This provides a Julia interface to some of the macOS Accelerate framework. At the moment, this package provides:

- Access to Accelerate BLAS and LAPACK using the libblastrampoline framework,
- An interface to the array-oriented functions, which provide a vectorised form for many common mathematical functions

The performance is significantly better than using standard libm functions in some cases, though there does appear to be some reduced accuracy.

MacOS 13.4 is required in order to run AppleAccelerate.jl, especially for the libblastrampoline forwarding. On older MacOS versions, your mileage may vary.

The following functions are supported:

*Rounding*:`ceil`

,`floor`

,`trunc`

,`round`

*Logarithmic*:`exp`

,`exp2`

,`expm1`

,`log`

,`log1p`

,`log2`

,`log10`

*Trigonometric*:`sin`

,`sinpi`

,`cos`

,`cospi`

,`tan`

,`tanpi`

,`asin`

,`acos`

,`atan`

,`atan2`

,`cis`

*Hyperbolic*:`sinh`

,`cosh`

,`tanh`

,`asinh`

,`acosh`

,`atanh`

*Convolution*:`conv`

,`xcorr`

*Other*:`sqrt`

,`copysign`

,`exponent`

,`abs`

,`rem`

Note there are some slight differences from behaviour in Base:

- No
`DomainError`

s are raised, instead`NaN`

values are returned. `round`

breaks ties (values with a fractional part of 0.5) by choosing the nearest even value.`exponent`

returns a floating point value of the same type (instead of an`Int`

).

Some additional functions that are also available:

`rec(x)`

: reciprocal (`1.0 ./ x`

)`rsqrt(x)`

: reciprocal square-root (`1.0 ./ sqrt(x)`

)`pow(x,y)`

: power (`x .^ y`

in Base)`fdiv(x,y)`

: divide (`x ./ y`

in Base)`sincos(x)`

: returns`(sin(x), cos(x))`

To use the Accelerate BLAS and LAPACK, simply load the library:

```
julia> peakflops(4096)
3.6024175318268243e11
julia> using AppleAccelerate
julia> peakflops(4096)
5.832806459434183e11
```

To avoid naming conflicts with Base, methods are not exported and so need to be accessed via the namespace:

```
using AppleAccelerate
using BenchmarkTools
X = randn(1_000_000);
@btime exp.($X); # standard libm function
@btime AppleAccelerate.exp($X); # Accelerate array-oriented function
```

The `@replaceBase`

macro replaces the relevant Base methods directly

```
@btime sin.($X); # standard libm function
AppleAccelerate.@replaceBase sin cos tan
@btime sin($X); # will use AppleAccelerate methods for vectorised operations
X = randn(1_000_000);
Y = fill(3.0, 1_000_000);
@btime $X .^ $Y;
AppleAccelerate.@replaceBase(^, /) # use parenthesised form for infix ops
@btime $X ^ $Y;
```

Output arrays can be specified as first arguments of the functions suffixed
with `!`

:

```
out = zeros(Float64, 1_000_000)
@btime AppleAccelerate.exp!($out, $X)
```

**Warning**: no dimension checks are performed on the `!`

functions, so ensure
your input and output arrays are of the same length.

Operations can be performed in-place by specifying the output array as the
input array (e.g. `AppleAccelerate.exp!(X,X)`

). This is not mentioned in the
Accelerate docs, but this comment by one of the authors indicates that it is safe.