copysign, drem, finite, logb, scalb - copysign, remainder, exponent manipulations
These functions are required for, or recommended by the IEEE standard 754 for floating-point arithmetic.
Copysign(x,y) returns x with its sign changed to y's.
Drem(x,y) returns the remainder r := x - n*y where n is the integer 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.
Finite(x) = 1 just when -infinity < x < +infinity,
= 0 otherwise (when |x| = infinity or x is NaN or
x is the VAX's reserved operand.)
Logb(x) returns x's exponent n, a signed integer converted to double-precision floating-point and so chosen that 1 <= |x|/2**n < 2 unless 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".
Scalb(x,n) = x*(2**n) computed, for integer n, without first computing 2**n.
IEEE 754 defines drem(x,0) and drem(infinity,y) to be invalid operations that produce a NaN. On a VAX, drem(x,0) returns the reserved op-
erand. No infinity exists on a VAX.
IEEE 754 defines logb(+-infinity) = +infinity and logb(0) = -infinity, 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(x,n) would overflow on a VAX, it returns the reserved oper-
and and sets errno to ERANGE.
floor(3M), math(3M), infnan(3M)
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 specifica-
tion 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 assumes 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 May 12, 1986 IEEE(3M)