gtsocial-umbx

precisevector.go (5569B)

---

 // 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 (
 	"fmt"
 	"math/big"
 )
 
 const (
 	// prec is the number of bits of precision to use for the Float values.
 	// To keep things simple, we use the maximum allowable precision on big
 	// values. This allows us to handle all values we expect in the s2 library.
 	prec = big.MaxPrec
 )
 
 // define some commonly referenced values.
 var (
 	precise0 = precInt(0)
 	precise1 = precInt(1)
 )
 
 // precStr wraps the conversion from a string into a big.Float. For results that
 // actually can be represented exactly, this should only be used on values that
 // are integer multiples of integer powers of 2.
 func precStr(s string) *big.Float {
 	// Explicitly ignoring the bool return for this usage.
 	f, _ := new(big.Float).SetPrec(prec).SetString(s)
 	return f
 }
 
 func precInt(i int64) *big.Float {
 	return new(big.Float).SetPrec(prec).SetInt64(i)
 }
 
 func precFloat(f float64) *big.Float {
 	return new(big.Float).SetPrec(prec).SetFloat64(f)
 }
 
 func precAdd(a, b *big.Float) *big.Float {
 	return new(big.Float).SetPrec(prec).Add(a, b)
 }
 
 func precSub(a, b *big.Float) *big.Float {
 	return new(big.Float).SetPrec(prec).Sub(a, b)
 }
 
 func precMul(a, b *big.Float) *big.Float {
 	return new(big.Float).SetPrec(prec).Mul(a, b)
 }
 
 // PreciseVector represents a point in ℝ³ using high-precision values.
 // Note that this is NOT a complete implementation because there are some
 // operations that Vector supports that are not feasible with arbitrary precision
 // math. (e.g., methods that need division like Normalize, or methods needing a
 // square root operation such as Norm)
 type PreciseVector struct {
 	X, Y, Z *big.Float
 }
 
 // PreciseVectorFromVector creates a high precision vector from the given Vector.
 func PreciseVectorFromVector(v Vector) PreciseVector {
 	return NewPreciseVector(v.X, v.Y, v.Z)
 }
 
 // NewPreciseVector creates a high precision vector from the given floating point values.
 func NewPreciseVector(x, y, z float64) PreciseVector {
 	return PreciseVector{
 		X: precFloat(x),
 		Y: precFloat(y),
 		Z: precFloat(z),
 	}
 }
 
 // Vector returns this precise vector converted to a Vector.
 func (v PreciseVector) Vector() Vector {
 	// The accuracy flag is ignored on these conversions back to float64.
 	x, _ := v.X.Float64()
 	y, _ := v.Y.Float64()
 	z, _ := v.Z.Float64()
 	return Vector{x, y, z}.Normalize()
 }
 
 // Equal reports whether v and ov are equal.
 func (v PreciseVector) Equal(ov PreciseVector) bool {
 	return v.X.Cmp(ov.X) == 0 && v.Y.Cmp(ov.Y) == 0 && v.Z.Cmp(ov.Z) == 0
 }
 
 func (v PreciseVector) String() string {
 	return fmt.Sprintf("(%10g, %10g, %10g)", v.X, v.Y, v.Z)
 }
 
 // Norm2 returns the square of the norm.
 func (v PreciseVector) Norm2() *big.Float { return v.Dot(v) }
 
 // IsUnit reports whether this vector is of unit length.
 func (v PreciseVector) IsUnit() bool {
 	return v.Norm2().Cmp(precise1) == 0
 }
 
 // Abs returns the vector with nonnegative components.
 func (v PreciseVector) Abs() PreciseVector {
 	return PreciseVector{
 		X: new(big.Float).Abs(v.X),
 		Y: new(big.Float).Abs(v.Y),
 		Z: new(big.Float).Abs(v.Z),
 	}
 }
 
 // Add returns the standard vector sum of v and ov.
 func (v PreciseVector) Add(ov PreciseVector) PreciseVector {
 	return PreciseVector{
 		X: precAdd(v.X, ov.X),
 		Y: precAdd(v.Y, ov.Y),
 		Z: precAdd(v.Z, ov.Z),
 	}
 }
 
 // Sub returns the standard vector difference of v and ov.
 func (v PreciseVector) Sub(ov PreciseVector) PreciseVector {
 	return PreciseVector{
 		X: precSub(v.X, ov.X),
 		Y: precSub(v.Y, ov.Y),
 		Z: precSub(v.Z, ov.Z),
 	}
 }
 
 // Mul returns the standard scalar product of v and f.
 func (v PreciseVector) Mul(f *big.Float) PreciseVector {
 	return PreciseVector{
 		X: precMul(v.X, f),
 		Y: precMul(v.Y, f),
 		Z: precMul(v.Z, f),
 	}
 }
 
 // MulByFloat64 returns the standard scalar product of v and f.
 func (v PreciseVector) MulByFloat64(f float64) PreciseVector {
 	return v.Mul(precFloat(f))
 }
 
 // Dot returns the standard dot product of v and ov.
 func (v PreciseVector) Dot(ov PreciseVector) *big.Float {
 	return precAdd(precMul(v.X, ov.X), precAdd(precMul(v.Y, ov.Y), precMul(v.Z, ov.Z)))
 }
 
 // Cross returns the standard cross product of v and ov.
 func (v PreciseVector) Cross(ov PreciseVector) PreciseVector {
 	return PreciseVector{
 		X: precSub(precMul(v.Y, ov.Z), precMul(v.Z, ov.Y)),
 		Y: precSub(precMul(v.Z, ov.X), precMul(v.X, ov.Z)),
 		Z: precSub(precMul(v.X, ov.Y), precMul(v.Y, ov.X)),
 	}
 }
 
 // LargestComponent returns the axis that represents the largest component in this vector.
 func (v PreciseVector) LargestComponent() Axis {
 	t := v.Abs()
 
 	if t.X.Cmp(t.Y) > 0 {
 		if t.X.Cmp(t.Z) > 0 {
 			return XAxis
 		}
 		return ZAxis
 	}
 	if t.Y.Cmp(t.Z) > 0 {
 		return YAxis
 	}
 	return ZAxis
 }
 
 // SmallestComponent returns the axis that represents the smallest component in this vector.
 func (v PreciseVector) SmallestComponent() Axis {
 	t := v.Abs()
 
 	if t.X.Cmp(t.Y) < 0 {
 		if t.X.Cmp(t.Z) < 0 {
 			return XAxis
 		}
 		return ZAxis
 	}
 	if t.Y.Cmp(t.Z) < 0 {
 		return YAxis
 	}
 	return ZAxis
 }