4 # This creates the tables used for distributions implemented using the
5 # ziggurat algorithm in `std::rand::distributions;`. They are
6 # (basically) the tables as used in the ZIGNOR variant (Doornik 2005).
7 # They are changed rarely, so the generated file should be checked in
10 # It creates 3 tables: X as in the paper, F which is f(x_i), and
11 # F_DIFF which is f(x_i) - f(x_{i-1}). The latter two are just cached
12 # values which is not done in that paper (but is done in other
13 # variants). Note that the adZigR table is unnecessary because of
16 # It is designed to be compatible with Python 2 and 3.
18 from math import exp, sqrt, log, floor
21 # The order should match the return value of `tables`
22 TABLE_NAMES = ['X', 'F', 'F_DIFF']
24 # The actual length of the table is 1 more, to stop
25 # index-out-of-bounds errors. This should match the bitwise operation
26 # to find `i` in `zigurrat` in `libstd/rand/mod.rs`. Also the *_R and
27 # *_V constants below depend on this value.
30 # equivalent to `zigNorInit` in Doornik2005, but generalised to any
31 # distribution. r = dR, v = dV, f = probability density function,
32 # f_inv = inverse of f
33 def tables(r, v, f, f_inv):
35 xvec = [0]*(TABLE_LEN+1)
40 for i in range(2, TABLE_LEN):
42 xvec[i] = f_inv(v / last + f(last))
45 fvec = [0]*(TABLE_LEN+1)
46 fdiff = [0]*(TABLE_LEN+1)
47 for i in range(TABLE_LEN+1):
50 fdiff[i] = fvec[i] - fvec[i-1]
52 return xvec, fvec, fdiff
59 return sqrt(-2.0*log(y))
61 NORM_R = 3.6541528853610088
62 NORM_V = 0.00492867323399
64 NORM = tables(NORM_R, NORM_V,
73 EXP_R = 7.69711747013104972
74 EXP_V = 0.0039496598225815571993
76 EXP = tables(EXP_R, EXP_V,
80 # Output the tables/constants/types
82 def render_static(name, type, value):
84 return 'pub static %s: %s =%s;\n' % (name, type, value)
86 # static `name`: [`type`, .. `len(values)`] =
87 # [values[0], ..., values[3],
88 # values[4], ..., values[7],
90 def render_table(name, values):
92 # 4 values on each row
93 for i in range(0, len(values), 4):
95 rows.append(', '.join('%.18f' % f for f in row))
97 rendered = '\n [%s]' % ',\n '.join(rows)
98 return render_static(name, '[f64, .. %d]' % len(values), rendered)
101 with open('ziggurat_tables.rs', 'w') as f:
102 f.write('''// Copyright 2013 The Rust Project Developers. See the COPYRIGHT
103 // file at the top-level directory of this distribution and at
104 // http://rust-lang.org/COPYRIGHT.
106 // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
107 // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
108 // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
109 // option. This file may not be copied, modified, or distributed
110 // except according to those terms.
112 // Tables for distributions which are sampled using the ziggurat
113 // algorithm. Autogenerated by `ziggurat_tables.py`.
115 pub type ZigTable = &\'static [f64, .. %d];
116 ''' % (TABLE_LEN + 1))
117 for name, tables, r in [('NORM', NORM, NORM_R),
118 ('EXP', EXP, EXP_R)]:
119 f.write(render_static('ZIG_%s_R' % name, 'f64', ' %.18f' % r))
120 for (tabname, table) in zip(TABLE_NAMES, tables):
121 f.write(render_table('ZIG_%s_%s' % (name, tabname), table))