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#!/usr/bin/env python
#
# Copyright 2018 Developers of the Rand project.
# Copyright 2013 The Rust Project Developers.
#
# Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
# https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
# <LICENSE-MIT or https://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 2018 Developers of the Rand project.
// Copyright 2013 The Rust Project Developers.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or https://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))
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