move hashing2 functions to their relevant files [NFC]

base/Base.jl

@@ -324,9 +324,6 @@ using .MPFR
 
 include("combinatorics.jl")
 
-# more hashing definitions
-include("hashing2.jl")
-
 # irrational mathematical constants
 include("irrationals.jl")
 include("mathconstants.jl")

base/float.jl

@@ -484,6 +484,110 @@ end
 hash(x::Float32, h::UInt) = hash(Float64(x), h)
 hash(x::Float16, h::UInt) = hash(Float64(x), h)
 
+## generic hashing for rational values ##
+
+function hash(x::Real, h::UInt)
+    # decompose x as num*2^pow/den
+    num, pow, den = decompose(x)
+
+    # handle special values
+    num == 0 && den == 0 && return hash(NaN, h)
+    num == 0 && return hash(ifelse(den > 0, 0.0, -0.0), h)
+    den == 0 && return hash(ifelse(num > 0, Inf, -Inf), h)
+
+    # normalize decomposition
+    if den < 0
+        num = -num
+        den = -den
+    end
+    z = trailing_zeros(num)
+    if z != 0
+        num >>= z
+        pow += z
+    end
+    z = trailing_zeros(den)
+    if z != 0
+        den >>= z
+        pow -= z
+    end
+
+    # handle values representable as Int64, UInt64, Float64
+    if den == 1
+        left = ndigits0z(num,2) + pow
+        right = trailing_zeros(num) + pow
+        if -1074 <= right
+            if 0 <= right && left <= 64
+                left <= 63                     && return hash(Int64(num) << Int(pow), h)
+                signbit(num) == signbit(den)   && return hash(UInt64(num) << Int(pow), h)
+            end # typemin(Int64) handled by Float64 case
+            left <= 1024 && left - right <= 53 && return hash(ldexp(Float64(num),pow), h)
+        end
+    end
+
+    # handle generic rational values
+    h = hash_integer(den, h)
+    h = hash_integer(pow, h)
+    h = hash_integer(num, h)
+    return h
+end
+
+#=
+`decompose(x)`: non-canonical decomposition of rational values as `num*2^pow/den`.
+
+The decompose function is the point where rational-valued numeric types that support
+hashing hook into the hashing protocol. `decompose(x)` should return three integer
+values `num, pow, den`, such that the value of `x` is mathematically equal to
+
+    num*2^pow/den
+
+The decomposition need not be canonical in the sense that it just needs to be *some*
+way to express `x` in this form, not any particular way – with the restriction that
+`num` and `den` may not share any odd common factors. They may, however, have powers
+of two in common – the generic hashing code will normalize those as necessary.
+
+Special values:
+
+ - `x` is zero: `num` should be zero and `den` should have the same sign as `x`
+ - `x` is infinite: `den` should be zero and `num` should have the same sign as `x`
+ - `x` is not a number: `num` and `den` should both be zero
+=#
+
+decompose(x::Integer) = x, 0, 1
+
+function decompose(x::Float16)::NTuple{3,Int}
+    isnan(x) && return 0, 0, 0
+    isinf(x) && return ifelse(x < 0, -1, 1), 0, 0
+    n = reinterpret(UInt16, x)
+    s = (n & 0x03ff) % Int16
+    e = ((n & 0x7c00) >> 10) % Int
+    s |= Int16(e != 0) << 10
+    d = ifelse(signbit(x), -1, 1)
+    s, e - 25 + (e == 0), d
+end
+
+function decompose(x::Float32)::NTuple{3,Int}
+    isnan(x) && return 0, 0, 0
+    isinf(x) && return ifelse(x < 0, -1, 1), 0, 0
+    n = reinterpret(UInt32, x)
+    s = (n & 0x007fffff) % Int32
+    e = ((n & 0x7f800000) >> 23) % Int
+    s |= Int32(e != 0) << 23
+    d = ifelse(signbit(x), -1, 1)
+    s, e - 150 + (e == 0), d
+end
+
+function decompose(x::Float64)::Tuple{Int64, Int, Int}
+    isnan(x) && return 0, 0, 0
+    isinf(x) && return ifelse(x < 0, -1, 1), 0, 0
+    n = reinterpret(UInt64, x)
+    s = (n & 0x000fffffffffffff) % Int64
+    e = ((n & 0x7ff0000000000000) >> 52) % Int
+    s |= Int64(e != 0) << 52
+    d = ifelse(signbit(x), -1, 1)
+    s, e - 1075 + (e == 0), d
+end
+
+
 """
     precision(num::AbstractFloat)
 

