1 files changed, 224 insertions, 0 deletions
diff --git a/src/math/big/bits_test.go b/src/math/big/bits_test.go
new file mode 100644
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--- /dev/null
+++ b/src/math/big/bits_test.go
@@ -0,0 +1,224 @@
+// Copyright 2015 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.
+
+// This file implements the Bits type used for testing Float operations
+// via an independent (albeit slower) representations for floating-point
+// numbers.
+
+package big
+
+import (
+	"fmt"
+	"sort"
+	"testing"
+)
+
+// A Bits value b represents a finite floating-point number x of the form
+//
+//	x = 2**b[0] + 2**b[1] + ... 2**b[len(b)-1]
+//
+// The order of slice elements is not significant. Negative elements may be
+// used to form fractions. A Bits value is normalized if each b[i] occurs at
+// most once. For instance Bits{0, 0, 1} is not normalized but represents the
+// same floating-point number as Bits{2}, which is normalized. The zero (nil)
+// value of Bits is a ready to use Bits value and represents the value 0.
+type Bits []int
+
+func (x Bits) add(y Bits) Bits {
+	return append(x, y...)
+}
+
+func (x Bits) mul(y Bits) Bits {
+	var p Bits
+	for _, x := range x {
+		for _, y := range y {
+			p = append(p, x+y)
+		}
+	}
+	return p
+}
+
+func TestMulBits(t *testing.T) {
+	for _, test := range []struct {
+		x, y, want Bits
+	}{
+		{nil, nil, nil},
+		{Bits{}, Bits{}, nil},
+		{Bits{0}, Bits{0}, Bits{0}},
+		{Bits{0}, Bits{1}, Bits{1}},
+		{Bits{1}, Bits{1, 2, 3}, Bits{2, 3, 4}},
+		{Bits{-1}, Bits{1}, Bits{0}},
+		{Bits{-10, -1, 0, 1, 10}, Bits{1, 2, 3}, Bits{-9, -8, -7, 0, 1, 2, 1, 2, 3, 2, 3, 4, 11, 12, 13}},
+	} {
+		got := fmt.Sprintf("%v", test.x.mul(test.y))
+		want := fmt.Sprintf("%v", test.want)
+		if got != want {
+			t.Errorf("%v * %v = %s; want %s", test.x, test.y, got, want)
+		}
+
+	}
+}
+
+// norm returns the normalized bits for x: It removes multiple equal entries
+// by treating them as an addition (e.g., Bits{5, 5} => Bits{6}), and it sorts
+// the result list for reproducible results.
+func (x Bits) norm() Bits {
+	m := make(map[int]bool)
+	for _, b := range x {
+		for m[b] {
+			m[b] = false
+			b++
+		}
+		m[b] = true
+	}
+	var z Bits
+	for b, set := range m {
+		if set {
+			z = append(z, b)
+		}
+	}
+	sort.Ints([]int(z))
+	return z
+}
+
+func TestNormBits(t *testing.T) {
+	for _, test := range []struct {
+		x, want Bits
+	}{
+		{nil, nil},
+		{Bits{}, Bits{}},
+		{Bits{0}, Bits{0}},
+		{Bits{0, 0}, Bits{1}},
+		{Bits{3, 1, 1}, Bits{2, 3}},
+		{Bits{10, 9, 8, 7, 6, 6}, Bits{11}},
+	} {
+		got := fmt.Sprintf("%v", test.x.norm())
+		want := fmt.Sprintf("%v", test.want)
+		if got != want {
+			t.Errorf("normBits(%v) = %s; want %s", test.x, got, want)
+		}
+
+	}
+}
+
+// round returns the Float value corresponding to x after rounding x
+// to prec bits according to mode.
+func (x Bits) round(prec uint, mode RoundingMode) *Float {
+	x = x.norm()
+
+	// determine range
+	var min, max int
+	for i, b := range x {
+		if i == 0 || b < min {
+			min = b
+		}
+		if i == 0 || b > max {
+			max = b
+		}
+	}
+	prec0 := uint(max + 1 - min)
+	if prec >= prec0 {
+		return x.Float()
+	}
+	// prec < prec0
+
+	// determine bit 0, rounding, and sticky bit, and result bits z
+	var bit0, rbit, sbit uint
+	var z Bits
+	r := max - int(prec)
+	for _, b := range x {
+		switch {
+		case b == r:
+			rbit = 1
+		case b < r:
+			sbit = 1
+		default:
+			// b > r
+			if b == r+1 {
+				bit0 = 1
+			}
+			z = append(z, b)
+		}
+	}
+
+	// round
+	f := z.Float() // rounded to zero
+	if mode == ToNearestAway {
+		panic("not yet implemented")
+	}
+	if mode == ToNearestEven && rbit == 1 && (sbit == 1 || sbit == 0 && bit0 != 0) || mode == AwayFromZero {
+		// round away from zero
+		f.SetMode(ToZero).SetPrec(prec)
+		f.Add(f, Bits{int(r) + 1}.Float())
+	}
+	return f
+}
+
+// Float returns the *Float z of the smallest possible precision such that
+// z = sum(2**bits[i]), with i = range bits. If multiple bits[i] are equal,
+// they are added: Bits{0, 1, 0}.Float() == 2**0 + 2**1 + 2**0 = 4.
+func (bits Bits) Float() *Float {
+	// handle 0
+	if len(bits) == 0 {
+		return new(Float)
+	}
+	// len(bits) > 0
+
+	// determine lsb exponent
+	var min int
+	for i, b := range bits {
+		if i == 0 || b < min {
+			min = b
+		}
+	}
+
+	// create bit pattern
+	x := NewInt(0)
+	for _, b := range bits {
+		badj := b - min
+		// propagate carry if necessary
+		for x.Bit(badj) != 0 {
+			x.SetBit(x, badj, 0)
+			badj++
+		}
+		x.SetBit(x, badj, 1)
+	}
+
+	// create corresponding float
+	z := new(Float).SetInt(x) // normalized
+	if e := int64(z.exp) + int64(min); MinExp <= e && e <= MaxExp {
+		z.exp = int32(e)
+	} else {
+		// this should never happen for our test cases
+		panic("exponent out of range")
+	}
+	return z
+}
+
+func TestFromBits(t *testing.T) {
+	for _, test := range []struct {
+		bits Bits
+		want string
+	}{
+		// all different bit numbers
+		{nil, "0"},
+		{Bits{0}, "0x.8p+1"},
+		{Bits{1}, "0x.8p+2"},
+		{Bits{-1}, "0x.8p+0"},
+		{Bits{63}, "0x.8p+64"},
+		{Bits{33, -30}, "0x.8000000000000001p+34"},
+		{Bits{255, 0}, "0x.8000000000000000000000000000000000000000000000000000000000000001p+256"},
+
+		// multiple equal bit numbers
+		{Bits{0, 0}, "0x.8p+2"},
+		{Bits{0, 0, 0, 0}, "0x.8p+3"},
+		{Bits{0, 1, 0}, "0x.8p+3"},
+		{append(Bits{2, 1, 0} /* 7 */, Bits{3, 1} /* 10 */ ...), "0x.88p+5" /* 17 */},
+	} {
+		f := test.bits.Float()
+		if got := f.Text('p', 0); got != test.want {
+			t.Errorf("setBits(%v) = %s; want %s", test.bits, got, test.want)
+		}
+	}
+}