问题
What is the purpose of the std::remquo function? What is an example of when you would use it instead of the regular std::remainder function?
回答1:
remquo first appeared in C99 before being in C++ and here is what the C99 rationale says about it:
The remquo functions are intended for implementing argument reductions which can exploit a few low-order bits of the quotient. Note that x may be so large in magnitude relative to y that an exact representation of the quotient is not practical.
回答2:
Suppose I am implementing a sine function. A typical way to implement sine is to design some polynomial s such that s(x) approximates sine of x, but the polynomial is only good for -π/4 <= x <= π/4. Outside of that interval, the polynomial deviates from sine(x) and is a bad approximation. (Making the polynomial good over a larger interval requires a polynomial with more terms, and, at some point, the polynomial becomes larger than is useful.) Commonly, we would also design a polynomial c such that c(x) approximates the cosine of x, in a similar interval.
The remquo function helps us use these polynomials to implement sine. We can use “r = remquo(x, pi/2, &q)” and use q to determine which portion of the circle x is in. (Note that sine is periodic with period 2π, so we only need to know the low few bits of the quotient. The higher bits just indicate x has wrapped around the circle and is repeating sine values.) Depending on which part of the circle x is in, the routine will return s(r), -s(r), c(r), or -c(r) for the sine of x.
There are embellishments, of course, but that is the basic idea. It only works for values of x that are small, not more than a few multiples of 2π. That is because each time x doubles, another bit of the divisor moves into the calculation of the exact result. However, we cannot pass π/2 exactly to remquo, because the precision of the double type is limited. So, as x grows, the error grows.
来源：https://stackoverflow.com/questions/11074865/stdremquo-purpose-and-usage