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simp.go
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package symexpr
import (
"math"
// "fmt"
)
type SimpRules struct {
GroupAddTerms bool
ConvertConsts bool
MulToPow bool
MaxPowPow int
MulInCoeff int // add must be >= to size, 0 == No
// state tracking
InTrig bool
}
func DefaultRules() SimpRules {
return SimpRules{true, true, true, 12, 0, false}
}
func (l *Leaf) Simplify(rules SimpRules) Expr { return nil }
func (u *Unary) Simplify(rules SimpRules) Expr { return nil }
func (n *N_ary) Simplify(rules SimpRules) Expr { return nil }
func (n *Time) Simplify(rules SimpRules) Expr { return n }
func (v *Var) Simplify(rules SimpRules) Expr { return v }
func (c *Constant) Simplify(rules SimpRules) Expr { return c }
func (c *ConstantF) Simplify(rules SimpRules) Expr {
if math.IsNaN(c.F) || math.IsInf(c.F, 0) {
return nil
}
// "close" to system value ??? TODO
return c
}
func (s *System) Simplify(rules SimpRules) Expr { return s }
func (u *Neg) Simplify(rules SimpRules) (ret Expr) {
if u.C == nil {
return nil
}
u.C = u.C.Simplify(rules)
if u.C == nil {
return nil
}
switch u.C.ExprType() {
case NULL:
ret = nil
u.C = nil
case NEG:
ret = u.C
u.C = nil
case CONSTANT:
ret = u.C
u.C = nil
case CONSTANTF:
c := u.C.(*ConstantF)
c.F *= -1.0
ret = u.C
u.C = nil
case MUL:
m := u.C.(*Mul)
if m.CS[0].ExprType() == CONSTANT { // Constants should always be first operand in Mul
ret = u.C
u.C = nil
} else if m.CS[0].ExprType() == CONSTANTF { // Constants should always be first operand in Mul
c := m.CS[0].(*ConstantF)
c.F *= -1.0
ret = u.C
u.C = nil
}
default: // no simplification
ret = u
}
return ret
}
func (u *Abs) Simplify(rules SimpRules) (ret Expr) {
if u.C == nil {
return nil
}
u.C = u.C.Simplify(rules)
if u.C == nil {
return nil
}
switch u.C.ExprType() {
case NULL:
ret = nil
u.C = nil
case ABS:
ret = u.C
u.C = nil
default: // no simplification
ret = u
}
return ret
}
func (u *Sqrt) Simplify(rules SimpRules) (ret Expr) {
if u.C == nil {
return nil
}
u.C = u.C.Simplify(rules)
if u.C == nil {
return nil
}
switch u.C.ExprType() {
case NULL:
ret = nil
u.C = nil
case SQRT:
s := u.C.(*Sqrt)
ret = NewPowF(s.C, 0.25)
u.C = nil
case CONSTANT:
ret = u.C
u.C = nil
case CONSTANTF:
ret = u.C
u.C = nil
ret.(*ConstantF).F = math.Sqrt(ret.(*ConstantF).F)
case POWF:
p := u.C.(*PowF)
p.Power *= 0.5
ret = p
u.C = nil
case POWI:
p := u.C.(*PowI)
if p.Power == 2 {
ret = p.Base
p.Base = nil
} else if p.Power%2 == 0 {
p.Power /= 2
ret = p
u.C = nil
} else {
f := NewPowF(p.Base, float64(p.Power)*0.5)
ret = f
p.Base = nil
}
default: // no simplification
ret = u
}
return ret
}
func (u *Sin) Simplify(rules SimpRules) (ret Expr) {
// fmt.Printf("Simp Sin: %v\n", u.C)
if !rules.InTrig {
rules.InTrig = true
} else {
tmp := u.C
u.C = nil
return tmp
}
if u.C == nil {
return nil
}
u.C = u.C.Simplify(rules)
if u.C == nil {
return nil
}
// fmt.Printf(" %v\n", u.C)
