digamma is type-unstable in Julia master

[giordano]

In Julia 0.7:

julia> Base.Test.@inferred digamma(3.0)
ERROR: return type Float64 does not match inferred return type Any
Stacktrace:
 [1] error(::String) at ./error.jl:28

julia> Base.Test.@inferred digamma(complex(3.0))
0.9227843350984687 + 0.0im

julia> @code_warntype digamma(3.0)
Variables:
  #self#::SpecialFunctions.#digamma
  z@_2::Float64
  x@_3::Float64
  n::Int64
  t::Float64
  ψ::Any
  x@_7::Any
  y::Any
  r::Any
  s::Any
  a6::Any
  a5::Any
  a4::Any
  a3::Any
  a2::Any
  a1::Any
  a0::Any
  tt::Float64
  #temp#@_19::Int64
  ν::Int64
  z@_21::Float64
  #temp#@_22::Any
  fy@_23::Float64
  #temp#@_24::Float64
  fy@_25::Float64
  #temp#@_26::Bool
  #temp#@_27::Int64
  #temp#@_28::Float64

Body:
  begin
      z@_21::Float64 = z@_2::Float64
      NewvarNode(:(n::Int64))
      NewvarNode(:(t::Float64))
      NewvarNode(:(ψ::Any))
      x@_3::Float64 = z@_21::Float64
      #= line 26 =#
      $(Expr(:inbounds, false))
      # meta: location float.jl <= 497
      fy@_23::Float64 = (Base.sitofp)(Float64, 0)::Float64
      # meta: pop location
      $(Expr(:inbounds, :pop))
      unless (Base.or_int)((Base.lt_float)(x@_3::Float64, fy@_23::Float64)::Bool, (Base.and_int)((Base.and_int)((Base.eq_float)(x@_3::Float64, fy@_23::Float64)::Bool, (Base.lt_float)(fy@_23::Float64, 9.223372036854776e18)::Bool)::Bool, (Base.sle_int)((Base.fptosi)(Int64, fy@_23::Float64)::Int64, 0)::Bool)::Bool)::Bool goto 35
      #= line 27 =#
      $(Expr(:inbounds, false))
      # meta: location special/trig.jl cot 324
      # meta: location math.jl tan 442
      SSAValue(8) = $(Expr(:foreigncall, ("tan", "libopenlibm"), Float64, svec(Float64), :(:ccall), 1, :((Base.mul_float)(3.141592653589793, z@_21)::Float64)))
      # meta: location math.jl nan_dom_err 323
      unless (Base.and_int)((Base.ne_float)(SSAValue(8), SSAValue(8))::Bool, (Base.not_int)((Base.ne_float)((Base.mul_float)(3.141592653589793, z@_21::Float64)::Float64, (Base.mul_float)(3.141592653589793, z@_21::Float64)::Float64)::Bool)::Bool)::Bool goto 22
      #temp#@_24::Float64 = (Base.Math.throw)($(Expr(:invoke, MethodInstance for DomainError(::Any, ::Any), :(Base.Math.DomainError), :((Base.mul_float)(3.141592653589793, z@_21)::Float64), "NaN result for non-NaN input."))::DomainError)::Union{}
      goto 24
      22: 
      #temp#@_24::Float64 = SSAValue(8)
      24: 
      # meta: pop location
      # meta: pop location
      # meta: pop location
      $(Expr(:inbounds, :pop))
      ψ::Any = (Base.mul_float)((Base.neg_float)(3.141592653589793)::Float64, (Base.div_float)((Base.sitofp)(Float64, 1)::Float64, #temp#@_24::Float64)::Float64)::Float64
      #= line 28 =#
      z@_21::Float64 = (Base.sub_float)((Base.sitofp)(Float64, 1)::Float64, z@_21::Float64)::Float64
      #= line 29 =#
      x@_3::Float64 = z@_21::Float64
      goto 38
      35: 
      #= line 31 =#
      ψ::Any = (Base.sitofp)(Float64, 0)::Float64
      38: 
      #= line 33 =#
      $(Expr(:inbounds, false))
      # meta: location float.jl < 493
      fy@_25::Float64 = (Base.sitofp)(Float64, 7)::Float64
      # meta: pop location
      $(Expr(:inbounds, :pop))
      unless (Base.or_int)((Base.lt_float)(x@_3::Float64, fy@_25::Float64)::Bool, (Base.and_int)((Base.and_int)((Base.eq_float)(x@_3::Float64, fy@_25::Float64)::Bool, (Base.lt_float)(fy@_25::Float64, 9.223372036854776e18)::Bool)::Bool, (Base.slt_int)((Base.fptosi)(Int64, fy@_25::Float64)::Int64, 7)::Bool)::Bool)::Bool goto 90
      #= line 35 =#
      $(Expr(:inbounds, false))
      # meta: location float.jl floor 334
      # meta: location float.jl trunc 671
      unless (Base.le_float)(-9.223372036854776e18, (Base.floor_llvm)(x@_3::Float64)::Float64)::Bool goto 53
      #temp#@_26::Bool = (Base.lt_float)((Base.floor_llvm)(x@_3::Float64)::Float64, 9.223372036854776e18)::Bool
      goto 55
      53: 
      #temp#@_26::Bool = false
      55: 
      unless #temp#@_26::Bool goto 60
      #= line 672 =#
      #temp#@_27::Int64 = (Base.fptosi)(Int64, (Base.floor_llvm)(x@_3::Float64)::Float64)::Int64
