Mercurial > octave
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,
DASRT-opts.in, DASRT.cc, DASRT.h, DASSL-opts.in, DASSL.cc, DASSL.h, DET.h,
EIG.cc, EIG.h, LSODE-opts.in, LSODE.cc, LSODE.h, ODE.h, ODEFunc.h, ODES.cc,
ODES.h, ODESFunc.h, Quad-opts.in, Quad.cc, Quad.h, aepbalance.cc, aepbalance.h,
base-dae.h, base-de.h, base-min.h, bsxfun-decl.h, bsxfun-defs.cc, bsxfun.h,
chol.cc, chol.h, eigs-base.cc, eigs-base.h, fEIG.cc, fEIG.h, gepbalance.cc,
gepbalance.h, gsvd.cc, gsvd.h, hess.cc, hess.h, lo-amos-proto.h,
lo-arpack-proto.h, lo-blas-proto.h, lo-fftpack-proto.h, lo-lapack-proto.h,
lo-mappers.cc, lo-mappers.h, lo-qrupdate-proto.h, lo-ranlib-proto.h,
lo-slatec-proto.h, lo-specfun.cc, lo-specfun.h, lu.cc, lu.h, oct-convn.cc,
oct-convn.h, oct-fftw.cc, oct-fftw.h, oct-norm.cc, oct-norm.h, oct-rand.cc,
oct-rand.h, oct-spparms.cc, oct-spparms.h, qr.cc, qr.h, qrp.cc, qrp.h,
randgamma.cc, randgamma.h, randmtzig.cc, randmtzig.h, randpoisson.cc,
randpoisson.h, schur.cc, schur.h, sparse-chol.cc, sparse-chol.h,
sparse-dmsolve.cc, sparse-dmsolve.h, sparse-lu.cc, sparse-lu.h, sparse-qr.cc,
sparse-qr.h, svd.cc, svd.h, Sparse-diag-op-defs.h, Sparse-op-decls.h,
Sparse-op-defs.h, Sparse-perm-op-defs.h, config-ops.sh, mk-ops.awk, mx-base.h,
mx-defs.h, mx-ext.h, mx-inlines.cc, mx-op-decl.h, mx-op-defs.h, mx-ops,
smx-ops, vx-ops, child-list.cc, child-list.h, cmach-info.c, cmach-info.h,
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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> |
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date | Sat, 06 Jan 2018 07:57:19 -0800 |
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rev | line source |
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7019 | 1 /* |
2 | |
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3 Copyright (C) 2006-2017 John W. Eaton |
7019 | 4 |
5 This file is part of Octave. | |
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. |
7019 | 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. |
7019 | 16 |
17 You should have received a copy of the GNU General Public License | |
18 along with Octave; see the file COPYING. If not, see | |
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19 <https://www.gnu.org/licenses/>. |
7019 | 20 |
21 */ | |
22 | |
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23 /* |
5742 | 24 A C-program for MT19937, with initialization improved 2002/2/10. |
25 Coded by Takuji Nishimura and Makoto Matsumoto. | |
26 This is a faster version by taking Shawn Cokus's optimization, | |
27 Matthe Bellew's simplification, Isaku Wada's real version. | |
28 David Bateman added normal and exponential distributions following | |
29 Marsaglia and Tang's Ziggurat algorithm. | |
30 | |
31 Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura, | |
32 Copyright (C) 2004, David Bateman | |
33 All rights reserved. | |
34 | |
35 Redistribution and use in source and binary forms, with or without | |
36 modification, are permitted provided that the following conditions | |
37 are met: | |
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38 |
5742 | 39 1. Redistributions of source code must retain the above copyright |
40 notice, this list of conditions and the following disclaimer. | |
41 | |
42 2. Redistributions in binary form must reproduce the above copyright | |
43 notice, this list of conditions and the following disclaimer in the | |
44 documentation and/or other materials provided with the distribution. | |
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 |
5742 | 48 permission. |
49 | |
50 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS | |
51 "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT | |
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 |
5742 | 54 OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, |
55 EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, | |
56 PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR | |
57 PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF | |
58 LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING | |
59 NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS | |
60 SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. | |
61 | |
62 | |
63 Any feedback is very welcome. | |
64 http://www.math.keio.ac.jp/matumoto/emt.html | |
65 email: matumoto@math.keio.ac.jp | |
66 | |
67 * 2004-01-19 Paul Kienzle | |
68 * * comment out main | |
69 * add init_by_entropy, get_state, set_state | |
70 * * converted to allow compiling by C++ compiler | |
71 * | |
72 * 2004-01-25 David Bateman | |
73 * * Add Marsaglia and Tsang Ziggurat code | |
74 * | |
75 * 2004-07-13 Paul Kienzle | |
76 * * make into an independent library with some docs. | |
77 * * introduce new main and test code. | |
78 * | |
79 * 2004-07-28 Paul Kienzle & David Bateman | |
80 * * add -DALLBITS flag for 32 vs. 53 bits of randomness in mantissa | |
81 * * make the naming scheme more uniform | |
82 * * add -DHAVE_X86 for faster support of 53 bit mantissa on x86 arch. | |
83 * | |
84 * 2005-02-23 Paul Kienzle | |
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 |
5742 | 95 */ |
96 | |
97 /* | |
98 === Build instructions === | |
99 | |
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100 Compile with -DHAVE_GETTIMEOFDAY if the gettimeofday function is |
5742 | 101 available. This is not necessary if your architecture has |
102 /dev/urandom defined. | |
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 |
