411 lines
11 KiB
Go
411 lines
11 KiB
Go
// Copyright 2015 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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// Package fixed implements fixed-point integer types.
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package fixed // import "golang.org/x/image/math/fixed"
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import (
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"fmt"
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)
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// TODO: implement fmt.Formatter for %f and %g.
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// I returns the integer value i as an Int26_6.
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//
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// For example, passing the integer value 2 yields Int26_6(128).
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func I(i int) Int26_6 {
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return Int26_6(i << 6)
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}
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// Int26_6 is a signed 26.6 fixed-point number.
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//
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// The integer part ranges from -33554432 to 33554431, inclusive. The
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// fractional part has 6 bits of precision.
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//
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// For example, the number one-and-a-quarter is Int26_6(1<<6 + 1<<4).
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type Int26_6 int32
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// String returns a human-readable representation of a 26.6 fixed-point number.
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//
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// For example, the number one-and-a-quarter becomes "1:16".
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func (x Int26_6) String() string {
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const shift, mask = 6, 1<<6 - 1
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if x >= 0 {
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return fmt.Sprintf("%d:%02d", int32(x>>shift), int32(x&mask))
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}
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x = -x
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if x >= 0 {
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return fmt.Sprintf("-%d:%02d", int32(x>>shift), int32(x&mask))
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}
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return "-33554432:00" // The minimum value is -(1<<25).
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}
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// Floor returns the greatest integer value less than or equal to x.
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//
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// Its return type is int, not Int26_6.
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func (x Int26_6) Floor() int { return int((x + 0x00) >> 6) }
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// Round returns the nearest integer value to x. Ties are rounded up.
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//
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// Its return type is int, not Int26_6.
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func (x Int26_6) Round() int { return int((x + 0x20) >> 6) }
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// Ceil returns the least integer value greater than or equal to x.
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//
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// Its return type is int, not Int26_6.
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func (x Int26_6) Ceil() int { return int((x + 0x3f) >> 6) }
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// Mul returns x*y in 26.6 fixed-point arithmetic.
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func (x Int26_6) Mul(y Int26_6) Int26_6 {
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return Int26_6((int64(x)*int64(y) + 1<<5) >> 6)
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}
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// Int52_12 is a signed 52.12 fixed-point number.
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//
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// The integer part ranges from -2251799813685248 to 2251799813685247,
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// inclusive. The fractional part has 12 bits of precision.
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//
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// For example, the number one-and-a-quarter is Int52_12(1<<12 + 1<<10).
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type Int52_12 int64
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// String returns a human-readable representation of a 52.12 fixed-point
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// number.
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//
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// For example, the number one-and-a-quarter becomes "1:1024".
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func (x Int52_12) String() string {
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const shift, mask = 12, 1<<12 - 1
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if x >= 0 {
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return fmt.Sprintf("%d:%04d", int64(x>>shift), int64(x&mask))
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}
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x = -x
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if x >= 0 {
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return fmt.Sprintf("-%d:%04d", int64(x>>shift), int64(x&mask))
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}
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return "-2251799813685248:0000" // The minimum value is -(1<<51).
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}
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// Floor returns the greatest integer value less than or equal to x.
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//
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// Its return type is int, not Int52_12.
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func (x Int52_12) Floor() int { return int((x + 0x000) >> 12) }
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// Round returns the nearest integer value to x. Ties are rounded up.
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//
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// Its return type is int, not Int52_12.
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func (x Int52_12) Round() int { return int((x + 0x800) >> 12) }
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// Ceil returns the least integer value greater than or equal to x.
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//
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// Its return type is int, not Int52_12.
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func (x Int52_12) Ceil() int { return int((x + 0xfff) >> 12) }
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// Mul returns x*y in 52.12 fixed-point arithmetic.
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func (x Int52_12) Mul(y Int52_12) Int52_12 {
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const M, N = 52, 12
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lo, hi := muli64(int64(x), int64(y))
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ret := Int52_12(hi<<M | lo>>N)
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ret += Int52_12((lo >> (N - 1)) & 1) // Round to nearest, instead of rounding down.
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return ret
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}
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// muli64 multiplies two int64 values, returning the 128-bit signed integer
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// result as two uint64 values.
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//
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// This implementation is similar to $GOROOT/src/runtime/softfloat64.go's mullu
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// function, which is in turn adapted from Hacker's Delight.
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func muli64(u, v int64) (lo, hi uint64) {
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const (
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s = 32
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mask = 1<<s - 1
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)
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u1 := uint64(u >> s)
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u0 := uint64(u & mask)
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v1 := uint64(v >> s)
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v0 := uint64(v & mask)
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w0 := u0 * v0
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t := u1*v0 + w0>>s
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w1 := t & mask
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w2 := uint64(int64(t) >> s)
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w1 += u0 * v1
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return uint64(u) * uint64(v), u1*v1 + w2 + uint64(int64(w1)>>s)
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}
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// P returns the integer values x and y as a Point26_6.
