make faster BigFloats

We can coalesce the two required allocations for the MFPR BigFloat API
design into one allocation, hopefully giving a easy performance boost.
It would have been slightly easier and more efficient if MPFR BigFloat
was already a VLA instead of containing a pointer here, but that does
not prevent the optimization.

base/Base.jl

@@ -306,7 +306,6 @@ end
 include("hashing.jl")
 include("rounding.jl")
 include("div.jl")
-include("rawbigints.jl")
 include("float.jl")
 include("twiceprecision.jl")
 include("complex.jl")

base/mpfr.jl

@@ -18,12 +18,10 @@ import
  setrounding, maxintfloat, widen, significand, frexp, tryparse, iszero,
  isone, big, _string_n, decompose, minmax, _precision_with_base_2,
  sinpi, cospi, sincospi, tanpi, sind, cosd, tand, asind, acosd, atand,
- uinttype, exponent_max, exponent_min, ieee754_representation, significand_mask,
- RawBigIntRoundingIncrementHelper, truncated, RawBigInt
-
+ uinttype, exponent_max, exponent_min, ieee754_representation, significand_mask
 
 using .Base.Libc
-import ..Rounding:
+import ..Rounding: Rounding,
  rounding_raw, setrounding_raw, rounds_to_nearest, rounds_away_from_zero,
  tie_breaker_is_to_even, correct_rounding_requires_increment
 
@@ -39,7 +37,6 @@ else
  const libmpfr = "libmpfr.so.6"
 end
 
-
 version() = VersionNumber(unsafe_string(ccall((:mpfr_get_version,libmpfr), Ptr{Cchar}, ())))
 patches() = split(unsafe_string(ccall((:mpfr_get_patches,libmpfr), Ptr{Cchar}, ())),' ')
 
@@ -120,69 +117,129 @@ const mpfr_special_exponent_zero = typemin(Clong) + true
 const mpfr_special_exponent_nan = mpfr_special_exponent_zero + true
 const mpfr_special_exponent_inf = mpfr_special_exponent_nan + true
 
+struct BigFloatLayout
+ prec::Clong
+ sign::Cint
+ exp::Clong
+ d::Ptr{Limb}
+ # possible padding
+ p::Limb # Tuple{Vararg{Limb}}
+end
+const offset_prec = fieldoffset(BigFloatLayout, 1) % Int
+const offset_sign = fieldoffset(BigFloatLayout, 2) % Int
+const offset_exp = fieldoffset(BigFloatLayout, 3) % Int
+const offset_d = fieldoffset(BigFloatLayout, 4) % Int
+const offset_p_limbs = ((fieldoffset(BigFloatLayout, 5) % Int + sizeof(Limb) - 1) ÷ sizeof(Limb))
+const offset_p = offset_p_limbs * sizeof(Limb)
+
 """
  BigFloat <: AbstractFloat
 
 Arbitrary precision floating point number type.
 """
-mutable struct BigFloat <: AbstractFloat
- prec::Clong
- sign::Cint
- exp::Clong
- d::Ptr{Limb}
- # _d::Buffer{Limb} # Julia gc handle for memory @ d
- _d::String # Julia gc handle for memory @ d (optimized)
+struct BigFloat <: AbstractFloat
+ d::Memory{Limb}
 
  # Not recommended for general use:
  # used internally by, e.g. deepcopy
- global function _BigFloat(prec::Clong, sign::Cint, exp::Clong, d::String)
- # ccall-based version, inlined below
- #z = new(zero(Clong), zero(Cint), zero(Clong), C_NULL, d)
- #ccall((:mpfr_custom_init,libmpfr), Cvoid, (Ptr{Limb}, Clong), d, prec) # currently seems to be a no-op in mpfr
- #NAN_KIND = Cint(0)
- #ccall((:mpfr_custom_init_set,libmpfr), Cvoid, (Ref{BigFloat}, Cint, Clong, Ptr{Limb}), z, NAN_KIND, prec, d)
- #return z
- return new(prec, sign, exp, pointer(d), d)
- end
+ global _BigFloat(d::Memory{Limb}) = new(d)
 
