#!/usr/bin/env python

import sys, math, string
from math import sqrt, pi, sin, cos

root2 = sqrt(2)

def progression(a0=0.0,b0=0.0,x=1,y=1):
	a0 = float(a0)
	b0 = float(b0)
	sys.stdout.write("\n")
	for a in range(0,y):
		ak = {}
		bk = {}
		for b in range(0,x):
			ak[b] = a0 + float(a)
			bk[b] = b0 + float(b)
			sys.stdout.write("k".rjust(4))
			sys.stdout.write("a_k".rjust(7))
			sys.stdout.write("norm a".rjust(7))
			sys.stdout.write("func a".rjust(7))
			sys.stdout.write("b_k".rjust(7))
			sys.stdout.write("norm b".rjust(7))
			sys.stdout.write("func b".rjust(7))
		sys.stdout.write( "\n")
		for k in range(0, 9):
			for b in range(0,x):
				sys.stdout.write(str("%d:" % k).rjust(4))
				sys.stdout.write(str("%0.3f" % ak[b]).rjust(7))
				sys.stdout.write(str("%0.3f" % \
					norm(ak[b],k)).rjust(7))
				sys.stdout.write(str("%0.3f" % \
					sinFormula(k,a0 + float(a),b0 + float(b)) \
					).rjust(7))
				
				sys.stdout.write(str("%0.3f" % bk[b]).rjust(7))
				sys.stdout.write(str("%0.3f" % \
					norm(bk[b],k)).rjust(7))
				sys.stdout.write(str("%0.3f" % \
					cosFormula(k,a0 + float(a),b0 + float(b)) \
					).rjust(7))
				ak[b] = ak[b] - bk[b]
				bk[b] = ak[b] + 2*bk[b]
			sys.stdout.write( "\n")
		sys.stdout.write( "\n")

def sinFormula(k,a,b):
	k = float(k)
	a = float(a)
	b = float(b)
	return pow(root2,k)*(a*cos(k*pi/4)-b*sin(k*pi/4))
def cosFormula(k,a,b):
	k = float(k)
	a = float(a)
	b = float(b)
	return pow(root2,k)*(b*cos(k*pi/4)+a*sin(k*pi/4))

def norm(n,k):
	return float(n) / pow(2,float(k)/2)

if (__name__ == "__main__"):
	import re
	count = 15
	if not len(sys.argv)>1:
		squareProgression(3,4)
	for arg in sys.argv[1:]:
		mo = re.match("^((?P<x>\d+),(?P<y>\d+),)?"+\
			"(?P<a>-?\d+(.\d+)?),(?P<b>-?\d+(.\d+)?)$", arg)
		if not mo:
			print "arg " + arg + " generated no match"
		else:
			x = 1
			y = 1
			a = float(mo.group("a"))
			b = float(mo.group("b"))
			if mo.group("x"):
				x = int(mo.group("x"))
				y = int(mo.group("y"))
			progression(a, b, x, y)