annotate liboctave/numeric/randmtzig.cc @ 24534:194eb4bd202b

maint: Update punctuation for GPL v3 license text. * COPYING, Makefile.am, README, bootstrap, bootstrap.conf, OctJavaQry.java, changelog.tmpl, check-subst-vars.in.sh, find-defun-files.sh, find-files-with-tests.sh, get-source-mtime.sh, mk-hg-id.sh, mk-octave-config-h.sh, mk-opts.pl, stl_algo.h-fixed, subst-config-vals.in.sh, subst-cross-config-vals.in.sh, subst-default-vals.in.sh, subst-script-vals.in.sh, configure.ac, Doxyfile.in, arith.txi, audio.txi, basics.txi, bugs.txi, config-images.sh, container.txi, cp-idx.txi, data.txi, debug.txi, diagperm.txi, diffeq.txi, add_to_aspell_dict, mk_undocumented_list, spellcheck, errors.txi, eval.txi, expr.txi, external.txi, fn-idx.txi, func.txi, genpropdoc.m, geometry.txi, geometryimages.m, grammar.txi, gui.txi, image.txi, images.awk, install.txi, interp.txi, interpimages.m, intro.txi, io.txi, linalg.txi, macros.texi, matrix.txi, mk-doc-cache.pl, mkcontrib.awk, mkoctfile.1, munge-texi.pl, nonlin.txi, numbers.txi, obsolete.txi, octave-cli.1, octave-config.1, octave.1, octave.css, octave.texi, oop.txi, op-idx.txi, optim.txi, package.txi, plot.txi, plotimages.m, poly.txi, preface.txi, quad.txi, set.txi, signal.txi, sparse.txi, sparseimages.m, splineimages.m, stats.txi, stmt.txi, strings.txi, system.txi, testfun.txi, var.txi, vectorize.txi, array.texi, bugs.texi, cp-idx.texi, dae.texi, diffeq.texi, error.texi, factor.texi, fn-idx.texi, gpl.texi, install.texi, intro.texi, liboctave.texi, matvec.texi, nleqn.texi, nlfunc.texi, ode.texi, optim.texi, preface.texi, quad.texi, range.texi, refcard-a4.tex, refcard-legal.tex, refcard-letter.tex, refcard.tex, HACKING.md, octave.appdata.xml.in, Backend.cc, Backend.h, BaseControl.cc, BaseControl.h, ButtonControl.cc, ButtonControl.h, ButtonGroup.cc, ButtonGroup.h, Canvas.cc, Canvas.h, CheckBoxControl.cc, CheckBoxControl.h, Container.cc, Container.h, ContextMenu.cc, ContextMenu.h, EditControl.cc, EditControl.h, Figure.cc, Figure.h, FigureWindow.cc, FigureWindow.h, GLCanvas.cc, GLCanvas.h, GenericEventNotify.h, KeyMap.cc, KeyMap.h, ListBoxControl.cc, ListBoxControl.h, Logger.cc, Logger.h, Menu.cc, Menu.h, MenuContainer.h, MouseModeActionGroup.cc, MouseModeActionGroup.h, Object.cc, Object.h, ObjectFactory.cc, ObjectFactory.h, ObjectProxy.cc, ObjectProxy.h, Panel.cc, Panel.h, PopupMenuControl.cc, PopupMenuControl.h, PushButtonControl.cc, PushButtonControl.h, PushTool.cc, PushTool.h, QtHandlesUtils.cc, QtHandlesUtils.h, RadioButtonControl.cc, RadioButtonControl.h, SliderControl.cc, SliderControl.h, TextControl.cc, TextControl.h, TextEdit.cc, TextEdit.h, ToggleButtonControl.cc, ToggleButtonControl.h, ToggleTool.cc, ToggleTool.h, ToolBar.cc, ToolBar.h, ToolBarButton.cc, ToolBarButton.h, __init_qt__.cc, __init_qt__.h, annotation-dialog.cc, annotation-dialog.h, gl-select.cc, gl-select.h, liboctgui-build-info.h, liboctgui-build-info.in.cc, mk-default-qt-settings.in.sh, QTerminal.cc, QTerminal.h, BlockArray.cpp, BlockArray.h, Character.h, CharacterColor.h, Emulation.cpp, Emulation.h, Filter.cpp, Filter.h, History.cpp, History.h, KeyboardTranslator.cpp, KeyboardTranslator.h, QUnixTerminalImpl.cpp, QUnixTerminalImpl.h, Screen.cpp, Screen.h, ScreenWindow.cpp, ScreenWindow.h, SelfListener.cpp, SelfListener.h, TerminalCharacterDecoder.cpp, TerminalCharacterDecoder.h, TerminalModel.cpp, TerminalModel.h, TerminalView.cpp, TerminalView.h, Vt102Emulation.cpp, Vt102Emulation.h, kpty.cpp, kpty.h, kpty_p.h, QTerminalColors.cpp, QTerminalColors.h, QWinTerminalImpl.cpp, QWinTerminalImpl.h, main.cpp, color-picker.cc, color-picker.h, dialog.cc, dialog.h, documentation-dock-widget.cc, documentation-dock-widget.h, external-editor-interface.cc, external-editor-interface.h, files-dock-widget.cc, files-dock-widget.h, find-files-dialog.cc, find-files-dialog.h, find-files-model.cc, find-files-model.h, history-dock-widget.cc, history-dock-widget.h, file-editor-interface.h, file-editor-tab.cc, file-editor-tab.h, file-editor.cc, file-editor.h, find-dialog.cc, find-dialog.h, marker.cc, marker.h, octave-qscintilla.cc, octave-qscintilla.h, octave-txt-lexer.cc, octave-txt-lexer.h, main-window.cc, main-window.h, octave-cmd.cc, octave-cmd.h, octave-dock-widget.cc, octave-dock-widget.h, octave-gui.cc, octave-gui.h, octave-qt-link.cc, octave-qt-link.h, octave-settings.h, texinfo-parser.cc, texinfo-parser.h, webinfo.cc, webinfo.h, resource-manager.cc, resource-manager.h, settings-dialog.cc, settings-dialog.h, shortcut-manager.cc, shortcut-manager.h, terminal-dock-widget.cc, terminal-dock-widget.h, thread-manager.cc, thread-manager.h, variable-editor-model.cc, variable-editor-model.h, variable-editor.cc, variable-editor.h, welcome-wizard.cc, welcome-wizard.h, workspace-model.cc, workspace-model.h, workspace-view.cc, workspace-view.h, build-env.h, build-env.in.cc, builtins.h, Cell.cc, Cell.h, __contourc__.cc, __dsearchn__.cc, __ichol__.cc, __ilu__.cc, __lin_interpn__.cc, __luinc__.cc, __magick_read__.cc, __pchip_deriv__.cc, __qp__.cc, balance.cc, base-text-renderer.h, besselj.cc, betainc.cc, bitfcns.cc, bsxfun.cc, c-file-ptr-stream.cc, c-file-ptr-stream.h, call-stack.cc, call-stack.h, cdisplay.c, cdisplay.h, cellfun.cc, coct-hdf5-types.c, colloc.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc, data.h, debug.cc, default-defs.in.h, defaults.cc, defaults.h, defun-dld.h, defun-int.h, defun.cc, defun.h, det.cc, dirfns.cc, dirfns.h, display.cc, display.h, dlmread.cc, dot.cc, dynamic-ld.cc, dynamic-ld.h, eig.cc, ellipj.cc, environment.cc, environment.h, error.cc, error.h, errwarn.cc, errwarn.h, event-queue.cc, event-queue.h, fcn-info.cc, fcn-info.h, fft.cc, fft2.cc, fftn.cc, file-io.cc, file-io.h, filter.cc, find.cc, ft-text-renderer.cc, ft-text-renderer.h, gammainc.cc, gcd.cc, genprops.awk, getgrent.cc, getpwent.cc, getrusage.cc, givens.cc, gl-render.cc, gl-render.h, gl2ps-print.cc, gl2ps-print.h, graphics-handle.h, graphics-toolkit.cc, graphics-toolkit.h, graphics.cc, graphics.in.h, gripes.cc, gripes.h, gsvd.cc, gtk-manager.cc, gtk-manager.h, hash.cc, help.cc, help.h, hess.cc, hex2num.cc, hook-fcn.cc, hook-fcn.h, input.cc, input.h, interpreter-private.cc, interpreter-private.h, interpreter.cc, interpreter.h, inv.cc, kron.cc, load-path.cc, load-path.h, load-save.cc, load-save.h, lookup.cc, ls-ascii-helper.cc, ls-ascii-helper.h, ls-hdf5.cc, ls-hdf5.h, ls-mat-ascii.cc, ls-mat-ascii.h, ls-mat4.cc, ls-mat4.h, ls-mat5.cc, ls-mat5.h, ls-oct-binary.cc, ls-oct-binary.h, ls-oct-text.cc, ls-oct-text.h, ls-utils.cc, ls-utils.h, lsode.cc, lu.cc, mappers.cc, matrix_type.cc, max.cc, mex.cc, mex.h, mexproto.h, mgorth.cc, mk-errno-list.sh, mk-mxarray-h.in.sh, mxarray.in.h, nproc.cc, oct-errno.h, oct-errno.in.cc, oct-fstrm.cc, oct-fstrm.h, oct-handle.h, oct-hdf5-types.cc, oct-hdf5-types.h, oct-hdf5.h, oct-hist.cc, oct-hist.h, oct-iostrm.cc, oct-iostrm.h, oct-map.cc, oct-map.h, oct-obj.h, oct-opengl.h, oct-prcstrm.cc, oct-prcstrm.h, oct-procbuf.cc, oct-procbuf.h, oct-stdstrm.h, oct-stream.cc, oct-stream.h, oct-strstrm.cc, oct-strstrm.h, oct-tex-lexer.in.ll, oct-tex-parser.in.yy, oct.h, octave-default-image.h, octave-link.cc, octave-link.h, ordschur.cc, pager.cc, pager.h, pinv.cc, pr-output.cc, pr-output.h, procstream.cc, procstream.h, psi.cc, quad.cc, quadcc.cc, qz.cc, rand.cc, rcond.cc, regexp.cc, schur.cc, sighandlers.cc, sighandlers.h, sparse-xdiv.cc, sparse-xdiv.h, sparse-xpow.cc, sparse-xpow.h, sparse.cc, spparms.cc, sqrtm.cc, str2double.