floating-point - Is this a visual representation of round-off errors in IEEE math

Question

In Wolfram Alpha:

plot -EXP(t)/2 LN((EXP(t)-1)/(EXP(t)+1)) from t=0 to t=40

Is this how round off errors appear in solutions when subtraction operand orders of magnitude differ more than 2^24 (32-bit float) ?

Link: Equation Plot

Link: What Every Computer Scientist Should Know About Floating-Point Arithmetic

Answer 1

基本上，是的，尽管减法隐藏在计算中，并且数据类型是双精度数，而不是浮点数。

对于大t，(exp(t)-1)/(exp(t)+1)本质上是1 - 2exp(-t)，其对数非常接近-2exp(-t)。但是，因为2exp(-t)与 相比是如此之小1，所以大多数精度位都会在传递给对数的值中丢失，这会导致您观察到的所有噪声。