5742 | 107 extra performance. Check whether -DUSE_X86_32=0 is faster on 64-bit |
108 x86 architectures. | |
109 | |
110 If you want to replace the Mersenne Twister with another | |
111 generator then redefine randi32 appropriately. | |
112 | |
113 === Usage instructions === | |
114 Before using any of the generators, initialize the state with one of | |
115 oct_init_by_int, oct_init_by_array or oct_init_by_entropy. | |
116 | |
117 All generators share the same state vector. | |
118 | |
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 |
5742 | 126 |
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) |
5742 | 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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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 |
5742 | 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 []) |
5742 | 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 []) |
5742 | 153 */ |
154 | |
155 #if defined (HAVE_CONFIG_H) | |
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156 # include "config.h" |
5742 | 157 #endif |
158 | |
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159 #include <cmath> |
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160 #include <cstdio> |
5742 | 161 |
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162 #include "oct-time.h" |
5742 | 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 |
5742 | 172 #endif |
173 | |
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174 /* ===== Mersenne Twister 32-bit generator ===== */ |
5742 | 175 |
176 #define MT_M 397 | |
177 #define MATRIX_A 0x9908b0dfUL /* constant vector a */ | |
178 #define UMASK 0x80000000UL /* most significant w-r bits */ | |
179 #define LMASK 0x7fffffffUL /* least significant r bits */ | |
180 #define MIXBITS(u,v) ( ((u) & UMASK) | ((v) & LMASK) ) | |
181 #define TWIST(u,v) ((MIXBITS(u,v) >> 1) ^ ((v)&1UL ? MATRIX_A : 0UL)) | |
182 | |
183 static uint32_t *next; | |
184 static uint32_t state[MT_N]; /* the array for the state vector */ | |
185 static int left = 1; | |
186 static int initf = 0; | |
187 static int initt = 1; | |
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188 static int inittf = 1; |
5742 | 189 |
190 /* initializes state[MT_N] with a seed */ | |
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191 void |
5742 | 192 oct_init_by_int (uint32_t s) |
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 */ |
5742 | 204 } |
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205 left = 1; |
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206 initf = 1; |
5742 | 207 } |
208 | |
209 /* initialize by an array with array-length */ | |
210 /* init_key is the array for initializing keys */ | |
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) |
5742 | 214 { |
215 int i, j, k; | |
216 oct_init_by_int (19650218UL); | |
217 i = 1; | |
218 j = 0; | |
219 k = (MT_N > key_length ? MT_N : key_length); | |
220 for (; k; k--) | |
221 { | |
222 state[i] = (state[i] ^ ((state[i-1] ^ (state[i-1] >> 30)) * 1664525UL)) | |
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223 + init_key[j] + j; /* non linear */ |
5742 | 224 state[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */ |
225 i++; | |
226 j++; | |
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 } |
5742 | 232 if (j >= key_length) |
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233 j = 0; |
5742 | 234 } |
235 for (k = MT_N - 1; k; k--) | |
236 { | |
237 state[i] = (state[i] ^ ((state[i-1] ^ (state[i-1] >> 30)) * 1566083941UL)) | |
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238 - i; /* non linear */ |
5742 | 239 state[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */ |
240 i++; | |
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 } |
5742 | 246 } |
247 | |
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248 state[0] = 0x80000000UL; /* MSB is 1; assuring nonzero initial array */ |
5742 | 249 left = 1; |
250 initf = 1; | |
251 } | |
252 | |
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253 void |
5742 | 254 oct_init_by_entropy (void) |
255 { | |
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256 uint32_t entropy[MT_N]; |
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257 int n = 0; |
5742 | 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 } |
5742 | 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); |
5742 | 289 } |
290 | |
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291 void |
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292 oct_set_state (uint32_t *save) |
5742 | 293 { |
294 int i; | |
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295 for (i = 0; i < MT_N; i++) |
5742 | 296 state[i] = save[i]; |
297 left = save[MT_N]; | |
298 next = state + (MT_N - left + 1); | |
299 } | |
300 | |
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301 void |
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302 oct_get_state (uint32_t *save) |
5742 | 303 { |
304 int i; | |
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305 for (i = 0; i < MT_N; i++) |
5742 | 306 save[i] = state[i]; |
307 save[MT_N] = left; | |
308 } | |
309 | |
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310 static void |
5742 | 311 next_state (void) |
312 { | |
313 uint32_t *p = state; | |
314 int j; | |
315 | |
316 /* if init_by_int() has not been called, */ | |
317 /* a default initial seed is used */ | |
318 /* if (initf==0) init_by_int(5489UL); */ | |
