浮点累加顺序：为什么同一份数据算两次不一样
What Every Computer Scientist Should Know About Floating-Point Arithmetic
David Goldberg · 1991
Foundation paper · permanent
1991
同一组数、同一个公式，换一个求和顺序，结果为什么会差？
What they did从舍入误差与结合律失效讲起，给出误差界与数值稳定算法的构造方法。
Evidence经典综述，结论可直接在小规模实验中复现。
Do not over-trust财务模型里 10 万行的累加误差可能吃掉两位小数；对账差异常被误判为“业务问题”。
Limits非新研究，但常被忽略；Kahan 求和等技巧有性能代价。
In-class task用三种求和顺序算同一份现金流 NPV，量化差异并给出可接受的对账阈值。
A foundation paper is the landmark work for a method and stays permanently: it explains why the method works, and is never replaced for being old.
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