From f87a960adf8a8ed71163055fe194af0e7bbb41a3 Mon Sep 17 00:00:00 2001
From: Rob Pike <r@golang.org>
Date: Fri, 18 Jul 2008 14:18:07 -0700
Subject: [PATCH] add doug's power series package

SVN=128063
---
 test/chan/powser1.go | 748 +++++++++++++++++++++++++++++++++++++++++++
 test/golden.out      |   2 +
 2 files changed, 750 insertions(+)
 create mode 100644 test/chan/powser1.go

diff --git a/test/chan/powser1.go b/test/chan/powser1.go
new file mode 100644
index 0000000000..1b25d7eefb
--- /dev/null
+++ b/test/chan/powser1.go
@@ -0,0 +1,748 @@
+// $G $D/$F.go && $L $F.$A && ./$A.out
+
+// Copyright 2009 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Power series package
+// A power series is a channel, along which flow rational
+// coefficients.  A denominator of zero signifies the end.
+// Original code in Newsqueak by Doug McIlroy.
+// See Squinting at Power Series by Doug McIlroy,
+//   http://www.cs.bell-labs.com/who/rsc/thread/squint.pdf
+
+package main
+
+type rat struct  {
+	num, den  int64;	// numerator, denominator
+}
+
+func (u *rat) pr(){
+	if u.den==1 { print u.num }
+	else { print u.num, "/", u.den }
+	print(" ")
+}
+
+func (u *rat) eq(c *rat) bool {
+	return u.num == c.num && u.den == c.den
+}
+
+type item *rat;
+
+type dch struct {
+	req *chan  int;
+	dat *chan  item;
+	nam int;
+}
+
+type dch2 [2] *dch
+
+var chnames string
+var chnameserial int
+var seqno int
+
+func Init();
+
+func mkdch() *dch {
+	c := chnameserial % len(chnames);
+	chnameserial++;
+	d := new(dch);
+	d.req = new(chan int);
+	d.dat = new(chan item);
+	d.nam = c;
+	return d;
+}
+
+func mkdch2() *dch2 {
+	d2 := new(dch2);
+	d2[0] = mkdch();
+	d2[1] = mkdch();
+	return d2;
+}
+
+// split reads a single demand channel and replicates its
+// output onto two, which may be read at different rates.
+// A process is created at first demand for an item and dies
+// after the item has been sent to both outputs.
+
+// When multiple generations of split exist, the newest
+// will service requests on one channel, which is
+// always renamed to be out[0]; the oldest will service
+// requests on the other channel, out[1].  All generations but the
+// newest hold queued data that has already been sent to
+// out[0].  When data has finally been sent to out[1],
+// a signal on the release-wait channel tells the next newer
+// generation to begin servicing out[1].
+
+func dosplit(in *dch, out *dch2, wait *chan int ){
+//print "dosplit ", wait, "\n";
+	var t *dch;
+	both := false;	// do not service both channels
+/*
+	select {
+	case <-out[0].req:
+		;
+	case <-wait:
+		both = 1;
+		select {
+		case <-out[0].req:
+			;
+		case <-out[1].req:
+			t=out[0]; out[0]=out[1]; out[1]=t;
+		};
+	}
+*/
+// select simulation
+	for {
+		var ok bool;
+		var dummy int;
+		dummy, ok = <-out[0].req;
+		if ok { goto OUT1 }
+		dummy, ok = <-wait;
+		if ok {
+			both = true;
+			// select simulation
+			for {
+				dummy, ok = <-out[0].req;
+				if ok { goto OUT1 }
+				dummy, ok = <-out[1].req;
+				if ok {
+					out[0], out[1] = out[1], out[0];
+					goto OUT1
+				}
+				sys.gosched();
+			}
+		}
+		sys.gosched();
+	}
+
+OUT1: //BUG
+
+	seqno++;
+	in.req -< seqno;
+	release := new(chan  int);
+	go dosplit(in, out, release);
+	dat := <-in.dat;
+	out[0].dat -< dat;
+	if !both {
+		<-wait
+	}
+	<-out[1].req;
+	out[1].dat -< dat;
+	release -< 0;
+}
+
+func split(in *dch, out *dch2){
+	release := new(chan int);
+	go dosplit(in, out, release);
+	release -< 0;
+}
+
+func put(dat item, out *dch){
+	<-out.req;
+	out.dat -< dat;
+}
+
+func get(in *dch) item{
