Merge aa070c4ec8 into d00399e161

decimal.go

@@ -19,6 +19,7 @@ package decimal
 import (
 	"database/sql/driver"
 	"encoding/binary"
+	"errors"
 	"fmt"
 	"math"
 	"math/big"
@@ -124,6 +125,26 @@ func NewFromBigInt(value *big.Int, exp int32) Decimal {
 	}
 }
 
+// NewFromBigRat returns a new Decimal from a big.Rat. The numerator and
+// denominator are divided and rounded to the given precision.
+//
+// Example:
+//
+//     d1 := NewFromBigRat(big.NewRat(0, 1), 0)    // output: "0"
+//     d2 := NewFromBigRat(big.NewRat(4, 5), 1)    // output: "0.8"
+//     d3 := NewFromBigRat(big.NewRat(1000, 3), 3) // output: "333.333"
+//     d4 := NewFromBigRat(big.NewRat(2, 7), 4)    // output: "0.2857"
+//
+func NewFromBigRat(value *big.Rat, precision int32) Decimal {
+	return Decimal{
+		value: new(big.Int).Set(value.Num()),
+		exp:   0,
+	}.DivRound(Decimal{
+		value: new(big.Int).Set(value.Denom()),
+		exp:   0,
+	}, precision)
+}
+
 // NewFromString returns a new Decimal from a string representation.
 // Trailing zeroes are not trimmed.
 //
@@ -2006,3 +2027,59 @@ func (d Decimal) Tan() Decimal {
 	}
 	return y
 }
+
+// More math
+
+// Sqrt returns the square root of d, accurate to DivisionPrecision decimal places.
+// Sqrt is only valid for non-negative numbers; it will return an error otherwise.
+func (d Decimal) Sqrt() (Decimal, error) {
+	s, _, err := d.SqrtRound(int32(DivisionPrecision))
+	return s, err
+}
+
+// ErrImaginaryResult indicates an operation that would produce an imaginary result.
+var ErrImaginaryResult = errors.New("The result of this operation is imaginary.")
+
+// SqrtMaxIter sets a limit for number of iterations for the Sqrt function
+const SqrtMaxIter = 1000000
+
+// SqrtRound returns the square root of d, accurate to precision decimal places.
+// The bool precise returns whether the precision was achieved.
+// SqrtRound is only valid for non-negative numbers; it will return an error otherwise.
+func (d Decimal) SqrtRound(precision int32) (Decimal, bool, error) {
+	var (
+		maxError = New(1, -precision)
+		one      = NewFromFloat(1)
+		lo, hi   Decimal
+	)
+
+	// Handle cases where d < 0, d = 0, 0 < d < 1, and d > 1
+	if d.GreaterThanOrEqual(one) {
+		lo = Zero
+		hi = d
+	} else if d.Equal(one) {
+		return one, true, nil
+	} else if d.LessThan(Zero) {
+		return Zero, false, ErrImaginaryResult
+	} else if d.Equal(Zero) {
+		return Zero, true, nil
+	} else {
+		// d is between 0 and 1. Therefore, 0 < d < Sqrt(d) < 1.
+		lo = d
+		hi = one
+	}
+
+	var mid Decimal
+	for i := 0; i < SqrtMaxIter; i++ {
+		mid = lo.Add(hi).Div(New(2, 0)) //mid = (lo+hi)/2;
+		if mid.Mul(mid).Sub(d).Abs().LessThan(maxError) {
+			return mid, true, nil
+		}
+		if mid.Mul(mid).GreaterThan(d) {
+			hi = mid
+		} else {
+			lo = mid
+		}
+	}
+	return mid, false, nil
+}

decimal_test.go

@@ -556,6 +556,51 @@ func TestNewFromBigIntWithExponent(t *testing.T) {
 	}
 }
 
+func TestNewFromBigRat(t *testing.T) {
+	mustParseRat := func(val string) *big.Rat {
+		num, _ := new(big.Rat).SetString(val)
+		return num
+	}
+
+	type Inp struct {
+		val  *big.Rat
+		prec int32
+	}
+
+	tests := map[Inp]string{
+		Inp{big.NewRat(0, 1), 16}:                                                     "0",
+		Inp{big.NewRat(4, 5), 16}:                                                     "0.8",
+		Inp{big.NewRat(10, 2), 16}:                                                    "5",
+		Inp{big.NewRat(1023427554493, 43432632), 16}:                                  "23563.5628642767953828", // rounded
+		Inp{big.NewRat(1, 434324545566634), 16}:                                       "0.0000000000000023",
+		Inp{big.NewRat(1, 3), 16}:                                                     "0.3333333333333333",
+		Inp{big.NewRat(2, 3), 2}:                                                      "0.67",               // rounded
+		Inp{big.NewRat(2, 3), 16}:                                                     "0.6666666666666667", // rounded
+		Inp{big.NewRat(10000, 3), 16}:                                                 "3333.3333333333333333",
+		Inp{mustParseRat("30702832066636633479"), 16}:                                 "30702832066636633479",
+		Inp{mustParseRat("487028320159896636679.1827512895753"), 16}:                  "487028320159896636679.1827512895753",
+		Inp{mustParseRat("127028320612589896636633479.173582751289575278357832"), -2}: "127028320612589896636633500",                  // rounded
+		Inp{mustParseRat("127028320612589896636633479.173582751289575278357832"), 16}: "127028320612589896636633479.1735827512895753", // rounded
+		Inp{mustParseRat("127028320612589896636633479.173582751289575278357832"), 32}: "127028320612589896636633479.173582751289575278357832",
+	}
+
+	// add negatives
+	for p, s := range tests {
+		if p.val.Cmp(new(big.Rat)) > 0 {
+			tests[Inp{p.val.Neg(p.val), p.prec}] = "-" + s
+		}
+	}
+
+	for input, s := range tests {
+		d := NewFromBigRat(input.val, input.prec)
+		if d.String() != s {
+			t.Errorf("expected %s, got %s (%s, %d)",
+				s, d.String(),
+				d.value.String(), d.exp)
+		}
+	}
+}
+
 func TestCopy(t *testing.T) {
 	origin := New(1, 0)
 	cpy := origin.Copy()
@@ -3194,6 +3239,40 @@ func TestAvg(t *testing.T) {
 	}
 }
 
+func TestSqrtRound(t *testing.T) {
+	i := NewFromFloat(-1)
+	if _, err := i.Sqrt(); err != ErrImaginaryResult {
+		t.Errorf("Square root of -1 should produce error")
+	}
+
+	var vals = map[string]string{
+		// value : Sqrt(value)
+		"0.0":       "0.0",
+		"0.002342":  "0.0483942145302514",
+		"1.0":       "1.0",
+		"3.0":       "1.7320508075688773",
+		"4.0":       "2.0",
+		"4.5":       "2.1213203435596426",
+		"3289854.0": "1813.7954680724064485",
+	}
+
+	for val, expected := range vals {
+		v, err := NewFromString(val)
+		if err != nil {
+			t.Errorf("error parsing test value into Decimal")
+		}
+
+		e, err := NewFromString(expected)
+		if err != nil {
+			t.Errorf("error parsing test expected value into Decimal")
+		}
+
+		if sqrt, err := v.Sqrt(); err != nil || !sqrt.Equal(e) {
+			t.Errorf("Square root of %s should be %s, not %s (error: %s)", v, e, sqrt, err)
+		}
+	}
+}
+
 func TestRoundBankAnomaly(t *testing.T) {
 	a := New(25, -1)
 	b := New(250, -2)