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+// run
+
+// 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.
+
+// Test concurrency primitives: power series.
+
+// Like powser1.go but uses channels of interfaces.
+// Has not been cleaned up as much as powser1.go, to keep
+// it distinct and therefore a different test.
+
+// 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,
+// https://swtch.com/~rsc/thread/squint.pdf
+
+package main
+
+import "os"
+
+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 mkdch() *dch {
+ c := chnameserial % len(chnames)
+ chnameserial++
+ d := new(dch)
+ d.req = make(chan int)
+ d.dat = make(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) {
+ 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:
+ out[0], out[1] = out[1], out[0]
+ }
+ }
+
+ seqno++
+ in.req <- seqno
+ release := make(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 := make(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).(*rat)
+}
+
+// Get one item from each of n demand channels
+
+func getn(in []*dch) []item {
+ n := len(in)
+ if n != 2 {
+ panic("bad n in getn")
+ }
+ req := make([]chan int, 2)
+ dat := make([]chan item, 2)
+ out := make([]item, 2)
+ 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 {
+ return getn([]*dch{in0, in1})
+}
+
+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].(*rat)) + 2*end(uv[1].(*rat)) {
+ case 0:
+ Z.dat <- add(uv[0].(*rat), uv[1].(*rat))
+ 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
+
+/*
+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].(*rat)) != 0 || end(uv[1].(*rat)) != 0 {
+ Z.dat <- finis
+ } else {
+ Z.dat <- mul(uv[0].(*rat), uv[1].(*rat))
+ UU := Split(U)
+ VV := Split(V)
+ W := Add(Cmul(uv[0].(*rat), VV[0]), Cmul(uv[1].(*rat), 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 Substitution: 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 len(os.Args) > 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 := make([]*rat, N)
+ d := Diff(Ones)
+ 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)
+ 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)
+ for i := 0; i < N; i++ {
+ a[i] = itor(int64(i + 1))
+ }
+ checka(m, a, "Mul") // 1 2 3 4 5
+ e := Exp(Ones)
+ 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))
+ 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)))
+ 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
+ */
+ }
+}
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-28 02:41:59 +0000