Document internal Ryu functions, remove duplicate functionality.

Also moved some functions from Math to Base.

base/float.jl

@@ -876,6 +876,11 @@ significand_mask(::Type{Float16}) = 0x03ff
 for T in (Float16, Float32, Float64)
     @eval significand_bits(::Type{$T}) = $(trailing_ones(significand_mask(T)))
     @eval exponent_bits(::Type{$T}) = $(sizeof(T)*8 - significand_bits(T) - 1)
+    @eval exponent_bias(::Type{$T}) = $(Int(exponent_one(T) >> significand_bits(T)))
+    # maximum float exponent
+    @eval exponent_max(::Type{$T}) = $(Int(exponent_mask(T) >> significand_bits(T)) - exponent_bias(T))
+    # maximum float exponent without bias
+    @eval exponent_raw_max(::Type{$T}) = $(Int(exponent_mask(T) >> significand_bits(T)))
 end
 
 # integer size of float

base/math.jl

@@ -22,7 +22,8 @@ import .Base: log, exp, sin, cos, tan, sinh, cosh, tanh, asin,
 
 using .Base: sign_mask, exponent_mask, exponent_one,
             exponent_half, uinttype, significand_mask,
-            significand_bits, exponent_bits
+            significand_bits, exponent_bits, exponent_bias,
+            exponent_max, exponent_max_raw
 
 using Core.Intrinsics: sqrt_llvm
 
@@ -38,14 +39,6 @@ end
                                 "Complex(x)^y, or similar.")))
 end
 
-for T in (Float16, Float32, Float64)
-    @eval exponent_bias(::Type{$T}) = $(Int(exponent_one(T) >> significand_bits(T)))
-    # maximum float exponent
-    @eval exponent_max(::Type{$T}) = $(Int(exponent_mask(T) >> significand_bits(T)) - exponent_bias(T))
-    # maximum float exponent without bias
-    @eval exponent_raw_max(::Type{$T}) = $(Int(exponent_mask(T) >> significand_bits(T)))
-end
-
 # non-type specific math functions
 
 """

base/ryu/Ryu.jl

@@ -1,10 +1,17 @@
 module Ryu
 
+import .Base: significand_bits, exponent_bits, exponent_bias
+
 include("utils.jl")
 include("shortest.jl")
 include("fixed.jl")
 include("exp.jl")
 
+"""
+    Ryu.neededdigits(T)
+
+Number of digits necessary to represent type `T` in fixed-precision decimal.
+"""
 neededdigits(::Type{Float64}) = 309 + 17
 neededdigits(::Type{Float32}) = 39 + 9 + 2
 neededdigits(::Type{Float16}) = 9 + 5 + 9
@@ -120,4 +127,4 @@ end
 
 Base.print(io::IO, x::Union{Float16, Float32}) = show(io, x, true)
 
-end # module
+end # module

base/ryu/shortest.jl

@@ -75,15 +75,15 @@
         return pos + neg + 3 + (typed && x isa Union{Float32, Float16} ? 2 : 0)
     end
 
-    bits = uint(x)
-    mant = bits & (oftype(bits, 1) << mantissabits(T) - oftype(bits, 1))
-    exp = Int((bits >> mantissabits(T)) & ((Int64(1) << exponentbits(T)) - 1))
-    m2 = oftype(bits, Int64(1) << mantissabits(T)) | mant
-    e2 = exp - bias(T) - mantissabits(T)
+    bits = reinterpret(Unsigned, x)
+    mant = bits & (oftype(bits, 1) << significand_bits(T) - oftype(bits, 1))
+    exp = Int((bits >> significand_bits(T)) & ((Int64(1) << exponent_bits(T)) - 1))
+    m2 = oftype(bits, Int64(1) << significand_bits(T)) | mant
+    e2 = exp - exponent_bias(T) - significand_bits(T)
     fraction = m2 & ((oftype(bits, 1) << -e2) - 1)
     if e2 > 0 || e2 < -52 || fraction != 0
         if exp == 0
-            e2 = 1 - bias(T) - mantissabits(T) - 2
+            e2 = 1 - exponent_bias(T) - significand_bits(T) - 2
             m2 = mant
         else
             e2 -= 2

base/ryu/utils.jl

@@ -1,25 +1,9 @@
-const MANTISSA_MASK = 0x000fffffffffffff
-const EXP_MASK = 0x00000000000007ff
+const MANTISSA_MASK = Base.significand_mask(Float64)
+const EXP_MASK = Base.exponent_mask(Float64) >> Base.significand_bits(Float64)
 
 memcpy(d, doff, s, soff, n) = ccall(:memcpy, Cvoid, (Ptr{Cvoid}, Ptr{Cvoid}, Int), d + doff - 1, s + soff - 1, n)
 memmove(d, doff, s, soff, n) = ccall(:memmove, Cvoid, (Ptr{Cvoid}, Ptr{Cvoid}, Int), d + doff - 1, s + soff - 1, n)
 