+	seqno++;
+	in.req -< seqno;
+	return <-in.dat;
+}
+
+// Get one item from each of n demand channels
+
+func getn(in *[]*dch, n int) *[]item {
+	// BUG n:=len(in);
+	if n != 2 { panic "bad n in getn" };
+	req := new([2] *chan int);
+	dat := new([2] *chan item);
+	out := new([2] item);
+	var i int;
+	var it item;
+	for i=0; i<n; i++ {
+		req[i] = in[i].req;
+		dat[i] = nil;
+	}
+	for n=2*n; n>0; n-- {
+		seqno++
+/*
+		select{
+		case req[i=] <-= seqno:
+			dat[i] = in[i].dat;
+			req[i] = nil;
+		case it = <-dat[i=]:
+			out[i] = it;
+			dat[i] = nil;
+		}
+*/
+
+		// simulation of select
+		sel:
+		for c1:=0; ; c1++ {
+			for i := 0; i < 2; i++ {
+				ok := false;
+				if req[i] != nil { ok = req[i] -< seqno }
+				if ok {
+					dat[i] = in[i].dat;
+					req[i] = nil;
+					goto OUT; // BUG
+					break sel;
+				}
+				ok = false;
+				if dat[i] != nil { it, ok = <-dat[i] }
+				if ok {
+					out[i] = it;
+					dat[i] = nil;
+					goto OUT;  // BUG
+					break sel;
+				}
+				sys.gosched();
+			}
+			sys.gosched();
+		}
+OUT:
+	}
+	return out;
+}
+
+// Get one item from each of 2 demand channels
+
+func get2(in0 *dch, in1 *dch)  *[]item {
+	x := new([2] *dch);
+	x[0] = in0;
+	x[1] = in1;
+	return getn(x, 2);
+}
+
+func copy(in *dch, out *dch){
+	for {
+		<-out.req;
+		out.dat -< get(in);
+	}
+}
+
+func repeat(dat item, out *dch){
+	for {
+		put(dat, out)
+	}
+}
+
+type PS *dch;	// power series
+type PS2 *[2] PS; // pair of power series
+
+var Ones PS
+var Twos PS
+
+func mkPS() *dch {
+	return mkdch()
+}
+
+func mkPS2() *dch2 {
+	return mkdch2()
+}
+
+// Conventions
+// Upper-case for power series.
+// Lower-case for rationals.
+// Input variables: U,V,...
+// Output variables: ...,Y,Z
+
+// Integer gcd; needed for rational arithmetic
+
+func gcd (u, v int64) int64{
+	if u < 0 { return gcd(-u, v) }
+	if u > v { return gcd(v, u) }
+	if u == 0 { return v }
+	return gcd(v%u, u)
+}
+
+// Make a rational from two ints and from one int
+
+func i2tor(u, v int64) *rat{
+	g := gcd(u,v);
+	r := new(rat);
+	if v > 0 {
+		r.num = u/g;
+		r.den = v/g;
+	} else {
+		r.num = -u/g;
+		r.den = -v/g;
+	}
+	return r;
+}
+
+func itor(u int64) *rat{
+	return i2tor(u, 1);
+}
+
+var zero *rat;
+var one *rat;
+
+
+// End mark and end test
+
+var finis *rat;
+
+func end(u *rat) int64 {
+	if u.den==0 { return 1 }
+	return 0
+}
+
+// Operations on rationals
+
+func add(u, v *rat) *rat {
+	g := gcd(u.den,v.den);
+	return  i2tor(u.num*(v.den/g)+v.num*(u.den/g),u.den*(v.den/g));
+}
+
+func mul(u, v *rat) *rat{
+	g1 := gcd(u.num,v.den);
+	g2 := gcd(u.den,v.num);
+	r := new(rat);
+	r.num =(u.num/g1)*(v.num/g2);
+	r.den = (u.den/g2)*(v.den/g1);
+	return r;
+}
+
+func neg(u *rat) *rat{
+	return i2tor(-u.num, u.den);
+}
+
+func sub(u, v *rat) *rat{
+	return add(u, neg(v));
+}
+
+func inv(u *rat) *rat{	// invert a rat
+	if u.num == 0 { panic "zero divide in inv" }
+	return i2tor(u.den, u.num);
+}
+
+// Print n terms of a power series
+
+func Printn(U PS, n int){
+	done := false;
+	for ; !done && n>0; n-- {
+		u := get(U);
+		if end(u) != 0 { done = true }
+		else { u.pr() }
+	}
+	print ("\n");
+}
+
+func Print(U PS){
+	Printn(U,1000000000);
+}
+
+// Evaluate n terms of power series U at x=c
+
+func eval(c *rat, U PS, n int) *rat{
+	if n==0 { return zero }
+	y := get(U);
+	if end(y) != 0 { return zero }
+	return add(y,mul(c,eval(c,U,n-1)));
+}
+
+// Power-series constructors return channels on which power
+// series flow.  They start an encapsulated generator that
+// puts the terms of the series on the channel.
