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add doug's power series package
SVN=128063
This commit is contained in:
Rob Pike
parent
dead164cc0
commit
f87a960adf
748
test/chan/powser1.go
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748
test/chan/powser1.go
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@ -0,0 +1,748 @@
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// $G $D/$F.go && $L $F.$A && ./$A.out
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// Copyright 2009 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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// Power series package
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// A power series is a channel, along which flow rational
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// coefficients. A denominator of zero signifies the end.
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// Original code in Newsqueak by Doug McIlroy.
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// See Squinting at Power Series by Doug McIlroy,
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// http://www.cs.bell-labs.com/who/rsc/thread/squint.pdf
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package main
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type rat struct {
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num, den int64; // numerator, denominator
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}
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func (u *rat) pr(){
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if u.den==1 { print u.num }
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else { print u.num, "/", u.den }
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print(" ")
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}
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func (u *rat) eq(c *rat) bool {
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return u.num == c.num && u.den == c.den
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}
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type item *rat;
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type dch struct {
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req *chan int;
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dat *chan item;
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nam int;
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}
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type dch2 [2] *dch
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var chnames string
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var chnameserial int
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var seqno int
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func Init();
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func mkdch() *dch {
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c := chnameserial % len(chnames);
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chnameserial++;
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d := new(dch);
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d.req = new(chan int);
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d.dat = new(chan item);
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d.nam = c;
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return d;
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}
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func mkdch2() *dch2 {
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d2 := new(dch2);
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d2[0] = mkdch();
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d2[1] = mkdch();
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return d2;
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}
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// split reads a single demand channel and replicates its
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// output onto two, which may be read at different rates.
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// A process is created at first demand for an item and dies
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// after the item has been sent to both outputs.
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// When multiple generations of split exist, the newest
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// will service requests on one channel, which is
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// always renamed to be out[0]; the oldest will service
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// requests on the other channel, out[1]. All generations but the
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// newest hold queued data that has already been sent to
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// out[0]. When data has finally been sent to out[1],
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// a signal on the release-wait channel tells the next newer
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// generation to begin servicing out[1].
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func dosplit(in *dch, out *dch2, wait *chan int ){
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//print "dosplit ", wait, "\n";
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var t *dch;
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both := false; // do not service both channels
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/*
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select {
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case <-out[0].req:
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;
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case <-wait:
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both = 1;
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select {
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case <-out[0].req:
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;
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case <-out[1].req:
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t=out[0]; out[0]=out[1]; out[1]=t;
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};
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}
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*/
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// select simulation
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for {
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var ok bool;
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var dummy int;
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dummy, ok = <-out[0].req;
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if ok { goto OUT1 }
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dummy, ok = <-wait;
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if ok {
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both = true;
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// select simulation
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for {
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dummy, ok = <-out[0].req;
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if ok { goto OUT1 }
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dummy, ok = <-out[1].req;
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if ok {
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out[0], out[1] = out[1], out[0];
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goto OUT1
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}
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sys.gosched();
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}
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}
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sys.gosched();
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}
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OUT1: //BUG
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seqno++;
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in.req -< seqno;
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release := new(chan int);
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go dosplit(in, out, release);
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dat := <-in.dat;
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out[0].dat -< dat;
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if !both {
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<-wait
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}
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<-out[1].req;
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out[1].dat -< dat;
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release -< 0;
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}
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func split(in *dch, out *dch2){
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release := new(chan int);
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go dosplit(in, out, release);
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release -< 0;
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}
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func put(dat item, out *dch){
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<-out.req;
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out.dat -< dat;
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}
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func get(in *dch) item{
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seqno++;
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in.req -< seqno;
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return <-in.dat;
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}
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// Get one item from each of n demand channels
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func getn(in *[]*dch, n int) *[]item {
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// BUG n:=len(in);
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if n != 2 { panic "bad n in getn" };
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req := new([2] *chan int);
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dat := new([2] *chan item);
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out := new([2] item);
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var i int;
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var it item;
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for i=0; i<n; i++ {
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req[i] = in[i].req;
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dat[i] = nil;
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}
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for n=2*n; n>0; n-- {
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seqno++
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/*
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select{
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case req[i=] <-= seqno:
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dat[i] = in[i].dat;
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req[i] = nil;
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case it = <-dat[i=]:
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out[i] = it;
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dat[i] = nil;
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}
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*/
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// simulation of select
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sel:
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for c1:=0; ; c1++ {
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for i := 0; i < 2; i++ {
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ok := false;
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if req[i] != nil { ok = req[i] -< seqno }
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if ok {
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dat[i] = in[i].dat;
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req[i] = nil;
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goto OUT; // BUG
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break sel;
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}
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ok = false;
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if dat[i] != nil { it, ok = <-dat[i] }
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if ok {
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out[i] = it;
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dat[i] = nil;
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goto OUT; // BUG
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break sel;
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}
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sys.gosched();
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}
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sys.gosched();
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}
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OUT:
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}
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return out;
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}
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// Get one item from each of 2 demand channels
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func get2(in0 *dch, in1 *dch) *[]item {
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x := new([2] *dch);
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x[0] = in0;
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x[1] = in1;
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return getn(x, 2);
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}
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func copy(in *dch, out *dch){
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for {
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<-out.req;
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out.dat -< get(in);
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}
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}
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func repeat(dat item, out *dch){
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for {
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put(dat, out)
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}
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}
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type PS *dch; // power series
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type PS2 *[2] PS; // pair of power series
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var Ones PS
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var Twos PS
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func mkPS() *dch {
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return mkdch()
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}
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func mkPS2() *dch2 {
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return mkdch2()
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}
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// Conventions
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// Upper-case for power series.