switch u.C.ExprType() {
case NULL, SIN, COS, TAN, CONSTANT:
ret = u.C
u.C = nil
case CONSTANTF:
ret = u.C
u.C = nil
ret.(*ConstantF).F = math.Sin(ret.(*ConstantF).F)
default: // no simplification
ret = u
}
return ret
}
func (u *Cos) Simplify(rules SimpRules) (ret Expr) {
if !rules.InTrig {
rules.InTrig = true
} else {
tmp := u.C
u.C = nil
return tmp
}
if u.C == nil {
return nil
}
u.C = u.C.Simplify(rules)
if u.C == nil {
return nil
}
switch u.C.ExprType() {
case NULL, SIN, COS, TAN, CONSTANT:
ret = u.C
u.C = nil
case CONSTANTF:
ret = u.C
u.C = nil
ret.(*ConstantF).F = math.Cos(ret.(*ConstantF).F)
default: // no simplification
ret = u
}
return ret
}
func (u *Tan) Simplify(rules SimpRules) (ret Expr) {
if !rules.InTrig {
rules.InTrig = true
} else {
tmp := u.C
u.C = nil
return tmp
}
if u.C == nil {
return nil
}
u.C = u.C.Simplify(rules)
if u.C == nil {
return nil
}
switch u.C.ExprType() {
case NULL, SIN, COS, TAN, CONSTANT:
ret = u.C
u.C = nil
case CONSTANTF:
ret = u.C
u.C = nil
ret.(*ConstantF).F = math.Tan(ret.(*ConstantF).F)
default: // no simplification
ret = u
}
return ret
}
func (u *Exp) Simplify(rules SimpRules) (ret Expr) {
if u.C == nil {
return nil
}
u.C = u.C.Simplify(rules)
if u.C == nil {
return nil
}
switch u.C.ExprType() {
case NULL, CONSTANT:
ret = u.C
u.C = nil
case CONSTANTF:
ret = u.C
u.C = nil
ret.(*ConstantF).F = math.Exp(ret.(*ConstantF).F)
default: // no simplification
ret = u
}
return ret
}
func (u *Log) Simplify(rules SimpRules) (ret Expr) {
if u.C == nil {
return nil
}
u.C = u.C.Simplify(rules)
if u.C == nil {
return nil
}
switch u.C.ExprType() {
case NULL, CONSTANT:
ret = u.C
u.C = nil
case CONSTANTF:
ret = u.C
u.C = nil
ret.(*ConstantF).F = math.Log(ret.(*ConstantF).F)
default: // no simplification
ret = u
}
return ret
}
func (u *PowI) Simplify(rules SimpRules) Expr {
var (
ret Expr = u
t ExprType = NULL
)
if u.Base != nil {
// serial := make([]int, 0, 64)
// serial = u.Base.Serial(serial)
// fmt.Printf("PowI-presort: %v %v\n", u.Base, serial)
u.Base = u.Base.Simplify(rules)
if u.Base == nil {
return nil
}
// serial2 := make([]int, 0, 64)
// serial2 = u.Base.Serial(serial2)
// fmt.Printf("PowI-postsort: %v %v\n", u.Base, serial2)
t = u.Base.ExprType()
}
if u.Power > rules.MaxPowPow {
u.Power = rules.MaxPowPow
} else if u.Power < -rules.MaxPowPow {
u.Power = -rules.MaxPowPow
}
if u.Power == 0 {
ret = &ConstantF{F: 1}
} else if u.Power == 1 {
ret = u.Base
u.Base = nil
} else {
switch t {
case NULL, CONSTANT:
ret = u.Base
u.Base = nil
case CONSTANTF:
ret = u.Base
u.Base = nil
ret.(*ConstantF).F = math.Pow(ret.(*ConstantF).F, float64(u.Power))
case MUL:
if u.Base.HasConst() {
m := u.Base.(*Mul)
mret := NewMul()
mret.Insert(m.CS[0])
m.CS[0] = nil
u.Base = m.Simplify(rules)
tmp := NewPowF(u.Base, float64(u.Power))
mret.Insert(tmp)
ret = mret
}
case POWI:
p := u.Base.(*PowI)
u.Base = p.Base
u.Power = u.Power * p.Power
if u.Power > rules.MaxPowPow {