-uint(x::Float16) = Core.bitcast(UInt16, x)
-uint(x::Float32) = Core.bitcast(UInt32, x)
-uint(x::Float64) = Core.bitcast(UInt64, x)
-
-mantissabits(::Type{Float16}) = 10
-mantissabits(::Type{Float32}) = 23
-mantissabits(::Type{Float64}) = 52
-
-exponentbits(::Type{Float16}) = 5
-exponentbits(::Type{Float32}) = 8
-exponentbits(::Type{Float64}) = 11
-
-bias(::Type{Float16}) = 15
-bias(::Type{Float32}) = 127
-bias(::Type{Float64}) = 1023
-
 pow5_bitcount(::Type{Float16}) = 30
 pow5_bitcount(::Type{Float32}) = 61
 pow5_bitcount(::Type{Float64}) = 121
@@ -36,16 +20,58 @@ qbound(::Type{Float16}) = 15
 qbound(::Type{Float32}) = 31
 qbound(::Type{Float64}) = 63
 
+"""
+    Ryu.log10pow2(e::Integer)
+
+Computes `floor(log10(2^e))`. This is valid for all `e < 1651`.
+"""
 log10pow2(e) = (e * 78913) >> 18
+
+
+"""
+    Ryu.log10pow2(e::Integer)
+
+Computes `floor(log10(5^e))`. This is valid for all `e < 2621`.
+"""
 log10pow5(e) = (e * 732923) >> 20
+
+"""
+    Ryu.pow5bits(e)
+
+Computes `e == 0 ? 1 : ceil(log2(5^e))`. This is valid for `e < 3529` (if performend in `Int32` arithmetic).
+"""
 pow5bits(e) = ((e * 1217359) >> 19) + 1
+
+""""
+     Ryu.mulshift(m::UInt64, mula, mulb, j)::UInt64
+
+Compute `(m * mul) >> j`, where `mul = mula + mulb<<64` and `j >= 64`.
+"""
 @inline mulshift(m::UInt64, mula, mulb, j) = ((((UInt128(m) * mula) >> 64) + UInt128(m) * mulb) >> (j - 64)) % UInt64
+
+""""
+     Ryu.mulshift(m::UInt32, mul, j)::UInt32
+
+Compute `(m * mul) >> j`, where `j >= 32`.
+"""
 @inline mulshift(m::UInt32, mul, j) = ((((UInt64(m) * (mul % UInt32)) >> 32) + (UInt64(m) * (mul >> 32))) >> (j - 32)) % UInt32
+
+""""
+     Ryu.mulshift(m::UInt16, mul, j)::UInt16
+
+Compute `(m * mul) >> j`, where `j >= 16`.
+"""
 @inline mulshift(m::UInt16, mul, j) = ((((UInt32(m) * (mul % UInt16)) >> 16) + (UInt32(m) * (mul >> 16))) >> (j - 16))
+
 indexforexp(e) = div(e + 15, 16)
 pow10bitsforindex(idx) = 16 * idx + 120
 lengthforindex(idx) = div(((Int64(16 * idx) * 1292913986) >> 32) + 1 + 16 + 8, 9)
 
+"""
+    Ryu.pow5(x, p)
+
+Return `true` if `5^p` is a divisor of `x`.
+"""
 @inline function pow5(x, p)
     count = 0
     while true
@@ -57,8 +83,18 @@ lengthforindex(idx) = div(((Int64(16 * idx) * 1292913986) >> 32) + 1 + 16 + 8, 9
     end
 end
 
+"""
+    Ryu.pow2(x, p)
+
+Return `true` if `2^p` is a divisor of `x`. In other words, if the trailing `p` bits of `x` are zero.
+"""
 pow2(x, p) = (x & ((Int64(1) << p) - 1)) == 0
 
+"""
+    Ryu.decimallength(v)
+
+The number of decimal digits of the integer `v`.
+"""
 @inline function decimallength(v)
     v >= 10000000000000000 && return 17
     v >= 1000000000000000 && return 16
@@ -78,7 +114,6 @@ pow2(x, p) = (x & ((Int64(1) << p) - 1)) == 0
     v >= 10 && return 2
     return 1
 end
-
 @inline function decimallength(v::UInt32)
     v >= 100000000 && return 9
     v >= 10000000 && return 8
@@ -90,7 +125,6 @@ end
     v >= 10 && return 2
     return 1
 end
-
 @inline function decimallength(v::UInt16)
     v >= 10000 && return 5
     v >= 1000 && return 4
@@ -147,6 +181,11 @@ end
     return vr, vp, vm
 end
 
+"""
+    Ryu.umul256(a::UInt128, bHi::UInt64, bLo::UInt64)::Tuple{UInt128, UInt128}
+
+Compute `p = a*b` where `b = bLo + bHi<<64`, returning the result as `pLo, pHi` where `p = pLo + pHi<<128`.
+"""
 @inline function umul256(a, bHi, bLo)
     aLo = a % UInt64
     aHi = (a >> 64) % UInt64
@@ -172,8 +211,18 @@ end
     return pLo, pHi
 end
 
+"""
+    Ryu.umul256_hi(a::UInt128, bHi::UInt64, bLo::UInt64)::UInt128
+
+Compute `pHi = (a*b)>>128` where `b = bLo + bHi<<64`.
+"""
 @inline umul256_hi(a, bHi, bLo) = umul256(a, bHi, bLo)[2]
 
+"""
+    Ryu.mulshiftmod1e9(m, mula, mulb, mulc, j)::UInt32
+
+Compute `(m * mul) >> j % 10^9` where `mul = mula + mulb<<64 + mulc<<128`, and `j >= 128`.
+"""
 @inline function mulshiftmod1e9(m, mula, mulb, mulc, j)
     b0 = UInt128(m) * mula
     b1 = UInt128(m) * mulb