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//
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// For example, passing the integer values (2, -3) yields Point26_6{128, -192}.
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func P(x, y int) Point26_6 {
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return Point26_6{Int26_6(x << 6), Int26_6(y << 6)}
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}
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// Point26_6 is a 26.6 fixed-point coordinate pair.
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//
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// It is analogous to the image.Point type in the standard library.
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type Point26_6 struct {
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X, Y Int26_6
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}
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// Add returns the vector p+q.
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func (p Point26_6) Add(q Point26_6) Point26_6 {
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return Point26_6{p.X + q.X, p.Y + q.Y}
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}
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// Sub returns the vector p-q.
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func (p Point26_6) Sub(q Point26_6) Point26_6 {
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return Point26_6{p.X - q.X, p.Y - q.Y}
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}
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// Mul returns the vector p*k.
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func (p Point26_6) Mul(k Int26_6) Point26_6 {
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return Point26_6{p.X * k / 64, p.Y * k / 64}
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}
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// Div returns the vector p/k.
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func (p Point26_6) Div(k Int26_6) Point26_6 {
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return Point26_6{p.X * 64 / k, p.Y * 64 / k}
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}
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// In returns whether p is in r.
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func (p Point26_6) In(r Rectangle26_6) bool {
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return r.Min.X <= p.X && p.X < r.Max.X && r.Min.Y <= p.Y && p.Y < r.Max.Y
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}
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// Point52_12 is a 52.12 fixed-point coordinate pair.
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//
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// It is analogous to the image.Point type in the standard library.
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type Point52_12 struct {
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X, Y Int52_12
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}
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// Add returns the vector p+q.
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func (p Point52_12) Add(q Point52_12) Point52_12 {
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return Point52_12{p.X + q.X, p.Y + q.Y}
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}
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// Sub returns the vector p-q.
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func (p Point52_12) Sub(q Point52_12) Point52_12 {
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return Point52_12{p.X - q.X, p.Y - q.Y}
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}
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// Mul returns the vector p*k.
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func (p Point52_12) Mul(k Int52_12) Point52_12 {
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return Point52_12{p.X * k / 4096, p.Y * k / 4096}
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}
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// Div returns the vector p/k.
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func (p Point52_12) Div(k Int52_12) Point52_12 {
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return Point52_12{p.X * 4096 / k, p.Y * 4096 / k}
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}
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// In returns whether p is in r.
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func (p Point52_12) In(r Rectangle52_12) bool {
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return r.Min.X <= p.X && p.X < r.Max.X && r.Min.Y <= p.Y && p.Y < r.Max.Y
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}
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// R returns the integer values minX, minY, maxX, maxY as a Rectangle26_6.
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//
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// For example, passing the integer values (0, 1, 2, 3) yields
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// Rectangle26_6{Point26_6{0, 64}, Point26_6{128, 192}}.
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//
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// Like the image.Rect function in the standard library, the returned rectangle
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// has minimum and maximum coordinates swapped if necessary so that it is
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// well-formed.
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func R(minX, minY, maxX, maxY int) Rectangle26_6 {
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if minX > maxX {
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minX, maxX = maxX, minX
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}
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if minY > maxY {
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minY, maxY = maxY, minY
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}
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return Rectangle26_6{
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Point26_6{
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Int26_6(minX << 6),
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Int26_6(minY << 6),
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},
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Point26_6{
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Int26_6(maxX << 6),
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Int26_6(maxY << 6),
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},
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}
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}
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// Rectangle26_6 is a 26.6 fixed-point coordinate rectangle. The Min bound is
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// inclusive and the Max bound is exclusive. It is well-formed if Min.X <=
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// Max.X and likewise for Y.
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//
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// It is analogous to the image.Rectangle type in the standard library.
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type Rectangle26_6 struct {
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Min, Max Point26_6
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}
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// Add returns the rectangle r translated by p.
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func (r Rectangle26_6) Add(p Point26_6) Rectangle26_6 {
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return Rectangle26_6{
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Point26_6{r.Min.X + p.X, r.Min.Y + p.Y},
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Point26_6{r.Max.X + p.X, r.Max.Y + p.Y},
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}
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}
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// Sub returns the rectangle r translated by -p.
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func (r Rectangle26_6) Sub(p Point26_6) Rectangle26_6 {
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return Rectangle26_6{
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Point26_6{r.Min.X - p.X, r.Min.Y - p.Y},
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Point26_6{r.Max.X - p.X, r.Max.Y - p.Y},
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}
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}
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// Intersect returns the largest rectangle contained by both r and s. If the
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// two rectangles do not overlap then the zero rectangle will be returned.