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc, sylvester.cc, symrec.cc, symrec.h, symscope.cc, symscope.h, symtab.cc, symtab.h, syscalls.cc, sysdep.cc, sysdep.h, text-renderer.cc, text-renderer.h, time.cc, toplev.cc, toplev.h, tril.cc, tsearch.cc, txt-eng.cc, txt-eng.h, typecast.cc, url-handle-manager.cc, url-handle-manager.h, urlwrite.cc, utils.cc, utils.h, variables.cc, variables.h, workspace-element.h, xdiv.cc, xdiv.h, xnorm.cc, xnorm.h, xpow.cc, xpow.h, zfstream.cc, zfstream.h, deprecated-config.h, __delaunayn__.cc, __eigs__.cc, __fltk_uigetfile__.cc, __glpk__.cc, __init_fltk__.cc, __init_gnuplot__.cc, __ode15__.cc, __osmesa_print__.cc, __voronoi__.cc, amd.cc, audiodevinfo.cc, audioread.cc, ccolamd.cc, chol.cc, colamd.cc, config-module.awk, config-module.sh, convhulln.cc, dmperm.cc, fftw.cc, gzip.cc, oct-qhull.h, qr.cc, symbfact.cc, symrcm.cc, liboctinterp-build-info.h, liboctinterp-build-info.in.cc, mk-build-env-features.sh, mk-builtins.pl, mk-doc.pl, mk-pkg-add.sh, mk-version-h.in.sh, ov-base-diag.cc, ov-base-diag.h, ov-base-int.cc, ov-base-int.h, ov-base-mat.cc, ov-base-mat.h, ov-base-scalar.cc, ov-base-scalar.h, ov-base-sparse.cc, ov-base-sparse.h, ov-base.cc, ov-base.h, ov-bool-mat.cc, ov-bool-mat.h, ov-bool-sparse.cc, ov-bool-sparse.h, ov-bool.cc, ov-bool.h, ov-builtin.cc, ov-builtin.h, ov-cell.cc, ov-cell.h, ov-ch-mat.cc, ov-ch-mat.h, ov-class.cc, ov-class.h, ov-classdef.cc, ov-classdef.h, ov-colon.cc, ov-colon.h, ov-complex.cc, ov-complex.h, ov-cs-list.cc, ov-cs-list.h, ov-cx-diag.cc, ov-cx-diag.h, ov-cx-mat.cc, ov-cx-mat.h, ov-cx-sparse.cc, ov-cx-sparse.h, ov-dld-fcn.cc, ov-dld-fcn.h, ov-fcn-handle.cc, ov-fcn-handle.h, ov-fcn-inline.cc, ov-fcn-inline.h, ov-fcn.cc, ov-fcn.h, ov-float.cc, ov-float.h, ov-flt-complex.cc, ov-flt-complex.h, ov-flt-cx-diag.cc, ov-flt-cx-diag.h, ov-flt-cx-mat.cc, ov-flt-cx-mat.h, ov-flt-re-diag.cc, ov-flt-re-diag.h, ov-flt-re-mat.cc, ov-flt-re-mat.h, ov-int-traits.h, ov-int16.cc, ov-int16.h, ov-int32.cc, ov-int32.h, ov-int64.cc, ov-int64.h, ov-int8.cc, ov-int8.h, ov-intx.h, ov-java.cc, ov-java.h, ov-lazy-idx.cc, ov-lazy-idx.h, ov-mex-fcn.cc, ov-mex-fcn.h, ov-null-mat.cc, ov-null-mat.h, ov-oncleanup.cc, ov-oncleanup.h, ov-perm.cc, ov-perm.h, ov-range.cc, ov-range.h, ov-re-diag.cc, ov-re-diag.h, ov-re-mat.cc, ov-re-mat.h, ov-re-sparse.cc, ov-re-sparse.h, ov-scalar.cc, ov-scalar.h, ov-str-mat.cc, ov-str-mat.h, ov-struct.cc, ov-struct.h, ov-typeinfo.cc, ov-typeinfo.h, ov-uint16.cc, ov-uint16.h, ov-uint32.cc, ov-uint32.h, ov-uint64.cc, ov-uint64.h, ov-uint8.cc, ov-uint8.h, ov-usr-fcn.cc, ov-usr-fcn.h, ov.cc, ov.h, ovl.cc, ovl.h, octave.cc, octave.h, op-kw-docs, mk-ops.sh, op-b-b.cc, op-b-bm.cc, op-b-sbm.cc, op-bm-b.cc, op-bm-bm.cc, op-bm-sbm.cc, op-cdm-cdm.cc, op-cdm-cm.cc, op-cdm-cs.cc, op-cdm-dm.cc, op-cdm-m.cc, op-cdm-s.cc, op-cell.cc, op-chm.cc, op-class.cc, op-cm-cdm.cc, op-cm-cm.cc, op-cm-cs.cc, op-cm-dm.cc, op-cm-m.cc, op-cm-pm.cc, op-cm-s.cc, op-cm-scm.cc, op-cm-sm.cc, op-cs-cm.cc, op-cs-cs.cc, op-cs-m.cc, op-cs-s.cc, op-cs-scm.cc, op-cs-sm.cc, op-dm-cdm.cc, op-dm-cm.cc, op-dm-cs.cc, op-dm-dm.cc, op-dm-m.cc, op-dm-s.cc, op-dm-scm.cc, op-dm-sm.cc, op-dm-template.cc, op-dms-template.cc, op-fcdm-fcdm.cc, op-fcdm-fcm.cc, op-fcdm-fcs.cc, op-fcdm-fdm.cc, op-fcdm-fm.cc, op-fcdm-fs.cc, op-fcm-fcdm.cc, op-fcm-fcm.cc, op-fcm-fcs.cc, op-fcm-fdm.cc, op-fcm-fm.cc, op-fcm-fs.cc, op-fcm-pm.cc, op-fcn.cc, op-fcs-fcm.cc, op-fcs-fcs.cc, op-fcs-fm.cc, op-fcs-fs.cc, op-fdm-fcdm.cc, op-fdm-fcm.cc, op-fdm-fcs.cc, op-fdm-fdm.cc, op-fdm-fm.cc, op-fdm-fs.cc, op-fm-fcdm.cc, op-fm-fcm.cc, op-fm-fcs.cc, op-fm-fdm.cc, op-fm-fm.cc, op-fm-fs.cc, op-fm-pm.cc, op-fs-fcm.cc, op-fs-fcs.cc, op-fs-fm.cc, op-fs-fs.cc, op-i16-i16.cc, op-i32-i32.cc, op-i64-i64.cc, op-i8-i8.cc, op-int-concat.cc, op-int.h, op-m-cdm.cc, op-m-cm.cc, op-m-cs.cc, op-m-dm.cc, op-m-m.cc, op-m-pm.cc, op-m-s.cc, op-m-scm.cc, op-m-sm.cc, op-pm-cm.cc, op-pm-fcm.cc, op-pm-fm.cc, op-pm-m.cc, op-pm-pm.cc, op-pm-scm.cc, op-pm-sm.cc, op-pm-template.cc, op-range.cc, op-s-cm.cc, op-s-cs.cc, op-s-m.cc, op-s-s.cc, op-s-scm.cc, op-s-sm.cc, op-sbm-b.cc, op-sbm-bm.cc, op-sbm-sbm.cc, op-scm-cm.cc, op-scm-cs.cc, op-scm-m.cc, op-scm-s.cc, op-scm-scm.cc, op-scm-sm.cc, op-sm-cm.cc, op-sm-cs.cc, op-sm-m.cc, op-sm-s.cc, op-sm-scm.cc, op-sm-sm.cc, op-str-m.cc, op-str-s.cc, op-str-str.cc, op-struct.cc, op-ui16-ui16.cc, op-ui32-ui32.cc, op-ui64-ui64.cc, op-ui8-ui8.cc, ops.h, options-usage.h, bp-table.cc, bp-table.h, comment-list.cc, comment-list.h, jit-ir.cc, jit-ir.h, jit-typeinfo.cc, jit-typeinfo.h, jit-util.cc, jit-util.h, lex.h, lex.ll, oct-lvalue.cc, oct-lvalue.h, oct-parse.in.yy, octave.gperf, parse.h, profiler.cc, profiler.h, pt-all.h, pt-arg-list.cc, pt-arg-list.h, pt-array-list.cc, pt-array-list.h, pt-assign.cc, pt-assign.h, pt-binop.cc, pt-binop.h, pt-bp.cc, pt-bp.h, pt-cbinop.cc, pt-cbinop.h, pt-cell.cc, pt-cell.h, pt-check.cc, pt-check.h, pt-classdef.cc, pt-classdef.h, pt-cmd.h, pt-colon.cc, pt-colon.h, pt-const.cc, pt-const.h, pt-decl.cc, pt-decl.h, pt-eval.cc, pt-eval.h, pt-except.cc, pt-except.h, pt-exp.cc, pt-exp.h, pt-fcn-handle.cc, pt-fcn-handle.h, pt-funcall.cc, pt-funcall.h, pt-id.cc, pt-id.h, pt-idx.cc, pt-idx.h, pt-jit.cc, pt-jit.h, pt-jump.cc, pt-jump.h, pt-loop.cc, pt-loop.h, pt-mat.cc, pt-mat.h, pt-misc.cc, pt-misc.h, pt-pr-code.cc, pt-pr-code.h, pt-select.cc, pt-select.h, pt-stmt.cc, pt-stmt.h, pt-tm-const.cc, pt-tm-const.h, pt-unop.cc, pt-unop.h, pt-walk.cc, pt-walk.h, pt.cc, pt.h, token.cc, token.h, Array-jit.cc, Array-tc.cc, version.cc, version.in.h, Array-C.cc, Array-b.cc, Array-ch.cc, Array-d.cc, Array-f.cc, Array-fC.cc, Array-i.cc, Array-idx-vec.cc, Array-s.cc, Array-str.cc, Array-util.cc, Array-util.h, Array-voidp.cc, Array.cc, Array.h, CColVector.cc, CColVector.h, CDiagMatrix.cc, CDiagMatrix.h, CMatrix.cc, CMatrix.h, CNDArray.cc, CNDArray.h, CRowVector.cc, CRowVector.h, CSparse.cc, CSparse.h, DiagArray2.cc, DiagArray2.h, MArray-C.cc, MArray-d.cc, MArray-f.cc, MArray-fC.cc, MArray-i.cc, MArray-s.cc, MArray.cc, MArray.h, MDiagArray2.cc, MDiagArray2.h, MSparse-C.cc, MSparse-d.cc, MSparse.cc, MSparse.h, Matrix.h, MatrixType.cc, MatrixType.h, PermMatrix.cc, PermMatrix.h, Range.cc, Range.h, Sparse-C.cc, Sparse-b.cc, Sparse-d.cc, Sparse.cc, Sparse.h, boolMatrix.cc, boolMatrix.h, boolNDArray.cc, boolNDArray.h, boolSparse.cc, boolSparse.h, chMatrix.cc, chMatrix.h, chNDArray.cc, chNDArray.h, dColVector.cc, dColVector.h, dDiagMatrix.cc, dDiagMatrix.h, dMatrix.cc, dMatrix.h, dNDArray.cc, dNDArray.h, dRowVector.cc, dRowVector.h, dSparse.cc, dSparse.h, dim-vector.cc, dim-vector.h, fCColVector.cc, fCColVector.h, fCDiagMatrix.cc, fCDiagMatrix.h, fCMatrix.cc, fCMatrix.h, fCNDArray.cc, fCNDArray.h, fCRowVector.cc, fCRowVector.h, fColVector.cc, fColVector.h, fDiagMatrix.cc, fDiagMatrix.h, fMatrix.cc, fMatrix.h, fNDArray.cc, fNDArray.h, fRowVector.cc, fRowVector.h, idx-vector.cc, idx-vector.h, int16NDArray.cc, int16NDArray.h, int32NDArray.cc, int32NDArray.h, int64NDArray.cc, int64NDArray.h, int8NDArray.cc, int8NDArray.h, intNDArray.cc, intNDArray.h, uint16NDArray.cc, uint16NDArray.h, uint32NDArray.cc, uint32NDArray.h, uint64NDArray.cc, uint64NDArray.h, uint8NDArray.cc, uint8NDArray.h, cconv2.f, cdotc3.f, cmatm3.f, csconv2.f, dconv2.f, ddot3.f, dmatm3.f, sconv2.f, sdot3.f, smatm3.f, zconv2.f, zdconv2.f, zdotc3.f, zmatm3.f, crsf2csf.f, zrsf2csf.f, mk-f77-def.in.sh, liboctave-build-info.h, liboctave-build-info.in.cc, CollocWt.cc, CollocWt.h, DAE.h, DAEFunc.h, DAERT.h, DAERTFunc.h, DASPK-opts.in, DASPK.cc, DASPK.h, 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compare_plot_demos.m, dump_demos.m, html_compare_plot_demos.m, rundemos.m, runtests.m, speed.m, test.m, addtodate.m, asctime.m, calendar.m, clock.m, ctime.m, date.m, datenum.m, datestr.m, datevec.m, eomday.m, etime.m, is_leap_year.m, now.m, weekday.m, display-available.c, display-available.h, main-cli.cc, main-gui.cc, main.in.cc, mkoctfile.in.cc, octave-build-info.h, octave-build-info.in.cc, octave-config.in.cc, shared-fcns.h, args.tst, bug-31371.tst, bug-35448.tst, bug-35881.tst, bug-36025.tst, bug-38236.tst, bug-38565.tst, bug-38576.tst, bug-38691.tst, bug-41723.tst, bug-44940.tst, bug-46330.tst, bug-46660.tst, bug-50014.tst, bug-50035.tst, bug-50716.tst, bug-51192.tst, bug-51532.tst, bug-51534.tst, bug-51599.tst, bug-52075.tst, class-concat.tst, classdef-multiple-inheritance.tst, classdef.tst, classes.tst, colormaps.tst, command.tst, complex.tst, ctor-vs-method.tst, deprecate-props.tst, diag-perm.tst, error.tst, eval-catch.tst, fcn-handle-derived-resolution.tst, fntests.m, for.tst, func.tst, global.tst, if.tst, index.tst, io.tst, jit.tst, leftdiv.tst, line-continue.tst, logical-index.tst, mk-bc-overloads-tst.sh, mk-conv-tst.sh, mk-sparse-tst.sh, nest.tst, null-assign.tst, parser.tst, prefer.tst, publish.tst, range.tst, recursion.tst, return.tst, show-failures.awk, single-index.tst, slice.tst, struct.tst, switch.tst, system.tst, transpose.tst, try.tst, unwind.tst, while.tst: Changed punctuation of GPL license text to match that suggested by FSF.
author Rik <rik@octave.org>
date Sat, 06 Jan 2018 07:57:19 -0800
parents bd77ab816e43
children 8bb0251fcfde
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1 /*
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2
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3 Copyright (C) 2006-2017 John W. Eaton
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4
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5 This file is part of Octave.
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6
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7 Octave is free software: you can redistribute it and/or modify it
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8 under the terms of the GNU General Public License as published by
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9 the Free Software Foundation, either version 3 of the License, or
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10 (at your option) any later version.
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11
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12 Octave is distributed in the hope that it will be useful, but
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13 WITHOUT ANY WARRANTY; without even the implied warranty of
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14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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15 GNU General Public License for more details.
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16
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17 You should have received a copy of the GNU General Public License
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18 along with Octave; see the file COPYING. If not, see
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19 <https://www.gnu.org/licenses/>.
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20
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21 */
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22
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23 /*
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24 A C-program for MT19937, with initialization improved 2002/2/10.
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25 Coded by Takuji Nishimura and Makoto Matsumoto.
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26 This is a faster version by taking Shawn Cokus's optimization,
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27 Matthe Bellew's simplification, Isaku Wada's real version.
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28 David Bateman added normal and exponential distributions following
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29 Marsaglia and Tang's Ziggurat algorithm.
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30
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31 Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
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32 Copyright (C) 2004, David Bateman
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33 All rights reserved.
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34
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35 Redistribution and use in source and binary forms, with or without
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36 modification, are permitted provided that the following conditions
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37 are met:
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38
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39 1. Redistributions of source code must retain the above copyright
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40 notice, this list of conditions and the following disclaimer.
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41
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42 2. Redistributions in binary form must reproduce the above copyright
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43 notice, this list of conditions and the following disclaimer in the
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44 documentation and/or other materials provided with the distribution.
