Optimize frombase/tobase for small integers

Author: edubart

Makefile

@@ -6,6 +6,7 @@ test:
 	lua examples/fibonacci.lua
 	lua examples/factorial.lua
 	lua examples/pi.lua
+	lua examples/e.lua
 	lua examples/rsa.lua
 
 docs:

bint.lua

@@ -276,27 +276,35 @@ function bint.frombase(s, base)
   if type(s) ~= 'string' then
     return nil
   end
-  s = s:lower()
   base = base or 10
   if not (base >= 2 and base <= 36) then
     -- number base is too large
     return nil
   end
-  local sign, int = s:match('^([+-]?)(%w+)$')
+  local step = getbasestep(base)
+  if #s < step then
+    -- string is small, use tonumber (faster)
+    return bint.frominteger(tonumber(s, base))
+  end
+  local sign, int = s:lower():match('^([+-]?)(%w+)$')
   if not (sign and int) then
     -- invalid integer string representation
     return nil
   end
   local n = bint.zero()
-  local step = getbasestep(base)
   for i=1,#int,step do
     local part = int:sub(i,i+step-1)
     local d = tonumber(part, base)
     if not d then
       -- invalid integer string representation
       return nil
     end
-    n = (n * ipow(1, base, #part)):_add(d)
+    if i > 1 then
+      n = n * ipow(1, base, #part)
+    end
+    if d ~= 0 then
+      n:_add(d)
+    end
   end
   if sign == '-' then
     n:_unm()
@@ -405,6 +413,18 @@ function bint.tobase(x, base, unsigned)
     -- number base is too large
     return nil
   end
+  if base == 10 or base == 16 then
+    local inluarange = x >= BIGINT_MATHMININTEGER and x <= BIGINT_MATHMAXINTEGER
+    if inluarange then
+      -- integer is small, use tostring or string.format (faster)
+      local n = x:tointeger()
+      if base == 10 then
+        return tostring(n)
+      else
+        return string.format('%x', n)
+      end
+    end
+  end
   local ss = {}
   if unsigned == nil then
     unsigned = base ~= 10

examples/bench.lua

@@ -26,28 +26,31 @@ local function bench2(n, name, f, a, b)
   print(string.format('fact %8s %10.02fx', name, factor))
 end
 
-bench2(100000, 'add', function(a, b) return a + b end, 1, 2)
-bench2(100000, 'sub', function(a, b) return a - b end, 1, 2)
-bench2(100000, 'mul', function(a, b) return a * b end, 1, 2)
+bench2(100000, 'add',  function(a, b) return a + b end, 1, 2)
+bench2(100000, 'sub',  function(a, b) return a - b end, 1, 2)
+bench2(100000, 'mul',  function(a, b) return a * b end, 1, 2)
 bench2(30000,  'idiv', function(a, b) return a // b end, 1, 2)
-bench2(30000,  'mod', function(a, b) return a % b end, 1, 2)
-bench2(30000,  'div', function(a, b) return a / b end, 1, 2)
-bench2(100000, 'shl', function(a, b) return a << b end, 1, 2)
-bench2(100000, 'shr', function(a, b) return a >> b end, 1, 2)
+bench2(30000,  'mod',  function(a, b) return a % b end, 1, 2)
+bench2(30000,  'div',  function(a, b) return a / b end, 1, 2)
+bench2(100000, 'shl',  function(a, b) return a << b end, 1, 2)
+bench2(100000, 'shr',  function(a, b) return a >> b end, 1, 2)
 bench2(100000, 'band', function(a, b) return a & b end, 1, 2)
-bench2(100000, 'bor', function(a, b) return a | b end, 1, 2)
+bench2(100000, 'bor',  function(a, b) return a | b end, 1, 2)
 bench2(100000, 'bxor', function(a, b) return a ~ b end, 1, 2)
 bench2(100000, 'bnot', function(a) return ~a end, 1)
-bench2(100000, 'unm', function(a) return -a end, 1)
-bench2(100000, 'eq', function(a, b) return a == b end, 1, 2)
-bench2(100000, 'lt', function(a, b) return a < b end, 1, 2)
-bench2(100000, 'le', function(a, b) return a <= b end, 1, 2)
-bench2(30000,   'pow', function(a, b) return a ^ b end, 1, 2)
-bench2(3000,   'tostring', function(a) return tostring(a) end, 1)
+bench2(100000, 'unm',  function(a) return -a end, 1)
+bench2(100000, 'eq',   function(a, b) return a == b end, 1, 2)
+bench2(100000, 'lt',   function(a, b) return a < b end, 1, 2)
+bench2(100000, 'le',   function(a, b) return a <= b end, 1, 2)
+bench2(30000,  'pow',  function(a, b) return a ^ b end, 1, 2)
 
-bench(100000, 'bint      abs', function(a) return bint.abs(a) end, 1)
-bench(100000, 'bint      dec', function(a) return bint.dec(a) end, 1)
-bench(100000, 'bint      inc', function(a) return bint.inc(a) end, 1)
-bench(30000,  'bint      ult', function(a, b) return bint.ult(a, b) end, 1, 2)
-bench(30000,  'bint      ule', function(a, b) return bint.ule(a, b) end, 1, 2)
-bench(30000,  'bint     ipow', function(a, b) return bint.ipow(a, b) end, 1, 2)
+bench(100000,  'bint      abs', function(a) return bint.abs(a) end, 1)
+bench(100000,  'bint      dec', function(a) return bint.dec(a) end, 1)
+bench(100000,  'bint      inc', function(a) return bint.inc(a) end, 1)
+bench(30000,   'bint      ult', function(a, b) return bint.ult(a, b) end, 1, 2)
+bench(30000,   'bint      ule', function(a, b) return bint.ule(a, b) end, 1, 2)
+bench(30000,   'bint     ipow', function(a, b) return bint.ipow(a, b) end, 1, 2)
+
+bench(30000,   'luab tonumber', function(a) return tonumber(a) end, '2147483648')
+bench(30000,   'bint frombase', function(a) return bint.frombase(a) end, '2147483648')
+bench2(30000,  'tostring',      function(a) return tostring(a) end, 1)

tests.lua

@@ -76,6 +76,10 @@ local function test(bits)
     assert(bint(1) <= 1.5 ==  true)
     assert(bint.isbint(1) == false)
     assert(bint.isbint(bint(1)) == true)
+    assert(tostring(bint.frombase('9223372036854775807')) == '9223372036854775807')
+    assert(tostring(bint.frombase('-9223372036854775808')) == '-9223372036854775808')
+    assert(bint.frombase('AAAAAAAAAAAAAAAAAAA') == nil)
+    assert(bint.frombase('AAAAAAAAAAAAAAAAAAA_') == nil)
 
     if bits > 96 then
       assert((bint(1) << 96):tonumber() > 1e28)