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#!/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:]))
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