--- /dev/null
+// $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
+// Like powser1.go but uses channels of interfaces.
+
+package main
+
+type rat struct {
+ num, den int64; // numerator, denominator
+}
+
+type item interface {
+ pr();
+ eq(c item) bool;
+}
+
+func (u *rat) pr(){
+ if u.den==1 { print(u.num) }
+ else { print(u.num, "/", u.den) }
+ print(" ")
+}
+
+func (u *rat) eq(c item) bool {
+ c1 := c.(*rat);
+ return u.num == c1.num && u.den == c1.den
+}
+
+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 ){
+ var t *dch;
+ both := false; // do not service both channels
+
+ select {
+ case <-out[0].req:
+ ;
+ case <-wait:
+ both = true;
+ select {
+ case <-out[0].req:
+ ;
+ case <-out[1].req:
+ t=out[0]; out[0]=out[1]; out[1]=t;
+ }
+ }
+
+ 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) *rat {
+ 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[0] <- seqno:
+ dat[0] = in[0].dat;
+ req[0] = nil;
+ case req[1] <- seqno:
+ dat[1] = in[1].dat;
+ req[1] = nil;
+ case it = <-dat[0]:
+ out[0] = it;
+ dat[0] = nil;
+ case it = <-dat[1]:
+ out[1] = it;
+ dat[1] = nil;
+ }
+ }
+ 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 == 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 eval in floating point of PS at x=c to n terms
+func
+Evaln(c *rat, U PS, n int)
+{
+ xn := float64(1);
+ x := float64(c.num)/float64(c.den);
+ val := float64(0);
+ for i:=0; i<n; i++ {
+ u := get(U);
+ if end(u) != 0 {
+ break;
+ }
+ val = val + x * float64(u.num)/float64(u.den);
+ xn = xn*x;
+ }
+ print(val, "\n");
+}
+
+// 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 *[] item;
+ 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{
+ return 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
+
+/* BUG: NEED LEN OF ARRAY
+func Poly(a [] *rat) PS{
+ Z:=mkPS();
+ 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)
+ }
+ }
+}
+
+const N=10
+func checka(U PS, a *[]*rat, str string) {
+ for i := 0; i < N; 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
+ a := new([N] *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
+}