base/gmp.jl

@@ -132,7 +132,7 @@ module MPZ
 # - a method modifying its input has a "!" appendend to its name, according to Julia's conventions
 # - some convenient methods are added (in addition to the pure MPZ ones), e.g. `add(a, b) = add!(BigInt(), a, b)`
 #   and `add!(x, a) = add!(x, x, a)`.
-using .Base.GMP: BigInt, Limb, BITS_PER_LIMB
+using ..GMP: BigInt, Limb, BITS_PER_LIMB
 
 const mpz_t = Ref{BigInt}
 const bitcnt_t = Culong
@@ -764,4 +764,77 @@ function Base.deepcopy_internal(x::BigInt, stackdict::IdDict)
     return y
 end
 
+## streamlined hashing for BigInt, by avoiding allocation from shifts ##
+
+if Limb === UInt
+    # this condition is true most (all?) of the time, and in this case we can define
+    # an optimized version of the above hash_integer(::Integer, ::UInt) method for BigInt
+    # used e.g. for Rational{BigInt}
+    function hash_integer(n::BigInt, h::UInt)
+        GC.@preserve n begin
+            s = n.size
+            s == 0 && return hash_integer(0, h)
+            p = convert(Ptr{UInt}, n.d)
+            b = unsafe_load(p)
+            h ⊻= hash_uint(ifelse(s < 0, -b, b) ⊻ h)
+            for k = 2:abs(s)
+                h ⊻= hash_uint(unsafe_load(p, k) ⊻ h)
+            end
+            return h
+        end
+    end
+
+    _divLimb(n) = UInt === UInt64 ? n >>> 6 : n >>> 5
+    _modLimb(n) = UInt === UInt64 ? n & 63 : n & 31
+
+    function hash(x::BigInt, h::UInt)
+        GC.@preserve x begin
+            sz = x.size
+            sz == 0 && return hash(0, h)
+            ptr = Ptr{UInt}(x.d)
+            if sz == 1
+                return hash(unsafe_load(ptr), h)
+            elseif sz == -1
+                limb = unsafe_load(ptr)
+                limb <= typemin(Int) % UInt && return hash(-(limb % Int), h)
+            end
+            pow = trailing_zeros(x)
+            nd = ndigits0z(x, 2)
+            idx = _divLimb(pow) + 1
+            shift = _modLimb(pow) % UInt
+            upshift = BITS_PER_LIMB - shift
+            asz = abs(sz)
+            if shift == 0
+                limb = unsafe_load(ptr, idx)
+            else
+                limb1 = unsafe_load(ptr, idx)
+                limb2 = idx < asz ? unsafe_load(ptr, idx+1) : UInt(0)
+                limb = limb2 << upshift | limb1 >> shift
+            end
+            if nd <= 1024 && nd - pow <= 53
+                return hash(ldexp(flipsign(Float64(limb), sz), pow), h)
+            end
+            h = hash_integer(1, h)
+            h = hash_integer(pow, h)
+            h ⊻= hash_uint(flipsign(limb, sz) ⊻ h)
+            for idx = idx+1:asz
+                if shift == 0
+                    limb = unsafe_load(ptr, idx)
+                else
+                    limb1 = limb2
+                    if idx == asz
+                        limb = limb1 >> shift
+                        limb == 0 && break # don't hash leading zeros
+                    else
+                        limb2 = unsafe_load(ptr, idx+1)
+                        limb = limb2 << upshift | limb1 >> shift
+                    end
+                end
+                h ⊻= hash_uint(limb ⊻ h)
+            end
+            return h
+        end
+    end
+end
+
 end # module

base/hashing.jl

@@ -66,6 +66,23 @@ else
     hash_uint(x::UInt)     = hash_32_32(x)
 end
 
+## efficient value-based hashing of integers ##
+
+hash(x::Int64,  h::UInt) = hash_uint64(bitcast(UInt64, x)) - 3h
+hash(x::UInt64, h::UInt) = hash_uint64(x) - 3h
+hash(x::Union{Bool,Int8,UInt8,Int16,UInt16,Int32,UInt32}, h::UInt) = hash(Int64(x), h)
+
+function hash_integer(n::Integer, h::UInt)
+    h ⊻= hash_uint((n % UInt) ⊻ h)
+    n = abs(n)
+    n >>>= sizeof(UInt) << 3
+    while n != 0
+        h ⊻= hash_uint((n % UInt) ⊻ h)
+        n >>>= sizeof(UInt) << 3
+    end
+    return h
+end
+
 ## symbol & expression hashing ##
 
 if UInt === UInt64