IEEE(3) BSD Programmer's Manual IEEE(3)
copysign, drem, finite, logb, scalb - IEEE 754 floating point support
copysign(double x, double y);
drem(double x, double y);
scalb(double x, int n);
These functions are required for, or recommended by the IEEE standard 754
for floating-point arithmetic.
The copysign() function returns x with its sign changed to y's.
The drem() function returns the remainder r := x - n*y where n is the in-
teger nearest the exact value of x/y; moreover if |n - x/y| = 1/2 then n
is even. Consequently the remainder is computed exactly and |r| <=
|y|/2. But drem(x, 0) is exceptional. (See below under DIAGNOSTICS.)
The finite() function returns the value 1 just when -infinity < x < +in-
finity; otherwise a zero is returned (when |x| = infinity or x is NaN or
is the VAX's reserved operand).
The logb() function returns x's exponent n, a signed integer converted to
double-precision floating-point and so chosen that 1 (<= |x|2**n < 2 un-
less x = 0 or (only on machines that conform to IEEE 754) |x| = infinity
or x lies between 0 and the Underflow Threshold. (See below under BUGS.)
The scalb() function returns x*(2**n) computed, for integer n, without
first computing 2*n.
The IEEE standard 754 defines drem(x, 0) and drem(infinity, y) to be in-
valid operations that produce a NaN. On the VAX, drem(x, 0) generates a
reserved operand fault. No infinity exists on a VAX.
IEEE 754 defines logb(+-infinity) = infinity and logb(0) = -infinity, and
requires the latter to signal Division-by-Zero. But on a VAX, logb(0) =
1.0 - 2.0**31 = -2,147,483,647.0. And if the correct value of scalb()
would overflow on a VAX, it generates a reserved operand fault and sets
the global variable errno to ERANGE.
floor(3), math(3), infnan(3)
The ieee functions appeared in 4.3BSD.
Should drem(x, 0) and logb(0) on a VAX signal invalidity by setting errno
= EDOM ? Should logb(0) return -1.7e38?
IEEE 754 currently specifies that logb(denormalized no.) = logb(tiniest
normalized no. > 0) but the consensus has changed to the specification in
the new proposed IEEE standard p854, namely that logb(x) satisfy
1 <= scalb(|x|, -logb(x)) < Radix ... = 2 for IEEE 754
for every x except 0, infinity and NaN. Almost every program that as-
sumes 754's specification will work correctly if logb() follows 854's
IEEE 754 requires copysign(x, NaN)) = +-x but says nothing else about the
sign of a NaN. A NaN (Not a Number) is similar in spirit to the VAX's
reserved operand, but very different in important details. Since the
sign bit of a reserved operand makes it look negative,
copysign(x, reserved operand) = -x;
should this return the reserved operand instead?
4.3 Berkeley Distribution June 4, 1993 2