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// Lower-case for rationals.
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// Input variables: U,V,...
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// Output variables: ...,Y,Z
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// Integer gcd; needed for rational arithmetic
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func gcd (u, v int64) int64{
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if u < 0 { return gcd(-u, v) }
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if u > v { return gcd(v, u) }
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if u == 0 { return v }
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return gcd(v%u, u)
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}
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// Make a rational from two ints and from one int
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func i2tor(u, v int64) *rat{
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g := gcd(u,v);
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r := new(rat);
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if v > 0 {
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r.num = u/g;
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r.den = v/g;
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} else {
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r.num = -u/g;
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r.den = -v/g;
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}
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return r;
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}
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func itor(u int64) *rat{
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return i2tor(u, 1);
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}
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var zero *rat;
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var one *rat;
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// End mark and end test
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var finis *rat;
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func end(u *rat) int64 {
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if u.den==0 { return 1 }
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return 0
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}
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// Operations on rationals
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func add(u, v *rat) *rat {
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g := gcd(u.den,v.den);
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return i2tor(u.num*(v.den/g)+v.num*(u.den/g),u.den*(v.den/g));
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}
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func mul(u, v *rat) *rat{
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g1 := gcd(u.num,v.den);
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g2 := gcd(u.den,v.num);
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r := new(rat);
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r.num =(u.num/g1)*(v.num/g2);
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r.den = (u.den/g2)*(v.den/g1);
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return r;
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}
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func neg(u *rat) *rat{
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return i2tor(-u.num, u.den);
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}
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func sub(u, v *rat) *rat{
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return add(u, neg(v));
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}
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func inv(u *rat) *rat{ // invert a rat
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if u.num == 0 { panic "zero divide in inv" }
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return i2tor(u.den, u.num);
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}
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// Print n terms of a power series
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func Printn(U PS, n int){
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done := false;
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for ; !done && n>0; n-- {
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u := get(U);
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if end(u) != 0 { done = true }
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else { u.pr() }
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}
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print ("\n");
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}
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func Print(U PS){
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Printn(U,1000000000);
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}
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// Evaluate n terms of power series U at x=c
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func eval(c *rat, U PS, n int) *rat{
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if n==0 { return zero }
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y := get(U);
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if end(y) != 0 { return zero }
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return add(y,mul(c,eval(c,U,n-1)));
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}
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// Power-series constructors return channels on which power
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// series flow. They start an encapsulated generator that
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// puts the terms of the series on the channel.
