Optimize integer-->string conversions

This avoids invalidations caused by invalidating `StringVector(::Integer)`.
This also makes `bin()`, `dec`() and `hex()` slightly faster,
but does not change the Printf.

base/intfuncs.jl

@@ -602,74 +602,111 @@ ndigits(x::Integer; base::Integer=10, pad::Integer=1) = max(pad, ndigits0z(x, ba
 ## integer to string functions ##
 
 function bin(x::Unsigned, pad::Integer, neg::Bool)
-    i = neg + max(pad,sizeof(x)<<3-leading_zeros(x))
-    a = StringVector(i)
+    m = 8sizeof(x) - leading_zeros(x)::Int
+    n = neg + max((pad % Int)::Int, m)
+    a = StringVector(n)
+    # for i in 0x0:UInt(n-1) # automatic vectorization produces redundant codes
+    #     @inbounds a[n - i] = 0x30 + (((x >> i) % UInt8)::UInt8 & 0x1)
+    # end
+    i = n
+    @inbounds while i >= 4
+        b = UInt32((x % UInt8)::UInt8)
+        d = 0x30303030 + ((b * 0x08040201) >> 0x3) & 0x01010101
+        a[i-3] = (d >> 0x00) % UInt8
+        a[i-2] = (d >> 0x08) % UInt8
+        a[i-1] = (d >> 0x10) % UInt8
+        a[i]   = (d >> 0x18) % UInt8
+        x >>= 0x4
+        i -= 4
+    end
     while i > neg
-        @inbounds a[i] = 48+(x&0x1)
-        x >>= 1
+        @inbounds a[i] = 0x30 + ((x % UInt8)::UInt8 & 0x1)
+        x >>= 0x1
         i -= 1
     end
     if neg; @inbounds a[1]=0x2d; end
     String(a)
 end
 
 function oct(x::Unsigned, pad::Integer, neg::Bool)
-    i = neg + max(pad,div((sizeof(x)<<3)-leading_zeros(x)+2,3))
-    a = StringVector(i)
+    m = div(8sizeof(x) - leading_zeros(x)::Int + 2, 3)
+    n = neg + max((pad % Int)::Int, m)
+    a = StringVector(n)
+    i = n
     while i > neg
-        @inbounds a[i] = 48+(x&0x7)
-        x >>= 3
+        @inbounds a[i] = 0x30 + ((x % UInt8)::UInt8 & 0x7)
+        x >>= 0x3
         i -= 1
     end
     if neg; @inbounds a[1]=0x2d; end
     String(a)
 end
 
+# 2-digit decimal characters ("00":"99")
+const _dec_d100 = UInt16[(0x30 + i % 10) << 0x8 + (0x30 + i ÷ 10) for i = 0:99]
+
 function dec(x::Unsigned, pad::Integer, neg::Bool)
-    i = neg + ndigits(x, base=10, pad=pad)
-    a = StringVector(i)
-    while i > neg
-        @inbounds a[i] = 48+rem(x,10)
-        x = oftype(x,div(x,10))
-        i -= 1
+    n = neg + ndigits(x, base=10, pad=(pad % Int)::Int)::Int
+    a = StringVector(n)
+    i = n
+    @inbounds while i >= 2
+        d, r = divrem(x, 0x64)
+        d100 = _dec_d100[(r % Int)::Int + 1]
+        a[i-1] = d100 % UInt8
+        a[i] = (d100 >> 0x8) % UInt8
+        x = oftype(x, d)
+        i -= 2
+    end
+    if i > neg
+        @inbounds a[i] = 0x30 + (rem(x, 0xa) % UInt8)::UInt8
     end
     if neg; @inbounds a[1]=0x2d; end
     String(a)
 end
 
 function hex(x::Unsigned, pad::Integer, neg::Bool)
-    i = neg + max(pad,(sizeof(x)<<1)-(leading_zeros(x)>>2))
-    a = StringVector(i)
-    while i > neg
-        d = x & 0xf
-        @inbounds a[i] = 48+d+39*(d>9)
-        x >>= 4
-        i -= 1
+    m = 2sizeof(x) - (leading_zeros(x)::Int >> 2)
+    n = neg + max((pad % Int)::Int, m)
+    a = StringVector(n)
+    i = n
+    while i >= 2
+        b = (x % UInt8)::UInt8
+        d1, d2 = b >> 0x4, b & 0xf
+        @inbounds a[i-1] = d1 + ifelse(d1 > 0x9, 0x57, 0x30)
+        @inbounds a[i]   = d2 + ifelse(d2 > 0x9, 0x57, 0x30)
+        x >>= 0x8
+        i -= 2
+    end
+    if i > neg
+        d = (x % UInt8)::UInt8 & 0xf
+        @inbounds a[i] = d + ifelse(d > 0x9, 0x57, 0x30)
     end
     if neg; @inbounds a[1]=0x2d; end
     String(a)
 end
 
-const base36digits = ['0':'9';'a':'z']
-const base62digits = ['0':'9';'A':'Z';'a':'z']
+const base36digits = UInt8['0':'9';'a':'z']
+const base62digits = UInt8['0':'9';'A':'Z';'a':'z']
 
-function _base(b::Integer, x::Integer, pad::Integer, neg::Bool)
-    (x >= 0) | (b < 0) || throw(DomainError(x, "For negative `x`, `b` must be negative."))
+function _base(base::Integer, x::Integer, pad::Integer, neg::Bool)
+    b = (base % Int)::Int
+    (x >= 0) | (b < 0) || throw(DomainError(x, "For negative `x`, `base` must be negative."))
     2 <= abs(b) <= 62 || throw(DomainError(b, "base must satisfy 2 ≤ abs(base) ≤ 62"))
     digits = abs(b) <= 36 ? base36digits : base62digits
-    i = neg + ndigits(x, base=b, pad=pad)
-    a = StringVector(i)
+    n = neg + ndigits(x, base=b, pad=(pad % Int)::Int)::Int
+    a = StringVector(n)
+    i = n
     @inbounds while i > neg
         if b > 0
-            a[i] = digits[1+rem(x,b)]
+            a[i] = digits[1 + (rem(x, b) % Int)::Int]
             x = div(x,b)
         else
-            a[i] = digits[1+mod(x,-b)]
+            a[i] = digits[1 + (mod(x, -b) % Int)::Int]
             x = cld(x,b)
         end
         i -= 1
     end
-    if neg; a[1]='-'; end
+    if neg; @inbounds a[1]=0x2d; end
     String(a)
 end