在没有条件比较的情况下以数学方式找到最大值 [英] Mathematically Find Max Value without Conditional Comparison

问题描述

----------更新了------------

到目前为止，codymanix和Moonshadow一直是一个很大的帮助.我能够使用方程式解决问题，而无需使用右移，而是除以29.因为32位有符号2 ^ 31 =溢出到29.有效！

PHP原型

$r = $x - (($x - $y) & (($x - $y) / (29)));

LEADS的实际代码(每行只能执行一个数学函数！!!! AHHHH !!!)

DERIVDE1 = IMAGE1 - IMAGE2;
DERIVED2 = DERIVED1 / 29;
DERIVED3 = DERIVED1 AND DERIVED2;
MAX = IMAGE1 - DERIVED3;

----------原始问题-----------
我认为应用程序的局限性不可能实现，但我认为值得一试.

我将尝试简化这一过程.我需要找到两个数字之间的最大值，而不能使用IF或任何条件语句.

为了找到MAX值，我只能执行以下功能

Divide, Multiply, Subtract, Add, NOT, AND ,OR

假设我有两个数字

A = 60;
B = 50;

现在，如果A始终大于B，则找到最大值很简单

MAX = (A - B) + B;
ex. 
10 = (60 - 50)
10 + 50 = 60 = MAX

问题是A并不总是大于B.我无法使用我正在使用的脚本应用程序执行ABS，MAX，MIN或条件检查.

使用上面的受限操作是否有可能找到非常接近最大值的值?

解决方案

找到最多2个变量:

max = a-((a-b)&((a-b)>>31))

其中>>是按位右移(也称为SHR或ASR依赖于签名).

您使用的位数是31，而不是31.

----------Updated ------------

codymanix and moonshadow have been a big help thus far. I was able to solve my problem using the equations and instead of using right shift I divided by 29. Because with 32bits signed 2^31 = overflows to 29. Which works!

Prototype in PHP

$r = $x - (($x - $y) & (($x - $y) / (29)));

Actual code for LEADS (you can only do one math function PER LINE!!! AHHHH!!!)

DERIVDE1 = IMAGE1 - IMAGE2;
DERIVED2 = DERIVED1 / 29;
DERIVED3 = DERIVED1 AND DERIVED2;
MAX = IMAGE1 - DERIVED3;

----------Original Question-----------
I don't think this is quite possible with my application's limitations but I figured it's worth a shot to ask.

I'll try to make this simple. I need to find the max values between two numbers without being able to use a IF or any conditional statement.

In order to find the the MAX values I can only perform the following functions

Divide, Multiply, Subtract, Add, NOT, AND ,OR

Let's say I have two numbers

A = 60;
B = 50;

Now if A is always greater than B it would be simple to find the max value

MAX = (A - B) + B;
ex. 
10 = (60 - 50)
10 + 50 = 60 = MAX

Problem is A is not always greater than B. I cannot perform ABS, MAX, MIN or conditional checks with the scripting applicaiton I am using.

Is there any way possible using the limited operation above to find a value VERY close to the max?

解决方案

finding the maximum of 2 variables:

max = a-((a-b)&((a-b)>>31))

where >> is bitwise right-shift (also called SHR or ASR depeding on signedness).

Instead of 31 you use the number of bits your numbers have minus one.

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