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infnan(3m) [bsd man page]

INFNAN(3M)																INFNAN(3M)

NAME
infnan - signals invalid floating-point operations on a VAX (temporary) SYNOPSIS
#include <math.h> double infnan(iarg) int iarg; DESCRIPTION
At some time in the future, some of the useful properties of the Infinities and NaNs in the IEEE standard 754 for Binary Floating-Point Arithmetic will be simulated in UNIX on the DEC VAX by using its Reserved Operands. Meanwhile, the Invalid, Overflow and Divide-by-Zero exceptions of the IEEE standard are being approximated on a VAX by calls to a procedure infnan in appropriate places in libm. When better exception-handling is implemented in UNIX, only infnan among the codes in libm will have to be changed. And users of libm can design their own infnan now to insulate themselves from future changes. Whenever an elementary function code in libm has to simulate one of the aforementioned IEEE exceptions, it calls infnan(iarg) with an appropriate value of iarg. Then a reserved operand fault stops computation. But infnan could be replaced by a function with the same name that returns some plausible value, assigns an apt value to the global variable errno, and allows computation to resume. Alternatively, the Reserved Operand Fault Handler could be changed to respond by returning that plausible value, etc. instead of aborting. In the table below, the first two columns show various exceptions signaled by the IEEE standard, and the default result it prescribes. The third column shows what value is given to iarg by functions in libm when they invoke infnan(iarg) under analogous circumstances on a VAX. Currently infnan stops computation under all those circumstances. The last two columns offer an alternative; they suggest a setting for errno and a value for a revised infnan to return. And a C program to implement that suggestion follows. IEEE IEEE Signal Default iarg errno infnan __________________________________________________ Invalid NaN EDOM EDOM 0 Overflow +-Infinity ERANGE ERANGEHUGE Div-by-0 +-Infinity +-ERANGE ERANGE or EDOM+-HUGE (HUGE = 1.7e38 ... nearly 2.0**127) ALTERNATIVE infnan: #include <math.h> #include <errno.h> extern int errno ; double infnan(iarg) int iarg ; { switch(iarg) { case ERANGE: errno = ERANGE; return(HUGE); case -ERANGE: errno = EDOM; return(-HUGE); default: errno = EDOM; return(0); } } SEE ALSO
math(3M), intro(2), signal(3). ERANGE and EDOM are defined in <errno.h>. See intro(2) for explanation of EDOM and ERANGE. 4.3 Berkeley Distribution May 27, 1986 INFNAN(3M)

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IEEE(3M)																  IEEE(3M)

NAME
copysign, drem, finite, logb, scalb - copysign, remainder, exponent manipulations SYNOPSIS
#include <math.h> double copysign(x,y) double x,y; double drem(x,y) double x,y; int finite(x) double x; double logb(x) double x; double scalb(x,n) double x; int n; DESCRIPTION
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. DIAGNOSTICS
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. SEE ALSO
floor(3M), math(3M), infnan(3M) AUTHOR
Kwok-Choi Ng BUGS
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 specification instead. 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)

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