Clean up digit_count lookup table generation

2021/06/03/generate.py

@@ -1,31 +1,35 @@
+from functools import partial
+import math
 
-from math import floor, log, ceil
-def log2(x):
-    return len(bin(x))-2
-table = []
-def mylog10(x):
-    return int(ceil(log(x)/log(10)))
-table.append(0)
-for j in range(1,33):
-    smallest = 2**(j-1)
-    largest = 2**(j) - 1
-    if(j < 31):
-      print("(1 << 32) -  "+str(10**mylog10(smallest)) + " + ("+str(mylog10(smallest))+ " << 32), // ceil(log10("+str(smallest)+")) = "+str(mylog10(smallest)))
-      table.append((2**32 - 10**mylog10(smallest)) + (mylog10(smallest) <<32))
-    else:
-      print(" ("+str(mylog10(smallest))+ " << 32), // ceil(log10("+str(smallest)+")) = "+str(mylog10(smallest)))
-      table.append((mylog10(smallest) <<32))
-
-
-
-print(table)
-print(len(table))
-def fast_digit_count(x):
-    return (x+table[log2(x)])//(2**32)#return (x+table[log2(x)]) >> 32
-#for x in range(1100):
-#    print(x, fast_digit_count(x))
-
-#print (mylog10(100))
-print(fast_digit_count(1073741824))
-print(mylog10(1073741824))
-print(log2(1073741824))
+def log2(n: int) -> int:
+  return int(math.log2(n | 1))
+
+def log10(n: int) -> int:
+  return int(math.log10(n | 1))
+
+def row(i: int, for_digit_count: bool = False) -> int:
+  d = log10(2**i)
+  # max(0, _) to avoid overflow
+  return ((d + for_digit_count) << 32) + max(0, ((1 << 32) - 10**(d + 1)))
+
+log10_table = list(map(row, range(32)))
+
+def log10_fast(n: int) -> int:
+  assert 0 <= n < 2**32, n
+  return (n + log10_table[log2(n)]) >> 32
+
+digit_count_table = list(map(partial(row, for_digit_count=True), range(32)))
+
+def digit_count(n: int) -> int:
+  assert 0 <= n < 2**32, n
+  return (n + digit_count_table[log2(n)]) >> 32
+
+tests = [
+  0, 1, 2, 3, 9, 10, 99, 100, 999, 1000, 9999, 10000, 99999, 100000, 999999, 1000000, 9999999,
+  10000000, 99999999, 100000000, 999999999, 1000000000, (1 << 32) - 1
+]
+
+for i in tests:
+  log10_ref, log10_res = log10(i), log10_fast(i)
+  dc_ref, dc_res = digit_count(i), digit_count(i)
+  assert log10_ref == log10_res == dc_ref - 1 == dc_res - 1