  function BigFloat(; precision::Integer=_precision_with_base_2(BigFloat))
  precision < 1 && throw(DomainError(precision, "`precision` cannot be less than 1."))
  nb = ccall((:mpfr_custom_get_size,libmpfr), Csize_t, (Clong,), precision)
- nb = (nb + Core.sizeof(Limb) - 1) ÷ Core.sizeof(Limb) # align to number of Limb allocations required for this
- #d = Vector{Limb}(undef, nb)
- d = _string_n(nb * Core.sizeof(Limb))
- EXP_NAN = mpfr_special_exponent_nan
- return _BigFloat(Clong(precision), one(Cint), EXP_NAN, d) # +NAN
+ nl = (nb + offset_p + sizeof(Limb) - 1) ÷ Core.sizeof(Limb) # align to number of Limb allocations required for this
+ d = Memory{Limb}(undef, nl % Int)
+ # ccall-based version, inlined below
+ z = _BigFloat(d) # initialize to +NAN
+ #ccall((:mpfr_custom_init,libmpfr), Cvoid, (Ptr{Limb}, Clong), BigFloatData(d), prec) # currently seems to be a no-op in mpfr
+ #NAN_KIND = Cint(0)
+ #ccall((:mpfr_custom_init_set,libmpfr), Cvoid, (Ref{BigFloat}, Cint, Clong, Ptr{Limb}), z, NAN_KIND, prec, BigFloatData(d))
+ z.prec = Clong(precision)
+ z.sign = one(Cint)
+ z.exp = mpfr_special_exponent_nan
+ return z
  end
 end
 
-# The rounding mode here shouldn't matter.
-significand_limb_count(x::BigFloat) = div(sizeof(x._d), sizeof(Limb), RoundToZero)
+"""
+Segment of raw words of bits interpreted as a big integer. Less
+significant words come first. Each word is in machine-native bit-order.
+"""
+struct BigFloatData{Limb}
+ d::Memory{Limb}
+end
+
+# BigFloat interface
+@inline function Base.getproperty(x::BigFloat, s::Symbol)
+ d = getfield(x, :d)
+ p = Base.unsafe_convert(Ptr{Limb}, d)
+ if s === :prec
+ return GC.@preserve d unsafe_load(Ptr{Clong}(p) + offset_prec)
+ elseif s === :sign
+ return GC.@preserve d unsafe_load(Ptr{Cint}(p) + offset_sign)
+ elseif s === :exp
+ return GC.@preserve d unsafe_load(Ptr{Clong}(p) + offset_exp)
+ elseif s === :d
+ return BigFloatData(d)
+ else
+ return throw(FieldError(typeof(x), s))
+ end
+end
+
+@inline function Base.setproperty!(x::BigFloat, s::Symbol, v)
+ d = getfield(x, :d)
+ p = Base.unsafe_convert(Ptr{Limb}, d)
+ if s === :prec
+ return GC.@preserve d unsafe_store!(Ptr{Clong}(p) + offset_prec, v)
+ elseif s === :sign
+ return GC.@preserve d unsafe_store!(Ptr{Cint}(p) + offset_sign, v)
+ elseif s === :exp
+ return GC.@preserve d unsafe_store!(Ptr{Clong}(p) + offset_exp, v)
+ #elseif s === :d # not mutable
+ else
+ return throw(FieldError(x, s))
+ end
+end
+
+# Ref interface: make sure the conversion to C is done properly
+Base.unsafe_convert(::Type{Ref{BigFloat}}, x::Ptr{BigFloat}) = error("not compatible with mpfr")
+Base.unsafe_convert(::Type{Ref{BigFloat}}, x::Ref{BigFloat}) = error("not compatible with mpfr")
+Base.cconvert(::Type{Ref{BigFloat}}, x::BigFloat) = x.d # BigFloatData is the Ref type for BigFloat
+function Base.unsafe_convert(::Type{Ref{BigFloat}}, x::BigFloatData)
+ d = getfield(x, :d)
+ p = Base.unsafe_convert(Ptr{Limb}, d)
+ GC.@preserve d unsafe_store!(Ptr{Ptr{Limb}}(p) + offset_d, p + offset_p, :monotonic) # :monotonic ensure that TSAN knows that this isn't a data race
+ return Ptr{BigFloat}(p)
+end
+Base.unsafe_convert(::Type{Ptr{Limb}}, fd::BigFloatData) = Base.unsafe_convert(Ptr{Limb}, getfield(fd, :d)) + offset_p
+function Base.setindex!(fd::BigFloatData, v, i)
+ d = getfield(fd, :d)
+ @boundscheck 1 <= i <= length(d) - offset_p_limbs || throw(BoundsError(fd, i))
+ @inbounds d[i + offset_p_limbs] = v
+ return fd
+end
+function Base.getindex(fd::BigFloatData, i)
+ d = getfield(fd, :d)
+ @boundscheck 1 <= i <= length(d) - offset_p_limbs || throw(BoundsError(fd, i))
+ @inbounds d[i + offset_p_limbs]
+end
+Base.length(fd::BigFloatData) = length(getfield(fd, :d)) - offset_p_limbs
+Base.copyto!(fd::BigFloatData, limbs) = copyto!(getfield(fd, :d), offset_p_limbs + 1, limbs) # for Random
+
+include("rawbigfloats.jl")
 
 rounding_raw(::Type{BigFloat}) = something(Base.ScopedValues.get(CURRENT_ROUNDING_MODE), ROUNDING_MODE[])
 setrounding_raw(::Type{BigFloat}, r::MPFRRoundingMode) = ROUNDING_MODE[]=r
 function setrounding_raw(f::Function, ::Type{BigFloat}, r::MPFRRoundingMode)
  Base.ScopedValues.@with(CURRENT_ROUNDING_MODE => r, f())
 end
 
