Curiosity

The built-in functions include round, floor, ceil, and trunc. Trunc rounds towards zero. For floats, the behavior of trunc is equivalent to the following:

float func trunc(float x)
  if x >= 0
    return floor(x)
  else
    return ceil(x)
  endif
endfunc

There is no equivalent function with < instead of >. In mathematics, I haven't even found a name for this. The best name that I could come up is "elong", a shortened version of elongate, as truncate is short for truncate.

Any comments?

I think we almost never have a need for it?

Yes, rarely, only in one of the Gaussian Integer coloring formulas or something similar.

(The email announcing your reply said that JVYV had replied.)

I think that's an effect of FPU rounding modes on x86. There are four total modes,

• to nearest
• towards zero
• downward
• upward

towards zero seems like the expected behavior of a truncation, since you'll always end up with the number before the decimal point as the result like you'd expect.

There's no actual "trunc" instruction in x87 or SSE (maybe there's a "fround" that avoids casting? I never messed with x87 much because it was a ridiculous mess) / AVX but casting to an integer and back will invoke FISTTP (SSSE3 but operating on x87 stack) / FISTP if the floating point x87 stack is in use and cause this rounding, or the SSE2 CVTTSD2SI can convert a double in a vector register or memory location to a truncated int in a GPR. I'm guessing most compilers generate that version for casts since everything that doesn't support SSE2 is effectively deprecated.

One possibility of getting this would be to just use

trunc(z) + sign(z)

Yes, good idea, except sign( ) isn't a built-in function in UF. In my version of Gaussian Integer, I've used

if x >= 0
  return ceil(x)
else
  return trunc(x)
endif