.\" Copyright (c) 1985 Regents of the University of California. .\" All rights reserved. The Berkeley software License Agreement .\" specifies the terms and conditions for redistribution. .\" .\" @(#)ieee.3m 6.2 (Berkeley) 5/12/86 .\" .TH IEEE 3M "May 12, 1986" .UC 6 .ds nn \fINaN\fR .SH NAME copysign, drem, finite, logb, scalb \- copysign, remainder, exponent manipulations .SH SYNOPSIS .nf .B #include <math.h> .PP .B double copysign(x,y) .B double x,y; .PP .B double drem(x,y) .B double x,y; .PP .B int finite(x) .B double x; .PP .B double logb(x) .B double x; .PP .B double scalb(x,n) .B double x; .B int n; .fi .SH DESCRIPTION These functions are required for, or recommended by the IEEE standard 754 for floating\-point arithmetic. .PP Copysign(x,y) returns x with its sign changed to y's. .PP 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. .PP .nf .ta \w'Finite(x)'u+1n +\w'= 0 otherwise'u+1n .if n \ Finite(x) = 1 just when \-infinity < x < +infinity, .if t \ Finite(x) = 1 just when \-\(if < x < +\(if, .if n \ = 0 otherwise (when |x| = infinity or x is \*(nn or .if t \ = 0 otherwise (when |x| = \(if or x is \*(nn or \0x is the VAX's reserved operand.) .ta .fi .PP Logb(x) returns x's exponent n, a signed integer converted to double\-precision floating\-point and so chosen that 1\0\(<=\0|x|/2**n\0<\02 unless x = 0 or (only on machines that conform to IEEE 754) .if n \ |x| = infinity .if t \ |x| = \(if or x lies between 0 and the Underflow Threshold; see below under "BUGS". .PP Scalb(x,n) = x\(**(2**n) computed, for integer n, without first computing 2**n. .SH DIAGNOSTICS IEEE 754 defines drem(x,0) and .if n \ drem(infinity,y) .if t \ drem(\(if,y) to be invalid operations that produce a \*(nn. On a VAX, drem(x,0) returns the reserved operand. No .if n \ infinity .if t \ \(if exists on a VAX. .PP IEEE 754 defines .if n \ logb(\(+-infinity) = +infinity and logb(0) = \-infinity, .if t \ logb(\(+-\(if) = +\(if and logb(0) = \-\(if, 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(x,n) would overflow on a VAX, it returns the reserved operand and sets \fIerrno\fR to ERANGE. .SH SEE ALSO floor(3M), math(3M), infnan(3M) .SH AUTHOR Kwok\-Choi Ng .SH BUGS Should drem(x,0) and logb(0) on a VAX signal invalidity by setting \fIerrno\fR = EDOM? Should logb(0) return \-1.7e38? .PP 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 .RS 1 \(<= scalb(|x|,\-logb(x)) < Radix\0\0\0... = 2 for IEEE 754 .RE for every x except 0, .if n \ infinity .if t \ \(if and \*(nn. Almost every program that assumes 754's specification will work correctly if logb follows 854's specification instead. .PP IEEE 754 requires copysign(x,\*(nn) = \(+-x but says nothing else about the sign of a \*(nn. A \*(nn (\fIN\fRot \fIa\fR \fIN\fRumber) 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, .RS copysign(x,reserved operand) = \-x; .RE should this return the reserved operand instead?