swift-mirror/stdlib/public/Darwin/simd/simd.swift.gyb

//===----------------------------------------------------------*- swift -*-===//
//
// This source file is part of the Swift.org open source project
//
// Copyright (c) 2014 - 2017 Apple Inc. and the Swift project authors
// Licensed under Apache License v2.0 with Runtime Library Exception
//
// See https://swift.org/LICENSE.txt for license information
// See https://swift.org/CONTRIBUTORS.txt for the list of Swift project authors
//
//===----------------------------------------------------------------------===//
// simd.h overlays for Swift
//===----------------------------------------------------------------------===//

import Swift
import Darwin
@_exported import simd

public extension SIMD {
  @available(swift, deprecated:5, renamed: "init(repeating:)")
  @_transparent
  init(_ scalar: Scalar) { self.init(repeating: scalar) }
}

internal extension SIMD2 {
  var _descriptionAsArray: String { return "[\(x), \(y)]" }
}

internal extension SIMD3 {
  var _descriptionAsArray: String { return "[\(x), \(y), \(z)]" }
}

internal extension SIMD4 {
  var _descriptionAsArray: String { return "[\(x), \(y), \(z), \(w)]" }
}

public extension SIMD where Scalar : FixedWidthInteger {
  @available(swift, deprecated:5, message: "use 0 &- rhs")
  @_transparent
  static prefix func -(rhs: Self) -> Self { return 0 &- rhs }
}

%{
component = ['x','y','z','w']
scalar_types = ['Float','Double','Int32','UInt32']
ctype = { 'Float':'float', 'Double':'double', 'Int32':'int', 'UInt32':'uint'}
floating_types = ['Float','Double']
}%

%for scalar in scalar_types:
% for count in [2, 3, 4]:
%  vectype = "SIMD" + str(count) + "<" + scalar + ">"
%  vecsize = (8 if scalar == 'Double' else 4) * (4 if count == 3 else count)
%  vecalign = (16 if vecsize > 16 else vecsize)
%  is_floating = scalar in floating_types
%  is_signed = scalar[0] != 'U'
%  wrap = "" if is_floating else "&"

@available(swift, deprecated: 5.1, message: "Use SIMD${count}<${scalar}>")
public typealias ${ctype[scalar]}${count} = ${vectype}

%  if is_signed:
/// Elementwise absolute value of a vector.  The result is a vector of the same
/// length with all elements positive.
@_transparent
public func abs(_ x: ${vectype}) -> ${vectype} {
  return simd_abs(x)
}
%  end

/// Elementwise minimum of two vectors.  Each component of the result is the
/// smaller of the corresponding component of the inputs.
@_transparent
public func min(_ x: ${vectype}, _ y: ${vectype}) -> ${vectype} {
  return simd_min(x, y)
}

/// Elementwise maximum of two vectors.  Each component of the result is the
/// larger of the corresponding component of the inputs.
@_transparent
public func max(_ x: ${vectype}, _ y: ${vectype}) -> ${vectype} {
  return simd_max(x, y)
}

/// Vector-scalar minimum.  Each component of the result is the minimum of the
/// corresponding element of the input vector and the scalar.
@_transparent
public func min(_ vector: ${vectype}, _ scalar: ${scalar}) -> ${vectype} {
  return min(vector, ${vectype}(repeating: scalar))
}

/// Vector-scalar maximum.  Each component of the result is the maximum of the
/// corresponding element of the input vector and the scalar.
@_transparent
public func max(_ vector: ${vectype}, _ scalar: ${scalar}) -> ${vectype} {
  return max(vector, ${vectype}(repeating: scalar))
}

/// Each component of the result is the corresponding element of `x` clamped to
/// the range formed by the corresponding elements of `min` and `max`.  Any
/// lanes of `x` that contain NaN will end up with the `min` value.
@_transparent
public func clamp(_ x: ${vectype}, min: ${vectype}, max: ${vectype})
  -> ${vectype} {
  return simd.min(simd.max(x, min), max)
}

/// Clamp each element of `x` to the range [`min`, max].  If any lane of `x` is
/// NaN, the corresponding lane of the result is `min`.
@_transparent
public func clamp(_ x: ${vectype}, min: ${scalar}, max: ${scalar})
  -> ${vectype} {
  return simd.min(simd.max(x, min), max)
}