319 /* Or better yet, a random seed! */ | |
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320 if (initf == 0) |
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321 oct_init_by_entropy (); |
5742 | 322 |
323 left = MT_N; | |
324 next = state; | |
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325 |
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326 for (j = MT_N - MT_M + 1; --j; p++) |
5742 | 327 *p = p[MT_M] ^ TWIST(p[0], p[1]); |
328 | |
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329 for (j = MT_M; --j; p++) |
5742 | 330 *p = p[MT_M-MT_N] ^ TWIST(p[0], p[1]); |
331 | |
332 *p = p[MT_M-MT_N] ^ TWIST(p[0], state[0]); | |
333 } | |
334 | |
335 /* generates a random number on [0,0xffffffff]-interval */ | |
5766 | 336 static uint32_t |
5742 | 337 randmt (void) |
338 { | |
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339 uint32_t y; |
5742 | 340 |
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341 if (--left == 0) |
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342 next_state (); |
5742 | 343 y = *next++; |
344 | |
345 /* Tempering */ | |
346 y ^= (y >> 11); | |
347 y ^= (y << 7) & 0x9d2c5680UL; | |
348 y ^= (y << 15) & 0xefc60000UL; | |
349 return (y ^ (y >> 18)); | |
350 } | |
351 | |
352 /* ===== Uniform generators ===== */ | |
353 | |
354 /* Select which 32 bit generator to use */ | |
355 #define randi32 randmt | |
356 | |
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357 static uint64_t |
5742 | 358 randi53 (void) |
359 { | |
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360 const uint32_t lo = randi32 (); |
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361 const uint32_t hi = randi32 () & 0x1FFFFF; |
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362 #if defined (HAVE_X86_32) |
5742 | 363 uint64_t u; |
364 uint32_t *p = (uint32_t *)&u; | |
365 p[0] = lo; | |
366 p[1] = hi; | |
367 return u; | |
368 #else | |
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369 return ((static_cast<uint64_t> (hi) << 32) | lo); |
5742 | 370 #endif |
371 } | |
372 | |
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373 static uint64_t |
5742 | 374 randi54 (void) |
375 { | |
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376 const uint32_t lo = randi32 (); |
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377 const uint32_t hi = randi32 () & 0x3FFFFF; |
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378 #if defined (HAVE_X86_32) |
5742 | 379 uint64_t u; |
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380 uint32_t *p = static_cast<uint32_t *> (&u); |
5742 | 381 p[0] = lo; |
382 p[1] = hi; | |
383 return u; | |
384 #else | |
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385 return ((static_cast<uint64_t> (hi) << 32) | lo); |
5742 | 386 #endif |
387 } | |
388 | |
389 /* generates a random number on (0,1)-real-interval */ | |
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390 static float |
5742 | 391 randu32 (void) |
392 { | |
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393 return (static_cast<float> (randi32 ()) + 0.5) * (1.0/4294967296.0); |
5742 | 394 /* divided by 2^32 */ |
395 } | |
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396 |
5742 | 397 /* generates a random number on (0,1) with 53-bit resolution */ |
5766 | 398 static double |
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399 randu53 (void) |
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400 { |
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401 const uint32_t a = randi32 () >> 5; |
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402 const uint32_t b = randi32 () >> 6; |
6959 | 403 return (a*67108864.0+b+0.4) * (1.0/9007199254740992.0); |
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404 } |
5742 | 405 |
406 /* Determine mantissa for uniform doubles */ | |
407 double | |
408 oct_randu (void) | |
409 { | |
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410 return randu53 (); |
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411 } |
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412 |
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413 /* Determine mantissa for uniform floats */ |
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414 float |
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415 oct_float_randu (void) |
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416 { |
6959 | 417 return randu32 (); |
5742 | 418 } |
419 | |
420 /* ===== Ziggurat normal and exponential generators ===== */ | |
421 | |
422 #define ZIGGURAT_TABLE_SIZE 256 | |
423 | |
424 #define ZIGGURAT_NOR_R 3.6541528853610088 | |
425 #define ZIGGURAT_NOR_INV_R 0.27366123732975828 | |
426 #define NOR_SECTION_AREA 0.00492867323399 | |
427 | |
428 #define ZIGGURAT_EXP_R 7.69711747013104972 | |
429 #define ZIGGURAT_EXP_INV_R 0.129918765548341586 | |
430 #define EXP_SECTION_AREA 0.0039496598225815571993 | |
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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438 |
5742 | 439 static ZIGINT ki[ZIGGURAT_TABLE_SIZE]; |
440 static double wi[ZIGGURAT_TABLE_SIZE], fi[ZIGGURAT_TABLE_SIZE]; | |
441 static ZIGINT ke[ZIGGURAT_TABLE_SIZE]; | |
442 static double we[ZIGGURAT_TABLE_SIZE], fe[ZIGGURAT_TABLE_SIZE]; | |
443 | |
444 /* | |
445 This code is based on the paper Marsaglia and Tsang, "The ziggurat method | |
446 for generating random variables", Journ. Statistical Software. Code was | |
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 |
