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