/// Sum of the elements of the vector.
@_transparent
public func reduce_add(_ x: ${vectype}) -> ${scalar} {
  return simd_reduce_add(x)
}

/// Minimum element of the vector.
@_transparent
public func reduce_min(_ x: ${vectype}) -> ${scalar} {
  return simd_reduce_min(x)
}

/// Maximum element of the vector.
@_transparent
public func reduce_max(_ x: ${vectype}) -> ${scalar} {
  return simd_reduce_max(x)
}

%  if is_floating:

/// Sign of a vector.  Each lane contains -1 if the corresponding lane of `x`
/// is less than zero, +1 if the corresponding lane of `x` is greater than
/// zero, and 0 otherwise.
@_transparent
public func sign(_ x: ${vectype}) -> ${vectype} {
  return simd_sign(x)
}

/// Linear interpolation between `x` (at `t=0`) and `y` (at `t=1`).  May be
/// used with `t` outside of [0, 1] as well.
@_transparent
public func mix(_ x: ${vectype}, _ y: ${vectype}, t: ${vectype}) -> ${vectype} {
  return x + t*(y-x)
}

/// Linear interpolation between `x` (at `t=0`) and `y` (at `t=1`).  May be
/// used with `t` outside of [0, 1] as well.
@_transparent
public func mix(_ x: ${vectype}, _ y: ${vectype}, t: ${scalar}) -> ${vectype} {
  return x + t*(y-x)
}

/// Elementwise reciprocal.
@_transparent
public func recip(_ x: ${vectype}) -> ${vectype} {
  return simd_recip(x)
}

/// Elementwise reciprocal square root.
@_transparent
public func rsqrt(_ x: ${vectype}) -> ${vectype} {
  return simd_rsqrt(x)
}

/// Alternate name for minimum of two floating-point vectors.
@_transparent
public func fmin(_ x: ${vectype}, _ y: ${vectype}) -> ${vectype} {
  return min(x, y)
}

/// Alternate name for maximum of two floating-point vectors.
@_transparent
public func fmax(_ x: ${vectype}, _ y: ${vectype}) -> ${vectype} {
  return max(x, y)
}

/// Each element of the result is the smallest integral value greater than or
/// equal to the corresponding element of the input.
@_transparent
public func ceil(_ x: ${vectype}) -> ${vectype} {
  return __tg_ceil(x)
}

/// Each element of the result is the largest integral value less than or equal
/// to the corresponding element of the input.
@_transparent
public func floor(_ x: ${vectype}) -> ${vectype} {
  return __tg_floor(x)
}

/// Each element of the result is the closest integral value with magnitude
/// less than or equal to that of the corresponding element of the input.
@_transparent
public func trunc(_ x: ${vectype}) -> ${vectype} {
  return __tg_trunc(x)
}

/// `x - floor(x)`, clamped to lie in the range [0,1).  Without this clamp step,
/// the result would be 1.0 when `x` is a very small negative number, which may
/// result in out-of-bounds table accesses in common usage.
@_transparent
public func fract(_ x: ${vectype}) -> ${vectype} {
  return simd_fract(x)
}

/// 0.0 if `x < edge`, and 1.0 otherwise.
@_transparent
public func step(_ x: ${vectype}, edge: ${vectype}) -> ${vectype} {
  return simd_step(edge, x)
}

/// 0.0 if `x < edge0`, 1.0 if `x > edge1`, and cubic interpolation between
/// 0 and 1 in the interval [edge0, edge1].
@_transparent
public func smoothstep(_ x: ${vectype}, edge0: ${vectype}, edge1: ${vectype})
  -> ${vectype} {
  return simd_smoothstep(edge0, edge1, x)
}

/// Dot product of `x` and `y`.
@_transparent
public func dot(_ x: ${vectype}, _ y: ${vectype}) -> ${scalar} {
  return reduce_add(x * y)
}

/// Projection of `x` onto `y`.
@_transparent
public func project(_ x: ${vectype}, _ y: ${vectype}) -> ${vectype} {
  return simd_project(x, y)
}

