Optimize tobase function using a better algorithm

Author: edubart

bint.lua

@@ -245,7 +245,7 @@ end
 
 local basesteps = {}
 
--- Compute the read/write step for frombase/tobase functions.
+-- Compute the read step for frombase function
 local function getbasestep(base)
  local step = basesteps[base]
  if step then
@@ -394,11 +394,18 @@ do
  end
 end
 
--- Get the quotient and remainder for a lua integer division
-local function idivmod(x, y)
- local quot = x // y
- local rem = x - (quot * y)
- return quot, rem
+-- Get the quotient and remainder for base digits
+local function xremainder(dividend, divisor)
+ local quo = bint_newempty()
+ local rem
+ local carry = 0
+ for i=BINT_SIZE,1,-1 do
+ carry = carry | dividend[i]
+ quo[i] = carry // divisor
+ rem = carry % divisor
+ carry = rem << BINT_WORDBITS
+ end
+ return quo, rem
 end
 
 --- Convert a bint to a string in the desired base.
@@ -441,26 +448,13 @@ function bint.tobase(x, base, unsigned)
  if neg then
  x = x:abs()
  end
- local step = getbasestep(base)
- local divisor = bint.new(ipow(1, base, step))
- local stop = x:iszero()
- if stop then
- return '0'
+ while not x:iszero() do
+ local d
+ x, d = xremainder(x, base)
+ table.insert(ss, 1, BASE_LETTERS[d])
  end
- while not stop do
- local ix
- x, ix = bint.udivmod(x, divisor)
- ix = ix:tointeger()
- stop = x:iszero()
- for _=1,step do
- local d
- ix, d = idivmod(ix, base)
- if stop and ix == 0 and d == 0 then
- -- stop on leading zeros
- break
- end
- table.insert(ss, 1, BASE_LETTERS[d])
- end
+ if #ss == 0 then
+ return '0'
  end
  if neg then
  table.insert(ss, 1, '-')
@@ -1063,12 +1057,12 @@ end
 function bint.udivmod(x, y)
  local dividend = bint.new(x)
  local divisor = bint_assert_convert(y)
- local quot = bint.zero()
+ local quo = bint.zero()
  assert(not divisor:iszero(), 'attempt to divide by zero')
  if divisor:isone() then
  return dividend, bint.zero()
  elseif dividend:ult(divisor) then
- return quot, dividend
+ return quo, dividend
  end
  -- align leftmost digits in dividend and divisor
  local divisorlbit = findleftbit(divisor)
@@ -1100,7 +1094,7 @@ function bint.udivmod(x, y)
  end
  -- concatenate 1 to the right bit of the quotient
  local i = (bit // BINT_WORDBITS) + 1
- quot[i] = quot[i] | (1 << (bit % BINT_WORDBITS))
+ quo[i] = quo[i] | (1 << (bit % BINT_WORDBITS))
  end
  -- shift right the divisor in one bit
  for i=1,divisorsize-1 do
@@ -1121,7 +1115,7 @@ function bint.udivmod(x, y)
  bit = bit - 1
  end
  -- the remaining dividend is the remainder
- return quot, dividend
+ return quo, dividend
 end
 
 --- Perform unsigned division between two integers considering bints.
@@ -1159,13 +1153,13 @@ function bint.idivmod(x, y)
  if iy:isminusone() then
  return -ix, bint.zero()
  end
- local quot, rem = bint.udivmod(ix:abs(), iy:abs())
+ local quo, rem = bint.udivmod(ix:abs(), iy:abs())
  local isnumneg, isdenomneg = ix:isneg(), iy:isneg()
  if isnumneg ~= isdenomneg then
- quot:_unm()
+ quo:_unm()
  -- round quotient towards minus infinity
  if not rem:iszero() then
- quot:_dec()
+ quo:_dec()
  -- adjust the remainder
  if isnumneg and not isdenomneg then
  rem:_unm():_add(y)
@@ -1177,9 +1171,10 @@ function bint.idivmod(x, y)
  -- adjust the remainder
  rem:_unm()
  end
- return quot, rem
+ return quo, rem
  else
- return idivmod(bint.tonumber(x), bint.tonumber(y))
+ local nx, ny = bint.tonumber(x), bint.tonumber(y)
+ return nx // ny, nx % ny
  end
 end
 

docs/index.html

@@ -2368,7 +2368,7 @@ <h2 class="section-header "><a name="Fields"></a>Fields</h2>
 </div> <!-- id="main" -->
 <div id="about">
 <i>generated by <a href="http://github.com/stevedonovan/LDoc">LDoc 1.4.6</a></i>
-<i style="float:right;">Last updated 2020-07-10 14:02:03 </i>
+<i style="float:right;">Last updated 2020-07-10 22:49:06 </i>
 </div> <!-- id="about" -->
 </div> <!-- id="container" -->
 </body>

tests.lua

@@ -614,9 +614,9 @@ local function test(bits, wordbits)
  end
 end
 
+test(64)
+test(64, 16)
 test(64, 4)
 test(64, 8)
-test(64, 16)
-test(64)
 test(128)
 test(256)