u.Power = rules.MaxPowPow
} else if u.Power < -rules.MaxPowPow {
u.Power = -rules.MaxPowPow
}
// ret = NewPowF(u.Base, float64(u.Power))
ret = u
default: // no simplification
// ret = NewPowF(u.Base, float64(u.Power))
ret = u
}
}
// serial := make([]int, 0, 64)
// serial = ret.Serial(serial)
// fmt.Printf("PowI-ret: %v %v\n", ret, serial)
return ret
}
func (u *PowF) Simplify(rules SimpRules) Expr {
var (
ret Expr = u
t ExprType = NULL
)
if u.Base != nil {
u.Base = u.Base.Simplify(rules)
if u.Base == nil {
return nil
}
t = u.Base.ExprType()
}
if u.Power == 0 {
ret = &ConstantF{F: 1}
} else if u.Power == 1 {
ret = u.Base
u.Base = nil
} else {
switch t {
case NULL, CONSTANT:
ret = u.Base
u.Base = nil
case CONSTANTF:
ret = u.Base
u.Base = nil
ret.(*ConstantF).F = math.Pow(ret.(*ConstantF).F, float64(u.Power))
default: // no simplification
ret = NewPowI(u.Base, int(u.Power))
}
}
return ret
}
func (n *PowE) Simplify(rules SimpRules) Expr {
var (
ret Expr = n
t1, t2 ExprType = NULL, NULL
)
if n.Base != nil {
n.Base = n.Base.Simplify(rules)
t1 = n.Base.ExprType()
}
if n.Power != nil {
n.Power = n.Power.Simplify(rules)
t2 = n.Power.ExprType()
}
if t1 == NULL && t2 == NULL {
return &Null{}
} else if t1 == NULL {
ret = n.Power
n.Base = nil
n.Power = nil
} else if t2 == NULL {
ret = n.Base
n.Base = nil
n.Power = nil
} else if n.Base.ExprType() == n.Power.ExprType() &&
n.Base.ExprType() == CONSTANTF {
ret = n.Base
ret.(*ConstantF).F = math.Pow(ret.(*ConstantF).F, n.Power.(*ConstantF).F)
n.Base = nil
n.Power = nil
}
return ret
}
func (n *Div) Simplify(rules SimpRules) Expr {
var (
ret Expr = n
t1, t2 ExprType = NULL, NULL
)
if n.Numer != nil {
n.Numer = n.Numer.Simplify(rules)
if n.Numer != nil {
t1 = n.Numer.ExprType()
}
}
if n.Denom != nil {
n.Denom = n.Denom.Simplify(rules)
if n.Denom != nil {
t2 = n.Denom.ExprType()
}
}
// check to see if nulls/nils
if t1 == NULL && t2 == NULL {
ret = nil
} else if t1 == NULL {
ret = n.Denom
n.Numer = nil
n.Denom = nil
return ret
} else if t2 == NULL {
ret = n.Numer
n.Numer = nil
n.Denom = nil
return ret
}
// check to see if divs
if t1 == DIV && t2 == DIV {
// a/b // c/d => ad/bc
ndiv := n.Numer.(*Div)
ddiv := n.Denom.(*Div)
nmul := NewMul()
nmul.Insert(ndiv.Numer)
nmul.Insert(ddiv.Denom)
dmul := NewMul()
dmul.Insert(ndiv.Denom)
dmul.Insert(ddiv.Numer)
ndiv.Numer = nil
ndiv.Denom = nil
ddiv.Numer = nil
ddiv.Denom = nil
n.Numer = nmul.Simplify(rules)
n.Denom = dmul.Simplify(rules)
t1 = n.Numer.ExprType()
t2 = n.Denom.ExprType()
} else if t1 == DIV {
// a/b // c => a/bc
div := n.Numer.(*Div)
n.Numer = div.Numer
mul := NewMul()
mul.Insert(div.Denom)
mul.Insert(n.Denom)
div.Numer = nil
div.Denom = nil
n.Denom = mul.Simplify(rules)
t1 = n.Numer.ExprType()
t2 = n.Denom.ExprType()
} else if t2 == DIV {
// a // c/d => ad/c
div := n.Denom.(*Div)
n.Denom = div.Numer
mul := NewMul()
mul.Insert(n.Numer)
mul.Insert(div.Denom)
div.Numer = nil
div.Denom = nil
