Y

#### Yousuf Khan

compatibility requirements from one generation to the next. The fix for

this problem was figured out quite a long time ago. In the excellent

paper The K5 transcendental functions by T. Lynch, A. Ahmed, M. Schulte,

T. Callaway, and R. Tisdale a technique is described for doing argument

reduction as if you had an infinitely precise value for pi. As far as I

know, the K5 is the only x86 family CPU that did sin/cos accurately. AMD

went back to being bit-for-bit compatibile with the old x87 behavior,

assumably because too many applications broke. Oddly enough, this is

fixed in Itanium.

What we do in the JVM on x86 is moderately obvious: we range check the

argument, and if it's outside the range [-pi/4, pi/4]we do the precise

range reduction by hand, and then call fsin.

So Java is accurate, but slower. I've never been a fan of "fast, but

wrong" when "wrong" is roughly random(). Benchmarks rarely test

accuracy. "double sin(double theta) { return 0; }" would be a great

benchmark-compatible implementation of sin(). For large values of theta,

0 would be arguably more accurate since the absolute error is never

greater than 1. fsin/fcos can have absolute errors as large as 2

(correct answer=1; returned result=-1). "

https://blogs.oracle.com/jag/entry/transcendental_meditation