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45
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46 3. The names of its contributors may not be used to endorse or promote
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47 products derived from this software without specific prior written
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48 permission.
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49
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50 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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51 "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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52 LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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53 A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
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54 OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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55 EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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56 PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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57 PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
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58 LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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59 NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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60 SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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61
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62
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63 Any feedback is very welcome.
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64 http://www.math.keio.ac.jp/matumoto/emt.html
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65 email: matumoto@math.keio.ac.jp
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66
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67 * 2004-01-19 Paul Kienzle
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68 * * comment out main
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69 * add init_by_entropy, get_state, set_state
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70 * * converted to allow compiling by C++ compiler
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71 *
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72 * 2004-01-25 David Bateman
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73 * * Add Marsaglia and Tsang Ziggurat code
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74 *
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75 * 2004-07-13 Paul Kienzle
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76 * * make into an independent library with some docs.
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77 * * introduce new main and test code.
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78 *
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79 * 2004-07-28 Paul Kienzle & David Bateman
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80 * * add -DALLBITS flag for 32 vs. 53 bits of randomness in mantissa
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81 * * make the naming scheme more uniform
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82 * * add -DHAVE_X86 for faster support of 53 bit mantissa on x86 arch.
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83 *
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84 * 2005-02-23 Paul Kienzle
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85 * * fix -DHAVE_X86_32 flag and add -DUSE_X86_32=0|1 for explicit control
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86 *
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87 * 2006-04-01 David Bateman
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88 * * convert for use in octave, declaring static functions only used
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89 * here and adding oct_ to functions visible externally
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90 * * inverse sense of ALLBITS
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91 *
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92 * 2012-05-18 David Bateman
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93 * * Remove randu64 and ALLBIT option
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94 * * Add the single precision generators
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95 */
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96
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97 /*
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98 === Build instructions ===
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99
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100 Compile with -DHAVE_GETTIMEOFDAY if the gettimeofday function is
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101 available. This is not necessary if your architecture has
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102 /dev/urandom defined.
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103
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104 Uses implicit -Di386 or explicit -DHAVE_X86_32 to determine if CPU=x86.
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105 You can force X86 behavior with -DUSE_X86_32=1, or suppress it with
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106 -DUSE_X86_32=0. You should also consider -march=i686 or similar for
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107 extra performance. Check whether -DUSE_X86_32=0 is faster on 64-bit
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108 x86 architectures.
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109
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110 If you want to replace the Mersenne Twister with another
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111 generator then redefine randi32 appropriately.
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112
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113 === Usage instructions ===
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114 Before using any of the generators, initialize the state with one of
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115 oct_init_by_int, oct_init_by_array or oct_init_by_entropy.
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116
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117 All generators share the same state vector.
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118
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119 === Mersenne Twister ===
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120 void oct_init_by_int (uint32_t s) 32-bit initial state
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121 void oct_init_by_array (uint32_t k[],int m) m*32-bit initial state
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122 void oct_init_by_entropy (void) random initial state
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123 void oct_get_state (uint32_t save[MT_N+1]) saves state in array
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124 void oct_set_state (uint32_t save[MT_N+1]) restores state from array
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125 static uint32_t randmt (void) returns 32-bit unsigned int
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126
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127 === inline generators ===
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128 static uint32_t randi32 (void) returns 32-bit unsigned int
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129 static uint64_t randi53 (void) returns 53-bit unsigned int
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130 static uint64_t randi54 (void) returns 54-bit unsigned int
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131 static float randu32 (void) returns 32-bit uniform in (0,1)
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132 static double randu53 (void) returns 53-bit uniform in (0,1)
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133
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134 double oct_randu (void) returns M-bit uniform in (0,1)
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135 double oct_randn (void) returns M-bit standard normal
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136 double oct_rande (void) returns N-bit standard exponential
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137
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138 float oct_float_randu (void) returns M-bit uniform in (0,1)
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139 float oct_float_randn (void) returns M-bit standard normal
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140 float oct_float_rande (void) returns N-bit standard exponential
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141
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142 === Array generators ===
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143 void oct_fill_randi32 (octave_idx_type, uint32_t [])
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144 void oct_fill_randi64 (octave_idx_type, uint64_t [])
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145
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146 void oct_fill_randu (octave_idx_type, double [])
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147 void oct_fill_randn (octave_idx_type, double [])
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148 void oct_fill_rande (octave_idx_type, double [])
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149
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150 void oct_fill_float_randu (octave_idx_type, float [])
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151 void oct_fill_float_randn (octave_idx_type, float [])
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152 void oct_fill_float_rande (octave_idx_type, float [])
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153 */
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154
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155 #if defined (HAVE_CONFIG_H)
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156 # include "config.h"
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157 #endif
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158
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159 #include <cmath>
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160 #include <cstdio>
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161
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162 #include "oct-time.h"
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163 #include "randmtzig.h"
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164
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165 /* FIXME: may want to suppress X86 if sizeof(long) > 4 */
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166 #if ! defined (USE_X86_32)
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167 # if defined (i386) || defined (HAVE_X86_32)
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168 # define USE_X86_32 1
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169 # else
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170 # define USE_X86_32 0
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171 # endif
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172 #endif
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173
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174 /* ===== Mersenne Twister 32-bit generator ===== */
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175
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176 #define MT_M 397
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177 #define MATRIX_A 0x9908b0dfUL /* constant vector a */
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178 #define UMASK 0x80000000UL /* most significant w-r bits */
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179 #define LMASK 0x7fffffffUL /* least significant r bits */
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180 #define MIXBITS(u,v) ( ((u) & UMASK) | ((v) & LMASK) )
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181 #define TWIST(u,v) ((MIXBITS(u,v) >> 1) ^ ((v)&1UL ? MATRIX_A : 0UL))
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182
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183 static uint32_t *next;
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184 static uint32_t state[MT_N]; /* the array for the state vector */
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185 static int left = 1;
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186 static int initf = 0;
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187 static int initt = 1;
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188 static int inittf = 1;
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189
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190 /* initializes state[MT_N] with a seed */
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191 void
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192 oct_init_by_int (uint32_t s)
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193 {
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194 int j;
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195 state[0] = s & 0xffffffffUL;
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196 for (j = 1; j < MT_N; j++)
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197 {
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198 state[j] = (1812433253UL * (state[j-1] ^ (state[j-1] >> 30)) + j);
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199 /* See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier. */
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200 /* In the previous versions, MSBs of the seed affect */
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201 /* only MSBs of the array state[]. */
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202 /* 2002/01/09 modified by Makoto Matsumoto */
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203 state[j] &= 0xffffffffUL; /* for >32 bit machines */
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204 }
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205 left = 1;
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206 initf = 1;
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207 }
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208
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209 /* initialize by an array with array-length */
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210 /* init_key is the array for initializing keys */
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211 /* key_length is its length */
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212 void
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213 oct_init_by_array (uint32_t *init_key, int key_length)
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214 {
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215 int i, j, k;
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216 oct_init_by_int (19650218UL);
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217 i = 1;
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218 j = 0;
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219 k = (MT_N > key_length ? MT_N : key_length);
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220 for (; k; k--)
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221 {
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222 state[i] = (state[i] ^ ((state[i-1] ^ (state[i-1] >> 30)) * 1664525UL))
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223 + init_key[j] + j; /* non linear */
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224 state[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */
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225 i++;
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226 j++;
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227 if (i >= MT_N)
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228 {
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229 state[0] = state[MT_N-1];
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230 i = 1;
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231 }
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232 if (j >= key_length)
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233 j = 0;
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234 }
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235 for (k = MT_N - 1; k; k--)
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236 {
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237 state[i] = (state[i] ^ ((state[i-1] ^ (state[i-1] >> 30)) * 1566083941UL))
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238 - i; /* non linear */
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239 state[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */
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240 i++;
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241 if (i >= MT_N)
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242 {
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243 state[0] = state[MT_N-1];
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244 i = 1;
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245 }
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246 }
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247
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248 state[0] = 0x80000000UL; /* MSB is 1; assuring nonzero initial array */
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249 left = 1;
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250 initf = 1;
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251 }
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252
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253 void
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254 oct_init_by_entropy (void)
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255 {
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256 uint32_t entropy[MT_N];
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257 int n = 0;
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258
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259 /* Look for entropy in /dev/urandom */
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260 FILE *urandom = std::fopen ("/dev/urandom", "rb");
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261 if (urandom)
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262 {
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263 while (n < MT_N)
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264 {
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265 unsigned char word[4];
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266 if (std::fread (word, 4, 1, urandom) != 1)
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267 break;
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268 entropy[n++] = word[0] + (word[1]<<8) + (word[2]<<16)
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269 + (static_cast<uint32_t> (word[3])<<24);
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270 }
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271 std::fclose (urandom);
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272 }
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273
