precisevector_test.go

// Copyright 2016 Google Inc. All rights reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

package r3

import (
	"math/big"
	"testing"
)

// preciseEq compares two big.Floats and checks if the are the same.
func preciseEq(a, b *big.Float) bool {
	return a.SetPrec(MaxPrec).Cmp(b.SetPrec(MaxPrec)) == 0
}

func TestPreciseRoundtrip(t *testing.T) {
	tests := []struct {
		v Vector
	}{
		{Vector{0, 0, 0}},
		{Vector{1, 2, 3}},
		{Vector{3, -4, 12}},
		{Vector{1, 1e-16, 1e-32}},
	}

	for _, test := range tests {
		if got, want := PreciseVectorFromVector(test.v).Vector(), test.v.Normalize(); !got.ApproxEqual(want) {
			t.Errorf("PreciseVectorFromVector(%v).Vector() = %v, want %v", test.v, got, want)
		}
	}
}

func TestPreciseIsUnit(t *testing.T) {
	const epsilon = 1e-14
	tests := []struct {
		v    PreciseVector
		want bool
	}{
		{
			v:    NewPreciseVector(0, 0, 0),
			want: false,
		},
		{
			v:    NewPreciseVector(1, 0, 0),
			want: true,
		},
		{
			v:    NewPreciseVector(0, 1, 0),
			want: true,
		},
		{
			v:    NewPreciseVector(0, 0, 1),
			want: true,
		},
		{
			v:    NewPreciseVector(1+2*epsilon, 0, 0),
			want: false,
		},
		{
			v:    NewPreciseVector(0*(1+epsilon), 0, 0),
			want: false,
		},
		{
			v:    NewPreciseVector(1, 1, 1),
			want: false,
		},
	}

	for _, test := range tests {
		if got := test.v.IsUnit(); got != test.want {
			t.Errorf("%v.IsUnit() = %v, want %v", test.v, got, test.want)
		}
	}
}

func TestPreciseNorm2(t *testing.T) {
	tests := []struct {
		v    PreciseVector
		want *big.Float
	}{
		{
			v:    NewPreciseVector(0, 0, 0),
			want: precise0,
		},
		{
			v:    NewPreciseVector(0, 1, 0),
			want: precise1,
		},
		{
			v:    NewPreciseVector(1, 1, 1),
			want: precStr("3"),
		},
		{
			v:    NewPreciseVector(1, 2, 3),
			want: precStr("14"),
		},
		{
			v:    NewPreciseVector(3, -4, 12),
			want: precStr("169"),
		},
	}

	for _, test := range tests {
		if got := test.v.Norm2(); !preciseEq(got, test.want) {
			t.Errorf("%v.Norm2() = %v, want %v", test.v, test.v.Norm2(), test.want)
		}
	}
}

func TestPreciseAdd(t *testing.T) {
	tests := []struct {
		v1, v2, want PreciseVector
	}{
		{
			v1:   NewPreciseVector(0, 0, 0),
			v2:   NewPreciseVector(0, 0, 0),
			want: NewPreciseVector(0, 0, 0),
		},
		{
			v1:   NewPreciseVector(1, 0, 0),
			v2:   NewPreciseVector(0, 0, 0),
			want: NewPreciseVector(1, 0, 0),
		},
		{
			v1:   NewPreciseVector(1, 2, 3),
			v2:   NewPreciseVector(4, 5, 7),
			want: NewPreciseVector(5, 7, 10),
		},
		{
			v1:   NewPreciseVector(1, -3, 5),
			v2:   NewPreciseVector(1, -6, -6),
			want: NewPreciseVector(2, -9, -1),
		},
	}

	for _, test := range tests {
		if got := test.v1.Add(test.v2); !got.Equal(test.want) {
			t.Errorf("%v + %v = %v, want %v", test.v1, test.v2, got, test.want)
		}
	}
}