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// Make a pair of power series identical to a given power series
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func Split(U PS) *dch2{
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UU := mkdch2();
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go split(U,UU);
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return UU;
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}
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// Add two power series
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func Add(U, V PS) PS{
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Z := mkPS();
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go func(U, V, Z PS){
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var uv *[2] *rat;
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for {
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<-Z.req;
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uv = get2(U,V);
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switch end(uv[0])+2*end(uv[1]) {
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case 0:
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Z.dat -< add(uv[0], uv[1]);
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case 1:
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Z.dat -< uv[1];
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copy(V,Z);
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case 2:
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Z.dat -< uv[0];
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copy(U,Z)
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case 3:
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Z.dat -< finis;
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}
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}
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}(U, V, Z);
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return Z;
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}
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// Multiply a power series by a constant
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func Cmul(c *rat,U PS) PS{
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Z := mkPS();
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go func(c *rat, U, Z PS){
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done := false;
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for !done {
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<-Z.req;
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u := get(U);
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if end(u) != 0 { done = true }
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else { Z.dat -< mul(c,u) }
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}
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Z.dat -< finis;
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}(c, U, Z);
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return Z;
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}
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// Subtract
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func Sub(U, V PS) PS{
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return Add(U, Cmul(neg(one), V));
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}
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// Multiply a power series by the monomial x^n
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func Monmul(U PS, n int) PS{
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Z := mkPS();
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go func(n int, U PS, Z PS){
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for ; n>0; n-- { put(zero,Z) }
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copy(U,Z);
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}(n, U, Z);
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return Z;
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}
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// Multiply by x
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func Xmul(U PS) PS{
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Monmul(U,1);
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}
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func Rep(c *rat) PS{
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Z := mkPS();
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go repeat(c,Z);
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return Z;
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}
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// Monomial c*x^n
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func Mon(c *rat, n int) PS{
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Z:=mkPS();
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go func(c *rat, n int, Z PS){
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if(c.num!=0) {
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for ; n>0; n=n-1 { put(zero,Z) }
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put(c,Z);
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}
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put(finis,Z);
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}(c, n, Z);
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return Z;
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}
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func Shift(c *rat, U PS) PS{
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Z := mkPS();
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go func(c *rat, U, Z PS){
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put(c,Z);
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copy(U,Z);
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}(c, U, Z);
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return Z;