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274 /* If there isn't enough entropy, gather some from various sources */
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275
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276 octave::sys::time now;
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277
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278 if (n < MT_N)
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279 entropy[n++] = now.unix_time (); /* Current time in seconds */
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280
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281 if (n < MT_N)
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282 entropy[n++] = clock (); /* CPU time used (usec) */
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283
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284 if (n < MT_N)
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285 entropy[n++] = now.usec (); /* Fractional part of current time */
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286
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287 /* Send all the entropy into the initial state vector */
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288 oct_init_by_array (entropy,n);
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289 }
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290
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291 void
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292 oct_set_state (uint32_t *save)
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293 {
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294 int i;
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295 for (i = 0; i < MT_N; i++)
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296 state[i] = save[i];
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297 left = save[MT_N];
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298 next = state + (MT_N - left + 1);
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299 }
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300
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301 void
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302 oct_get_state (uint32_t *save)
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303 {
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304 int i;
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305 for (i = 0; i < MT_N; i++)
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306 save[i] = state[i];
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307 save[MT_N] = left;
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308 }
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309
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310 static void
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311 next_state (void)
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312 {
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313 uint32_t *p = state;
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diff changeset
314 int j;
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315
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316 /* if init_by_int() has not been called, */
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317 /* a default initial seed is used */
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318 /* if (initf==0) init_by_int(5489UL); */
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319 /* Or better yet, a random seed! */
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320 if (initf == 0)
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diff changeset
321 oct_init_by_entropy ();
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322
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323 left = MT_N;
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324 next = state;
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325
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326 for (j = MT_N - MT_M + 1; --j; p++)
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327 *p = p[MT_M] ^ TWIST(p[0], p[1]);
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328
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329 for (j = MT_M; --j; p++)
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330 *p = p[MT_M-MT_N] ^ TWIST(p[0], p[1]);
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331
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332 *p = p[MT_M-MT_N] ^ TWIST(p[0], state[0]);
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333 }
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334
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335 /* generates a random number on [0,0xffffffff]-interval */
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336 static uint32_t
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337 randmt (void)
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338 {
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diff changeset
339 uint32_t y;
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340
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341 if (--left == 0)
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342 next_state ();
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343 y = *next++;
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344
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345 /* Tempering */
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346 y ^= (y >> 11);
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347 y ^= (y << 7) & 0x9d2c5680UL;
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348 y ^= (y << 15) & 0xefc60000UL;
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349 return (y ^ (y >> 18));
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350 }
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351
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352 /* ===== Uniform generators ===== */
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353
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354 /* Select which 32 bit generator to use */
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355 #define randi32 randmt
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
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356
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357 static uint64_t
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358 randi53 (void)
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359 {
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diff changeset
360 const uint32_t lo = randi32 ();
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diff changeset
361 const uint32_t hi = randi32 () & 0x1FFFFF;
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diff changeset
362 #if defined (HAVE_X86_32)
5742
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363 uint64_t u;
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364 uint32_t *p = (uint32_t *)&u;
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365 p[0] = lo;
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366 p[1] = hi;
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367 return u;
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368 #else
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369 return ((static_cast<uint64_t> (hi) << 32) | lo);
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370 #endif
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371 }
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372
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373 static uint64_t
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374 randi54 (void)
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375 {
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diff changeset
376 const uint32_t lo = randi32 ();
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377 const uint32_t hi = randi32 () & 0x3FFFFF;
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diff changeset
378 #if defined (HAVE_X86_32)
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379 uint64_t u;
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380 uint32_t *p = static_cast<uint32_t *> (&u);
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381 p[0] = lo;
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382 p[1] = hi;
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
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383 return u;
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384 #else
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diff changeset
385 return ((static_cast<uint64_t> (hi) << 32) | lo);
5742
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386 #endif
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387 }
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388
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389 /* generates a random number on (0,1)-real-interval */
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43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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diff changeset
390 static float
5742
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391 randu32 (void)
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392 {
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diff changeset
393 return (static_cast<float> (randi32 ()) + 0.5) * (1.0/4294967296.0);
5742
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394 /* divided by 2^32 */
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diff changeset
395 }
14655
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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diff changeset
396
5742
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397 /* generates a random number on (0,1) with 53-bit resolution */
5766
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diff changeset
398 static double
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diff changeset
399 randu53 (void)
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diff changeset
400 {
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diff changeset
401 const uint32_t a = randi32 () >> 5;
1b9a36a66b01 maint: Octave coding convention cleanups.
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diff changeset
402 const uint32_t b = randi32 () >> 6;
6959
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diff changeset
403 return (a*67108864.0+b+0.4) * (1.0/9007199254740992.0);
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diff changeset
404 }
5742
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diff changeset
405
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diff changeset
406 /* Determine mantissa for uniform doubles */
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407 double
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diff changeset
408 oct_randu (void)
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409 {
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diff changeset
410 return randu53 ();
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parents: 14138
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411 }
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parents: 14138
diff changeset
412
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413 /* Determine mantissa for uniform floats */
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
414 float
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
415 oct_float_randu (void)
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David Bateman <dbateman@free.fr>
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diff changeset
416 {
6959
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417 return randu32 ();
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418 }
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419
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420 /* ===== Ziggurat normal and exponential generators ===== */
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421
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422 #define ZIGGURAT_TABLE_SIZE 256
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423
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424 #define ZIGGURAT_NOR_R 3.6541528853610088
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diff changeset
425 #define ZIGGURAT_NOR_INV_R 0.27366123732975828
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426 #define NOR_SECTION_AREA 0.00492867323399
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427
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428 #define ZIGGURAT_EXP_R 7.69711747013104972
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429 #define ZIGGURAT_EXP_INV_R 0.129918765548341586
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430 #define EXP_SECTION_AREA 0.0039496598225815571993
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431
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432 #define ZIGINT uint64_t
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433 #define EMANTISSA 9007199254740992.0 /* 53 bit mantissa */
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434 #define ERANDI randi53() /* 53 bits for mantissa */
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435 #define NMANTISSA EMANTISSA
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436 #define NRANDI randi54() /* 53 bits for mantissa + 1 bit sign */
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437 #define RANDU randu53()
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David Bateman <dbateman@free.fr>
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438
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439 static ZIGINT ki[ZIGGURAT_TABLE_SIZE];
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440 static double wi[ZIGGURAT_TABLE_SIZE], fi[ZIGGURAT_TABLE_SIZE];
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441 static ZIGINT ke[ZIGGURAT_TABLE_SIZE];
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442 static double we[ZIGGURAT_TABLE_SIZE], fe[ZIGGURAT_TABLE_SIZE];
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443
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444 /*
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445 This code is based on the paper Marsaglia and Tsang, "The ziggurat method
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446 for generating random variables", Journ. Statistical Software. Code was
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447 presented in this paper for a Ziggurat of 127 levels and using a 32 bit
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448 integer random number generator. This version of the code, uses the
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449 Mersenne Twister as the integer generator and uses 256 levels in the
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450 Ziggurat. This has several advantages.
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451
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452 1) As Marsaglia and Tsang themselves states, the more levels the few
5742
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453 times the expensive tail algorithm must be called
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454 2) The cycle time of the generator is determined by the integer
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455 generator, thus the use of a Mersenne Twister for the core random
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456 generator makes this cycle extremely long.
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457 3) The license on the original code was unclear, thus rewriting the code
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458 from the article means we are free of copyright issues.
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459 4) Compile flag for full 53-bit random mantissa.
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460
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
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461 It should be stated that the authors made my life easier, by the fact that
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462 the algorithm developed in the text of the article is for a 256 level
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463 ziggurat, even if the code itself isn't...
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464
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465 One modification to the algorithm developed in the article, is that it is
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466 assumed that 0 <= x < Inf, and "unsigned long"s are used, thus resulting in
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467 terms like 2^32 in the code. As the normal distribution is defined between
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468 -Inf < x < Inf, we effectively only have 31 bit integers plus a sign. Thus
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469 in Marsaglia and Tsang, terms like 2^32 become 2^31. We use NMANTISSA for
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470 this term. The exponential distribution is one sided so we use the
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471 full 32 bits. We use EMANTISSA for this term.
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472
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473 It appears that I'm slightly slower than the code in the article, this
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474 is partially due to a better generator of random integers than they
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475 use. But might also be that the case of rapid return was optimized by
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476 inlining the relevant code with a #define. As the basic Mersenne
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477 Twister is only 25% faster than this code I suspect that the main
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478 reason is just the use of the Mersenne Twister and not the inlining,
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479 so I'm not going to try and optimize further.
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480 */
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481
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482 static void
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483 create_ziggurat_tables (void)
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484 {
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485 int i;
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486 double x, x1;
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diff changeset
487
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488 /* Ziggurat tables for the normal distribution */
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489 x1 = ZIGGURAT_NOR_R;
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490 wi[255] = x1 / NMANTISSA;
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491 fi[255] = exp (-0.5 * x1 * x1);
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492
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493 /* Index zero is special for tail strip, where Marsaglia and Tsang
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494 * defines this as
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495 * k_0 = 2^31 * r * f(r) / v, w_0 = 0.5^31 * v / f(r), f_0 = 1,
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496 * where v is the area of each strip of the ziggurat.