n.Numer = mul.Simplify(rules)
t1 = n.Numer.ExprType()
t2 = n.Denom.ExprType()
}
// cancel / simp like terms
if t1 == t2 && t1 == CONSTANT {
ret = n.Numer
n.Numer = nil
n.Denom = nil
return ret
} else if t1 == CONSTANT && t2 == MUL {
d := n.Denom.(*Mul)
if d.CS[0].ExprType() == CONSTANT {
d.CS[0] = nil
n.Denom = d.Simplify(rules)
}
return ret
} else if t2 == CONSTANT && t1 == MUL {
d := n.Numer.(*Mul)
if d.CS[0].ExprType() != CONSTANT {
d.Insert(NewConstant(-1))
}
ret = n.Numer
n.Numer = nil
n.Denom = nil
return ret
} else if t1 == t2 && t1 == CONSTANTF {
c := n.Numer.(*ConstantF)
c.F /= n.Denom.(*ConstantF).F
ret = n.Numer
n.Numer = nil
n.Denom = nil
return ret
} else if t1 == CONSTANTF && t2 == MUL {
d := n.Denom.(*Mul)
if d.CS[0].ExprType() == CONSTANTF {
c := n.Numer.(*ConstantF)
c.F /= d.CS[0].(*ConstantF).F
d.CS[0] = nil
n.Denom = d.Simplify(rules)
}
return ret
} else if t2 == CONSTANTF && t1 == MUL {
d := n.Numer.(*Mul)
if d.CS[0].ExprType() != CONSTANTF {
c := NewConstantF(1.0)
c.F /= n.Denom.(*ConstantF).F
d.Insert(c)
} else {
c := d.CS[0].(*ConstantF)
c.F /= n.Denom.(*ConstantF).F
}
ret = n.Numer
n.Numer = nil
n.Denom = nil
return ret
} else {
ret = n.cancelLikeTerms(rules)
}
return ret
}
func (D *Div) cancelLikeTerms(rules SimpRules) Expr {
t1 := D.Numer.ExprType()
t2 := D.Denom.ExprType()
var ret Expr = D
// fmt.Println("cancel", t1, t2)
if D.Numer.AmISame(D.Denom) {
return NewConstantF(1.0)
}
changed := false
if t1 == t2 && t1 == MUL {
mn := D.Numer.(*Mul)
md := D.Denom.(*Mul)
for i, n := range mn.CS {
if n == nil {
continue
}
for j, d := range md.CS {
if d == nil {
continue
}
// fmt.Println("cancel", i, n.ExprType(), j, d.ExprType())
if n.AmISame(d) {
mn.CS[i] = nil
md.CS[j] = nil
changed = true
break
}
if n.ExprType() == POWI && d.ExprType() == POWI {
np, dp := n.(*PowI), d.(*PowI)
if np.Base.AmISame(dp.Base) {
if np.Power > dp.Power {
np.Power -= dp.Power
md.CS[j] = nil
changed = true
continue
} else if np.Power < dp.Power {
dp.Power -= np.Power
mn.CS[i] = nil
changed = true
break
} else { // same and should cancel
mn.CS[i] = nil
md.CS[j] = nil
changed = true
break
}
}
} else if n.ExprType() == POWI {
np := n.(*PowI)
if np.Base.AmISame(d) {
np.Power -= 1
md.CS[j] = nil
changed = true
continue
}
} else if d.ExprType() == POWI {
nd := d.(*PowI)
if nd.Base.AmISame(n) {
nd.Power -= 1
mn.CS[i] = nil
changed = true
break
}
}
}
}
} else if t1 == MUL {
if D.Numer.AmIAlmostSame(D.Denom) {
return NewConstantF(1.0)
}
mn := D.Numer.(*Mul)
d := D.Denom
for i, n := range mn.CS {
if n.AmISame(d) {
mn.CS[i] = nil
D.Denom = nil
changed = true
break
}
if n.ExprType() == POWI && d.ExprType() == POWI {
np, dp := n.(*PowI), d.(*PowI)
if np.Base.AmISame(dp.Base) {
if np.Power > dp.Power {
np.Power -= dp.Power
D.Denom = nil
changed = true
break
} else if np.Power < dp.Power {
dp.Power -= np.Power
mn.CS[i] = nil
changed = true
break
} else { // same and should cancel
// will we even get here?