5742 | 450 Ziggurat. This has several advantages. |
451 | |
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452 1) As Marsaglia and Tsang themselves states, the more levels the few |
5742 | 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 |
5742 | 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 |
5742 | 458 from the article means we are free of copyright issues. |
459 4) Compile flag for full 53-bit random mantissa. | |
460 | |
461 It should be stated that the authors made my life easier, by the fact that | |
462 the algorithm developed in the text of the article is for a 256 level | |
463 ziggurat, even if the code itself isn't... | |
464 | |
465 One modification to the algorithm developed in the article, is that it is | |
466 assumed that 0 <= x < Inf, and "unsigned long"s are used, thus resulting in | |
467 terms like 2^32 in the code. As the normal distribution is defined between | |
468 -Inf < x < Inf, we effectively only have 31 bit integers plus a sign. Thus | |
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 |
5742 | 471 full 32 bits. We use EMANTISSA for this term. |
472 | |
473 It appears that I'm slightly slower than the code in the article, this | |
474 is partially due to a better generator of random integers than they | |
475 use. But might also be that the case of rapid return was optimized by | |
476 inlining the relevant code with a #define. As the basic Mersenne | |
477 Twister is only 25% faster than this code I suspect that the main | |
478 reason is just the use of the Mersenne Twister and not the inlining, | |
479 so I'm not going to try and optimize further. | |
480 */ | |
481 | |
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482 static void |
5742 | 483 create_ziggurat_tables (void) |
484 { | |
485 int i; | |
486 double x, x1; | |
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487 |
5742 | 488 /* Ziggurat tables for the normal distribution */ |
489 x1 = ZIGGURAT_NOR_R; | |
490 wi[255] = x1 / NMANTISSA; | |
491 fi[255] = exp (-0.5 * x1 * x1); | |
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 |
5742 | 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. |
5742 | 497 */ |
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498 ki[0] = static_cast<ZIGINT> (x1 * fi[255] / NOR_SECTION_AREA * NMANTISSA); |
5742 | 499 wi[0] = NOR_SECTION_AREA / fi[255] / NMANTISSA; |
500 fi[0] = 1.; | |
501 | |
502 for (i = 254; i > 0; i--) | |
503 { | |
504 /* New x is given by x = f^{-1}(v/x_{i+1} + f(x_{i+1})), thus | |
505 * need inverse operator of y = exp(-0.5*x*x) -> x = sqrt(-2*ln(y)) | |
506 */ | |
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507 x = std::sqrt (-2. * std::log (NOR_SECTION_AREA / x1 + fi[i+1])); |
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508 ki[i+1] = static_cast<ZIGINT> (x / x1 * NMANTISSA); |
5742 | 509 wi[i] = x / NMANTISSA; |
510 fi[i] = exp (-0.5 * x * x); | |
511 x1 = x; | |
512 } | |
513 | |
514 ki[1] = 0; | |
515 | |
516 /* Zigurrat tables for the exponential distribution */ | |
517 x1 = ZIGGURAT_EXP_R; | |
518 we[255] = x1 / EMANTISSA; | |
519 fe[255] = exp (-x1); | |
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 |
5742 | 523 * k_0 = 2^32 * r * f(r) / v, w_0 = 0.5^32 * v / f(r), f_0 = 1, |
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524 * where v is the area of each strip of the ziggurat. |
5742 | 525 */ |
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526 ke[0] = static_cast<ZIGINT> (x1 * fe[255] / EXP_SECTION_AREA * EMANTISSA); |
5742 | 527 we[0] = EXP_SECTION_AREA / fe[255] / EMANTISSA; |
528 fe[0] = 1.; | |
529 | |
530 for (i = 254; i > 0; i--) | |
531 { | |
532 /* New x is given by x = f^{-1}(v/x_{i+1} + f(x_{i+1})), thus | |
533 * need inverse operator of y = exp(-x) -> x = -ln(y) | |
534 */ | |
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535 x = - std::log (EXP_SECTION_AREA / x1 + fe[i+1]); |
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536 ke[i+1] = static_cast<ZIGINT> (x / x1 * EMANTISSA); |
5742 | 537 we[i] = x / EMANTISSA; |
538 fe[i] = exp (-x); | |
539 x1 = x; | |
540 } | |
541 ke[1] = 0; | |
542 | |
543 initt = 0; | |
544 } | |
545 | |
546 /* | |
547 * Here is the guts of the algorithm. As Marsaglia and Tsang state the | |
548 * algorithm in their paper | |
549 * | |
550 * 1) Calculate a random signed integer j and let i be the index | |
551 * provided by the rightmost 8-bits of j | |
552 * 2) Set x = j * w_i. If j < k_i return x | |
553 * 3) If i = 0, then return x from the tail | |
554 * 4) If [f(x_{i-1}) - f(x_i)] * U < f(x) - f(x_i), return x | |
555 * 5) goto step 1 | |
556 * | |
557 * Where f is the functional form of the distribution, which for a normal | |
558 * distribution is exp(-0.5*x*x) | |
559 */ | |
560 | |
561 double | |
562 oct_randn (void) | |
563 { | |
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564 if (initt) |
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565 create_ziggurat_tables (); |
5742 | 566 |
567 while (1) | |
568 { | |
569 /* The following code is specialized for 32-bit mantissa. | |
570 * Compared to the arbitrary mantissa code, there is a performance | |
571 * gain for 32-bits: PPC: 2%, MIPS: 8%, x86: 40% | |
572 * There is a bigger performance gain compared to using a full | |
573 * 53-bit mantissa: PPC: 60%, MIPS: 65%, x86: 240% | |
574 * Of course, different compilers and operating systems may | |
575 * have something to do with this. | |
