ceph/src/seastar/fmt/support/compute-powers.py

   1 #!/usr/bin/env python
   2 # Compute 10 ** exp with exp in the range [min_exponent, max_exponent] and print
   3 # normalized (with most-significant bit equal to 1) significands in hexadecimal.
   4
   5 from __future__ import print_function
   6
   7 min_exponent = -348
   8 max_exponent = 340
   9 step = 8
  10 significand_size = 64
  11 exp_offset = 2000
  12
  13 class fp:
  14     pass
  15
  16 powers = []
  17 for i, exp in enumerate(range(min_exponent, max_exponent + 1, step)):
  18     result = fp()
  19     n = 10 ** exp if exp >= 0 else 2 ** exp_offset / 10 ** -exp
  20     k = significand_size + 1
  21     # Convert to binary and round.
  22     binary = '{:b}'.format(n)
  23     result.f = (int('{:0<{}}'.format(binary[:k], k), 2) + 1) / 2
  24     result.e = len(binary) - (exp_offset if exp < 0 else 0) - significand_size
  25     powers.append(result)
  26     # Sanity check.
  27     exp_offset10 = 400
  28     actual = result.f * 10 ** exp_offset10
  29     if result.e > 0:
  30         actual *= 2 ** result.e
  31     else:
  32         for j in range(-result.e):
  33             actual /= 2
  34     expected = 10 ** (exp_offset10 + exp)
  35     precision = len('{}'.format(expected)) - len('{}'.format(actual - expected))
  36     if precision < 19:
  37         print('low precision:', precision)
  38         exit(1)
  39
  40 print('Significands:', end='')
  41 for i, fp in enumerate(powers):
  42     if i % 3 == 0:
  43         print(end='\n ')
  44     print(' {:0<#16x}'.format(fp.f, ), end=',')
  45
  46 print('\n\nExponents:', end='')
  47 for i, fp in enumerate(powers):
  48     if i % 11 == 0:
  49         print(end='\n ')
  50     print(' {:5}'.format(fp.e), end=',')
  51
  52 print('\n\nMax exponent difference:',
  53       max([x.e - powers[i - 1].e for i, x in enumerate(powers)][1:]))