mn.CS[i] = nil
D.Denom = nil
changed = true
break
}
}
} else if n.ExprType() == POWI {
np := n.(*PowI)
if np.Base.AmISame(d) {
np.Power -= 1
D.Denom = nil
changed = true
break
}
} else if d.ExprType() == POWI {
nd := d.(*PowI)
if nd.Base.AmISame(n) {
nd.Power -= 1
mn.CS[i] = nil
changed = true
break
}
}
}
} else if t2 == MUL {
if D.Denom.AmIAlmostSame(D.Numer) {
return NewConstantF(1.0)
}
n := D.Numer
md := D.Denom.(*Mul)
for i, d := range md.CS {
if n.AmISame(d) {
D.Numer = NewConstantF(1.0)
md.CS[i] = nil
changed = true
break
}
if n.ExprType() == POWI && d.ExprType() == POWI {
np, dp := n.(*PowI), d.(*PowI)
if np.Base.AmISame(dp.Base) {
if np.Power > dp.Power {
np.Power -= dp.Power
md.CS[i] = nil
changed = true
break
} else if np.Power < dp.Power {
dp.Power -= np.Power
D.Numer = NewConstantF(1.0)
changed = true
break
} else { // same and should cancel
// will we even get here?
D.Numer = nil
md.CS[i] = nil
changed = true
break
}
}
} else if n.ExprType() == POWI {
np := n.(*PowI)
if np.Base.AmISame(d) {
np.Power -= 1
md.CS[i] = nil
changed = true
break
}
} else if d.ExprType() == POWI {
nd := d.(*PowI)
if nd.Base.AmISame(n) {
nd.Power -= 1
D.Numer = NewConstantF(1.0)
changed = true
break
}
}
}
} else {
n, d := D.Numer, D.Denom
if n.AmISame(d) {
D.Numer = NewConstantF(1.0)
D.Denom = nil
changed = true
} else if n.ExprType() == POWI && d.ExprType() == POWI {
// fmt.Println("Got Here 1")
np, dp := n.(*PowI), d.(*PowI)
if np.Base.AmISame(dp.Base) {
if np.Power > dp.Power {
np.Power -= dp.Power
D.Denom = nil
changed = true
} else if np.Power < dp.Power {
dp.Power -= np.Power
D.Numer = NewConstantF(1.0)
changed = true
} else { // same and should cancel
// will we even get here?
D.Numer = NewConstantF(1.0)
D.Denom = nil
changed = true
}
}
} else if n.ExprType() == POWI {
// fmt.Println("Got Here 2")
np := n.(*PowI)
if np.Base.AmISame(d) {
np.Power -= 1
D.Denom = nil
changed = true
}
} else if d.ExprType() == POWI {
// fmt.Println("Got Here 3")
nd := d.(*PowI)
if nd.Base.AmISame(n) {
nd.Power -= 1
D.Numer = NewConstantF(1.0)
changed = true
}
}
}
if changed {
t1, t2 = NULL, NULL
if D.Numer != nil {
D.Numer = D.Numer.Simplify(rules)
if D.Numer != nil {
t1 = D.Numer.ExprType()
}
}
if D.Denom != nil {
D.Denom = D.Denom.Simplify(rules)
if D.Denom != nil {
t2 = D.Denom.ExprType()
}
}
// check to see if nulls/nils
if t1 == NULL && t2 == NULL {
ret = nil
} else if t1 == NULL {
D.Numer = NewConstantF(1.0)
ret = D
return ret
} else if t2 == NULL {
ret = D.Numer
D.Numer = nil
D.Denom = nil
return ret
}
}
return ret
}
func (n *Add) Simplify(rules SimpRules) Expr {
var ret Expr = n
hasSome := false
// fmt.Printf("n.CS = %v\n",n.CS)
for i, C := range n.CS {
if C != nil {
n.CS[i] = C.Simplify(rules)
if n.CS[i] == nil {
continue
}
if n.CS[i].ExprType() == NULL {
