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Diffstat (limited to 'rand/utils')
-rwxr-xr-x | rand/utils/ziggurat_tables.py | 127 |
1 files changed, 127 insertions, 0 deletions
diff --git a/rand/utils/ziggurat_tables.py b/rand/utils/ziggurat_tables.py new file mode 100755 index 0000000..762f956 --- /dev/null +++ b/rand/utils/ziggurat_tables.py @@ -0,0 +1,127 @@ +#!/usr/bin/env python +# +# Copyright 2013 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. + +# This creates the tables used for distributions implemented using the +# ziggurat algorithm in `rand::distributions;`. They are +# (basically) the tables as used in the ZIGNOR variant (Doornik 2005). +# They are changed rarely, so the generated file should be checked in +# to git. +# +# It creates 3 tables: X as in the paper, F which is f(x_i), and +# F_DIFF which is f(x_i) - f(x_{i-1}). The latter two are just cached +# values which is not done in that paper (but is done in other +# variants). Note that the adZigR table is unnecessary because of +# algebra. +# +# It is designed to be compatible with Python 2 and 3. + +from math import exp, sqrt, log, floor +import random + +# The order should match the return value of `tables` +TABLE_NAMES = ['X', 'F'] + +# The actual length of the table is 1 more, to stop +# index-out-of-bounds errors. This should match the bitwise operation +# to find `i` in `zigurrat` in `libstd/rand/mod.rs`. Also the *_R and +# *_V constants below depend on this value. +TABLE_LEN = 256 + +# equivalent to `zigNorInit` in Doornik2005, but generalised to any +# distribution. r = dR, v = dV, f = probability density function, +# f_inv = inverse of f +def tables(r, v, f, f_inv): + # compute the x_i + xvec = [0]*(TABLE_LEN+1) + + xvec[0] = v / f(r) + xvec[1] = r + + for i in range(2, TABLE_LEN): + last = xvec[i-1] + xvec[i] = f_inv(v / last + f(last)) + + # cache the f's + fvec = [0]*(TABLE_LEN+1) + for i in range(TABLE_LEN+1): + fvec[i] = f(xvec[i]) + + return xvec, fvec + +# Distributions +# N(0, 1) +def norm_f(x): + return exp(-x*x/2.0) +def norm_f_inv(y): + return sqrt(-2.0*log(y)) + +NORM_R = 3.6541528853610088 +NORM_V = 0.00492867323399 + +NORM = tables(NORM_R, NORM_V, + norm_f, norm_f_inv) + +# Exp(1) +def exp_f(x): + return exp(-x) +def exp_f_inv(y): + return -log(y) + +EXP_R = 7.69711747013104972 +EXP_V = 0.0039496598225815571993 + +EXP = tables(EXP_R, EXP_V, + exp_f, exp_f_inv) + + +# Output the tables/constants/types + +def render_static(name, type, value): + # no space or + return 'pub static %s: %s =%s;\n' % (name, type, value) + +# static `name`: [`type`, .. `len(values)`] = +# [values[0], ..., values[3], +# values[4], ..., values[7], +# ... ]; +def render_table(name, values): + rows = [] + # 4 values on each row + for i in range(0, len(values), 4): + row = values[i:i+4] + rows.append(', '.join('%.18f' % f for f in row)) + + rendered = '\n [%s]' % ',\n '.join(rows) + return render_static(name, '[f64, .. %d]' % len(values), rendered) + + +with open('ziggurat_tables.rs', 'w') as f: + f.write('''// Copyright 2013 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. + +// Tables for distributions which are sampled using the ziggurat +// algorithm. Autogenerated by `ziggurat_tables.py`. + +pub type ZigTable = &\'static [f64, .. %d]; +''' % (TABLE_LEN + 1)) + for name, tables, r in [('NORM', NORM, NORM_R), + ('EXP', EXP, EXP_R)]: + f.write(render_static('ZIG_%s_R' % name, 'f64', ' %.18f' % r)) + for (tabname, table) in zip(TABLE_NAMES, tables): + f.write(render_table('ZIG_%s_%s' % (name, tabname), table)) |