New blog post: Degenerate Conic | Sign, Sign, Everywhere a Sign
I think there was a comment here in this forum somewhere (which i can no longer find) about how the sign() function arguments are confusing. So, don’t feel bad, even the giants of the 1980s apparently were also confused. 
Also curious if anyone here ever actually used ALGOL. I’ve only seen it in old books and papers. I didn’t realize that Backus was also one of its creators.
The Fortran definition of SIGN pre-dates the ALGOL-60 definition, though it was called SIGNF in early Fortrans. ALGOL probably should have called theirs “signum”.
C has a similar function, but with a better name:
#include <math.h>
double copysign(double x, double y);
The copysign functions produce a value with the magnitude of x and the sign of y. If x or y is an unsigned value, the sign (if any) of the result is implementation-defined. On implementations that represent a signed zero but do not treat negative zero consistently in arithmetic operations, the copysign functions should regard the sign of zero as positive.
(C2023 standard)