/// Length of `x`, squared.  This is more efficient to compute than the length,
/// so you should use it if you only need to compare lengths to each other.
/// I.e. instead of writing:
///
///   if (length(x) < length(y)) { ... }
///
/// use:
///
///   if (length_squared(x) < length_squared(y)) { ... }
///
/// Doing it this way avoids one or two square roots, which is a fairly costly
/// operation.
@_transparent
public func length_squared(_ x: ${vectype}) -> ${scalar} {
  return dot(x, x)
}

/// Length (two-norm or "Euclidean norm") of `x`.
@_transparent
public func length(_ x: ${vectype}) -> ${scalar} {
  return sqrt(length_squared(x))
}

/// The one-norm (or "taxicab norm") of `x`.
@_transparent
public func norm_one(_ x: ${vectype}) -> ${scalar} {
  return reduce_add(abs(x))
}

/// The infinity-norm (or "sup norm") of `x`.
@_transparent
public func norm_inf(_ x: ${vectype}) -> ${scalar} {
  return reduce_max(abs(x))
}

/// Distance between `x` and `y`, squared.
@_transparent
public func distance_squared(_ x: ${vectype}, _ y: ${vectype}) -> ${scalar} {
  return length_squared(x - y)
}

/// Distance between `x` and `y`.
@_transparent
public func distance(_ x: ${vectype}, _ y: ${vectype}) -> ${scalar} {
  return length(x - y)
}

/// Unit vector pointing in the same direction as `x`.
@_transparent
public func normalize(_ x: ${vectype}) -> ${vectype} {
  return simd_normalize(x)
}

/// `x` reflected through the hyperplane with unit normal vector `n`, passing
/// through the origin.  E.g. if `x` is [1,2,3] and `n` is [0,0,1], the result
/// is [1,2,-3].
@_transparent
public func reflect(_ x: ${vectype}, n: ${vectype}) -> ${vectype} {
  return simd_reflect(x, n)
}

/// The refraction direction given unit incident vector `x`, unit surface
/// normal `n`, and index of refraction `eta`.  If the angle between the
/// incident vector and the surface is so small that total internal reflection
/// occurs, zero is returned.
@_transparent
public func refract(_ x: ${vectype}, n: ${vectype}, eta: ${scalar})
  -> ${vectype} {
  return simd_refract(x, n, eta)
}

%  end # if is_floating
% end # for count in [2, 3, 4]
% if is_floating:
//  Scalar versions of common operations:

/// Returns -1 if `x < 0`, +1 if `x > 0`, and 0 otherwise (`sign(NaN)` is 0).
@_transparent
public func sign(_ x: ${scalar}) -> ${scalar} {
  return simd_sign(x)
}

/// Reciprocal.
@_transparent
public func recip(_ x: ${scalar}) -> ${scalar} {
  return simd_recip(x)
}

/// Reciprocal square root.
@_transparent
public func rsqrt(_ x: ${scalar}) -> ${scalar} {
  return simd_rsqrt(x)
}

/// Returns 0.0 if `x < edge`, and 1.0 otherwise.
@_transparent
public func step(_ x: ${scalar}, edge: ${scalar}) -> ${scalar} {
  return simd_step(edge, x)
}

/// Interprets two two-dimensional vectors as three-dimensional vectors in the
/// xy-plane and computes their cross product, which lies along the z-axis.
@_transparent
public func cross(_ x: SIMD2<${scalar}>, _ y: SIMD2<${scalar}>) -> SIMD3<${scalar}> {
  return simd_cross(x,y)
}

/// Cross-product of two three-dimensional vectors.  The resulting vector is
/// perpendicular to the plane determined by `x` and `y`, with length equal to
/// the oriented area of the parallelogram they determine.
@_transparent
public func cross(_ x: SIMD3<${scalar}>, _ y: SIMD3<${scalar}>) -> SIMD3<${scalar}> {
  return simd_cross(x,y)
}

