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SIMD additions

Introduction

Early adopters of SIMD types and protocols have encountered a few missing things as they've started to write more code that uses them. In addition, there are some features we punted out of the original review because we were up against a hard time deadline to which we would like to give further consideration.

This is a bit of a grab bag of SIMD features, so I'm deviating from the usual proposal structure. Each new addition has its own motivation, proposed solution, and alternatives considered section.

Table of Contents

  1. Static scalarCount
  2. Extending Vectors
  3. Swizzling
  4. Reductions
  5. Lanewise min, max, and clamp
  6. .one
  7. any and all

Static scalarCount

Motivation

In functions that construct new SIMD vectors, especially initializers, one frequently wants to perform some validation involving scalarCount before doing the work to create the vector. Currently, scalarCount is defined as an instance property (following the pattern of count on collection).

However, all SIMD vectors of a given type have the same scalarCount, so semantically it makes sense to have available as a static property as well. There's precedent for having this duplication in the .bitWidth property on fixed-width integers.

Detailed Design

extension SIMDStorage {
  /// The number of scalars, or elements, in a vector of this type.
  public static var scalarCount: Int {
    return Self().scalarCount
  }
}

The property is defined as an extension on SIMDStorage because it makes semantic sense there (SIMD refines SIMDStorage). It is defined in terms of the existing member property (instead of the apparently more-logical vise-versa) because that way it automatically works for all existing SIMD types with no changes. In practice this introduces no extra overhead at runtime.

Alternatives Considered

Not doing anything. Users can always fall back on the weird-but-effective Self().scalarCount.

Extending vectors

Motivation

When working with homogeneous coordinates in graphics, the last component frequently needs to be treated separately--this means that you frequently want to extract the first (n-1) components, do arithmetic on them and the final component separately, and then re-assemble them. At API boundaries, you frequently take in (n-1) component vectors, immediately extend them to perform math, and then return out only the first (n-1) components.

Detailed design

In order to support extending vectors from (n-1) to n components, add the following two initializers:

extension SIMD3 {
  public init(_ xy: SIMD2<Scalar>, _ z: Scalar) {
    self.init(xy.x, xy.y, z)
  }
}

extension SIMD4 {
  public init(_ xyz: SIMD3<Scalar>, _ w: Scalar) {
    self.init(xyz.x, xyz.y, xyz.z, w)
  }
}

Alternatives Considered

These could alternatively be spelled like xy.appending(z); there are two reasons that I'm avoiding that:

  • I would expect appending( ) to return the same type; but the result type is different.
  • I would expect appending( ) to be available on all SIMD types, but it breaks down beyond SIMD4, because there is no SIMD5 in the standard library.

We could have also used an explicit parameter label.

let v = SIMD3(...)
let x = SIMD4(v, 1)            // proposed above
let y = SIMD4(v, appending: 1) // with parameter label

My feeling is that the behavior is clear without the label, but it's very reasonable to argue for an explicit label instead.

Swizzling

Motivation

In C-family languages, clang defines "vector swizzles" (aka permutes, aka shuffles, ... ) that let you select and re-arrange elements from a vector:

#import <simd/simd.h>
simd_float4 x = { 1, 2, 3, 4};
x.zyx; // (simd_float3){3, 2, 1};

This comes from an identical feature in graphics shader-languages, where it is very heavily used.

Detailed design

For Swift, we want to restrict the feature somewhat, but also make it more powerful. In shader languages and clang extensions, you can even use swizzled vectors as lvalues, so long as the same element does not appear twice. I proposed to define general permutes as get-only subscripts. By restricting them from appearing as setters, we gain the flexibility to not require they be compile-time constants:

extension SIMD {
  /// Extracts the scalars at specified indices to form a SIMD2.
	///
	/// The elements of the index vector are wrapped modulo the count of elements
	/// in this vector. Because of this, the index is always in-range and no trap
	/// can occur.
  public subscript<Index>(index: SIMD2<Index>) -> SIMD2<Scalar>
  where Index: FixedWidthInteger {
    var result = SIMD2<Scalar>()
    for i in result.indices {
      result[i] = self[Int(index[i]) % scalarCount]
    }
    return result
  }
}

let v = SIMD4<Float>(1,2,3,4)
let xyz = SIMD3(2,1,0)
let w = v[xyz] // SIMD3<Float>(3,2,1)

Alternatives Considered

  1. We might want an explicit label on this subscript, but as with the extending inits, I believe that its use is generally clear enough in context.

  2. The main question is "what should the behavior for out-of-range indices be?" The definition I have chosen here is simple to explain and maps efficiently to the hardware, but there are at least two other good options: it could be a precondition failure, or it could fill the vector with zero in lanes that have out of range indices. The first option (trapping) is undesirable because it's less efficient with dynamic indices. The second would be slightly more efficient on some architectures, but is also significantly more magic. I believe that the proposed alternative has the best balance of explainable behavior and efficiency.

Reductions (or "Horizontal Operations")

Motivation

Generally in SIMD programming you try to avoid horizontal operations as much as possible, but frequently you need to do a few of them at the end of a chain of computations. For example, if you're summing an array, you would sum into a bank of vector accumulators first, then sum those down to a single vector. Now you need to get from that vector to a scalar by summing the elements. This is where reductions enter.

sum is also a basic building block for things like the dot product (and hence matrix multiplication), so it's very valuable to have an efficient implementation provided by the standard library. Similarly you want to have min and max to handle things like rescaling for computational geometry.