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}
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// simple pole at 1: 1/(1-x) = 1 1 1 1 1 ...
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// Convert array of coefficients, constant term first
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// to a (finite) power series
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func Poly(a [] *rat) PS{
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Z:=mkPS();
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/* BUG: NEED LEN OF ARRAY
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begin func(a [] *rat, Z PS){
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j:=0;
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done:=0;
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for j=len(a); !done&&j>0; j=j-1)
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if(a[j-1].num!=0) done=1;
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i:=0;
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for(; i<j; i=i+1) put(a[i],Z);
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put(finis,Z);
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}();
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*/
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return Z;
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}
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// Multiply. The algorithm is
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// let U = u + x*UU
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// let V = v + x*VV
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// then UV = u*v + x*(u*VV+v*UU) + x*x*UU*VV
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func Mul(U, V PS) PS{
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Z:=mkPS();
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go func(U, V, Z PS){
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<-Z.req;
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uv := get2(U,V);
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if end(uv[0])!=0 || end(uv[1]) != 0 {
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Z.dat -< finis;
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} else {
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Z.dat -< mul(uv[0],uv[1]);
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UU := Split(U);
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VV := Split(V);
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W := Add(Cmul(uv[0],VV[0]),Cmul(uv[1],UU[0]));
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<-Z.req;
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Z.dat -< get(W);
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copy(Add(W,Mul(UU[1],VV[1])),Z);
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}
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}(U, V, Z);
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return Z;
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}
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// Differentiate
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func Diff(U PS) PS{
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Z:=mkPS();
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go func(U, Z PS){
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<-Z.req;
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u := get(U);
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if end(u) == 0 {
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done:=false;
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for i:=1; !done; i++ {
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u = get(U);
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if end(u) != 0 { done=true }
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else {
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Z.dat -< mul(itor(int64(i)),u);
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<-Z.req;
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}
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}
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}
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Z.dat -< finis;
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}(U, Z);
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return Z;
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}
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// Integrate, with const of integration
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func Integ(c *rat,U PS) PS{
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Z:=mkPS();
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go func(c *rat, U, Z PS){
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put(c,Z);
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done:=false;
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for i:=1; !done; i++ {
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<-Z.req;
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u := get(U);
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if end(u) != 0 { done= true }
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Z.dat -< mul(i2tor(1,int64(i)),u);
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}
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Z.dat -< finis;
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}(c, U, Z);
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return Z;
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}
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// Binomial theorem (1+x)^c
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func Binom(c *rat) PS{
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Z:=mkPS();
|
||||
go func(c *rat, Z PS){
|
||||
n := 1;
|
||||
t := itor(1);
|
||||
for c.num!=0 {
|
||||
put(t,Z);
|
||||
t = mul(mul(t,c),i2tor(1,int64(n)));
|
||||
c = sub(c,one);
|
||||
n++;
|
||||