func TestPreciseSub(t *testing.T) {
	tests := []struct {
		v1, v2, want PreciseVector
	}{
		{
			v1:   NewPreciseVector(0, 0, 0),
			v2:   NewPreciseVector(0, 0, 0),
			want: NewPreciseVector(0, 0, 0),
		},
		{
			v1:   NewPreciseVector(1, 0, 0),
			v2:   NewPreciseVector(0, 0, 0),
			want: NewPreciseVector(1, 0, 0),
		},
		{
			v1:   NewPreciseVector(1, 2, 3),
			v2:   NewPreciseVector(4, 5, 7),
			want: NewPreciseVector(-3, -3, -4),
		},
		{
			v1:   NewPreciseVector(1, -3, 5),
			v2:   NewPreciseVector(1, -6, -6),
			want: NewPreciseVector(0, 3, 11),
		},
	}

	for _, test := range tests {
		if got := test.v1.Sub(test.v2); !got.Equal(test.want) {
			t.Errorf("%v - %v = %v, want %v", test.v1, test.v2, got, test.want)
		}
	}
}

func TestPreciseMul(t *testing.T) {
	tests := []struct {
		v    PreciseVector
		f    *big.Float
		want PreciseVector
	}{
		{
			v:    NewPreciseVector(0, 0, 0),
			f:    precFloat(3),
			want: NewPreciseVector(0, 0, 0),
		},
		{
			v:    NewPreciseVector(1, 0, 0),
			f:    precFloat(1),
			want: NewPreciseVector(1, 0, 0),
		},
		{
			v:    NewPreciseVector(1, 0, 0),
			f:    precFloat(0),
			want: NewPreciseVector(0, 0, 0),
		},
		{
			v:    NewPreciseVector(1, 0, 0),
			f:    precFloat(3),
			want: NewPreciseVector(3, 0, 0),
		},
		{
			v:    NewPreciseVector(1, -3, 5),
			f:    precFloat(-1),
			want: NewPreciseVector(-1, 3, -5),
		},
		{
			v:    NewPreciseVector(1, -3, 5),
			f:    precFloat(2),
			want: NewPreciseVector(2, -6, 10),
		},
	}

	for _, test := range tests {
		if got := test.v.Mul(test.f); !got.Equal(test.want) {
			t.Errorf("%v.Mul(%v) = %v, want %v", test.v, test.f, got, test.want)
		}
	}
}

func TestPreciseMulByFloat64(t *testing.T) {
	tests := []struct {
		v    PreciseVector
		f    float64
		want PreciseVector
	}{
		{
			v:    NewPreciseVector(0, 0, 0),
			f:    3,
			want: NewPreciseVector(0, 0, 0),
		},
		{
			v:    NewPreciseVector(1, 0, 0),
			f:    1,
			want: NewPreciseVector(1, 0, 0),
		},
		{
			v:    NewPreciseVector(1, 0, 0),
			f:    0,
			want: NewPreciseVector(0, 0, 0),
		},
		{
			v:    NewPreciseVector(1, 0, 0),
			f:    3,
			want: NewPreciseVector(3, 0, 0),
		},
		{
			v:    NewPreciseVector(1, -3, 5),
			f:    -1,
			want: NewPreciseVector(-1, 3, -5),
		},
		{
			v:    NewPreciseVector(1, -3, 5),
			f:    2,
			want: NewPreciseVector(2, -6, 10),
		},
	}

	for _, test := range tests {
		if got := test.v.MulByFloat64(test.f); !got.Equal(test.want) {
			t.Errorf("%v.MulByFloat64(%v) = %v, want %v", test.v, test.f, got, test.want)
		}
	}
}

