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NaNs
When a numeric operation cannot produce a meaningful result,
the operation delivers a special bit pattern called a NaN (Not-a-
Number). For example, zero divided by zero, +° added to -°,
and Ã-1 yield NaNs. A NaN can occur in any of the numeric data
formats (single, double, and double-double), but generally,
system-specific integer types (non-numeric types exclusively for
integer values) have no representation for NaNs.
A NaN may have an associated code that indicates its origin.
NaN Meaning
1 Invalid square root, such as Ã-1
2 Invalid addition, such as (+°) + (-°)
4 Invalid division, such as 0Ö0
8 Invalid multiplication, such as 0x°
9 Invalid remainder or modulo, such as
x rem 0
17 Attempt to convert invalid ASCII string
21 Attempt to create a NaN with a zero code
33 Invalid argument to trigonometric function (such as cos,
sin, tan)
34 Invalid argument to inverse trigonometric function (such
as acos, asin, atan)
36 Invalid argument to logarithmic function (such as log,
log
10
)
37 Invalid argument to exponential function (such as exp,
expm1)
38 Invalid argument to financial function (compound or
annuity)
40 Invalid argument to inverse hyperbolic function (such as
acosh, asinh)
42 Invalid argument to gamma function (gamma or lgamma)
Zeroes
Each floating-point format has two representations for zero: +0
and -0. Although the two zeros compare as equal (+0)=(-0),
their behaviours in IEEE arithmetic are slightly different.
Ordinarily, the sign of zero does not matter except (possibly) for
a function discontinuous at zero. Though the two forms are
numerically equal, a program can distinguish +0 from -0 by
operations such as division by zero or by performing the
numeric copysign function.
The sign of zero obeys the usual sign laws for multiplication and
division. For example, (+0)x(-1) = -0 and 1/(-0)= -°. Because
Technical Considerations
iMalc Manual
Technical Considerations
39