Detailed design

extension SIMD where Scalar: Comparable {
  /// The least element in the vector.
  public func min() -> Scalar

  /// The greatest element in the vector.
  public func max() -> Scalar
}
 
extension SIMD where Scalar: FixedWidthInteger { 
  /// Returns the sum of the scalars in the vector, computed with
  /// wrapping addition.
  ///
  /// Equivalent to indices.reduce(into: 0) { $0 &+= self[$1] }.
  public func wrappedSum() -> Scalar
}

extension SIMD where Scalar: FloatingPoint {
  /// Returns the sum of the scalars in the vector.
  public func sum() -> Scalar
}

Alternatives Considered

We could call the integer operation sum as well, but it seems better to reserve that name for the trapping operation in case we ever want to add it (just like we use &+ for integer addition on vectors, even though there is no +). We may want to define a floating-point sum with relaxed semantics for accumulation ordering at some point in the future (I plan to define sum as the binary tree sum here--that's the best tradeoff between reproducibility and performance).

I dropped indexOfMinValue and indexOfMaxValue from this proposal for two reasons:

  • there's some disagreement about whether or not they're important enough to include
  • it's not clear what we should name them; If they're sufficiently important, we probably want to have them on Collection some day, too, so the bar for the naming pattern that we establish is somewhat higher.

any and all

Motivation

any and all are special reductions that operate on boolean vectors (SIMDMask). They return true if and only if any (or all) lanes of the boolean vector are true. These are used to do things like branch around edge-case fixup:

if any(x .< 0) { // handle negative x }

Detailed design

any and all are free functions:

public func any<Storage>(_ mask: SIMDMask<Storage>) -> Bool {
  return mask._storage.min() < 0
}

public func all<Storage>(_ mask: SIMDMask<Storage>) -> Bool {
  return mask._storage.max() < 0
}

Alternatives Considered

Why are any and all free functions while max and min and sum are member properties? Because of readability in their typical use sites. min, max, and sum are frequently applied to a named value:

let accumulator = /* do some work */
return accumulator.sum

any and all are most often used with nameless comparison results:

if any(x .< minValue .| x .> maxValue) {
  // handle special cases
}

To my mind, this would read significantly less clearly as

if (x .< minValue .| x .> maxValue).any` {

or

if (x .< minValue .| x .> maxValue).anyIsTrue` {

because there's no "noun" that the property applies to. There was a proposal in the fall to make them static functions on Bool so that one could write

if .any(x .< minValue) {
}

but I'm not convinced that's actually better than a free function.

min, max, and clamp

Motivation

We have lanewise arithmetic on SIMD types, but we don't have lanewise min and max. We're also missing clamp to restrict values to a specified range.

Detailed design

extension SIMD where Scalar: Comparable {
  /// Replace any values less than lowerBound with lowerBound, and any
  /// values greater than upperBound with upperBound.
  ///
  /// For floating-point vectors, `.nan` is replaced with `lowerBound`.
  public mutating func clamp(lowerBound: Self, upperBound: Self) {
    self = self.clamped(lowerBound: lowerBound, upperBound: upperBound)
  }
  
  /// The vector formed by replacing any values less than lowerBound
  /// with lowerBound, and any values greater than upperBound with
  /// upperBound.
  ///
  /// For floating-point vectors, `.nan` is replaced with `lowerBound`.
  public func clamped(lowerBound: Self, upperBound: Self) -> Self {
    return Self.min(upperBound, Self.max(lowerBound, self))
  }
}

/// The lanewise minimum of two vectors.
///
/// Each element of the result is the minimum of the corresponding
/// elements of the inputs.
public func min<V>(_ lhs: V, _ rhs: V) -> V where V: SIMD, V.Scalar: Comparable

/// The lanewise maximum of two vectors.
///
/// Each element of the result is the maximum of the corresponding
/// elements of the inputs.
public func max<V>(_ lhs: V, _ rhs: V) -> V where V: SIMD, V.Scalar: Comparable

Alternatives Considered

These could be spelled out lanewiseMaximum or similar, to clarify that they operate lanewise (Chris suggested this in the pitch thread), but we don't spell out + as "lanewise-plus", so it seems weird to do it here. The default assumption is that SIMD operations are lanewise.

.one

Motivation

SIMD types cannot be ExpressibleByIntegerLiteral (it results in type system ambiguity for common expressions). We already have .zero, so adding .one makes sense as a convenience.

Detailed design

extension SIMD where Scalar: ExpressibleByIntegerLiteral {
  public static var one: Self {
    return Self(repeating: 1)
  }
}

Alternatives Considered

  • Do nothing. We don't need this, but it has turned out to be a useful convenience.
  • Why stop at one? Why not two? Because that way lies madness.

Source compatibility

These are all purely additive changes with no effect on source stability.

Effect on ABI stability

These are all purely additive changes with no effect on source stability.

Effect on API resilience

These are all purely additive changes with no effect on source stability.

Alternatives Considered

The pitch for this proposal included some operations for loading and storing from a collection. As Jordan pointed out in the pitch thread, we already have an init from Sequence, which together with slices makes the load mostly irrelevant. The store operation did not have satisfactory naming, and I would like to come up with a better pattern for these that handles iterating over a sequence of SIMD vectors loaded from a collection of scalars and storing them out as a single pattern, rather than building it up one piece at a time.

Implementation Notes

Due to a desire to avoid collision between the min(u, v) (pointwise minimum on SIMD vectors) and min(u, v) (minimum defined on Comparable, if a user adds a retroactive conformance), the core team decided to rename the SIMD operations to pointwiseMin(u, v) and pointwiseMax(u, v).

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