func TestPreciseDot(t *testing.T) {
	tests := []struct {
		v1, v2 PreciseVector
		want   *big.Float
	}{
		{
			// Dot with self should be 1.
			v1:   NewPreciseVector(1, 0, 0),
			v2:   NewPreciseVector(1, 0, 0),
			want: precise1,
		},
		{
			// Dot with self should be 1.
			v1:   NewPreciseVector(0, 1, 0),
			v2:   NewPreciseVector(0, 1, 0),
			want: precise1,
		},
		{
			// Dot with self should be 1.
			v1:   NewPreciseVector(0, 0, 1),
			v2:   NewPreciseVector(0, 0, 1),
			want: precise1,
		},
		{
			// Perpendicular should be 0.
			v1:   NewPreciseVector(1, 0, 0),
			v2:   NewPreciseVector(0, 1, 0),
			want: precise0,
		},
		{
			// Perpendicular should be 0.
			v1:   NewPreciseVector(1, 0, 0),
			v2:   NewPreciseVector(0, 1, 1),
			want: precise0,
		},
		{
			v1:   NewPreciseVector(1, 1, 1),
			v2:   NewPreciseVector(-1, -1, -1),
			want: precStr("-3"),
		},
	}

	for _, test := range tests {
		if got := test.v1.Dot(test.v2); !preciseEq(got, test.want) {
			t.Errorf("%v · %v = %v, want %v", test.v1, test.v2, got, test.want)
		}
		if got := test.v2.Dot(test.v1); !preciseEq(got, test.want) {
			t.Errorf("%v · %v = %v, want %v", test.v2, test.v1, got, test.want)
		}
	}
}

func TestPreciseCross(t *testing.T) {
	tests := []struct {
		v1, v2, want PreciseVector
	}{
		{
			// Cross with self should be 0.
			v1:   NewPreciseVector(1, 0, 0),
			v2:   NewPreciseVector(1, 0, 0),
			want: NewPreciseVector(0, 0, 0),
		},
		{
			// Cross with perpendicular should give the remaining axis.
			v1:   NewPreciseVector(1, 0, 0),
			v2:   NewPreciseVector(0, 1, 0),
			want: NewPreciseVector(0, 0, 1),
		},
		{
			// Cross with perpendicular should give the remaining axis.
			v1:   NewPreciseVector(0, 1, 0),
			v2:   NewPreciseVector(0, 0, 1),
			want: NewPreciseVector(1, 0, 0),
		},
		{
			// Cross with perpendicular should give the remaining axis.
			v1:   NewPreciseVector(0, 0, 1),
			v2:   NewPreciseVector(1, 0, 0),
			want: NewPreciseVector(0, 1, 0),
		},
		{
			v1:   NewPreciseVector(0, 1, 0),
			v2:   NewPreciseVector(1, 0, 0),
			want: NewPreciseVector(0, 0, -1),
		},
		{
			v1:   NewPreciseVector(1, 2, 3),
			v2:   NewPreciseVector(-4, 5, -6),
			want: NewPreciseVector(-27, -6, 13),
		},
	}

	for _, test := range tests {
		if got := test.v1.Cross(test.v2); !got.Equal(test.want) {
			t.Errorf("%v ⨯ %v = %v, want %v", test.v1, test.v2, got, test.want)
		}
	}
}

func TestPreciseIdentities(t *testing.T) {
	tests := []struct {
		v1, v2 PreciseVector
	}{
		{
			v1: NewPreciseVector(0, 0, 0),
			v2: NewPreciseVector(0, 0, 0),
		},
		{
			v1: NewPreciseVector(0, 0, 0),
			v2: NewPreciseVector(0, 1, 2),
		},
		{
			v1: NewPreciseVector(1, 0, 0),
			v2: NewPreciseVector(0, 1, 0),
		},
		{
			v1: NewPreciseVector(1, 0, 0),
			v2: NewPreciseVector(0, 1, 1),
		},
		{
			v1: NewPreciseVector(1, 1, 1),
			v2: NewPreciseVector(-1, -1, -1),
		},
		{
			v1: NewPreciseVector(1, 2, 2),
			v2: NewPreciseVector(-0.3, 0.4, -1.2),
		},
	}

	for _, test := range tests {
		c1 := test.v1.Cross(test.v2)
		c2 := test.v2.Cross(test.v1)
		d1 := test.v1.Dot(test.v2)
		d2 := test.v2.Dot(test.v1)