n.CS[i] = nil
} else {
hasSome = true
}
}
}
if !hasSome {
return nil
}
changed := true
for changed {
// fmt.Printf("iter = %v\n",n.CS)
// fmt.Printf("ADD: %v\n", n)
changed = false
if rules.ConvertConsts {
changed = changed || gatherAddTerms(n)
// fmt.Printf("GTH: %v\n", n)
changed = changed || groupAddTerms(n)
// fmt.Printf("GRP: %v\n", n)
} else {
changed = changed || gatherAddTerms(n)
// fmt.Printf("GTH: %v\n", n)
changed = changed || groupAddTermsF(n)
// fmt.Printf("GRP: %v\n", n)
}
n.Sort()
// fmt.Printf("SRT: %v\n", n)
}
// fmt.Printf("POST: %v\n\n\n", n)
cnt := countTerms(n.CS)
if cnt == 0 {
ret = nil
}
if cnt == 1 {
ret = n.CS[0]
n.CS[0] = nil
}
// fmt.Printf("exit = %v\n",n.CS)
return ret
}
func (n *Mul) Simplify(rules SimpRules) Expr {
var ret Expr = n
changed := true
for changed {
for i, C := range n.CS {
if C != nil {
n.CS[i] = C.Simplify(rules)
if n.CS[i] == nil {
continue
}
if n.CS[i].ExprType() == NULL {
n.CS[i] = nil
}
}
}
// fmt.Printf("MUL: %v\n", n)
changed = false
if rules.ConvertConsts {
changed = changed || gatherMulTerms(n)
// fmt.Printf("GTH: %v\n", n)
changed = changed || groupMulTerms(n)
// fmt.Printf("GRP: %v\n", n)
} else {
changed = changed || gatherMulTermsF(n)
// fmt.Printf("GTH: %v\n", n)
changed = changed || groupMulTermsF(n)
// fmt.Printf("GRP: %v\n", n)
}
n.Sort()
// fmt.Printf("SRT: %v\n", n)
}
// fmt.Printf("POST: %v\n\n\n", n)
cnt := countTerms(n.CS)
if cnt == 0 {
ret = nil
}
if cnt == 1 {
// fmt.Printf("ARRRRGGGGG %v\n", n.CS)
ret = n.CS[0]
n.CS[0] = nil
}
return ret
}
func countTerms(terms []Expr) int {
cnt := 0
for _, e := range terms {
if e != nil {
cnt++
}
}
return cnt
}
// this function left aligns children terms ( ie move nils to end of terms[] )
// and returns the number of children
func leftAlignTerms(terms []Expr) int {
cnt, nilp := 0, -1
for i, e := range terms {
if e != nil {
// fmt.Printf( "TERMS(%d/%d): %v\n", i,nilp, terms )
cnt++
if nilp >= 0 {
terms[nilp], terms[i] = terms[i], nil
nilp++
// find next nil spot
for nilp < len(terms) {
if terms[nilp] == nil {
break
} else {
nilp++
}
}
if nilp >= len(terms) {
break
} // the outer loop
}
} else if nilp < 0 {
nilp = i
}
}
return cnt
}
// pulls recursive adds into the current add
func gatherAddTerms(n *Add) (changed bool) {
terms := make([]Expr, 0)
// terms := n.CS
// fmt.Printf("n.CS: %v\n", n.CS[:])
for i, e := range n.CS {
if e == nil {
continue
}
if e.ExprType() == ADD {
// fmt.Printf("got here\n")
changed = true
a := e.(*Add)
for j, E := range a.CS {
if E == nil {
continue
}
terms = append(terms, E)
a.CS[j] = nil
}
// rem := leftAlignTerms(a.CS[:])
// if rem == 0 {
n.CS[i] = nil
// }
// leftAlignTerms(terms)
} else {
terms = append(terms, e)
}
}
// fmt.Printf("terms: %v\n", terms)
n.CS = terms
return changed
}