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 5from __future__ import print_function 6 7min_exponent = -348 8max_exponent = 340 9step = 8 10significand_size = 64 11exp_offset = 2000 12 13class fp: 14 pass 15 16powers = [] 17for 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 40print('Significands:', end='') 41for i, fp in enumerate(powers): 42 if i % 3 == 0: 43 print(end='\n ') 44 print(' {:0<#16x}'.format(fp.f, ), end=',') 45 46print('\n\nExponents:', end='') 47for i, fp in enumerate(powers): 48 if i % 11 == 0: 49 print(end='\n ') 50 print(' {:5}'.format(fp.e), end=',') 51 52print('\n\nMax exponent difference:', 53 max([x.e - powers[i - 1].e for i, x in enumerate(powers)][1:])) 54