src/etc/dec2flt_table.py

   1 #!/usr/bin/env python2.7
   2 #
   3 # Copyright 2015 The Rust Project Developers. See the COPYRIGHT
   4 # file at the top-level directory of this distribution and at
   5 # http://rust-lang.org/COPYRIGHT.
   6 #
   7 # Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
   8 # http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
   9 # <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
  10 # option. This file may not be copied, modified, or distributed
  11 # except according to those terms.
  12
  13 """
  14 Generate powers of ten using William Clinger's ``AlgorithmM`` for use in
  15 decimal to floating point conversions.
  16
  17 Specifically, computes and outputs (as Rust code) a table of 10^e for some
  18 range of exponents e. The output is one array of 64 bit significands and
  19 another array of corresponding base two exponents. The approximations are
  20 normalized and rounded perfectly, i.e., within 0.5 ULP of the true value.
  21
  22 The representation ([u64], [i16]) instead of the more natural [(u64, i16)]
  23 is used because (u64, i16) has a ton of padding which would make the table
  24 even larger, and it's already uncomfortably large (6 KiB).
  25 """
  26 from __future__ import print_function
  27 import sys
  28 from fractions import Fraction
  29 from collections import namedtuple
  30
  31
  32 N = 64  # Size of the significand field in bits
  33 MIN_SIG = 2 ** (N - 1)
  34 MAX_SIG = (2 ** N) - 1
  35
  36
  37 # Hand-rolled fp representation without arithmetic or any other operations.
  38 # The significand is normalized and always N bit, but the exponent is
  39 # unrestricted in range.
  40 Fp = namedtuple('Fp', 'sig exp')
  41
  42
  43 def algorithm_m(f, e):
  44     assert f > 0
  45     if e < 0:
  46         u = f
  47         v = 10 ** abs(e)
  48     else:
  49         u = f * 10 ** e
  50         v = 1
  51     k = 0
  52     x = u // v
  53     while True:
  54         if x < MIN_SIG:
  55             u <<= 1
  56             k -= 1
  57         elif x >= MAX_SIG:
  58             v <<= 1
  59             k += 1
  60         else:
  61             break
  62         x = u // v
  63     return ratio_to_float(u, v, k)
  64
  65
  66 def ratio_to_float(u, v, k):
  67     q, r = divmod(u, v)
  68     v_r = v - r
  69     z = Fp(q, k)
  70     if r < v_r:
  71         return z
  72     elif r > v_r:
  73         return next_float(z)
  74     elif q % 2 == 0:
  75         return z
  76     else:
  77         return next_float(z)
  78
  79
  80 def next_float(z):
  81     if z.sig == MAX_SIG:
  82         return Fp(MIN_SIG, z.exp + 1)
  83     else:
  84         return Fp(z.sig + 1, z.exp)
  85
  86
  87 def error(f, e, z):
  88     decimal = f * Fraction(10) ** e
  89     binary = z.sig * Fraction(2) ** z.exp
  90     abs_err = abs(decimal - binary)
  91     # The unit in the last place has value z.exp
  92     ulp_err = abs_err / Fraction(2) ** z.exp
  93     return float(ulp_err)
  94
  95 LICENSE = """
  96 // Copyright 2015 The Rust Project Developers. See the COPYRIGHT
  97 // file at the top-level directory of this distribution and at
  98 // http://rust-lang.org/COPYRIGHT.
  99 //
 100 // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
 101 // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
 102 // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
 103 // option. This file may not be copied, modified, or distributed
 104 // except according to those terms.
 105 """
 106
 107 def main():
 108     MIN_E = -305
 109     MAX_E = 305
 110     e_range = range(MIN_E, MAX_E+1)
 111     powers = []
 112     for e in e_range:
 113         z = algorithm_m(1, e)
 114         err = error(1, e, z)
 115         assert err < 0.5
 116         powers.append(z)
 117     typ = "([u64; {0}], [i16; {0}])".format(len(e_range))
 118     print(LICENSE.strip())
 119     print("// Table of approximations of powers of ten.")
 120     print("// DO NOT MODIFY: Generated by a src/etc/dec2flt_table.py")
 121     print("pub const MIN_E: i16 = {};".format(MIN_E))
 122     print("pub const MAX_E: i16 = {};".format(MAX_E))
 123     print()
 124     print("pub const POWERS: ", typ, " = ([", sep='')
 125     for z in powers:
 126         print("    0x{:x},".format(z.sig))
 127     print("], [")
 128     for z in powers:
 129         print("    {},".format(z.exp))
 130     print("]);")
 131
 132
 133 if __name__ == '__main__':
 134     main()