7高效的方式乘 [英] Multiply by 7 in efficient way
问题描述
最近，我遇到了以下面试问题：
I recently encountered the following interview question:
你怎么能由7以高效，优化的方式繁衍多少？
How can you multiply a number by 7 in an efficient and optimized way?
我知道，我可以通过8（或左移三个位）相乘，然后减去原始值：
I know that I can multiply by 8 (or left-shift by three bits) and then subtract the original value:
num = (num << 3) - num;
但是否有任何其他的解决方案。
but are there any other solutions.
推荐答案
要获得7的倍数以有效的方式：
To get a multiple of 7 in an efficient way:
7
7的7，回答你问的问题多，但我敢肯定它不会回答你的意思是问的问题。
7 is a multiple of 7. That answers the question you asked, but I'm sure it doesn't answer the question you mean to ask.
的编辑：以上是根据问题的原题，我刚刚修正的
要乘的按的7高效，只写，例如：
To multiply by 7 efficiently, just write, for example:
x * 7
和调用与优化的编译器。让编译器弄清楚是否一个MUL指令或类似的东西（X＆LT;＆LT; 3） - X 更有效的当前计算机的。
and invoke your compiler with optimization. Let the compiler figure out whether a single MUL instruction or something like (x<<3) - x is more efficient for the current machine.
还有另一个隐含的问题在这里：什么答案面试官想要？我的希望的说：让这件事编译器无忧将是一个可以接受的答案。 （X＆LT;＆LT; 3） - X 可能是最明显的微型优化 - 但它可以产生不正确的答案，如果
There's yet another implicit question here: what answer was the interviewer looking for? I hope that "let the compiler worry about it" would be an acceptable answer. (x<<3) - x is probably the most obvious micro-optimization -- but it can yield incorrect answers if x<<3 overflows, and depending on the system it might be slower than a MUL instruction.
（如果我是面试官，我会用的问题比任何具体的答案一个很好的解释和理解pssed更多IM $ P $）。
(If I were the interviewer, I'd be more impressed by a good explanation and understanding of the issues than by any specific answer.)
修改
在进一步的思考，已经在这里讨论的各种微型优化的可能的，如果你知道更多关于 X 比编译器。如果你知道，因为你的程序逻辑的性质，即 X 将永远范围0..10，然后查找表可以很容易地比乘快操作。或者，如果你知道 X 中的时间范围的99％，也可能降低为一个实际的乘法查找表可能只是事情。
On further thought, the kinds of micro-optimizations that have been discussed here might be useful if you know more about the possible values of x than the compiler does. If you know, because of the nature of your program's logic, that x will always be in the range 0..10, then a lookup table could easily be faster than a multiply operation. Or if you know that x is in that range 99% of the time, a lookup table with a fallback to an actual multiplication might be just the thing.
但是，如果你的程序流程的编译器的分析并没有允许它的证明的是 X 总是在这个范围内，那么它可以'T执行这种优化。
But if the compiler's analysis of your program flow doesn't allow it to prove that x is always in that range, then it can't perform this kind of optimization.
不过，这样的情况下是非常罕见的。当你的code在一个新的环境中运行，其中 X 可以是11（也许这是一个更大的显示设备上运行）的 KABOOM 。和性能的改善很可能是不首先显著
But such circumstances are very rare. And when your code runs in a new environment where x can be 11 (perhaps it's running on a device with a larger display), kaboom. And the performance improvement very likely wasn't significant in the first place.
有时候微优化是合适的，但在开发和测试时间大幅成本。做到这一点只有在实际的测量的指示，这是值得的。
There are times when micro-optimization is appropriate, but there is a substantial cost in development and testing time. Do it only if actual measurements indicate that it's worth it.
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