operator-fraction.go: many new functions supporting fraction operations

operator-fraction.go

@@ -5,7 +5,9 @@
 package expr
 
 import (
+	"errors"
 	"fmt"
+	"strconv"
 	"strings"
 )
 
@@ -13,9 +15,57 @@ type fraction struct {
 	num, den int64
 }
 
+func newFraction(num, den int64) *fraction {
+	if den < 0 {
+		den = -den
+		num = -num
+	}
+	return &fraction{num, den}
+}
+
+func (f *fraction) toFloat() float64 {
+	return float64(f.num) / float64(f.den)
+}
+
+func (f *fraction) String() string {
+	return f.ToString(0)
+}
+
 func (f *fraction) ToString(opt FmtOpt) string {
 	var sb strings.Builder
-	sb.WriteString(fmt.Sprintf("%d|%d", f.num, f.den))
+	if opt&MultiLine == 0 {
+		sb.WriteString(fmt.Sprintf("%d|%d", f.num, f.den))
+	} else {
+		var s, num string
+		if f.num < 0 && opt&TTY == 0 {
+			num = strconv.FormatInt(-f.num, 10)
+			s = "-"
+		} else {
+			num = strconv.FormatInt(f.num, 10)
+		}
+		den := strconv.FormatInt(f.den, 10)
+		size := max(len(num), len(den))
+		if opt&TTY != 0 {
+			sb.WriteString(fmt.Sprintf("\x1b[4m%[1]*s\x1b[0m\n", -size, fmt.Sprintf("%[1]*s", (size+len(num))/2, s+num)))
+		} else {
+			if len(s) > 0 {
+				sb.WriteString("  ")
+			}
+			sb.WriteString(fmt.Sprintf("%[1]*s", -size, fmt.Sprintf("%[1]*s", (size+len(num))/2, num)))
+			sb.WriteByte('\n')
+			if len(s) > 0 {
+				sb.WriteString(s)
+				sb.WriteByte(' ')
+			}
+			sb.WriteString(strings.Repeat("-", size))
+			sb.WriteByte('\n')
+			if len(s) > 0 {
+				sb.WriteString("  ")
+			}
+		}
+		sb.WriteString(fmt.Sprintf("%[1]*s", -size, fmt.Sprintf("%[1]*s", (size+len(den))/2, den)))
+	}
+
 	return sb.String()
 }
 
@@ -42,15 +92,182 @@ func evalFraction(ctx ExprContext, self *term) (v any, err error) {
 	}
 	if num, ok = numValue.(int64); !ok {
 		err = fmt.Errorf("numerator must be integer, got %T (%v)", numValue, numValue)
+		return
 	}
 	if den, ok = denValue.(int64); !ok {
 		err = fmt.Errorf("denominator must be integer, got %T (%v)", denValue, denValue)
+		return
+	}
+	if den == 0 {
+		err = errors.New("division by zero")
+		return
 	}
 
-	v = &fraction{num, den}
+	if den < 0 {
+		den = -den
+		num = -num
+	}
+	g := gcd(num, den)
+	num = num / g
+	den = den / g
+	if den == 1 {
+		v = num
+	} else {
+		v = &fraction{num, den}
+	}
 	return
 }
 
+func gcd(a, b int64) (g int64) {
+	if a < 0 {
+		a = -a
+	}
+	if b < 0 {
+		b = -b
+	}
+	if a < b {
+		a, b = b, a
+	}
+	r := a % b
+	for r > 0 {
+		a, b = b, r
+		r = a % b
+	}
+	g = b
+	return
+}
+
+func lcm(a, b int64) (l int64) {
+	g := gcd(a, b)
+	l = a * b / g
+	return
+}
+
+func sumFract(f1, f2 *fraction) (sum *fraction) {
+	m := lcm(f1.den, f2.den)
+	sum = &fraction{f1.num*(m/f1.den) + f2.num*(m/f2.den), m}
+	return
+}
+
+func mulFract(f1, f2 *fraction) (prod *fraction) {
+	prod = &fraction{f1.num * f2.num, f1.den * f2.den}
+	return
+}
+
+func anyToFract(v any) (f *fraction, err error) {
+	var ok bool
+	if f, ok = v.(*fraction); !ok {
+		if n, ok := v.(int64); ok {
+			f = intToFraction(n)
+		}
+	}
+	if f == nil {
+		err = errExpectedGot("fract", typeFraction, v)
+	}
+	return
+}
+
+func anyPairToFract(v1, v2 any) (f1, f2 *fraction, err error) {
+	if f1, err = anyToFract(v1); err != nil {
+		return
+	}
+	if f2, err = anyToFract(v2); err != nil {
+		return
+	}
+	return
+}
+
+func sumAnyFract(af1, af2 any) (sum any, err error) {
+	var f1, f2 *fraction
+	if f1, f2, err = anyPairToFract(af1, af2); err != nil {
+		return
+	}
+	f := sumFract(f1, f2)
+	if f.num == 0 {
+		sum = 0
+	} else {
+		sum = simplifyFraction(f)
+	}
+	return
+}
+
+func subAnyFract(af1, af2 any) (sum any, err error) {
+	var f1, f2 *fraction
+	if f1, f2, err = anyPairToFract(af1, af2); err != nil {
+		return
+	}
+	f2.num = -f2.num
+	f := sumFract(f1, f2)
+	if f.num == 0 {
+		sum = 0
+	} else {
+		sum = simplifyFraction(f)
+	}
+	return
+}
+
+func mulAnyFract(af1, af2 any) (prod any, err error) {
+	var f1, f2 *fraction
+	if f1, f2, err = anyPairToFract(af1, af2); err != nil {
+		return
+	}
+	if f1.num == 0 || f2.num == 0 {
+		prod = 0
+	} else {
+		f := &fraction{f1.num * f2.num, f1.den * f2.den}
+		prod = simplifyFraction(f)
+	}
+	return
+}
+
+func divAnyFract(af1, af2 any) (quot any, err error) {
+	var f1, f2 *fraction
+	if f1, f2, err = anyPairToFract(af1, af2); err != nil {
+		return
+	}
+	if f2.num == 0 {
+		err = errors.New("division by zero")
+		return
+		return
+	}
+	if f1.num == 0 || f2.den == 0 {
+		quot = 0
+	} else {
+		f := &fraction{f1.num * f2.den, f1.den * f2.num}
+		quot = simplifyFraction(f)
+	}
+	return
+}
+
+func simplifyFraction(f *fraction) any {
+	return simplifyIntegers(f.num, f.den)
+}
+
+func simplifyIntegers(num, den int64) (v any) {
+	if den < 0 {
+		den = -den
+		num = -num
+	}
+	g := gcd(num, den)
+	num = num / g
+	den = den / g
+	if den == 1 {
+		v = num
+	} else {
+		v = &fraction{num, den}
+	}
+	return
+}
+
+func intToFraction(n int64) *fraction {
+	return &fraction{n, 1}
+}
+
+func isFraction(v any) (ok bool) {
+	_, ok = v.(*fraction)
+	return ok
+}
+
 // init
 func init() {
 	registerTermConstructor(SymVertBar, newFractionTerm)