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Source file test/chan/powser1.go

  // 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,
  //   http://www.cs.bell-labs.com/who/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 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() {
  		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
  */
  	}
  }
  

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