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497 */
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498 ki[0] = static_cast<ZIGINT> (x1 * fi[255] / NOR_SECTION_AREA * NMANTISSA);
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499 wi[0] = NOR_SECTION_AREA / fi[255] / NMANTISSA;
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500 fi[0] = 1.;
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501
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502 for (i = 254; i > 0; i--)
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diff changeset
503 {
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
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diff changeset
504 /* New x is given by x = f^{-1}(v/x_{i+1} + f(x_{i+1})), thus
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505 * need inverse operator of y = exp(-0.5*x*x) -> x = sqrt(-2*ln(y))
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diff changeset
506 */
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diff changeset
507 x = std::sqrt (-2. * std::log (NOR_SECTION_AREA / x1 + fi[i+1]));
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diff changeset
508 ki[i+1] = static_cast<ZIGINT> (x / x1 * NMANTISSA);
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509 wi[i] = x / NMANTISSA;
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510 fi[i] = exp (-0.5 * x * x);
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511 x1 = x;
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512 }
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513
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514 ki[1] = 0;
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515
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516 /* Zigurrat tables for the exponential distribution */
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517 x1 = ZIGGURAT_EXP_R;
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518 we[255] = x1 / EMANTISSA;
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519 fe[255] = exp (-x1);
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520
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521 /* Index zero is special for tail strip, where Marsaglia and Tsang
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522 * defines this as
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523 * k_0 = 2^32 * r * f(r) / v, w_0 = 0.5^32 * v / f(r), f_0 = 1,
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diff changeset
524 * where v is the area of each strip of the ziggurat.
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525 */
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diff changeset
526 ke[0] = static_cast<ZIGINT> (x1 * fe[255] / EXP_SECTION_AREA * EMANTISSA);
5742
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527 we[0] = EXP_SECTION_AREA / fe[255] / EMANTISSA;
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528 fe[0] = 1.;
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diff changeset
529
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diff changeset
530 for (i = 254; i > 0; i--)
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diff changeset
531 {
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
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diff changeset
532 /* New x is given by x = f^{-1}(v/x_{i+1} + f(x_{i+1})), thus
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diff changeset
533 * need inverse operator of y = exp(-x) -> x = -ln(y)
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534 */
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diff changeset
535 x = - std::log (EXP_SECTION_AREA / x1 + fe[i+1]);
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diff changeset
536 ke[i+1] = static_cast<ZIGINT> (x / x1 * EMANTISSA);
5742
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537 we[i] = x / EMANTISSA;
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538 fe[i] = exp (-x);
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
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539 x1 = x;
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diff changeset
540 }
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diff changeset
541 ke[1] = 0;
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diff changeset
542
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
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diff changeset
543 initt = 0;
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
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544 }
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diff changeset
545
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diff changeset
546 /*
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
547 * Here is the guts of the algorithm. As Marsaglia and Tsang state the
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
548 * algorithm in their paper
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
549 *
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
550 * 1) Calculate a random signed integer j and let i be the index
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
551 * provided by the rightmost 8-bits of j
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
552 * 2) Set x = j * w_i. If j < k_i return x
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
553 * 3) If i = 0, then return x from the tail
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
554 * 4) If [f(x_{i-1}) - f(x_i)] * U < f(x) - f(x_i), return x
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
555 * 5) goto step 1
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
556 *
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
557 * Where f is the functional form of the distribution, which for a normal
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
558 * distribution is exp(-0.5*x*x)
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
559 */
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
560
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
561 double
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
562 oct_randn (void)
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
563 {
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
564 if (initt)
14846
460a3c6d8bf1 maint: Use Octave coding convention for cuddled parenthis in function calls with empty argument lists.
Rik <octave@nomad.inbox5.com>
parents: 14655
diff changeset
565 create_ziggurat_tables ();
5742
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
566
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
567 while (1)
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
568 {
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
569 /* The following code is specialized for 32-bit mantissa.
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
570 * Compared to the arbitrary mantissa code, there is a performance
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
571 * gain for 32-bits: PPC: 2%, MIPS: 8%, x86: 40%
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
572 * There is a bigger performance gain compared to using a full
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
573 * 53-bit mantissa: PPC: 60%, MIPS: 65%, x86: 240%
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
574 * Of course, different compilers and operating systems may
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
575 * have something to do with this.
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
576 */
21724
aba2e6293dd8 use "#if ..." consistently instead of "#ifdef" and "#ifndef"
John W. Eaton <jwe@octave.org>
parents: 21720
diff changeset
577 # if defined (HAVE_X86_32)
5742
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
578 /* 53-bit mantissa, 1-bit sign, x86 32-bit architecture */
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
579 double x;
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
580 int si,idx;
21332
db574711df78 eliminate deprecated register storage class specifier
John W. Eaton <jwe@octave.org>
parents: 21308
diff changeset
581 uint32_t lo, hi;
5742
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
582 int64_t rabs;
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
583 uint32_t *p = (uint32_t *)&rabs;
14846
460a3c6d8bf1 maint: Use Octave coding convention for cuddled parenthis in function calls with empty argument lists.
Rik <octave@nomad.inbox5.com>
parents: 14655
diff changeset
584 lo = randi32 ();
21661
1b9a36a66b01 maint: Octave coding convention cleanups.
Rik <rik@octave.org>
parents: 21332
diff changeset
585 idx = lo & 0xFF;
14846
460a3c6d8bf1 maint: Use Octave coding convention for cuddled parenthis in function calls with empty argument lists.
Rik <octave@nomad.inbox5.com>
parents: 14655
diff changeset
586 hi = randi32 ();
21661
1b9a36a66b01 maint: Octave coding convention cleanups.
Rik <rik@octave.org>
parents: 21332
diff changeset
587 si = hi & UMASK;
5742
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
588 p[0] = lo;
21661
1b9a36a66b01 maint: Octave coding convention cleanups.
Rik <rik@octave.org>
parents: 21332
diff changeset
589 p[1] = hi & 0x1FFFFF;
5742
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
590 x = ( si ? -rabs : rabs ) * wi[idx];
22188
1344509a480c style fixes
John W. Eaton <jwe@octave.org>
parents: 22022
diff changeset
591 # else
5742
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
592 /* arbitrary mantissa (selected by NRANDI, with 1 bit for sign) */
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
593 const uint64_t r = NRANDI;
21661
1b9a36a66b01 maint: Octave coding convention cleanups.
Rik <rik@octave.org>
parents: 21332
diff changeset
594 const int64_t rabs = r >> 1;
21720
b28c26ae737c use C++ for random number generator sources
John W. Eaton <jwe@octave.org>
parents: 21661
diff changeset
595 const int idx = static_cast<int> (rabs & 0xFF);
21661
1b9a36a66b01 maint: Octave coding convention cleanups.
Rik <rik@octave.org>
parents: 21332
diff changeset
596 const double x = ( (r & 1) ? -rabs : rabs) * wi[idx];
22188
1344509a480c style fixes
John W. Eaton <jwe@octave.org>
parents: 22022
diff changeset
597 # endif
21720
b28c26ae737c use C++ for random number generator sources
John W. Eaton <jwe@octave.org>
parents: 21661
diff changeset
598 if (rabs < static_cast<int64_t> (ki[idx]))
10317
42d098307c30 untabify additional source files
John W. Eaton <jwe@octave.org>
parents: 10158
diff changeset
599 return x; /* 99.3% of the time we return here 1st try */
5742
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
600 else if (idx == 0)
10317
42d098307c30 untabify additional source files
John W. Eaton <jwe@octave.org>
parents: 10158
diff changeset
601 {
42d098307c30 untabify additional source files
John W. Eaton <jwe@octave.org>
parents: 10158
diff changeset
602 /* As stated in Marsaglia and Tsang
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
603 *
10317
42d098307c30 untabify additional source files
John W. Eaton <jwe@octave.org>
parents: 10158
diff changeset
604 * For the normal tail, the method of Marsaglia[5] provides:
42d098307c30 untabify additional source files
John W. Eaton <jwe@octave.org>
parents: 10158
diff changeset
605 * generate x = -ln(U_1)/r, y = -ln(U_2), until y+y > x*x,
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
606 * then return r+x. Except that r+x is always in the positive
10317
42d098307c30 untabify additional source files
John W. Eaton <jwe@octave.org>
parents: 10158
diff changeset
607 * tail!!!! Any thing random might be used to determine the
42d098307c30 untabify additional source files
John W. Eaton <jwe@octave.org>
parents: 10158
diff changeset
608 * sign, but as we already have r we might as well use it
42d098307c30 untabify additional source files
John W. Eaton <jwe@octave.org>
parents: 10158
diff changeset
609 *
42d098307c30 untabify additional source files
John W. Eaton <jwe@octave.org>
parents: 10158
diff changeset
610 * [PAK] but not the bottom 8 bits, since they are all 0 here!