576 */ | |
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577 # if defined (HAVE_X86_32) |
5742 | 578 /* 53-bit mantissa, 1-bit sign, x86 32-bit architecture */ |
579 double x; | |
580 int si,idx; | |
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581 uint32_t lo, hi; |
5742 | 582 int64_t rabs; |
583 uint32_t *p = (uint32_t *)&rabs; | |
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584 lo = randi32 (); |
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585 idx = lo & 0xFF; |
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586 hi = randi32 (); |
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587 si = hi & UMASK; |
5742 | 588 p[0] = lo; |
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589 p[1] = hi & 0x1FFFFF; |
5742 | 590 x = ( si ? -rabs : rabs ) * wi[idx]; |
22188 | 591 # else |
5742 | 592 /* arbitrary mantissa (selected by NRANDI, with 1 bit for sign) */ |
593 const uint64_t r = NRANDI; | |
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594 const int64_t rabs = r >> 1; |
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595 const int idx = static_cast<int> (rabs & 0xFF); |
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596 const double x = ( (r & 1) ? -rabs : rabs) * wi[idx]; |
22188 | 597 # endif |
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598 if (rabs < static_cast<int64_t> (ki[idx])) |
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599 return x; /* 99.3% of the time we return here 1st try */ |
5742 | 600 else if (idx == 0) |
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601 { |
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602 /* As stated in Marsaglia and Tsang |
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603 * |
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604 * For the normal tail, the method of Marsaglia[5] provides: |
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605 * generate x = -ln(U_1)/r, y = -ln(U_2), until y+y > x*x, |
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606 * then return r+x. Except that r+x is always in the positive |
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607 * tail!!!! Any thing random might be used to determine the |
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608 * sign, but as we already have r we might as well use it |
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609 * |
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610 * [PAK] but not the bottom 8 bits, since they are all 0 here! |
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611 */ |
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612 double xx, yy; |
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613 do |
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614 { |
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615 xx = - ZIGGURAT_NOR_INV_R * std::log (RANDU); |
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616 yy = - std::log (RANDU); |
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617 } |
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618 while ( yy+yy <= xx*xx); |
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619 return ((rabs & 0x100) ? -ZIGGURAT_NOR_R-xx : ZIGGURAT_NOR_R+xx); |
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620 } |
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621 else if ((fi[idx-1] - fi[idx]) * RANDU + fi[idx] < exp (-0.5*x*x)) |
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622 return x; |
5742 | 623 } |
624 } | |
625 | |
626 double | |
627 oct_rande (void) | |
628 { | |
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629 if (initt) |
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630 create_ziggurat_tables (); |
5742 | 631 |
632 while (1) | |
633 { | |
634 ZIGINT ri = ERANDI; | |
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635 const int idx = static_cast<int> (ri & 0xFF); |
5742 | 636 const double x = ri * we[idx]; |
637 if (ri < ke[idx]) | |
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638 return x; /* 98.9% of the time we return here 1st try */ |
5742 | 639 else if (idx == 0) |
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640 { |
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641 /* As stated in Marsaglia and Tsang |
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642 * |
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643 * For the exponential tail, the method of Marsaglia[5] provides: |
5742 | 644 * x = r - ln(U); |
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645 */ |
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646 return ZIGGURAT_EXP_R - std::log (RANDU); |
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647 } |
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648 else if ((fe[idx-1] - fe[idx]) * RANDU + fe[idx] < exp (-x)) |
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649 return x; |
5742 | 650 } |
651 } | |
652 | |
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653 #undef ZIGINT |
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654 #undef EMANTISSA |
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655 #undef ERANDI |
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656 #undef NMANTISSA |
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657 #undef NRANDI |
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658 #undef RANDU |
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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659 |