% end # is_floating
%end # for scalar in scalar_types

%for type in floating_types:
% for rows in [2,3,4]:
%  for cols in [2,3,4]:
%   mattype = 'simd_' + ctype[type] + str(cols) + 'x' + str(rows)
%   diagsize = rows if rows < cols else cols
%   coltype = "SIMD" + str(rows) + "<" + type + ">"
%   rowtype = "SIMD" + str(cols) + "<" + type + ">"
%   diagtype = "SIMD" + str(diagsize) + "<" + type + ">"
%   transtype = ctype[type] + str(rows) + 'x' + str(cols)

public typealias ${ctype[type]}${cols}x${rows} = ${mattype}

extension ${mattype} {

  /// Initialize matrix to have `scalar` on main diagonal, zeros elsewhere.
  public init(_ scalar: ${type}) {
    self.init(diagonal: ${diagtype}(repeating: scalar))
  }

  /// Initialize matrix to have specified `diagonal`, and zeros elsewhere.
  public init(diagonal: ${diagtype}) {
    self.init()
%   for i in range(diagsize):
    self.columns.${i}.${component[i]} = diagonal.${component[i]}
%   end
  }

  /// Initialize matrix to have specified `columns`.
  public init(_ columns: [${coltype}]) {
    precondition(columns.count == ${cols}, "Requires array of ${cols} vectors")
    self.init()
%   for i in range(cols):
    self.columns.${i} = columns[${i}]
%   end
  }

  /// Initialize matrix to have specified `rows`.
  public init(rows: [${rowtype}]) {
    precondition(rows.count == ${rows}, "Requires array of ${rows} vectors")
    self = ${transtype}(rows).transpose
  }

  /// Initialize matrix to have specified `columns`.
  public init(${', '.join(['_ col' + str(i) + ': ' + coltype
                          for i in range(cols)])}) {
    self.init()
%   for i in range(cols):
      self.columns.${i} = col${i}
%   end
  }

  /// Initialize matrix from corresponding C matrix type.
  @available(swift, deprecated: 4, message: "This conversion is no longer necessary; use `cmatrix` directly.")
  @_transparent
  public init(_ cmatrix: ${mattype}) {
    self = cmatrix
  }

  /// Get the matrix as the corresponding C matrix type.
  @available(swift, deprecated: 4, message: "This property is no longer needed; use the matrix itself.")
  @_transparent
  public var cmatrix: ${mattype} {
    return self
  }

  /// Access to individual columns.
  public subscript(column: Int) -> ${coltype} {
    get {
      switch(column) {
%   for i in range(cols):
      case ${i}: return columns.${i}
%   end
      default: preconditionFailure("Column index out of range")
      }
    }
    set (value) {
      switch(column) {
%   for i in range(cols):
      case ${i}: columns.${i} = value
%   end
      default: preconditionFailure("Column index out of range")
      }
    }
  }

  /// Access to individual elements.
  public subscript(column: Int, row: Int) -> ${type} {
    get { return self[column][row] }
    set (value) { self[column][row] = value }
  }
}

extension ${mattype} : CustomDebugStringConvertible {
  public var debugDescription: String {
    return "${mattype}([${', '.join(map(lambda i: \
                        '\(columns.' + str(i) + '._descriptionAsArray)',
                        range(cols)))}])"
  }
}

extension ${mattype} : Equatable {
  @_transparent
  public static func ==(lhs: ${mattype}, rhs: ${mattype}) -> Bool {
    return simd_equal(lhs, rhs)
  }
}

extension ${mattype} {

  /// Transpose of the matrix.
  @_transparent
  public var transpose: ${transtype} {
    return simd_transpose(self)
  }

%   if rows == cols:
  /// Inverse of the matrix if it exists, otherwise the contents of the
  /// resulting matrix are undefined.
  @available(macOS 10.10, iOS 8.0, tvOS 10.0, watchOS 3.0, *)
  @_transparent
  public var inverse: ${mattype} {
    return simd_inverse(self)
  }

  /// Determinant of the matrix.
  @_transparent
  public var determinant: ${type} {
    return simd_determinant(self)
  }
%   end

  /// Sum of two matrices.
  @_transparent
  public static func +(lhs: ${mattype}, rhs: ${mattype}) -> ${mattype} {
    return simd_add(lhs, rhs)
  }

  /// Negation of a matrix.
  @_transparent
  public static prefix func -(rhs: ${mattype}) -> ${mattype} {
    return ${mattype}() - rhs
  }

  /// Difference of two matrices.
  @_transparent
  public static func -(lhs: ${mattype}, rhs: ${mattype}) -> ${mattype} {
    return simd_sub(lhs, rhs)
  }

