Script for generating the powers-of-ten tables necessary for correct and

fast decimal-to-float conversions.

Author: Robin Kruppe

src/etc/dec2flt_table.py

@@ -0,0 +1,134 @@
+#!/usr/bin/env python2.7
+#
+# Copyright 2015 The Rust Project Developers. See the COPYRIGHT
+# file at the top-level directory of this distribution and at
+# http://rust-lang.org/COPYRIGHT.
+#
+# Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
+# http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
+# <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
+# option. This file may not be copied, modified, or distributed
+# except according to those terms.
+
+"""
+Generate powers of ten using William Clinger's ``AlgorithmM`` for use in
+decimal to floating point conversions.
+
+Specifically, computes and outputs (as Rust code) a table of 10^e for some
+range of exponents e. The output is one array of 64 bit significands and
+another array of corresponding base two exponents. The approximations are
+normalized and rounded perfectly, i.e., within 0.5 ULP of the true value.
+
+The representation ([u64], [i16]) instead of the more natural [(u64, i16)]
+is used because (u64, i16) has a ton of padding which would make the table
+even larger, and it's already uncomfortably large (6 KiB).
+"""
+from __future__ import print_function
+import sys
+from fractions import Fraction
+from collections import namedtuple
+
+
+N = 64  # Size of the significand field in bits
+MIN_SIG = 2 ** (N - 1)
+MAX_SIG = (2 ** N) - 1
+
+
+# Hand-rolled fp representation without arithmetic or any other operations.
+# The significand is normalized and always N bit, but the exponent is
+# unrestricted in range.
+Fp = namedtuple('Fp', 'sig exp')
+
+
+def algorithm_m(f, e):
+    assert f > 0
+    if e < 0:
+        u = f
+        v = 10 ** abs(e)
+    else:
+        u = f * 10 ** e
+        v = 1
+    k = 0
+    x = u // v
+    while True:
+        if x < MIN_SIG:
+            u <<= 1
+            k -= 1
+        elif x >= MAX_SIG:
+            v <<= 1
+            k += 1
+        else:
+            break
+        x = u // v
+    return ratio_to_float(u, v, k)
+
+
+def ratio_to_float(u, v, k):
+    q, r = divmod(u, v)
+    v_r = v - r
+    z = Fp(q, k)
+    if r < v_r:
+        return z
+    elif r > v_r:
+        return next_float(z)
+    elif q % 2 == 0:
+        return z
+    else:
+        return next_float(z)
+
+
+def next_float(z):
+    if z.sig == MAX_SIG:
+        return Fp(MIN_SIG, z.exp + 1)
+    else:
+        return Fp(z.sig + 1, z.exp)
+
+
+def error(f, e, z):
+    decimal = f * Fraction(10) ** e
+    binary = z.sig * Fraction(2) ** z.exp
+    abs_err = abs(decimal - binary)
+    # The unit in the last place has value z.exp
+    ulp_err = abs_err / Fraction(2) ** z.exp
+    return float(ulp_err)
+
+LICENSE = """
+// Copyright 2015 The Rust Project Developers. See the COPYRIGHT
+// file at the top-level directory of this distribution and at
+// http://rust-lang.org/COPYRIGHT.
+//
+// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
+// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
+// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
+// option. This file may not be copied, modified, or distributed
+// except according to those terms.
+"""
+
+def main():
+    MIN_E = -305
+    MAX_E = 305
+    e_range = range(MIN_E, MAX_E+1)
+    powers = []
+    for e in e_range:
+        z = algorithm_m(1, e)
+        err = error(1, e, z)
+        assert err < 0.5
+        powers.append(z)
+    typ = "([u64; {0}], [i16; {0}])".format(len(e_range))
+    print(LICENSE.strip())
+    print("// Table of approximations of powers of ten.")
+    print("// DO NOT MODIFY: Generated by a src/etc/dec2flt_table.py")
+    print("pub const MIN_E: i16 = {};".format(MIN_E))
+    print("pub const MAX_E: i16 = {};".format(MAX_E))
+    print()
+    print("pub const POWERS: ", typ, " = ([", sep='')
+    for z in powers:
+        print("    0x{:x},".format(z.sig))
+    print("], [")
+    for z in powers:
+        print("    {},".format(z.exp))
+    print("]);")
+
+
+if __name__ == '__main__':
+    main()