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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660 #define ZIGINT uint32_t |
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661 #define EMANTISSA 4294967296.0 /* 32 bit mantissa */ |
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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662 #define ERANDI randi32() /* 32 bits for mantissa */ |
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663 #define NMANTISSA 2147483648.0 /* 31 bit mantissa */ |
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664 #define NRANDI randi32() /* 31 bits for mantissa + 1 bit sign */ |
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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665 #define RANDU randu32() |
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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666 |
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667 static ZIGINT fki[ZIGGURAT_TABLE_SIZE]; |
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668 static float fwi[ZIGGURAT_TABLE_SIZE], ffi[ZIGGURAT_TABLE_SIZE]; |
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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669 static ZIGINT fke[ZIGGURAT_TABLE_SIZE]; |
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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)
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|
671 |
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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|
672 static void |
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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673 create_ziggurat_float_tables (void) |
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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|
674 { |
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675 int i; |
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David Bateman <dbateman@free.fr>
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676 float x, x1; |
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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|
677 |
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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|
678 /* Ziggurat tables for the normal distribution */ |
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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679 x1 = ZIGGURAT_NOR_R; |
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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|
680 fwi[255] = x1 / NMANTISSA; |
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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|
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>
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|
682 |
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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|
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>
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|
684 * defines this as |
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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parents:
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diff
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|
685 * k_0 = 2^31 * r * f(r) / v, w_0 = 0.5^31 * v / f(r), f_0 = 1, |
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
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|
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>
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|
687 */ |
21720
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use C++ for random number generator sources
John W. Eaton <jwe@octave.org>
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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
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|
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:
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|
690 ffi[0] = 1.; |
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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|
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:
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|
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:
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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
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|
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:
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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:
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diff
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|
701 x1 = x; |
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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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:
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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:
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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:
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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:
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diff
changeset
|
746 * |
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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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:
