helper script to generate tables needed for string-to-number conversion

src/gennumdigits.py

@@ -0,0 +1,46 @@
+#!/usr/bin/python
+#
+#  Generate a table indicating how many digits should be considered
+#  significant for each radix (2 to 36) when doing string-to-number
+#  conversion.
+#
+#  For decimal, the E5/E5.1 specification indicates that anything
+#  after the 20th digit can be ignored (treated as zero) and the
+#  20th digit can be rounded upwards.  We estimate the significant
+#  bits of precision from this and compute similar values for other
+#  radix values.
+#
+#  Also generate a table of minimum and maximum radix-specific
+#  exponent values above and below which a number is guaranteed
+#  to overflow to Infinity or underflow to zero.  This allows the
+#  C code to quick reject such exponent values, and to keep bigint
+#  values bounded.  The exponent limit is relative to an integer
+#  significand padded to the precision-related digit count (e.g.
+#  20 for decimal).
+
+import math
+
+digits_table = []
+limits_table = []
+
+for radix in xrange(2, 36+1):
+	bits_per_digit = math.log(radix, 2)
+
+	if radix == 10:
+		prec_digits = 20
+	else:
+		target_bits = math.ceil(math.log(10, 2) * 20) + 2  # +2 is extra, just in case
+		prec_digits = int(math.ceil(target_bits / bits_per_digit))
+	digits_table.append(prec_digits)
+
+	# these are conservative (details are off by one etc); +/- 2 is the extra
+	overflow_limit = int(math.ceil(1024.0 / bits_per_digit)) + 2 - prec_digits
+	underflow_limit = int(math.floor((-1024.0 - 52.0) / bits_per_digit)) - 2 - prec_digits
+
+	limits_table.append(overflow_limit)
+	limits_table.append(underflow_limit)
+
+print repr(digits_table)
+print repr(limits_table)
+
+