问题描述
在两个理论上相等的双精度数之间进行减法时，我应该预期哪个数量级的差异？
我有两个双精度数组。预计它们在理论上是相同的。它们都是由两种完全不同的方法计算出来的，所以它们之间有一些数值上的差异。我逐个检查了它们，我的最大差异是
6.5557799910909154E-008。我的老板说，对于双精度这是一个非常高的差异，但我认为，如果E-008的顺序如果差别，那么它的好。
谢谢，
Pradeep
具有以下格式：
具有以下格式
- 符号位：1位
- 指数宽度：8位
- 显着性和精确性：24（显式存储23）
- Sign bit: 1 bit
- Exponent width: 11 bits
- Significand precision: 53 bits (52 explicitly stored)
- Sign bit: 1 bit
- Exponent width: 8 bits
- Significand precision: 24 (23 explicitly stored)
您遇到的最大差异表示类似于转换为单精度的精度损失。 p>
你知道哪两种方法更准确吗？它是计算速度与精度之间的一个折衷，它是主要区别还是算法之一在数值上不太稳定？输入的精度是多少？如果您的输入不是那么精确，那么精度的8位小数的差值可能不相关......或者它可能意味着行星轨迹上没有火星。
What order of magnitude difference should I be expecting for a subtraction between two theoretically equal double precision numbers?
I have two double precision arrays. They are expected to be theoretically same. They are both calculated by two completely different methodologies, so there is some numerical difference between them. I checked them element by element and my maximum difference is coming out to be6.5557799910909154E-008. My boss says that for a double precision this is a very high difference, but I thought that if the difference if of the order of E-008, then its alright.
Thank you,Pradeep
Double precision floating point has the following format
Single precision floating point has the following format
The maximum difference you are encountering indicates a loss of precision akin to converting to single precision.
Do you know which of the two methods is more accurate? Is it a trade-off between speed of computation and precision that is the main difference or is one of the algorithms less numerically stable? What is the precision of the inputs? A difference of 8 decimal digits of precision may not be relevant if your inputs aren't that precise... or it could mean missing Mars on a planetary trajectory.
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