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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:
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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
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David Bateman <dbateman@free.fr>
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753 { |
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David Bateman <dbateman@free.fr>
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|
754 if (inittf) |
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maint: Use Octave coding convention for cuddled parenthis in function calls with empty argument lists.
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14655
diff
changeset
|
755 create_ziggurat_float_tables (); |
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David Bateman <dbateman@free.fr>
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|
756 |
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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|
757 while (1) |
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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parents:
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diff
changeset
|
758 { |
43db83eff9db
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David Bateman <dbateman@free.fr>
parents:
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759 /* 32-bit mantissa */ |
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|
760 const uint32_t r = randi32 (); |
21661
1b9a36a66b01
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|
761 const uint32_t rabs = r & LMASK; |
21720
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parents:
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762 const int idx = static_cast<int> (r & 0xFF); |
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John W. Eaton <jwe@octave.org>
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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)
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764 if (rabs < fki[idx]) |
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David Bateman <dbateman@free.fr>
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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)
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|
766 else if (idx == 0) |
43db83eff9db
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767 { |
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768 /* As stated in Marsaglia and Tsang |
43db83eff9db
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parents:
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769 * |
43db83eff9db
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David Bateman <dbateman@free.fr>
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770 * For the normal tail, the method of Marsaglia[5] provides: |
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David Bateman <dbateman@free.fr>
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diff
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|
771 * generate x = -ln(U_1)/r, y = -ln(U_2), until y+y > x*x, |
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David Bateman <dbateman@free.fr>
parents:
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|
772 * then return r+x. Except that r+x is always in the positive |
43db83eff9db
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David Bateman <dbateman@free.fr>
parents:
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773 * tail!!!! Any thing random might be used to determine the |
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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|
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:
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|
775 * |
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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|
776 * [PAK] but not the bottom 8 bits, since they are all 0 here! |
43db83eff9db
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David Bateman <dbateman@free.fr>
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changeset
|
777 */ |
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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|
778 float xx, yy; |
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David Bateman <dbateman@free.fr>
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|
779 do |
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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parents:
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changeset
|
780 { |
21942
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21928
diff
changeset
|
781 xx = - ZIGGURAT_NOR_INV_R * std::log (RANDU); |
aab79a1885cc
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John W. Eaton <jwe@octave.org>
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|
782 yy = - std::log (RANDU); |
14655
43db83eff9db
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parents:
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diff
changeset
|
783 } |
43db83eff9db
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David Bateman <dbateman@free.fr>
parents:
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|
784 while ( yy+yy <= xx*xx); |
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1b9a36a66b01
maint: Octave coding convention cleanups.