  @_transparent
  public static func +=(lhs: inout ${mattype}, rhs: ${mattype}) -> Void {
    lhs = lhs + rhs
  }

  @_transparent
  public static func -=(lhs: inout ${mattype}, rhs: ${mattype}) -> Void {
    lhs = lhs - rhs
  }

  /// Scalar-Matrix multiplication.
  @_transparent
  public static func *(lhs: ${type}, rhs: ${mattype}) -> ${mattype} {
    return simd_mul(lhs, rhs)
  }

  /// Matrix-Scalar multiplication.
  @_transparent
  public static func *(lhs: ${mattype}, rhs: ${type}) -> ${mattype} {
    return rhs*lhs
  }

  @_transparent
  public static func *=(lhs: inout ${mattype}, rhs: ${type}) -> Void {
    lhs = lhs*rhs
  }

  /// Matrix-Vector multiplication.  Keep in mind that matrix types are named
  /// `${type}NxM` where `N` is the number of *columns* and `M` is the number of
  /// *rows*, so we multiply a `${type}3x2 * ${type}3` to get a `${type}2`, for
  /// example.
  @_transparent
  public static func *(lhs: ${mattype}, rhs: ${rowtype}) -> ${coltype} {
    return simd_mul(lhs, rhs)
  }

  /// Vector-Matrix multiplication.
  @_transparent
  public static func *(lhs: ${coltype}, rhs: ${mattype}) -> ${rowtype} {
    return simd_mul(lhs, rhs)
  }

%   for k in [2,3,4]:
  /// Matrix multiplication (the "usual" matrix product, not the elementwise
  /// product).
%    restype = ctype[type] + str(k) + 'x' + str(rows)
%    rhstype = ctype[type] + str(k) + 'x' + str(cols)
  @_transparent
  public static func *(lhs: ${mattype}, rhs: ${rhstype}) -> ${restype} {
    return simd_mul(lhs, rhs)
  }

%   end # for k in [2,3,4]

%   rhstype = ctype[type] + str(cols) + 'x' + str(cols)
  /// Matrix multiplication (the "usual" matrix product, not the elementwise
  /// product).
  @_transparent
  public static func *=(lhs: inout ${mattype}, rhs: ${rhstype}) -> Void {
    lhs = lhs*rhs
  }
}

// Make old-style C free functions with the `matrix_` prefix available but
// deprecated in Swift 4.

%   if rows == cols:
@available(swift, deprecated: 4, renamed: "${mattype}(diagonal:)")
public func matrix_from_diagonal(_ d: ${diagtype}) -> ${mattype} {
  return ${mattype}(diagonal: d)
}

@available(swift, deprecated: 4, message: "Use the .inverse property instead.")
@available(macOS 10.10, iOS 8.0, tvOS 10.0, watchOS 3.0, *)
public func matrix_invert(_ x: ${mattype}) -> ${mattype} {
  return x.inverse
}

@available(swift, deprecated: 4, message: "Use the .determinant property instead.")
public func matrix_determinant(_ x: ${mattype}) -> ${type} {
  return x.determinant
}

%   end # rows == cols
@available(swift, deprecated: 4, renamed: "${mattype}")
public func matrix_from_columns(${', '.join(['_ col' + str(i) + ': ' + coltype
                                for i in range(cols)])}) -> ${mattype} {
  return ${mattype}(${', '.join(['col' + str(i) for i in range(cols)])})
}

public func matrix_from_rows(${', '.join(['_ row' + str(i) + ': ' + rowtype
                             for i in range(rows)])}) -> ${mattype} {
  return ${transtype}(${', '.join(['row' + str(i) for i in range(rows)])}).transpose
}

@available(swift, deprecated: 4, message: "Use the .transpose property instead.")
public func matrix_transpose(_ x: ${mattype}) -> ${transtype} {
  return x.transpose
}

@available(swift, deprecated: 4, renamed: "==")
public func matrix_equal(_ lhs: ${mattype}, _ rhs: ${mattype}) -> Bool {
  return lhs == rhs
}

%  end # for cols in [2,3,4]
% end # for rows in [2,3,4]
%end # for type in floating_types