-
 rounding(::Type{BigFloat}) = convert(RoundingMode, rounding_raw(BigFloat))
 setrounding(::Type{BigFloat}, r::RoundingMode) = setrounding_raw(BigFloat, convert(MPFRRoundingMode, r))
 setrounding(f::Function, ::Type{BigFloat}, r::RoundingMode) =
  setrounding_raw(f, BigFloat, convert(MPFRRoundingMode, r))
 
 
-# overload the definition of unsafe_convert to ensure that `x.d` is assigned
-# it may have been dropped in the event that the BigFloat was serialized
-Base.unsafe_convert(::Type{Ref{BigFloat}}, x::Ptr{BigFloat}) = x
-@inline function Base.unsafe_convert(::Type{Ref{BigFloat}}, x::Ref{BigFloat})
- x = x[]
- if x.d == C_NULL
- x.d = pointer(x._d)
- end
- return convert(Ptr{BigFloat}, Base.pointer_from_objref(x))
-end
-
 """
  BigFloat(x::Union{Real, AbstractString} [, rounding::RoundingMode=rounding(BigFloat)]; [precision::Integer=precision(BigFloat)])
 
@@ -283,17 +340,18 @@ function BigFloat(x::Float64, r::MPFRRoundingMode=rounding_raw(BigFloat); precis
  nlimbs = (precision + 8*Core.sizeof(Limb) - 1) ÷ (8*Core.sizeof(Limb))
 
  # Limb is a CLong which is a UInt32 on windows (thank M$) which makes this more complicated and slower.
+ zd = z.d
  if Limb === UInt64
  for i in 1:nlimbs-1
- unsafe_store!(z.d, 0x0, i)
+ @inbounds setindex!(zd, 0x0, i)
  end
- unsafe_store!(z.d, val, nlimbs)
+ @inbounds setindex!(zd, val, nlimbs)
  else
  for i in 1:nlimbs-2
- unsafe_store!(z.d, 0x0, i)
+ @inbounds setindex!(zd, 0x0, i)
  end
- unsafe_store!(z.d, val % UInt32, nlimbs-1)
- unsafe_store!(z.d, (val >> 32) % UInt32, nlimbs)
+ @inbounds setindex!(zd, val % UInt32, nlimbs-1)
+ @inbounds setindex!(zd, (val >> 32) % UInt32, nlimbs)
  end
  z
 end
@@ -440,12 +498,12 @@ function to_ieee754(::Type{T}, x::BigFloat, rm) where {T<:AbstractFloat}
  ret_u = if is_regular & !rounds_to_inf & !rounds_to_zero
  if !exp_is_huge_p
  # significand
- v = RawBigInt{Limb}(x._d, significand_limb_count(x))
+ v = x.d::BigFloatData
  len = max(ieee_precision + min(exp_diff, 0), 0)::Int
  signif = truncated(U, v, len) & significand_mask(T)
 
  # round up if necessary
- rh = RawBigIntRoundingIncrementHelper(v, len)
+ rh = BigFloatDataRoundingIncrementHelper(v, len)
  incr = correct_rounding_requires_increment(rh, rm, sb)
 
  # exponent
@@ -1193,10 +1251,8 @@ set_emin!(x) = check_exponent_err(ccall((:mpfr_set_emin, libmpfr), Cint, (Clong,
 
 function Base.deepcopy_internal(x::BigFloat, stackdict::IdDict)
  get!(stackdict, x) do
- # d = copy(x._d)
- d = x._d
- d′ = GC.@preserve d unsafe_string(pointer(d), sizeof(d)) # creates a definitely-new String
- y = _BigFloat(x.prec, x.sign, x.exp, d′)
+ d′ = copy(getfield(x, :d))
+ y = _BigFloat(d′)
  #ccall((:mpfr_custom_move,libmpfr), Cvoid, (Ref{BigFloat}, Ptr{Limb}), y, d) # unnecessary
  return y
  end::BigFloat
@@ -1210,7 +1266,8 @@ function decompose(x::BigFloat)::Tuple{BigInt, Int, Int}
  s.size = cld(x.prec, 8*sizeof(Limb)) # limbs
  b = s.size * sizeof(Limb) # bytes
  ccall((:__gmpz_realloc2, libgmp), Cvoid, (Ref{BigInt}, Culong), s, 8b) # bits
- memcpy(s.d, x.d, b)
+ xd = x.d
+ GC.@preserve xd memcpy(s.d, Base.unsafe_convert(Ptr{Limb}, xd), b)
  s, x.exp - 8b, x.sign
 end