Initial commit: Go 1.23 release state

test/chan/powser1.go

@@ -0,0 +1,741 @@
+// 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.
+
+// 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
+}
+
+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 dch struct {
+	req chan int
+	dat chan rat
+	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 rat)
+	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 a rat and dies
+// after the rat 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 rat, out *dch) {
+	<-out.req
+	out.dat <- dat
+}
+
+func get(in *dch) rat {
+	seqno++
+	in.req <- seqno
+	return <-in.dat
+}
+
+// Get one rat from each of n demand channels
+
+func getn(in []*dch) []rat {
+	n := len(in)
+	if n != 2 {
+		panic("bad n in getn")
+	}
+	req := new([2]chan int)
+	dat := new([2]chan rat)
+	out := make([]rat, 2)
+	var i int
+	var it rat
+	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 rat from each of 2 demand channels
+
+func get2(in0 *dch, in1 *dch) []rat {
+	return getn([]*dch{in0, in1})
+}
+
+func copy(in *dch, out *dch) {
+	for {
+		<-out.req
+		out.dat <- get(in)
+	}
+}
+
+func repeat(dat rat, 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)
+	var r 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)
+	var r 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"))
+}
+
+// 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() {
+		var uv []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
+			}
+		}
+	}()
+	return Z
+}
+
+// Multiply a power series by a constant
+func Cmul(c rat, U PS) PS {
+	Z := mkPS()
+	go func() {
+		done := false
+		for !done {
+			<-Z.req
+			u := get(U)
+			if end(u) != 0 {
+				done = true
+			} else {
+				Z.dat <- mul(c, u)
+			}
+		}
+		Z.dat <- finis
+	}()
+	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() {
+		for ; n > 0; n-- {
+			put(zero, Z)
+		}
+		copy(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() {
+		if c.num != 0 {
+			for ; n > 0; n = n - 1 {
+				put(zero, Z)
+			}
+			put(c, Z)
+		}
+		put(finis, Z)
+	}()
+	return Z
+}
+
+func Shift(c rat, U PS) PS {
+	Z := mkPS()
+	go func() {
+		put(c, Z)
+		copy(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() {
+		<-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)
+		}
+	}()
+	return Z
+}
+
+// Differentiate
+
+func Diff(U PS) PS {
+	Z := mkPS()
+	go func() {
+		<-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
+	}()
+	return Z
+}
+
+// Integrate, with const of integration
+func Integ(c rat, U PS) PS {
+	Z := mkPS()
+	go func() {
+		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
+	}()
+	return Z
+}
+
+// Binomial theorem (1+x)^c
+
+func Binom(c rat) PS {
+	Z := mkPS()
+	go func() {
+		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)
+	}()
+	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() {
+		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)
+	}()
+	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() {
+		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)
+			}
+		}
+	}()
+	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() {
+		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
+			}
+		}
+	}()
+	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
+		*/
+	}
+}