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#!/usr/bin/env python2
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#
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# Generate a table indicating how many digits should be considered
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# significant for each radix (2 to 36) when doing string-to-number
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# conversion.
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#
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# For decimal, the E5/E5.1 specification indicates that anything
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# after the 20th digit can be ignored (treated as zero) and the
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# 20th digit can be rounded upwards. We estimate the significant
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# bits of precision from this and compute similar values for other
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# radix values.
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#
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# Also generate a table of minimum and maximum radix-specific
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# exponent values above and below which a number is guaranteed
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# to overflow to Infinity or underflow to zero. This allows the
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# C code to quick reject such exponent values, and to keep bigint
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# values bounded. The exponent limit is relative to an integer
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# significand padded to the precision-related digit count (e.g.
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# 20 for decimal).
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#
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import math
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digits_table = []
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limits_table = []
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for radix in xrange(2, 36+1):
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bits_per_digit = math.log(radix, 2)
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if radix == 10:
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prec_digits = 20
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else:
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target_bits = math.ceil(math.log(10, 2) * 20) + 2 # +2 is extra, just in case
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prec_digits = int(math.ceil(target_bits / bits_per_digit))
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digits_table.append(prec_digits)
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# these are conservative (details are off by one etc); +/- 2 is the extra
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overflow_limit = int(math.ceil(1024.0 / bits_per_digit)) + 2 - prec_digits
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underflow_limit = int(math.floor((-1024.0 - 52.0) / bits_per_digit)) - 2 - prec_digits
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limits_table.append(overflow_limit)
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limits_table.append(underflow_limit)
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print repr(digits_table)
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print repr(limits_table)
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