Add Python script for calculating Freicoin demurrage parameters.

contrib/freicoin/demurrage_parameters_arithmetic.py

@@ -0,0 +1,51 @@
+#!/usr/bin/env python
+
+from __future__ import division
+
+try:
+    from gmpy2 import mpq as Fraction
+except ImportError:
+    from fractions import Fraction
+
+TOTAL_SUPPLY   = 10**16 - 1
+EQ_HEIGHT      = 161280
+TITHE_RATIO    = Fraction(4,5)
+TITHE_AMOUNT   = TOTAL_SUPPLY * TITHE_RATIO / EQ_HEIGHT
+DEMURRAGE_RATE = 2**20
+
+def sample_run(subsidy):
+  def get_block_value(height):
+    if height < EQ_HEIGHT:
+        return Fraction(TOTAL_SUPPLY, DEMURRAGE_RATE) + TITHE_AMOUNT + \
+               Fraction((EQ_HEIGHT - height) * subsidy, EQ_HEIGHT)
+    else:
+        return Fraction(TOTAL_SUPPLY, DEMURRAGE_RATE)
+  total=0
+  for i in xrange(EQ_HEIGHT):
+    total = total + get_block_value(i) - Fraction(total, DEMURRAGE_RATE)
+  return total
+
+print "Performing binary search..."
+
+low,high = 0, TOTAL_SUPPLY
+while True:
+  if (high-low) <= 1:
+    break
+  sample = (low+high)//2
+  result = sample_run(sample)
+  if result < TOTAL_SUPPLY:
+    low = sample
+  else:
+    high = sample
+  print(high - low)
+initial = low
+if sample_run(initial) >= TOTAL_SUPPLY:
+  initial = initial - 1
+print "Tithe amount:    %d" % TITHE_AMOUNT
+print "Initial subsidy: %d" % initial
+print "Initial reward:  %d" % (initial + TOTAL_SUPPLY//DEMURRAGE_RATE)
+print "Final subsidy:   %d" % 0
+print "Final reward:    %d" % (TOTAL_SUPPLY//DEMURRAGE_RATE)
+print "Equilibrium:     Block #%d" % EQ_HEIGHT
+print "Approx delta:    %f" % (initial / EQ_HEIGHT / 100000000)
+print "Max coins:       %d" % sample_run(initial)