+
+// Make a pair of power series identical to a given power series
+
+func Split(U PS) *dch2{
+	UU := mkdch2();
+	go split(U,UU);
+	return UU;
+}
+
+// Add two power series
+func Add(U, V PS) PS{
+	Z := mkPS();
+	go func(U, V, Z PS){
+		var uv *[2] *rat;
+		for {
+			<-Z.req;
+			uv = get2(U,V);
+			switch end(uv[0])+2*end(uv[1]) {
+			case 0:
+				Z.dat -< add(uv[0], uv[1]);
+			case 1:
+				Z.dat -< uv[1];
+				copy(V,Z);
+			case 2:
+				Z.dat -< uv[0];
+				copy(U,Z)
+			case 3:
+				Z.dat -< finis;
+			}
+		}
+	}(U, V, Z);
+	return Z;
+}
+
+// Multiply a power series by a constant
+func Cmul(c *rat,U PS) PS{
+	Z := mkPS();
+	go func(c *rat, U, Z PS){
+		done := false;
+		for !done {
+			<-Z.req;
+			u := get(U);
+			if end(u) != 0 { done = true }
+			else { Z.dat -< mul(c,u) }
+		}
+		Z.dat -< finis;
+	}(c, U, Z);
+	return Z;
+}
+
+// Subtract
+
+func Sub(U, V PS) PS{
+	return Add(U, Cmul(neg(one), V));
+}
+
+// Multiply a power series by the monomial x^n
+
+func Monmul(U PS, n int) PS{
+	Z := mkPS();
+	go func(n int, U PS, Z PS){
+		for ; n>0; n-- { put(zero,Z) }
+		copy(U,Z);
+	}(n, U, Z);
+	return Z;
+}
+
+// Multiply by x
+
+func Xmul(U PS) PS{
+	Monmul(U,1);
+}
+
+func Rep(c *rat) PS{
+	Z := mkPS();
+	go repeat(c,Z);
+	return Z;
+}
+
+// Monomial c*x^n
+
+func Mon(c *rat, n int) PS{
+	Z:=mkPS();
+	go func(c *rat, n int, Z PS){
+		if(c.num!=0) {
+			for ; n>0; n=n-1 { put(zero,Z) }
+			put(c,Z);
+		}
+		put(finis,Z);
+	}(c, n, Z);
+	return Z;
+}
+
+func Shift(c *rat, U PS) PS{
+	Z := mkPS();
+	go func(c *rat, U, Z PS){
+		put(c,Z);
+		copy(U,Z);
+	}(c, U, Z);
+	return Z;
+}
+
+// simple pole at 1: 1/(1-x) = 1 1 1 1 1 ...
+
+// Convert array of coefficients, constant term first
+// to a (finite) power series
+
+func Poly(a [] *rat) PS{
+	Z:=mkPS();
+/* BUG: NEED LEN OF ARRAY
+	begin func(a [] *rat, Z PS){
+		j:=0;
+		done:=0;
+		for j=len(a); !done&&j>0; j=j-1) 
+			if(a[j-1].num!=0) done=1;
+		i:=0;
+		for(; i<j; i=i+1) put(a[i],Z);
+		put(finis,Z);
+	}();
+*/
+	return Z;
+}
+
+// Multiply. The algorithm is
+// 	let U = u + x*UU
+//	let V = v + x*VV
+//	then UV = u*v + x*(u*VV+v*UU) + x*x*UU*VV
+
+func Mul(U, V PS) PS{
+	Z:=mkPS();
+	go func(U, V, Z PS){
+		<-Z.req;
+		uv := get2(U,V);
+		if end(uv[0])!=0 || end(uv[1]) != 0 {
+			Z.dat -< finis;
+		} else {
+			Z.dat -< mul(uv[0],uv[1]);
+			UU := Split(U);
+			VV := Split(V);
+			W := Add(Cmul(uv[0],VV[0]),Cmul(uv[1],UU[0]));
+			<-Z.req;
+			Z.dat -< get(W);
+			copy(Add(W,Mul(UU[1],VV[1])),Z);
+		}
+	}(U, V, Z);
+	return Z;
+}
+
+// Differentiate
+
+func Diff(U PS) PS{
+	Z:=mkPS();
+	go func(U, Z PS){
+		<-Z.req;
+		u := get(U);
+		if end(u) == 0 {
+			done:=false;
+			for i:=1; !done; i++ {
+				u = get(U);
+				if end(u) != 0 { done=true }
+				else {
+					Z.dat -< mul(itor(int64(i)),u);
+					<-Z.req;
+				}
+			}
+		}
+		Z.dat -< finis;
+	}(U, Z);
+	return Z;
+}
+
+// Integrate, with const of integration
+func Integ(c *rat,U PS) PS{
+	Z:=mkPS();
+	go func(c *rat, U, Z PS){
+		put(c,Z);
+		done:=false;
+		for i:=1; !done; i++ {
+			<-Z.req;
+			u := get(U);
+			if end(u) != 0 { done= true }
+			Z.dat -< mul(i2tor(1,int64(i)),u);
+		}
+		Z.dat -< finis;
+	}(c, U, Z);
+	return Z;
+}
+
+// Binomial theorem (1+x)^c
+
+func Binom(c *rat) PS{
+	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
+}
diff --git a/test/golden.out b/test/golden.out
index 746175239f..66ad449086 100644
--- a/test/golden.out
+++ b/test/golden.out
@@ -119,6 +119,8 @@ abcxyz-abcxyz-abcxyz-abcxyz-abcxyz-abcxyz-abcxyz
 =========== chan/nonblock.go
 PASS
 
+=========== chan/powser1.go
+
 =========== chan/sieve.go
 
 =========== bugs/bug010.go
-- 
2.48.1