@@ -34,6 +34,7 @@ import SwiftShims
3434/// ElementaryFunctions and FloatingPoint.
3535///
3636/// [elfn]: http://en.wikipedia.org/wiki/Elementary_function
37+ @available ( macOS 9999 , iOS 9999 , tvOS 9999 , watchOS 9999 , * )
3738public protocol ElementaryFunctions {
3839
3940% for func in ElementaryFunctions:
@@ -59,77 +60,12 @@ public protocol ElementaryFunctions {
5960 static func root( _ x: Self , _ n: Int ) -> Self
6061}
6162
62- /// A type that models the real numbers.
63- ///
64- /// Conformance to this protocol means that all the FloatingPoint operations
65- /// are available, as well as the ElementaryFunctions, plus the following
66- /// additional math functions: atan2, erf, erc, hypot, tgamma.
67- ///
68- /// logGamma and signGamma are also available on non-Windows platforms.
69- public protocol Real : ElementaryFunctions , FloatingPoint {
70- % for func in RealFunctions:
71-
72- ${ func . comment}
73- static func ${ func . decl( " Self " ) }
74- % end
75-
76- /// `atan(y/x)` with quadrant fixup.
77- ///
78- /// There is an infinite family of angles whose tangent is `y/x`. `atan2`
79- /// selects the representative that is the angle between the vector `(x, y)`
80- /// and the real axis in the range [-π, π].
81- static func atan2( y: Self , x: Self ) -> Self
82-
83- #if !os(Windows)
84- // lgamma is not available on Windows.
85- // TODO: provide an implementation of lgamma with the stdlib to support
86- // Windows so we can vend a uniform interface.
87-
88- /// `log(gamma(x))` computed without undue overflow.
89- ///
90- /// `log(abs(gamma(x)))` is returned. To get the sign of `gamma(x)` cheaply,
91- /// use `signGamma(x)`.
92- static func logGamma( _ x: Self) -> Self
93- #endif
94- }
95-
96- extension Real {
97- #if !os(Windows)
98- // lgamma is not available on Windows; no lgamma means signGamma
99- // is basically useless, so don't bother exposing it.
100-
101- /// The sign of `gamma(x)`.
102- ///
103- /// This function is typically used in conjunction with `logGamma(x)`, which
104- /// computes `log(abs(gamma(x)))`, to recover the sign information that is
105- /// lost to the absolute value.
106- ///
107- /// `gamma(x)` has a simple pole at each non-positive integer and an
108- /// essential singularity at infinity; we arbitrarily choose to return
109- /// `.plus` for the sign in those cases. For all other values, `signGamma(x)`
110- /// is `.plus` if `x >= 0` or `trunc(x)` is odd, and `.minus` otherwise.
111- @_alwaysEmitIntoClient
112- public static func signGamma( _ x: Self ) -> FloatingPointSign {
113- if x >= 0 { return . plus }
114- let trunc = x. rounded ( . towardZero)
115- // Treat poles as gamma(x) == +inf. This is arbitrary, but we need to
116- // pick one sign or the other.
117- if x == trunc { return . plus }
118- // Result is .minus if trunc is even, .plus otherwise. To figure out if
119- // trunc is even or odd, check if trunc/2 is an integer.
120- let halfTrunc = trunc/ 2
121- if halfTrunc == halfTrunc. rounded ( . towardZero) { return . minus }
122- return . plus
123- }
124- #endif
125- }
126-
12763% for type in all_floating_point_types( ) :
12864% if type. bits == 80 :
12965#if (arch(i386) || arch(x86_64)) && !os(Windows)
13066% end
13167% Self = type. stdlib_name
132- extension ${ Self} : Real {
68+ extension ${ Self} : ElementaryFunctions {
13369% for func in ElementaryFunctions + RealFunctions:
13470
13571 @_alwaysEmitIntoClient
@@ -172,9 +108,66 @@ extension ${Self}: Real {
172108 public static func logGamma( _ x: ${ Self} ) -> ${ Self} {
173109 return _swift_stdlib_lgamma ${ type. cFuncSuffix} ( x)
174110 }
111+
112+ @_alwaysEmitIntoClient
113+ public static func signGamma( _ x: ${ Self} ) -> FloatingPointSign {
114+ if x >= 0 { return . plus }
115+ let trunc = x. rounded ( . towardZero)
116+ if x == trunc { return . plus }
117+ let halfTrunc = trunc/ 2
118+ if halfTrunc == halfTrunc. rounded ( . towardZero) { return . minus }
119+ return . plus
120+ }
175121#endif
176122}
177123% if type. bits == 80 :
178124#endif
179125% end
180126% end
127+
128+ @available ( macOS 9999 , iOS 9999 , tvOS 9999 , watchOS 9999 , * )
129+ extension SIMD where Scalar: ElementaryFunctions {
130+ % for func in ElementaryFunctions:
131+
132+ @_alwaysEmitIntoClient
133+ public static func ${ func . decl( " Self " ) } {
134+ var r = Self ( )
135+ for i in r. indices {
136+ r [ i] = Scalar . ${ func . swiftName} ( ${ func . params( suffix= " [i] " ) } )
137+ }
138+ return r
139+ }
140+ % end
141+
142+ @_alwaysEmitIntoClient
143+ public static func pow( _ x: Self , _ y: Self ) -> Self {
144+ var r = Self ( )
145+ for i in r. indices {
146+ r [ i] = Scalar . pow ( x [ i] , y [ i] )
147+ }
148+ return r
149+ }
150+
151+ @_alwaysEmitIntoClient
152+ public static func pow( _ x: Self , _ n: Int ) -> Self {
153+ var r = Self ( )
154+ for i in r. indices {
155+ r [ i] = Scalar . pow ( x [ i] , n)
156+ }
157+ return r
158+ }
159+
160+ @_alwaysEmitIntoClient
161+ public static func root( _ x: Self , _ n: Int ) -> Self {
162+ var r = Self ( )
163+ for i in r. indices {
164+ r [ i] = Scalar . root ( x [ i] , n)
165+ }
166+ return r
167+ }
168+ }
169+
170+ % for n in [ 2 , 3 , 4 , 8 , 16 , 32 , 64 ] :
171+ @available ( macOS 9999 , iOS 9999 , tvOS 9999 , watchOS 9999 , * )
172+ extension SIMD ${ n} : ElementaryFunctions where Scalar: ElementaryFunctions { }
173+ % end
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