File: frapp.py
   1 #!/usr/bin/python3
   2 
   3 # The MIT License (MIT)
   4 #
   5 # Copyright © 2024 pacman64
   6 #
   7 # Permission is hereby granted, free of charge, to any person obtaining a copy
   8 # of this software and associated documentation files (the “Software”), to deal
   9 # in the Software without restriction, including without limitation the rights
  10 # to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  11 # copies of the Software, and to permit persons to whom the Software is
  12 # furnished to do so, subject to the following conditions:
  13 #
  14 # The above copyright notice and this permission notice shall be included in
  15 # all copies or substantial portions of the Software.
  16 #
  17 # THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  18 # IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  19 # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  20 # AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  21 # LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  22 # OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  23 # SOFTWARE.
  24 
  25 
  26 # frapp [floating-point values...]
  27 #
  28 # FRactional APProximations tries to find fractions which are close to the
  29 # floating-point value(s) given.
  30 
  31 
  32 from fractions import Fraction
  33 from math import ceil, floor, isinf, isnan
  34 from sys import argv, exit, stderr, stdout
  35 
  36 
  37 # info is the help message shown when asked to
  38 info = '''
  39 frapp [floating-point values...]
  40 
  41 FRactional APProximations tries to find fractions which are close to the
  42 floating-point value(s) given.
  43 '''.strip()
  44 
  45 # handle standard help cmd-line options, quitting right away in that case
  46 if len(argv) == 2 and argv[1] in ('-h', '--h', '-help', '--help'):
  47     print(info, file=stderr)
  48     exit(0)
  49 
  50 
  51 def run(s: str) -> None:
  52     '''Show fractions approximating the target value given.'''
  53 
  54     # handle invalid inputs: NaNs and the infinities are unmatchable
  55     value = float(s)
  56     if isnan(value) or isinf(value):
  57         raise ValueError(f'invalid number {value}')
  58 
  59     # show exact fraction first, with its 0-difference from the target
  60     print(f'{Fraction(s)}\t{s}\t0')
  61     # if it's an integer, don't bother searching for approximations
  62     if Fraction(s).denominator == 1:
  63         return
  64 
  65     posvalue = abs(value)
  66     min_diff = posvalue
  67 
  68     for den in range(1, 1_000_000):
  69         # restrict loop-range of numerators for a noticeable speed-up
  70         start = int(floor(posvalue * den))
  71         stop = int(ceil(posvalue * den))
  72 
  73         for num in range(start, stop + 1):
  74             f = num / den
  75             diff = (f - posvalue) / posvalue
  76             if abs(diff) < min_diff:
  77                 if value < 0:
  78                     print('-', end='')
  79                 print(f'{num}/{den}\t{f}\t{diff}')
  80                 min_diff = abs(diff)
  81 
  82 
  83 if len(argv) < 2:
  84     print(info, file=stderr)
  85     msg = '\x1b[31mexpected floating-point values as arguments\x1b[0m'
  86     print(msg, file=stderr)
  87     exit(1)
  88 
  89 try:
  90     stdout.reconfigure(newline='\n', encoding='utf-8')
  91     # running inside a func speeds things up in older versions of python
  92     if len(argv) == 2:
  93         run(argv[1])
  94     else:
  95         for e in argv[1:]:
  96             # print(e, file=stderr)
  97             print(f'\x1b[38;5;26m{e}\x1b[0m', file=stderr)
  98             run(e)
  99 except (BrokenPipeError, KeyboardInterrupt):
 100     # quit quietly, instead of showing a confusing error message
 101     stderr.flush()
 102     stderr.close()
 103 except Exception as err:
 104     print(f'\x1b[31m{err}\x1b[0m', file=stderr)
 105     exit(1)