}
|
||||
put(finis,Z);
|
||||
}(c, Z);
|
||||
return Z;
|
||||
}
|
||||
|
||||
// Reciprocal of a power series
|
||||
// let U = u + x*UU
|
||||
// let Z = z + x*ZZ
|
||||
// (u+x*UU)*(z+x*ZZ) = 1
|
||||
// z = 1/u
|
||||
// u*ZZ + z*UU +x*UU*ZZ = 0
|
||||
// ZZ = -UU*(z+x*ZZ)/u;
|
||||
|
||||
func Recip(U PS) PS{
|
||||
Z:=mkPS();
|
||||
go func(U, Z PS){
|
||||
ZZ:=mkPS2();
|
||||
<-Z.req;
|
||||
z := inv(get(U));
|
||||
Z.dat -< z;
|
||||
split(Mul(Cmul(neg(z),U),Shift(z,ZZ[0])),ZZ);
|
||||
copy(ZZ[1],Z);
|
||||
}(U, Z);
|
||||
return Z;
|
||||
}
|
||||
|
||||
// Exponential of a power series with constant term 0
|
||||
// (nonzero constant term would make nonrational coefficients)
|
||||
// bug: the constant term is simply ignored
|
||||
// Z = exp(U)
|
||||
// DZ = Z*DU
|
||||
// integrate to get Z
|
||||
|
||||
func Exp(U PS) PS{
|
||||
ZZ := mkPS2();
|
||||
split(Integ(one,Mul(ZZ[0],Diff(U))),ZZ);
|
||||
return ZZ[1];
|
||||
}
|
||||
|
||||
// Substitute V for x in U, where the leading term of V is zero
|
||||
// let U = u + x*UU
|
||||
// let V = v + x*VV
|
||||
// then S(U,V) = u + VV*S(V,UU)
|
||||
// bug: a nonzero constant term is ignored
|
||||
|
||||
func Subst(U, V PS) PS {
|
||||
Z:= mkPS();
|
||||
go func(U, V, Z PS) {
|
||||
VV := Split(V);
|
||||
<-Z.req;
|
||||
u := get(U);
|
||||
Z.dat -< u;
|
||||
if end(u) == 0 {
|
||||
if end(get(VV[0])) != 0 { put(finis,Z); }
|
||||
else { copy(Mul(VV[0],Subst(U,VV[1])),Z); }
|
||||
}
|
||||
}(U, V, Z);
|
||||
return Z;
|
||||
}
|
||||
|
||||
// Monomial Substition: U(c x^n)
|
||||
// Each Ui is multiplied by c^i and followed by n-1 zeros
|
||||
|
||||
func MonSubst(U PS, c0 *rat, n int) PS {
|
||||
Z:= mkPS();
|
||||
go func(U, Z PS, c0 *rat, n int) {
|
||||
c := one;
|
||||
for {
|
||||
<-Z.req;
|
||||
u := get(U);
|
||||
Z.dat -< mul(u, c);
|
||||
c = mul(c, c0);
|
||||
if end(u) != 0 {
|
||||
Z.dat -< finis;
|
||||
break;
|
||||
}
|
||||
for i := 1; i < n; i++ {
|
||||
<-Z.req;
|
||||
Z.dat -< zero;
|
||||
}
|
||||
}
|
||||
}(U, Z, c0, n);
|
||||
return Z;
|
||||
}
|
||||
|
||||
|
||||
func Init() {
|
||||
chnameserial = -1;
|
||||
seqno = 0;
|
||||
chnames = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz";
|
||||
zero = itor(0);
|
||||
one = itor(1);
|
||||
finis = i2tor(1,0);
|
||||
Ones = Rep(one);
|
||||
Twos = Rep(itor(2));
|
||||
}
|
||||
|
||||
func check(U PS, c *rat, count int, str string) {
|
||||
for i := 0; i < count; i++ {
|
||||
r := get(U)
|
||||
if !r.eq(c) {
|
||||
print "got: ";
|
||||
r.pr();
|
||||
print "should get ";
|
||||
c.pr();
|
||||
print "\n";
|
||||
panic str
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func checka(U PS, a *[]*rat, str string) {
|
||||
for i := 0; i < len(a); i++ {
|
||||
check(U, a[i], 1, str);
|
||||
}
|
||||
}
|
||||
|
||||
func main() {
|
||||
Init();
|
||||
if sys.argc() > 1 { // print
|
||||
print "Ones: "; Printn(Ones, 10);
|
||||
print "Twos: "; Printn(Twos, 10);
|
||||
print "Add: "; Printn(Add(Ones, Twos), 10);
|
||||
print "Diff: "; Printn(Diff(Ones), 10);
|
||||
print "Integ: "; Printn(Integ(zero, Ones), 10);
|
||||
print "CMul: "; Printn(Cmul(neg(one), Ones), 10);
|
||||
print "Sub: "; Printn(Sub(Ones, Twos), 10);
|
||||
print "Mul: "; Printn(Mul(Ones, Ones), 10);
|
||||
print "Exp: "; Printn(Exp(Ones), 15);
|
||||
print "MonSubst: "; Printn(MonSubst(Ones, neg(one), 2), 10);
|
||||
print "ATan: "; Printn(Integ(zero, MonSubst(Ones, neg(one), 2)), 10);
|
||||
} else { // test
|
||||
check(Ones, one, 5, "Ones");
|
||||
check(Add(Ones, Ones), itor(2), 0, "Add Ones Ones"); // 1 1 1 1 1
|
||||
check(Add(Ones, Twos), itor(3), 0, "Add Ones Twos"); // 3 3 3 3 3
|
||||
const N = 5;
|
||||
a := new([10] *rat);
|
||||
d := Diff(Ones);
|
||||
// BUG: want array initializer
|
||||
for i:=0; i < N; i++ {
|
||||
a[i] = itor(int64(i+1))
|
||||
}
|
||||
checka(d, a, "Diff"); // 1 2 3 4 5
|
||||
in := Integ(zero, Ones);
|
||||
// BUG: want array initializer
|
||||
a[0] = zero; // integration constant
|
||||
for i:=1; i < N; i++ {
|
||||
a[i] = i2tor(1, int64(i))
|
||||
}
|
||||
checka(in, a, "Integ"); // 0 1 1/2 1/3 1/4 1/5
|
||||
check(Cmul(neg(one), Twos), itor(-2), 10, "CMul"); // -1 -1 -1 -1 -1
|
||||
check(Sub(Ones, Twos), itor(-1), 0, "Sub Ones Twos"); // -1 -1 -1 -1 -1
|
||||
m := Mul(Ones, Ones)
|
||||
// BUG: want array initializer
|
||||
for i:=0; i < N; i++ {
|
||||
a[i] = itor(int64(i+1))
|
||||
}
|
||||
checka(m, a, "Mul"); // 1 2 3 4 5
|
||||
e := Exp(Ones);
|
||||
// BUG: want array initializer
|
||||
a[0] = itor(1);
|
||||
a[1] = itor(1);
|
||||
a[2] = i2tor(3,2);
|
||||
a[3] = i2tor(13,6);
|
||||
a[4] = i2tor(73,24);
|
||||
a[5] = i2tor(167,40);
|
||||
a[6] = i2tor(4051,720);
|
||||
a[7] = i2tor(37633,5040);
|
||||
a[8] = i2tor(43817,4480);
|
||||
a[9] = i2tor(4596553,362880);
|
||||
checka(e, a, "Exp"); // 1 1 3/2 13/6 73/24
|
||||
at := Integ(zero, MonSubst(Ones, neg(one), 2));
|
||||
// BUG: want array initializer
|
||||
for c, i := 1, 0; i < N; i++ {
|
||||
if i%2 == 0 {
|
||||
a[i] = zero
|
||||
} else {
|
||||
a[i] = i2tor(int64(c), int64(i));
|
||||
c *= -1
|
||||
}
|
||||
}
|
||||
checka(at, a, "ATan"); // 0 -1 0 -1/3 0 -1/5
|
||||
/*
|
||||
t := Revert(Integ(zero, MonSubst(Ones, neg(one), 2)));
|
||||
// BUG: want array initializer
|
||||
a[0] = zero;
|
||||
a[1] = itor(1);
|
||||
a[2] = zero;
|
||||
a[3] = i2tor(1,3);
|
||||
a[4] = zero;
|
||||
a[5] = i2tor(2,15);
|
||||
a[6] = zero;
|
||||
a[7] = i2tor(17,315);
|
||||
a[8] = zero;
|
||||
a[9] = i2tor(62,2835);
|
||||
checka(t, a, "Tan"); // 0 1 0 1/3 0 2/15
|
||||
*/
|
||||
}
|
||||
sys.exit(0); // BUG: force waiting goroutines to exit
|
||||
}
|
||||
@ -119,6 +119,8 @@ abcxyz-abcxyz-abcxyz-abcxyz-abcxyz-abcxyz-abcxyz
|
||||
=========== chan/nonblock.go
|
||||
PASS
|
||||
|
||||
=========== chan/powser1.go
|
||||
|
||||
=========== chan/sieve.go
|
||||
|
||||
=========== bugs/bug010.go
|
||||
|
||||
Loading…
Reference in New Issue
Block a user