| #!/usr/bin/env python |
| # Compute 10 ** exp with exp in the range [min_exponent, max_exponent] and print |
| # normalized (with most-significant bit equal to 1) significands in hexadecimal. |
| |
| from __future__ import print_function |
| |
| min_exponent = -348 |
| max_exponent = 340 |
| step = 8 |
| significand_size = 64 |
| exp_offset = 2000 |
| |
| class fp: |
| pass |
| |
| powers = [] |
| for i, exp in enumerate(range(min_exponent, max_exponent + 1, step)): |
| result = fp() |
| n = 10 ** exp if exp >= 0 else 2 ** exp_offset / 10 ** -exp |
| k = significand_size + 1 |
| # Convert to binary and round. |
| binary = '{:b}'.format(n) |
| result.f = (int('{:0<{}}'.format(binary[:k], k), 2) + 1) / 2 |
| result.e = len(binary) - (exp_offset if exp < 0 else 0) - significand_size |
| powers.append(result) |
| # Sanity check. |
| exp_offset10 = 400 |
| actual = result.f * 10 ** exp_offset10 |
| if result.e > 0: |
| actual *= 2 ** result.e |
| else: |
| for j in range(-result.e): |
| actual /= 2 |
| expected = 10 ** (exp_offset10 + exp) |
| precision = len('{}'.format(expected)) - len('{}'.format(actual - expected)) |
| if precision < 19: |
| print('low precision:', precision) |
| exit(1) |
| |
| print('Significands:', end='') |
| for i, fp in enumerate(powers): |
| if i % 3 == 0: |
| print(end='\n ') |
| print(' {:0<#16x}'.format(fp.f, ), end=',') |
| |
| print('\n\nExponents:', end='') |
| for i, fp in enumerate(powers): |
| if i % 11 == 0: |
| print(end='\n ') |
| print(' {:5}'.format(fp.e), end=',') |
| |
| print('\n\nMax exponent difference:', |
| max([x.e - powers[i - 1].e for i, x in enumerate(powers)][1:])) |