minimal inlining of x^Val{p} for p=0,1,2,3 and x::Number (#20648)

NEWS.md

@@ -76,6 +76,8 @@ Language changes
  * Experimental feature: `x^n` for integer literals `n` (e.g. `x^3`
  or `x^-3`) is now lowered to `x^Val{n}`, to enable compile-time
  specialization for literal integer exponents ([#20530]).
+ `x^p` for `x::Number` and a literal `p=0,1,2,3` is now lowered to
+ `one(x)`, `x`, `x*x`, and `x*x*x`, respectively ([#20648]).
 
 Breaking changes
 ----------------

base/gmp.jl

@@ -443,6 +443,9 @@ end
 ^(x::Integer, y::BigInt ) = bigint_pow(BigInt(x), y)
 ^(x::Bool , y::BigInt ) = Base.power_by_squaring(x, y)
 
+# override default inlining of x^2 and x^3 etc.
+^{p}(x::BigInt, ::Type{Val{p}}) = x^Culong(p)
+
 function powermod(x::BigInt, p::BigInt, m::BigInt)
  r = BigInt()
  ccall((:__gmpz_powm, :libgmp), Void,

base/intfuncs.jl

@@ -197,8 +197,18 @@ end
 
 # x^p for any literal integer p is lowered to x^Val{p},
 # to enable compile-time optimizations specialized to p.
-# However, we still need a fallback that calls the general ^:
-^{p}(x, ::Type{Val{p}}) = x^p
+# However, we still need a fallback that calls the general ^.
+# To avoid ambiguities for methods that dispatch on the
+# first argument, we dispatch the fallback via internal_pow:
+^(x, p) = internal_pow(x, p)
+internal_pow{p}(x, ::Type{Val{p}}) = x^p
+
+# inference.jl has complicated logic to inline x^2 and x^3 for
+# numeric types. In terms of Val we can do it much more simply:
+internal_pow(x::Number, ::Type{Val{0}}) = one(x)
+internal_pow(x::Number, ::Type{Val{1}}) = x
+internal_pow(x::Number, ::Type{Val{2}}) = x*x
+internal_pow(x::Number, ::Type{Val{3}}) = x*x*x
 
 # b^p mod m
 

base/irrationals.jl

@@ -212,6 +212,7 @@ catalan
 for T in (Irrational, Rational, Integer, Number)
  ^(::Irrational{:e}, x::T) = exp(x)
 end
+^{p}(::Irrational{:e}, ::Type{Val{p}}) = exp(p)
 
 log(::Irrational{:e}) = 1 # use 1 to correctly promote expressions like log(x)/log(e)
 log(::Irrational{:e}, x::Number) = log(x)

base/math.jl

@@ -676,6 +676,7 @@ end
 ^(x::Float32, y::Integer) = x^Int32(y)
 ^(x::Float32, y::Int32) = powi_llvm(x, y)
 ^(x::Float16, y::Integer) = Float16(Float32(x)^y)
+^{p}(x::Float16, ::Type{Val{p}}) = Float16(Float32(x)^Val{p})
 
 function angle_restrict_symm(theta)
  const P1 = 4 * 7.8539812564849853515625e-01

base/mpfr.jl

@@ -504,6 +504,9 @@ end
 ^(x::BigFloat, y::Integer) = typemin(Clong) <= y <= typemax(Clong) ? x^Clong(y) : x^BigInt(y)
 ^(x::BigFloat, y::Unsigned) = typemin(Culong) <= y <= typemax(Culong) ? x^Culong(y) : x^BigInt(y)
 
+# override default inlining of x^2 etc.
+^{p}(x::BigFloat, ::Type{Val{p}}) = x^Culong(p)
+
 for f in (:exp, :exp2, :exp10, :expm1, :cosh, :sinh, :tanh, :sech, :csch, :coth, :cbrt)
  @eval function $f(x::BigFloat)
  z = BigFloat()