Initial commit.

LICENSE

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+Copyright (c) 2014 by Philip Nelson
+
+Some rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+- Redistributions of source code must retain the above copyright notice, this
+  list of conditions and the following disclaimer.
+
+- Redistributions in binary form must reproduce the above copyright notice,
+  this list of conditions and the following disclaimer in the documentation
+  and/or other materials provided with the distribution.
+
+- The names of the contributors may not be used to endorse or promote products
+  derived from this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
+FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

README

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+fraction
+========
+
+Approximate fractions from floats.
+
+Modeled after https://www.ics.uci.edu/~eppstein/numth/frap.c.
+
+Note
+----
+
+I feel like this is probably already implemented in the standard library. I
+took a look at `Rat` from `math/big` but didn't have any luck.
+
+http://play.golang.org/p/6ht0tn5xKH

fraction.go

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+// Package fraction finds rational approximations to real numbers.
+package fraction
+
+// Fraction returns the numerator, denominator and error of v, limiting the
+// denominator to a maximum of d. If the provided value of d is less than 1, it
+// defaults to 10. If v is negative, the numerator will be negative.
+func Fraction(v float64, d int64) (int64, int64, float64) {
+	sign := int64(1)
+	ai := int64(0)
+	m := [2][2]int64{{1, 0}, {0, 1}}
+
+	if v < 0 {
+		sign = -1
+		v *= -1.0
+	}
+
+	if d < 1 {
+		d = 10
+	}
+
+	x := v
+
+	// Find terms until denominator gets too large.
+	for m[1][0]*ai+m[1][1] <= d {
+		m[0][1], m[0][0] = m[0][0], m[0][0]*ai+m[0][1]
+		m[1][1], m[1][0] = m[1][0], m[1][0]*ai+m[1][1]
+
+		// Handle division by 0.
+		if x == float64(ai) {
+			break
+		}
+
+		x = 1 / (x - float64(ai))
+		ai = int64(x)
+
+		// Handle representation failure.
+		if x > float64(0x7FFFFFFF) {
+			break
+		}
+	}
+
+	return m[0][0] * sign, m[1][0], v - (float64(m[0][0]) / float64(m[1][0]))
+}
+
+// WholeFraction returns the whole, numerator, denominator and error of v,
+// limiting the denominator to a maximum of d. If the provided value of d is
+// less than 1, it defaults to 10. The whole number will take the sign unless
+// it is 0, in which case the numerator will.
+func WholeFraction(v float64, d int64) (int64, int64, int64, float64) {
+	whole := int64(v)
+	v -= float64(whole)
+	num, den, e := Fraction(v, d)
+	if num < 0 && whole != 0 {
+		num *= -1
+	}
+	return whole, num, den, e
+}

fraction_test.go

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+package fraction
+
+import (
+	"fmt"
+	"math"
+	"testing"
+)
+
+var fractionTest = []struct {
+	v   float64
+	d   int64
+	num int64
+	den int64
+}{
+	{0.33, 10, 1, 3},
+	{0.33, -1, 1, 3},
+	{-0.33, 10, -1, 3},
+}
+
+var wholeFractionTest = []struct {
+	v     float64
+	d     int64
+	whole int64
+	num   int64
+	den   int64
+}{
+	{2.33, 10, 2, 1, 3},
+	{2.33, -1, 2, 1, 3},
+	{-2.33, 10, -2, 1, 3},
+	{-0.33, 10, 0, -1, 3},
+}
+
+func TestFraction(t *testing.T) {
+	for i, tt := range fractionTest {
+		num, den, e := Fraction(tt.v, tt.d)
+		if num != tt.num {
+			t.Errorf("%d. Fraction num = %v, want %v", i, num, tt.num)
+		}
+		if den != tt.den {
+			t.Errorf("%d. Fraction den = %v, want %v", i, den, tt.den)
+		}
+		if abs := math.Abs(e); abs > 0.01 {
+			t.Errorf("%d. Fraction math.Abs(%v) = %v > 0.01", i, e, abs)
+		}
+	}
+}
+
+func TestWholeFraction(t *testing.T) {
+	for i, tt := range wholeFractionTest {
+		whole, num, den, e := WholeFraction(tt.v, tt.d)
+		if whole != tt.whole {
+			t.Errorf("%d. WholeFraction whole = %v, want %v", i, whole, tt.whole)
+		}
+		if num != tt.num {
+			t.Errorf("%d. WholeFraction num = %v, want %v", i, num, tt.num)
+		}
+		if den != tt.den {
+			t.Errorf("%d. WholeFraction den = %v, want %v", i, den, tt.den)
+		}
+		if abs := math.Abs(e); abs > 0.01 {
+			t.Errorf("%d. WholeFraction math.Abs(%v) = %v > 0.01", i, e, abs)
+		}
+	}
+}
+
+func ExampleFraction() {
+	num, den, e := Fraction(0.33, -1)
+	fmt.Println(num)
+	fmt.Println(den)
+	fmt.Println(e)
+	// Output:
+	// 1
+	// 3
+	// -0.0033333333333332993
+}
+
+func ExampleWholeFraction() {
+	whole, num, den, e := WholeFraction(2.5, -1)
+	fmt.Println(whole)
+	fmt.Println(num)
+	fmt.Println(den)
+	fmt.Println(e)
+	// Output:
+	// 2
+	// 1
+	// 2
+	// 0
+}