在计算机程序设计艺术中approximatelyEqual和essentiallyEqual差异 [英] Difference among approximatelyEqual and essentiallyEqual in The art of computer programming

问题描述

我得到这个code段从一些别的地方。据站长，在code从<拾取href="http://books.google.ca/books?ei=KRkLSYLZEJ7ktQOX3-ChBQ&id=T89QAAAAMAAJ&dq=%22essentially+equal%22+%22approximately+equal%22+knuth&q=%22essentially+equal%22+%22approximately+equal%22+%22definitely+less+than%22&pgis=1#search"相对=nofollow>计算机编程由克努特

由于我没有这本书的副本，可我知道什么是两个功能之间的区别是什么？

 布尔approximatelyEqual（浮起，浮动B，浮动小量）
{
    返回晶圆厂（A  -  B）＆LT; =（（晶圆厂（一）LT;晶圆厂（二）晶圆厂（二）：晶圆厂（一））*小量？）;
}

布尔essentiallyEqual（浮起，浮动B，浮动小量）
{
    返回晶圆厂（A  -  B）＆LT; =（（晶圆厂（一）＆GT;晶圆厂（二）晶圆厂（二）：晶圆厂（一））*小量？）;
}
 

解决方案

要举一个例子：

 双A = 95.1，B = 100.0;
断言（approximatelyEqual（A，B，0.05））;
断言（essentiallyEqual（A，B，0.05）！）;
 

即，小量为5％，95.1是约100，因为它落在100值（最大）的5％的范围之内。另一方面，95.1没有本质100中，100是不从95.1 5％的差异（最小值）内。

I get this code snippet from some where else. According to the webmaster, the code is picked from The art of computer programming by Knuth

Since I do not have a copy of that book, may I know what is the difference among the two functions?

bool approximatelyEqual(float a, float b, float epsilon)
{
    return fabs(a - b) <= ( (fabs(a) < fabs(b) ? fabs(b) : fabs(a)) * epsilon);
}

bool essentiallyEqual(float a, float b, float epsilon)
{
    return fabs(a - b) <= ( (fabs(a) > fabs(b) ? fabs(b) : fabs(a)) * epsilon);
}

解决方案

To give an example:

double a = 95.1, b = 100.0;
assert( approximatelyEqual( a, b, 0.05 ) );
assert( !essentiallyEqual( a, b, 0.05 ) );

That is, with epsilon being a 5%, 95.1 is approximately 100, as it falls within the 5% margin of the 100 value (biggest). On the other hand, 95.1 is not essentially 100, as 100 is not within a 5% difference from 95.1 (smallest value).

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