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func (r Rectangle26_6) Intersect(s Rectangle26_6) Rectangle26_6 {
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if r.Min.X < s.Min.X {
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r.Min.X = s.Min.X
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}
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if r.Min.Y < s.Min.Y {
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r.Min.Y = s.Min.Y
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}
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if r.Max.X > s.Max.X {
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r.Max.X = s.Max.X
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}
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if r.Max.Y > s.Max.Y {
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r.Max.Y = s.Max.Y
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}
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// Letting r0 and s0 be the values of r and s at the time that the method
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// is called, this next line is equivalent to:
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//
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// if max(r0.Min.X, s0.Min.X) >= min(r0.Max.X, s0.Max.X) || likewiseForY { etc }
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if r.Empty() {
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return Rectangle26_6{}
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}
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return r
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}
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// Union returns the smallest rectangle that contains both r and s.
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func (r Rectangle26_6) Union(s Rectangle26_6) Rectangle26_6 {
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if r.Empty() {
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return s
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}
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if s.Empty() {
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return r
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}
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if r.Min.X > s.Min.X {
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r.Min.X = s.Min.X
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}
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if r.Min.Y > s.Min.Y {
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r.Min.Y = s.Min.Y
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}
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if r.Max.X < s.Max.X {
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r.Max.X = s.Max.X
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}
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if r.Max.Y < s.Max.Y {
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r.Max.Y = s.Max.Y
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}
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return r
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}
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// Empty returns whether the rectangle contains no points.
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func (r Rectangle26_6) Empty() bool {
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return r.Min.X >= r.Max.X || r.Min.Y >= r.Max.Y
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}
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// In returns whether every point in r is in s.
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func (r Rectangle26_6) In(s Rectangle26_6) bool {
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if r.Empty() {
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return true
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}
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// Note that r.Max is an exclusive bound for r, so that r.In(s)
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// does not require that r.Max.In(s).
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return s.Min.X <= r.Min.X && r.Max.X <= s.Max.X &&
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s.Min.Y <= r.Min.Y && r.Max.Y <= s.Max.Y
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}
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// Rectangle52_12 is a 52.12 fixed-point coordinate rectangle. The Min bound is
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// inclusive and the Max bound is exclusive. It is well-formed if Min.X <=
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// Max.X and likewise for Y.
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//
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// It is analogous to the image.Rectangle type in the standard library.
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type Rectangle52_12 struct {
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Min, Max Point52_12
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}
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// Add returns the rectangle r translated by p.
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func (r Rectangle52_12) Add(p Point52_12) Rectangle52_12 {
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return Rectangle52_12{
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Point52_12{r.Min.X + p.X, r.Min.Y + p.Y},
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Point52_12{r.Max.X + p.X, r.Max.Y + p.Y},
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}
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}
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// Sub returns the rectangle r translated by -p.
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func (r Rectangle52_12) Sub(p Point52_12) Rectangle52_12 {
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return Rectangle52_12{
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Point52_12{r.Min.X - p.X, r.Min.Y - p.Y},
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Point52_12{r.Max.X - p.X, r.Max.Y - p.Y},
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}
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}
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// Intersect returns the largest rectangle contained by both r and s. If the
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// two rectangles do not overlap then the zero rectangle will be returned.
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func (r Rectangle52_12) Intersect(s Rectangle52_12) Rectangle52_12 {
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if r.Min.X < s.Min.X {
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r.Min.X = s.Min.X
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}
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if r.Min.Y < s.Min.Y {
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r.Min.Y = s.Min.Y
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}
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if r.Max.X > s.Max.X {
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r.Max.X = s.Max.X
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}
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if r.Max.Y > s.Max.Y {
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r.Max.Y = s.Max.Y
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}
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// Letting r0 and s0 be the values of r and s at the time that the method
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// is called, this next line is equivalent to:
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//
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// if max(r0.Min.X, s0.Min.X) >= min(r0.Max.X, s0.Max.X) || likewiseForY { etc }
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if r.Empty() {
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return Rectangle52_12{}
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}
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return r
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}
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// Union returns the smallest rectangle that contains both r and s.
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func (r Rectangle52_12) Union(s Rectangle52_12) Rectangle52_12 {
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if r.Empty() {
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return s
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}
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if s.Empty() {
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return r
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}
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if r.Min.X > s.Min.X {
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r.Min.X = s.Min.X
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}
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if r.Min.Y > s.Min.Y {
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r.Min.Y = s.Min.Y
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}
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if r.Max.X < s.Max.X {
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r.Max.X = s.Max.X
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}
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if r.Max.Y < s.Max.Y {
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r.Max.Y = s.Max.Y
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}
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return r
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}
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// Empty returns whether the rectangle contains no points.
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func (r Rectangle52_12) Empty() bool {
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return r.Min.X >= r.Max.X || r.Min.Y >= r.Max.Y
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}
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// In returns whether every point in r is in s.
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func (r Rectangle52_12) In(s Rectangle52_12) bool {
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if r.Empty() {
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return true
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}
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// Note that r.Max is an exclusive bound for r, so that r.In(s)
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// does not require that r.Max.In(s).
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return s.Min.X <= r.Min.X && r.Max.X <= s.Max.X &&
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s.Min.Y <= r.Min.Y && r.Max.Y <= s.Max.Y
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}
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