42d098307c30 untabify additional source files
John W. Eaton <jwe@octave.org>
parents: 10158
diff changeset
611 */
42d098307c30 untabify additional source files
John W. Eaton <jwe@octave.org>
parents: 10158
diff changeset
612 double xx, yy;
42d098307c30 untabify additional source files
John W. Eaton <jwe@octave.org>
parents: 10158
diff changeset
613 do
42d098307c30 untabify additional source files
John W. Eaton <jwe@octave.org>
parents: 10158
diff changeset
614 {
21942
aab79a1885cc limit gnulib headers to liboctave/wrappers directory
John W. Eaton <jwe@octave.org>
parents: 21928
diff changeset
615 xx = - ZIGGURAT_NOR_INV_R * std::log (RANDU);
aab79a1885cc limit gnulib headers to liboctave/wrappers directory
John W. Eaton <jwe@octave.org>
parents: 21928
diff changeset
616 yy = - std::log (RANDU);
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
617 }
10317
42d098307c30 untabify additional source files
John W. Eaton <jwe@octave.org>
parents: 10158
diff changeset
618 while ( yy+yy <= xx*xx);
21661
1b9a36a66b01 maint: Octave coding convention cleanups.
Rik <rik@octave.org>
parents: 21332
diff changeset
619 return ((rabs & 0x100) ? -ZIGGURAT_NOR_R-xx : ZIGGURAT_NOR_R+xx);
10317
42d098307c30 untabify additional source files
John W. Eaton <jwe@octave.org>
parents: 10158
diff changeset
620 }
15018
3d8ace26c5b4 maint: Use Octave coding conventions for cuddled parentheses in liboctave/.
Rik <rik@octave.org>
parents: 14846
diff changeset
621 else if ((fi[idx-1] - fi[idx]) * RANDU + fi[idx] < exp (-0.5*x*x))
10317
42d098307c30 untabify additional source files
John W. Eaton <jwe@octave.org>
parents: 10158
diff changeset
622 return x;
5742
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
623 }
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
624 }
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
625
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
626 double
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
627 oct_rande (void)
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
628 {
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
629 if (initt)
14846
460a3c6d8bf1 maint: Use Octave coding convention for cuddled parenthis in function calls with empty argument lists.
Rik <octave@nomad.inbox5.com>
parents: 14655
diff changeset
630 create_ziggurat_tables ();
5742
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
631
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
632 while (1)
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
633 {
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
634 ZIGINT ri = ERANDI;
21720
b28c26ae737c use C++ for random number generator sources
John W. Eaton <jwe@octave.org>
parents: 21661
diff changeset
635 const int idx = static_cast<int> (ri & 0xFF);
5742
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
636 const double x = ri * we[idx];
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
637 if (ri < ke[idx])
15970
ca6202597201 Use C-style comments in C code.
Mike Miller <mtmiller@ieee.org>
parents: 15408
diff changeset
638 return x; /* 98.9% of the time we return here 1st try */
5742
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
639 else if (idx == 0)
10317
42d098307c30 untabify additional source files
John W. Eaton <jwe@octave.org>
parents: 10158
diff changeset
640 {
42d098307c30 untabify additional source files
John W. Eaton <jwe@octave.org>
parents: 10158
diff changeset
641 /* As stated in Marsaglia and Tsang
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
642 *
10317
42d098307c30 untabify additional source files
John W. Eaton <jwe@octave.org>
parents: 10158
diff changeset
643 * For the exponential tail, the method of Marsaglia[5] provides:
5742
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
644 * x = r - ln(U);
10317
42d098307c30 untabify additional source files
John W. Eaton <jwe@octave.org>
parents: 10158
diff changeset
645 */
21942
aab79a1885cc limit gnulib headers to liboctave/wrappers directory
John W. Eaton <jwe@octave.org>
parents: 21928
diff changeset
646 return ZIGGURAT_EXP_R - std::log (RANDU);
10317
42d098307c30 untabify additional source files
John W. Eaton <jwe@octave.org>
parents: 10158
diff changeset
647 }
15018
3d8ace26c5b4 maint: Use Octave coding conventions for cuddled parentheses in liboctave/.
Rik <rik@octave.org>
parents: 14846
diff changeset
648 else if ((fe[idx-1] - fe[idx]) * RANDU + fe[idx] < exp (-x))
10317
42d098307c30 untabify additional source files
John W. Eaton <jwe@octave.org>
parents: 10158
diff changeset
649 return x;
5742
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
650 }
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
651 }
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
652
14655
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
653 #undef ZIGINT
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
654 #undef EMANTISSA
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
655 #undef ERANDI
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
656 #undef NMANTISSA
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
657 #undef NRANDI
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
658 #undef RANDU
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
659
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
660 #define ZIGINT uint32_t
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
661 #define EMANTISSA 4294967296.0 /* 32 bit mantissa */
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
662 #define ERANDI randi32() /* 32 bits for mantissa */
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
663 #define NMANTISSA 2147483648.0 /* 31 bit mantissa */
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
664 #define NRANDI randi32() /* 31 bits for mantissa + 1 bit sign */
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
665 #define RANDU randu32()
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
666
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
667 static ZIGINT fki[ZIGGURAT_TABLE_SIZE];
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
668 static float fwi[ZIGGURAT_TABLE_SIZE], ffi[ZIGGURAT_TABLE_SIZE];
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
669 static ZIGINT fke[ZIGGURAT_TABLE_SIZE];
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
670 static float fwe[ZIGGURAT_TABLE_SIZE], ffe[ZIGGURAT_TABLE_SIZE];
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
671
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
672 static void
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
673 create_ziggurat_float_tables (void)
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
674 {
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
675 int i;
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
676 float x, x1;
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
677
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
678 /* Ziggurat tables for the normal distribution */
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
679 x1 = ZIGGURAT_NOR_R;
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
680 fwi[255] = x1 / NMANTISSA;
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
681 ffi[255] = exp (-0.5 * x1 * x1);
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
682
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
683 /* Index zero is special for tail strip, where Marsaglia and Tsang
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
684 * defines this as
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
685 * k_0 = 2^31 * r * f(r) / v, w_0 = 0.5^31 * v / f(r), f_0 = 1,
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
686 * where v is the area of each strip of the ziggurat.
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
687 */
21720
b28c26ae737c use C++ for random number generator sources
John W. Eaton <jwe@octave.org>
parents: 21661
diff changeset
688 fki[0] = static_cast<ZIGINT> (x1 * ffi[255] / NOR_SECTION_AREA * NMANTISSA);
14655
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
689 fwi[0] = NOR_SECTION_AREA / ffi[255] / NMANTISSA;
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
690 ffi[0] = 1.;
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
691
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
692 for (i = 254; i > 0; i--)
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
693 {
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
694 /* New x is given by x = f^{-1}(v/x_{i+1} + f(x_{i+1})), thus
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
695 * need inverse operator of y = exp(-0.5*x*x) -> x = sqrt(-2*ln(y))
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
696 */
23649
aabf6cd222ac Use sqrt from C++ std library in liboctave.
Rik <rik@octave.org>
parents: 23449
diff changeset
697 x = std::sqrt (-2. * std::log (NOR_SECTION_AREA / x1 + ffi[i+1]));
21720
b28c26ae737c use C++ for random number generator sources
John W. Eaton <jwe@octave.org>
parents: 21661
diff changeset
698 fki[i+1] = static_cast<ZIGINT> (x / x1 * NMANTISSA);
14655
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
699 fwi[i] = x / NMANTISSA;
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
700 ffi[i] = exp (-0.5 * x * x);
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
701 x1 = x;
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
702 }
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
703
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
704 fki[1] = 0;
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
705
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
706 /* Zigurrat tables for the exponential distribution */
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
707 x1 = ZIGGURAT_EXP_R;
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
708 fwe[255] = x1 / EMANTISSA;
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
709 ffe[255] = exp (-x1);
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
710
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
711 /* Index zero is special for tail strip, where Marsaglia and Tsang
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
712 * defines this as
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
713 * k_0 = 2^32 * r * f(r) / v, w_0 = 0.5^32 * v / f(r), f_0 = 1,
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
714 * where v is the area of each strip of the ziggurat.
