更快地转换1D->；使用2维幂的3D

我正在尝试优化对3D环境数据的访问和更改，因为有些操作必须执行数百万次。目前，我有以下优化：

• 使用平面阵列（1D）
• 尺寸单位为2的幂
• 在可能的情况下进行位移位，而不是乘法/除法

三维矢量的索引如下所示：

• X向量的变化将使指数增加/减少1
• Y向量的更改将使索引增加/减少3DEnvironmentSize.X
• Z向量的更改将使索引增加/减少3DEnvironmentSize.X*3DEnvironmentSize.Y

给定以下伪代码：

mapSize.X = 4
mapSize.Y = 4
mapSize.Z = 2

Xdif = 1
Ydif = mapSize.X = 4
Zdif = mapSize.X * mapSize.Y = 16

Xexponent = log2(Xdif) = log2(1) = 0 (2^0 = 1 = Xdif)
Yexponent = log2(Ydif) = log2(4) = 2 (2^2 = 4 = Ydif)
Zexponent = log2(Zdif) = log2(16) = 4 (2^4 = 16 = Zdif)

可以使用以下公式从3D->1D给定向量（1,2,1）开始：

location.X = 1
location.Y = 2
location.Z = 1

shiftIndex.X = location.X << Xexponent = 1 << 0 = 1
shiftIndex.Y = location.Y << YExponent = 2 << 2 = 8
shiftIndex.Z = location.Z << Zexponent = 1 << 4 = 16

index = shiftIndex.X + shiftIndex.Y + shiftIndex.Z = 1 + 8 + 16 = 25

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有没有任何方法可以利用位移位（或其他相关的方法）来加快速度？我已经试着处理这个问题有一段时间了，但如果一开始可能的话，我无法破解它。

你只是想把3个数字打包成一个更大的数字吗

如果是这样的话，你为什么不换个面具呢

ThreeToOne(v3) -> v3.x | (v3.y << 8 ) | (v3.z << 16)

OneToThree(v) -> v3(v & 0xFF, v >> 8 & 0xFF, v >> 16 & 0xFF)

ThreeToOne（v3）->v3.x（v3.y>8&0xFF，v>>16&0xFF）

我在别处得到了答案

当你除以一个2次幂的数字时，你可以用一个2次幂指数的右移运算来代替这个除法。 模运算可以用位and运算符和n-1替换（如果是2的幂次运算，则再次替换）。其中n是您潜水时使用的数字。 因此，总结该准则：

mapSize.X = 4
mapSize.Y = 4
mapSize.Z = 2

Xdif = 1
Ydif = mapSize.X = 4
Zdif = mapSize.X * mapSize.Y = 16

XDifExponent = log2(Xdif) = log2(1) = 0 (2^0 = 1 = Xdif)
YDifExponent = log2(Ydif) = log2(4) = 2 (2^2 = 4 = Ydif)
ZDifExponent = log2(Zdif) = log2(16) = 4 (2^4 = 16 = Zdif)

XSizeExponent = log2(mapSize.X) = log2(4) = 2 (2^2 = 4 = mapSize.X)
YSizeExponent = log2(mapSize.Y) = log2(4) = 2 (2^2 = 4 = mapSize.Y)
ZSizeExponent = log2(mapSize.Z) = log2(2) = 1 (2^1 = 2 = mapSize.Z)

Vector3D -> Index example:
location.X = 1
location.Y = 2
location.Z = 1

shiftIndex.X = location.X << XDifExponent = 1 << 0 = 1
shiftIndex.Y = location.Y << YDifExponent = 2 << 2 = 8
shiftIndex.Z = location.Z << ZDifExponent = 1 << 4 = 16

index = shiftIndex.X + shiftIndex.Y + shiftIndex.Z = 1 + 8 + 16 = 25

Index -> Vector3D example:
index = 30

location.X = index & (mapSize.X - 1) = 2
location.Y = (index >> XSizeExponent) & (mapSize.Y - 1) = 3
location.Z = ((index >> XSizeExponent) >> YSizeExponent) & (mapSize.Z - 1) = 1

mapSize.X=4
mapSize.Y=4
mapSize.Z=2
Xdif=1
Ydif=mapSize.X=4
Zdif=mapSize.X*mapSize.Y=16
XDifExponent=log2（Xdif）=log2（1）=0（2^0=1=Xdif）
YDifExponent=log2（Ydif）=log2（4）=2（2^2=4=Ydif）
Zdif指数=log2（Zdif）=log2（16）=4（2^4=16=Zdif）
XSizeExponent=log2（mapSize.X）=log2（4）=2（2^2=4=mapSize.X）
YSizeExponent=log2（mapSize.Y）=log2（4）=2（2^2=4=mapSize.Y）
ZSizeExponent=log2（mapSize.Z）=log2（2）=1（2^1=2=mapSize.Z）
Vector3D->索引示例：
位置X=1
位置Y=2
位置Z=1
shiftIndex.X=location.X>ysizeindex）和（mapSize.Z-1）=1

感谢您的回答，但不，我正在尝试更快地访问数组中的元素。但是，使用1D数组的缺点是需要根据索引计算坐标。我正在尝试优化完成这项工作的方式（使之尽可能快）。

mapSize.X = 4
mapSize.Y = 4
mapSize.Z = 2

Xdif = 1
Ydif = mapSize.X = 4
Zdif = mapSize.X * mapSize.Y = 16

XDifExponent = log2(Xdif) = log2(1) = 0 (2^0 = 1 = Xdif)
YDifExponent = log2(Ydif) = log2(4) = 2 (2^2 = 4 = Ydif)
ZDifExponent = log2(Zdif) = log2(16) = 4 (2^4 = 16 = Zdif)

XSizeExponent = log2(mapSize.X) = log2(4) = 2 (2^2 = 4 = mapSize.X)
YSizeExponent = log2(mapSize.Y) = log2(4) = 2 (2^2 = 4 = mapSize.Y)
ZSizeExponent = log2(mapSize.Z) = log2(2) = 1 (2^1 = 2 = mapSize.Z)

Vector3D -> Index example:
location.X = 1
location.Y = 2
location.Z = 1

shiftIndex.X = location.X << XDifExponent = 1 << 0 = 1
shiftIndex.Y = location.Y << YDifExponent = 2 << 2 = 8
shiftIndex.Z = location.Z << ZDifExponent = 1 << 4 = 16

index = shiftIndex.X + shiftIndex.Y + shiftIndex.Z = 1 + 8 + 16 = 25

Index -> Vector3D example:
index = 30

location.X = index & (mapSize.X - 1) = 2
location.Y = (index >> XSizeExponent) & (mapSize.Y - 1) = 3
location.Z = ((index >> XSizeExponent) >> YSizeExponent) & (mapSize.Z - 1) = 1