		// Dot commutes
		if !preciseEq(d1, d2) {
			t.Errorf("%v = %v · %v != %v · %v = %v", d1, test.v1, test.v2, test.v2, test.v1, d2)
		}
		// Cross anti-commutes
		if !c1.Equal(c2.MulByFloat64(-1.0)) {
			t.Errorf("%v = %v ⨯ %v != -(%v ⨯ %v) = -%v", c1, test.v1, test.v2, test.v2, test.v1, c2)
		}
		// Cross is orthogonal to original vectors
		if got := test.v1.Dot(c1); !preciseEq(got, precise0) {
			t.Errorf("%v · (%v ⨯ %v) = %v, want %v", test.v1, test.v1, test.v2, got, precise0)
		}
		if got := test.v2.Dot(c1); !preciseEq(got, precise0) {
			t.Errorf("%v · (%v ⨯ %v) = %v, want %v", test.v2, test.v1, test.v2, got, precise0)
		}
	}
}

func TestPreciseLargestSmallestComponents(t *testing.T) {
	tests := []struct {
		v                 PreciseVector
		largest, smallest Axis
	}{
		{
			v:        NewPreciseVector(0, 0, 0),
			largest:  ZAxis,
			smallest: ZAxis,
		},
		{
			v:        NewPreciseVector(1, 0, 0),
			largest:  XAxis,
			smallest: ZAxis,
		},
		{
			v:        NewPreciseVector(1, -1, 0),
			largest:  YAxis,
			smallest: ZAxis,
		},
		{
			v:        NewPreciseVector(-1, -1.1, -1.1),
			largest:  ZAxis,
			smallest: XAxis,
		},
		{
			v:        NewPreciseVector(0.5, -0.4, -0.5),
			largest:  ZAxis,
			smallest: YAxis,
		},
		{
			v:        NewPreciseVector(1e-15, 1e-14, 1e-13),
			largest:  ZAxis,
			smallest: XAxis,
		},
	}

	for _, test := range tests {
		if got := test.v.LargestComponent(); got != test.largest {
			t.Errorf("%v.LargestComponent() = %v, want %v", test.v, got, test.largest)
		}
		if got := test.v.SmallestComponent(); got != test.smallest {
			t.Errorf("%v.SmallestComponent() = %v, want %v", test.v, got, test.smallest)
		}
	}
}

func TestPreciseVectorIsZero(t *testing.T) {

	x := NewPreciseVector(1e20, 0, 0)
	y := NewPreciseVector(1, 0, 0)
	xy := x.Add(y)

	tests := []struct {
		have PreciseVector
		want bool
	}{
		{
			have: NewPreciseVector(0, 0, 0),
			want: true,
		},
		{
			// Test with one element being negatively signed 0.
			have: NewPreciseVector(0, -0, 0),
			want: true,
		},
		{
			// Test a non-zero value.
			have: NewPreciseVector(0, 0, 1),
			want: false,
		},
		{
			// 1e20+1-1e20 should equal 1.  Testing the case where the
			// numbers are outside the range a traditional double would
			// be able to handle correctly.
			have: x.Add(y).Add(x.Mul(precFloat(-1))),
			want: false,
		},
		{
			// (1e20+1) - (1e20+1) should be zero. Test the same case
			// where a non-representable double minus itself is 0.
			have: xy.Sub(xy),
			want: true,
		},
	}

	for _, test := range tests {
		if got := test.have.IsZero(); got != test.want {
			t.Errorf("%s.IsZero() = %v, want %v", test.have, got, test.want)
		}
	}
}