      goto 63
      60: 
      #= line 674 =#
      #temp#@_27::Int64 = (Base.throw)($(Expr(:invoke, MethodInstance for InexactError(::Symbol, ::Any, ::Any), :(Base.InexactError), :(:trunc), Int64, :((Base.floor_llvm)(x@_3)::Float64)))::InexactError)::Union{}
      63: 
      # meta: pop location
      # meta: pop location
      $(Expr(:inbounds, :pop))
      n::Int64 = (Base.sub_int)(7, #temp#@_27::Int64)::Int64
      #= line 36 =#
      $(Expr(:inbounds, false))
      # meta: location range.jl colon 5
      # meta: pop location
      $(Expr(:inbounds, :pop))
      SSAValue(11) = (Base.select_value)((Base.sle_int)(1, (Base.sub_int)(n::Int64, 1)::Int64)::Bool, (Base.sub_int)(n::Int64, 1)::Int64, (Base.sub_int)(1, 1)::Int64)::Int64
      #temp#@_19::Int64 = 1
      75: 
      unless (Base.not_int)((#temp#@_19::Int64 === (Base.add_int)(SSAValue(11), 1)::Int64)::Bool)::Bool goto 85
      SSAValue(12) = #temp#@_19::Int64
      SSAValue(13) = (Base.add_int)(#temp#@_19::Int64, 1)::Int64
      ν::Int64 = SSAValue(12)
      #temp#@_19::Int64 = SSAValue(13)
      #= line 37 =#
      ψ::Any = (Base.sub_float)(ψ::Float64, (Base.div_float)((Base.sitofp)(Float64, 1)::Float64, (Base.add_float)(z@_21::Float64, (Base.sitofp)(Float64, ν::Int64)::Float64)::Float64)::Float64)::Float64
      83: 
      goto 75
      85: 
      #= line 39 =#
      ψ::Any = (Base.sub_float)(ψ::Float64, (Base.div_float)((Base.sitofp)(Float64, 1)::Float64, z@_21::Float64)::Float64)::Float64
      #= line 40 =#
      z@_21::Float64 = (Base.add_float)(z@_21::Float64, (Base.sitofp)(Float64, n::Int64)::Float64)::Float64
      90: 
      #= line 42 =#
      t::Float64 = (Base.div_float)((Base.sitofp)(Float64, 1)::Float64, z@_21::Float64)::Float64
      #= line 43 =#
      $(Expr(:inbounds, false))
      # meta: location math.jl log 442
      SSAValue(10) = $(Expr(:foreigncall, ("log", "libopenlibm"), Float64, svec(Float64), :(:ccall), 1, :(z@_21)))
      # meta: location math.jl nan_dom_err 323
      unless (Base.and_int)((Base.ne_float)(SSAValue(10), SSAValue(10))::Bool, (Base.not_int)((Base.ne_float)(z@_21::Float64, z@_21::Float64)::Bool)::Bool)::Bool goto 101
      #temp#@_28::Float64 = (Base.Math.throw)($(Expr(:invoke, MethodInstance for DomainError(::Any, ::Any), :(Base.Math.DomainError), :(z@_21), "NaN result for non-NaN input."))::DomainError)::Union{}
      goto 103
      101: 
      #temp#@_28::Float64 = SSAValue(10)
      103: 
      # meta: pop location
      # meta: pop location
      $(Expr(:inbounds, :pop))
      ψ::Any = (Base.add_float)(ψ::Float64, (Base.sub_float)(#temp#@_28::Float64, (Base.mul_float)(0.5, t::Float64)::Float64)::Float64)::Float64
      #= line 44 =#
      t::Float64 = (Base.mul_float)(t::Float64, t::Float64)::Float64
      #= line 46 =#
      SSAValue(2) = ψ::Float64
      SSAValue(3) = t::Float64
      tt::Float64 = t::Float64
      # meta: location math.jl
      #= line 139 =#
      goto 117
      117: 
      Base.Math.t = tt::Float64
      #temp#@_22::Any = (Base.Math.muladd)(Base.Math.t, (Base.Math.muladd)(Base.Math.t, (Base.Math.muladd)(Base.Math.t, (Base.Math.muladd)(Base.Math.t, (Base.Math.muladd)(Base.Math.t, (Base.Math.muladd)(Base.Math.t, (Base.Math.muladd)(Base.Math.t, -0.4432598039215686, 0.08333333333333333)::Any, -0.021092796092796094)::Any, 0.007575757575757576)::Any, -0.004166666666666667)::Any, 0.003968253968253968)::Any, -0.008333333333333333)::Any, 0.08333333333333333)::Any
      120: 
      # meta: pop location
      SSAValue(5) = (SSAValue(3) * #temp#@_22::Any)::Any
      SSAValue(6) = (SSAValue(2) - SSAValue(5))::Any
      ψ::Any = SSAValue(6)
      return SSAValue(6)
  end::Any

The same function is type-stable in Julia 0.6, so it has probably to do with some change in Julia base code.

[giordano]

By git-bisecting Julia, I found that the type-instability pops up after JuliaLang/julia#22985 😕

[stevengj]

I filed a Julia issue, since it seems to occur for any @evalpoly invocation.

[giordano]

Fixed by JuliaLang/julia#23247