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// $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

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
*/
        }
}