there is a corresponding
"dot" operation `.^` that is *automatically* defined
to perform `^` element-by-element on arrays. For example,
`[1,2,3] ^ 3` is not defined, since there is no standard
`[1, 2, 3] ^ 3` is not defined, since there is no standard
mathematical meaning to "cubing" a (non-square) array, but
`[1,2,3] .^ 3` is defined as computing the elementwise
`[1, 2, 3] .^ 3` is defined as computing the elementwise
(or "vectorized") result `[1^3, 2^3, 3^3]`. Similarly for unary
operators like `!` or `√`, there is a corresponding `.√` that
applies the operator elementwise.

```jldoctest
julia> [1,2,3] .^ 3
julia> [1, 2, 3] .^ 3
3-element Vector{Int64}:
1
8
Expand Down Expand Up @@ -524,43 +524,43 @@ See [Conversion and Promotion](@ref conversion-and-promotion) for how to define

### Division functions

| Function | Description |
|:------------------------- |:--------------------------------------------------------------------------------------------------------- |
| [`div(x,y)`](@ref), `x÷y` | truncated division; quotient rounded towards zero |
| [`fld(x,y)`](@ref) | floored division; quotient rounded towards `-Inf` |
| [`cld(x,y)`](@ref) | ceiling division; quotient rounded towards `+Inf` |
| [`rem(x,y)`](@ref), `x%y` | remainder; satisfies `x == div(x,y)*y + rem(x,y)`; sign matches `x` |
| [`mod(x,y)`](@ref) | modulus; satisfies `x == fld(x,y)*y + mod(x,y)`; sign matches `y` |
| [`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))` |
| [`gcd(x,y...)`](@ref) | greatest positive common divisor of `x`, `y`,... |
| [`lcm(x,y...)`](@ref) | least positive common multiple of `x`, `y`,... |
| Function | Description |
|:-------------------------- |:--------------------------------------------------------------------------------------------------------- |
| [`div(x, y)`](@ref), `x÷y` | truncated division; quotient rounded towards zero |
| [`fld(x, y)`](@ref) | floored division; quotient rounded towards `-Inf` |
| [`cld(x, y)`](@ref) | ceiling division; quotient rounded towards `+Inf` |
| [`rem(x, y)`](@ref), `x%y` | remainder; satisfies `x == div(x, y)*y + rem(x, y)`; sign matches `x` |
| [`mod(x, y)`](@ref) | modulus; satisfies `x == fld(x, y)*y + mod(x, y)`; sign matches `y` |
| [`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 ))` |
| [`gcd(x, y...)`](@ref) | greatest positive common divisor of `x`, `y`,... |
| [`lcm(x, y...)`](@ref) | least positive common multiple of `x`, `y`,... |

### Sign and absolute value functions

| Function | Description |
|:----------------------- |:---------------------------------------------------------- |
| [`abs(x)`](@ref) | a positive value with the magnitude of `x` |
| [`abs2(x)`](@ref) | the squared magnitude of `x` |
| [`sign(x)`](@ref) | indicates the sign of `x`, returning -1, 0, or +1 |
| [`signbit(x)`](@ref) | indicates whether the sign bit is on (true) or off (false) |
| [`copysign(x,y)`](@ref) | a value with the magnitude of `x` and the sign of `y` |
| [`flipsign(x,y)`](@ref) | a value with the magnitude of `x` and the sign of `x*y` |
| Function | Description |
|:------------------------ |:---------------------------------------------------------- |
| [`abs(x)`](@ref) | a positive value with the magnitude of `x` |
| [`abs2(x)`](@ref) | the squared magnitude of `x` |
| [`sign(x)`](@ref) | indicates the sign of `x`, returning -1, 0, or +1 |
| [`signbit(x)`](@ref) | indicates whether the sign bit is on (true) or off (false) |
| [`copysign(x, y)`](@ref) | a value with the magnitude of `x` and the sign of `y` |
| [`flipsign(x, y)`](@ref) | a value with the magnitude of `x` and the sign of `x*y` |

### Powers, logs and roots

| Function | Description |
|:------------------------ |:-------------------------------------------------------------------------- |
| [`sqrt(x)`](@ref), `√x` | square root of `x` |
| [`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` |
| [`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` |
| [`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` |
| [`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 |
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