# Surge

Surge is a Swift library that uses the Accelerate framework to provide high-performance functions for matrix math, digital signal processing, and image manipulation.

Accelerate exposes SIMD instructions available in modern CPUs to significantly improve performance of certain calculations. Because of its relative obscurity and inconvenient APIs, Accelerate is not commonly used by developers, which is a shame, since many applications could benefit from these performance optimizations.

**Surge aims to bring Accelerate to the mainstream, making it as easy (and nearly as fast, in most cases) to perform computation over a set of numbers as for a single member.**

Though, keep in mind: *Accelerate is not a silver bullet*. Under certain conditions, such as performing simple calculations over a small data set, Accelerate can be out-performed by conventional algorithms. Always benchmark to determine the performance characteristics of each potential approach.

Curious about the name

Surge? Back in the mid 90's, Apple, IBM, and Motorola teamed up to create AltiVec (a.k.a the Velocity Engine), which provided a SIMD instruction set for the PowerPC architecture. When Apple made the switch to Intel CPUs, AltiVec was ported to the x86 architecture and rechristened Accelerate. The derivative of Accelerate (and second derivative of Velocity) is known as either jerk, jolt, surge, or lurch, hence the name of this library.

## Performance

Initial benchmarks on iOS devices and the iOS simulator indicate significant performance improvements over a conventional Swift implementation.

```
import Surge
let numbers: [Double] = ...
var sum: Double = 0.0
// Naïve Swift Implementation
sum = reduce(numbers, 0.0, +)
// Surge Implementation
sum = Surge.sum(numbers)
```

*(Time in milliseconds, Optimization Level -Ofast)*

n |
Swift | Surge | Δ |
---|---|---|---|

100 | 0.269081 | 0.004453 | ~60x |

100000 | 251.037254 | 0.028687 | ~9000x |

100000000 | 239474.689326 | 57.009841 | ~4000x |

Surge's performance characteristics have not yet been thoroughly evaluated, though initial benchmarks show incredible promise. Further investigation is definitely warranted.

## Installation

*The infrastructure and best practices for distributing Swift libraries are currently in flux during this beta period of Swift & Xcode. In the meantime, you can add Surge as a git submodule, drag the Surge.xcodeproj file into your Xcode project, and add Surge.framework as a dependency for your target.*

## Inventory

Surge functions are named according to their corresponding "Math.h" functions, where applicable (omitting

`f`

and`d`

affixes, since type information is communicated and enforced by the language's type system).

### Arithmetic

`sum`

`asum`

`max`

`min`

`mean`

`meamg`

`measq`

`add`

`sub`

`mul`

`div`

`mod`

`remainder`

`sqrt`

### Auxilliary

`abs`

`ceil`

`copysign`

`floor`

`rec`

`round`

`trunc`

### Convolution

`conv`

`xcorr`

### Exponential

`exp`

`exp2`

`log`

`log2`

`log10`

`logb`

### FFT

`fft`

### Hyperbolic

`sinh`

`cosh`

`tanh`

`asinh`

`acosh`

`atanh`

### Matrix

`add`

`mul`

`inv`

`transpose`

### Power

`pow`

### Trigonometric

`sincos`

`sin`

`cos`

`tan`

`asin`

`acos`

`atan`

`rad2deg`

`deg2rad`

## Usage

`[Double]`

Computing Sum of ```
import Surge
let n = [1.0, 2.0, 3.0, 4.0, 5.0]
let sum = Surge.sum(n) // 15.0
```

`[Double]`

s

Computing Product of Two ```
import Surge
let a = [1.0, 3.0, 5.0, 7.0]
let b = [2.0, 4.0, 6.0, 8.0]
let product = Surge.mul(a, b) // [2.0, 12.0, 30.0, 56.0]
```

## License

Surge is available under the MIT license. See the LICENSE file for more info.