# vim: set fileencoding=utf-8 :
#    Copyright © 2008 Jeff Epler <jepler@unpythonic.net)
#
#    This program is free software; you can redistribute it and/or modify
#    it under the terms of the GNU General Public License as published by
#    the Free Software Foundation; either version 2 of the License, or
#    (at your option) any later version.
#
#    This program is distributed in the hope that it will be useful,
#    but WITHOUT ANY WARRANTY; without even the implied warranty of
#    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#    GNU General Public License for more details.
#
#    You should have received a copy of the GNU General Public License
#    along with this program; if not, write to the Free Software
#    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

"""Extend the 1-2-5 progression to real numbers.

lurg(epic(x)) = x except for rounding errors

epic(0) = 1, epic(1) = 2, epic(2) = 5
epic(3+x) = 10*epic(x)

between integer values, the progression is exponential
"""

import math, sys

__all__ = ['lurg', 'epic']
def powers(start=1):
    m = int(math.floor(math.log(start, 10)))
    l = 10**m
    while 1:
        yield 3*m,   l
        yield 3*m+1, l*2
        yield 3*m+2, l*5
        l *= 10
        m += 1

def lb(x):
    for m, p in powers(x):
        if p == x: return m, p
        if p > x: return m-1, op
        op = p

def lurg(x):
    """A log-like function using the 1-2-5 progression."""
    lm, lo = lb(x)
    hi = iepic(lm+1)

    return lm + math.log(x/lo, hi*1./lo)

def iepic(x):
    m = x/3
    n = [1,2,5][x%3]
    return n * 10.**m
    
def epic(x):
    """An exponent-like function using the 1-2-5 progression."""
    whole = int(math.floor(x))
    frac = x - whole

    lo = iepic(whole)
    hi = iepic(whole+1)
    
    return lo * (hi/lo) ** frac

if __name__ == '__main__':
    worsterr = 0
    for i in range(-100, 100):
        j = i*.1
        e = epic(j)
        l = lurg(e)
        err = abs(l-j)
        if err > worsterr: worsterr = err
        print j, e, l, err, worsterr