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785 return ((rabs & 0x100) ? -ZIGGURAT_NOR_R-xx : ZIGGURAT_NOR_R+xx); |
14655
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David Bateman <dbateman@free.fr>
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|
786 } |
15018
3d8ace26c5b4
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|
787 else if ((ffi[idx-1] - ffi[idx]) * RANDU + ffi[idx] < exp (-0.5*x*x)) |
14655
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changeset
|
788 return x; |
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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changeset
|
789 } |
43db83eff9db
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changeset
|
790 } |
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|
791 |
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|
792 float |
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|
793 oct_float_rande (void) |
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|
794 { |
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|
795 if (inittf) |
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|
796 create_ziggurat_float_tables (); |
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changeset
|
797 |
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|
798 while (1) |
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|
799 { |
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changeset
|
800 ZIGINT ri = ERANDI; |
21720
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|
801 const int idx = static_cast<int> (ri & 0xFF); |
14655
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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|
802 const float x = ri * fwe[idx]; |
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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changeset
|
803 if (ri < fke[idx]) |
15970
ca6202597201
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Mike Miller <mtmiller@ieee.org>
parents:
15408
diff
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|
804 return x; /* 98.9% of the time we return here 1st try */ |
14655
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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|
805 else if (idx == 0) |
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|
806 { |
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|
807 /* As stated in Marsaglia and Tsang |
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changeset
|
808 * |
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changeset
|
809 * For the exponential tail, the method of Marsaglia[5] provides: |
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|
810 * x = r - ln(U); |
43db83eff9db
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|
811 */ |
21942
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21928
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|
812 return ZIGGURAT_EXP_R - std::log (RANDU); |
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|
813 } |
15018
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|
814 else if ((ffe[idx-1] - ffe[idx]) * RANDU + ffe[idx] < exp (-x)) |
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815 return x; |
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816 } |
43db83eff9db
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|
817 } |
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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|
818 |
5742 | 819 /* Array generators */ |
11586
12df7854fa7c
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|
820 void |
5742 | 821 oct_fill_randu (octave_idx_type n, double *p) |
822 { | |
823 octave_idx_type i; | |
11586
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strip trailing whitespace from source files
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|
824 for (i = 0; i < n; i++) |
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|
825 p[i] = oct_randu (); |
5742 | 826 } |
827 | |
11586
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John W. Eaton <jwe@octave.org>
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|
828 void |
5742 | 829 oct_fill_randn (octave_idx_type n, double *p) |
830 { | |
831 octave_idx_type i; | |
11586
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John W. Eaton <jwe@octave.org>
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|
832 for (i = 0; i < n; i++) |
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maint: Use Octave coding convention for cuddled parenthis in function calls with empty argument lists.
Rik <octave@nomad.inbox5.com>
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|
833 p[i] = oct_randn (); |
5742 | 834 } |
835 | |
11586
12df7854fa7c
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John W. Eaton <jwe@octave.org>
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|
836 void |
5742 | 837 oct_fill_rande (octave_idx_type n, double *p) |
838 { | |
839 octave_idx_type i; | |
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840 for (i = 0; i < n; i++) |
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|
841 p[i] = oct_rande (); |
5742 | 842 } |
14655
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|
843 |
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|
844 void |
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|
845 oct_fill_float_randu (octave_idx_type n, float *p) |
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|
846 { |
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|
847 octave_idx_type i; |
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848 for (i = 0; i < n; i++) |
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changeset
|
849 p[i] = oct_float_randu (); |
14655
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|
850 } |
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|
851 |
43db83eff9db
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|
852 void |
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David Bateman <dbateman@free.fr>
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changeset
|
853 oct_fill_float_randn (octave_idx_type n, float *p) |
43db83eff9db
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|
854 { |
43db83eff9db
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David Bateman <dbateman@free.fr>
parents:
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changeset
|
855 octave_idx_type i; |
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diff
changeset
|
856 for (i = 0; i < n; i++) |
14846
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Rik <octave@nomad.inbox5.com>
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14655
diff
changeset
|
857 p[i] = oct_float_randn (); |
14655
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changeset
|
858 } |
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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changeset
|
859 |
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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|
860 void |
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|
861 oct_fill_float_rande (octave_idx_type n, float *p) |
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|
862 { |
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|
863 octave_idx_type i; |
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|
864 for (i = 0; i < n; i++) |
14846
460a3c6d8bf1
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|
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
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