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
715 */
21720
b28c26ae737c use C++ for random number generator sources
John W. Eaton <jwe@octave.org>
parents: 21661
diff changeset
716 fke[0] = static_cast<ZIGINT> (x1 * ffe[255] / EXP_SECTION_AREA * EMANTISSA);
14655
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
717 fwe[0] = EXP_SECTION_AREA / ffe[255] / EMANTISSA;
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
718 ffe[0] = 1.;
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
719
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
720 for (i = 254; i > 0; i--)
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
721 {
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
722 /* New x is given by x = f^{-1}(v/x_{i+1} + f(x_{i+1})), thus
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
723 * need inverse operator of y = exp(-x) -> x = -ln(y)
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
724 */
21942
aab79a1885cc limit gnulib headers to liboctave/wrappers directory
John W. Eaton <jwe@octave.org>
parents: 21928
diff changeset
725 x = - std::log (EXP_SECTION_AREA / x1 + ffe[i+1]);
21720
b28c26ae737c use C++ for random number generator sources
John W. Eaton <jwe@octave.org>
parents: 21661
diff changeset
726 fke[i+1] = static_cast<ZIGINT> (x / x1 * EMANTISSA);
14655
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
727 fwe[i] = x / EMANTISSA;
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
728 ffe[i] = exp (-x);
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
729 x1 = x;
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
730 }
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
731 fke[1] = 0;
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
732
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
733 inittf = 0;
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
734 }
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
735
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
736 /*
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
737 * Here is the guts of the algorithm. As Marsaglia and Tsang state the
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
738 * algorithm in their paper
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
739 *
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
740 * 1) Calculate a random signed integer j and let i be the index
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
741 * provided by the rightmost 8-bits of j
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
742 * 2) Set x = j * w_i. If j < k_i return x
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
743 * 3) If i = 0, then return x from the tail
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
744 * 4) If [f(x_{i-1}) - f(x_i)] * U < f(x) - f(x_i), return x
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
745 * 5) goto step 1
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
746 *
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
747 * Where f is the functional form of the distribution, which for a normal
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
748 * distribution is exp(-0.5*x*x)
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
749 */
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
750
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
751 float
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
752 oct_float_randn (void)
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
753 {
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
754 if (inittf)
14846
460a3c6d8bf1 maint: Use Octave coding convention for cuddled parenthis in function calls with empty argument lists.
Rik <octave@nomad.inbox5.com>
parents: 14655
diff changeset
755 create_ziggurat_float_tables ();
14655
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
756
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
757 while (1)
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
758 {
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
759 /* 32-bit mantissa */
14846
460a3c6d8bf1 maint: Use Octave coding convention for cuddled parenthis in function calls with empty argument lists.
Rik <octave@nomad.inbox5.com>
parents: 14655
diff changeset
760 const uint32_t r = randi32 ();
21661
1b9a36a66b01 maint: Octave coding convention cleanups.
Rik <rik@octave.org>
parents: 21332
diff changeset
761 const uint32_t rabs = r & LMASK;
21720
b28c26ae737c use C++ for random number generator sources
John W. Eaton <jwe@octave.org>
parents: 21661
diff changeset
762 const int idx = static_cast<int> (r & 0xFF);
b28c26ae737c use C++ for random number generator sources
John W. Eaton <jwe@octave.org>
parents: 21661
diff changeset
763 const float x = static_cast<int32_t> (r) * fwi[idx];
14655
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
764 if (rabs < fki[idx])
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
765 return x; /* 99.3% of the time we return here 1st try */
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
766 else if (idx == 0)
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
767 {
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
768 /* As stated in Marsaglia and Tsang
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
769 *
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
770 * For the normal tail, the method of Marsaglia[5] provides:
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
771 * generate x = -ln(U_1)/r, y = -ln(U_2), until y+y > x*x,
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
772 * then return r+x. Except that r+x is always in the positive
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
773 * tail!!!! Any thing random might be used to determine the
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
774 * sign, but as we already have r we might as well use it
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
775 *
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
776 * [PAK] but not the bottom 8 bits, since they are all 0 here!
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
777 */
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
778 float xx, yy;
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
779 do
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
780 {
21942
aab79a1885cc limit gnulib headers to liboctave/wrappers directory
John W. Eaton <jwe@octave.org>
parents: 21928
diff changeset
781 xx = - ZIGGURAT_NOR_INV_R * std::log (RANDU);
aab79a1885cc limit gnulib headers to liboctave/wrappers directory
John W. Eaton <jwe@octave.org>
parents: 21928
diff changeset
782 yy = - std::log (RANDU);
14655
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
783 }
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
784 while ( yy+yy <= xx*xx);
21661
1b9a36a66b01 maint: Octave coding convention cleanups.
Rik <rik@octave.org>
parents: 21332
diff changeset
785 return ((rabs & 0x100) ? -ZIGGURAT_NOR_R-xx : ZIGGURAT_NOR_R+xx);
14655
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
786 }
15018
3d8ace26c5b4 maint: Use Octave coding conventions for cuddled parentheses in liboctave/.
Rik <rik@octave.org>
parents: 14846
diff changeset
787 else if ((ffi[idx-1] - ffi[idx]) * RANDU + ffi[idx] < exp (-0.5*x*x))
14655
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
788 return x;
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
789 }
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
790 }
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
791
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
792 float
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
793 oct_float_rande (void)
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
794 {
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
795 if (inittf)
14846
460a3c6d8bf1 maint: Use Octave coding convention for cuddled parenthis in function calls with empty argument lists.
Rik <octave@nomad.inbox5.com>
parents: 14655
diff changeset
796 create_ziggurat_float_tables ();
14655
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
797
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
798 while (1)
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
799 {
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
800 ZIGINT ri = ERANDI;
21720
b28c26ae737c use C++ for random number generator sources
John W. Eaton <jwe@octave.org>
parents: 21661
diff changeset
801 const int idx = static_cast<int> (ri & 0xFF);
14655
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
802 const float x = ri * fwe[idx];
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
803 if (ri < fke[idx])
15970
ca6202597201 Use C-style comments in C code.
Mike Miller <mtmiller@ieee.org>
parents: 15408
diff changeset
804 return x; /* 98.9% of the time we return here 1st try */
14655
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
805 else if (idx == 0)
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
806 {
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
807 /* As stated in Marsaglia and Tsang
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
808 *
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
809 * For the exponential tail, the method of Marsaglia[5] provides:
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
810 * x = r - ln(U);
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
811 */
21942
aab79a1885cc limit gnulib headers to liboctave/wrappers directory
John W. Eaton <jwe@octave.org>
parents: 21928
diff changeset
812 return ZIGGURAT_EXP_R - std::log (RANDU);
14655
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
813 }
15018
3d8ace26c5b4 maint: Use Octave coding conventions for cuddled parentheses in liboctave/.
Rik <rik@octave.org>
parents: 14846
diff changeset
814 else if ((ffe[idx-1] - ffe[idx]) * RANDU + ffe[idx] < exp (-x))
14655
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
815 return x;
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
816 }
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
817 }
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
818
5742
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
819 /* Array generators */
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
820 void
5742
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
821 oct_fill_randu (octave_idx_type n, double *p)
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
822 {
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
823 octave_idx_type i;
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
824 for (i = 0; i < n; i++)
14846
460a3c6d8bf1 maint: Use Octave coding convention for cuddled parenthis in function calls with empty argument lists.
Rik <octave@nomad.inbox5.com>
parents: 14655
diff changeset
825 p[i] = oct_randu ();
5742
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
826 }
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
827
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
828 void
5742
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
829 oct_fill_randn (octave_idx_type n, double *p)
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
830 {
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
831 octave_idx_type i;
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
832 for (i = 0; i < n; i++)
14846
460a3c6d8bf1 maint: Use Octave coding convention for cuddled parenthis in function calls with empty argument lists.
Rik <octave@nomad.inbox5.com>
parents: 14655
diff changeset
833 p[i] = oct_randn ();
5742
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
834 }
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
835
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
836 void
5742
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
837 oct_fill_rande (octave_idx_type n, double *p)
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
838 {
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
839 octave_idx_type i;
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
840 for (i = 0; i < n; i++)
14846
460a3c6d8bf1 maint: Use Octave coding convention for cuddled parenthis in function calls with empty argument lists.
Rik <octave@nomad.inbox5.com>
parents: 14655
diff changeset
841 p[i] = oct_rande ();
5742
2cd0af543e7a [project @ 2006-04-06 08:15:49 by jwe]
jwe
parents:
diff changeset
842 }
14655
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
843
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
844 void
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
845 oct_fill_float_randu (octave_idx_type n, float *p)
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
846 {
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
847 octave_idx_type i;
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
848 for (i = 0; i < n; i++)
14846
460a3c6d8bf1 maint: Use Octave coding convention for cuddled parenthis in function calls with empty argument lists.
Rik <octave@nomad.inbox5.com>
parents: 14655
diff changeset
849 p[i] = oct_float_randu ();
14655
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
850 }
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
851
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
852 void
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
853 oct_fill_float_randn (octave_idx_type n, float *p)
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
854 {
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
855 octave_idx_type i;
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
856 for (i = 0; i < n; i++)
14846
460a3c6d8bf1 maint: Use Octave coding convention for cuddled parenthis in function calls with empty argument lists.
Rik <octave@nomad.inbox5.com>
parents: 14655
diff changeset
857 p[i] = oct_float_randn ();
14655
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
858 }
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
859
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
860 void
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
861 oct_fill_float_rande (octave_idx_type n, float *p)
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
862 {
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
863 octave_idx_type i;
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
864 for (i = 0; i < n; i++)
14846
460a3c6d8bf1 maint: Use Octave coding convention for cuddled parenthis in function calls with empty argument lists.
Rik <octave@nomad.inbox5.com>
parents: 14655
diff changeset
865 p[i] = oct_float_rande ();
14655
43db83eff9db Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents: 14138
diff changeset
866 }