4.27.2.4 IEEE 754 floating point arithmetic

The Prolog ISO standard defines that floating point arithmetic returns a valid floating point number or raises an exception. IEEE floating point arithmetic defines two modes: raising exceptions and propagating the special float values NaN, Inf, -Inf and -0.0. SWI-Prolog implements a part of the ECLiPSe proposal to support non-exception based processing of floating point numbers. There are four flags that define handling the four exceptional events in floating point arithmetic, providing the choice between error and returning the IEEE special value. Note that these flags only apply for floating point arithmetic. For example rational division by zero always raises an exception.

Flag	Default	Alternative
float_overflow	error	infinity
float_zero_div	error	infinity
float_undefined	error	nan
float_underflow	ignore	error

The Prolog flag float_rounding and the function roundtoward/2 control the rounding mode for floating point arithmetic. The default rounding is to_nearest and the following alternatives are provided: to_positive, to_negative and to_zero.

[det]float_class(+Float, -Class)

Wraps C99 fpclassify() to access the class of a floating point number. Raises a type error if Float is not a float. Defined classes are below.

nan

Float is “Not a number''. See nan/0. May be produced if the Prolog flag float_undefined is set to nan. Although IEEE 754 allows NaN to carry a payload and have a sign, SWI-Prolog has only a single NaN values. Note that two NaN terms compare equal in the standard order of terms (==/2, etc.), they compare non-equal for arithmetic (=:=/2, etc.).

infinite

Float is positive or negative infinity. See inf/0. May be produced if the Prolog flag float_overflow or the flag float_zero_div is set to infinity.

zero

Float is zero (0.0 or -0.0)

subnormal

Float is too small to be represented in normalized format. May not be produced if the Prolog flag float_underflow is set to error.

normal

Float is a normal floating point number.

[det]float_parts(+Float, -Mantissa, -Base, -Exponent)

True when Mantissa is the normalized fraction of Float, Base is the radix and Exponent is the exponent. This uses the C function frexp(). If Float is NaN or ±Inf Mantissa has the same value and Exponent is 0 (zero). In the current implementation Base is always 2. The following relation is always true:

Float =:= Mantissa × Base^Exponent

[det]bounded_number(?Low, ?High, +Num)

True if Low < Num < High. Raises a type error if Num is not a number. This predicate can be used both to check and generate bounds across the various numeric types. Note that a number cannot be bounded by itself and NaN, Inf, and -Inf are not bounded numbers.

If Low and/or High are variables they will be unified with tightest values that still meet the bounds criteria. The generated bounds will be integers if Num is an integer; otherwise they will be floats (also see nexttoward/2 for generating float bounds). Some examples:

?- bounded_number(0,10,1).
true.

?- bounded_number(0.0,1.0,1r2).
true.

?- bounded_number(L,H,1.0).
L = 0.9999999999999999,
H = 1.0000000000000002.

?- bounded_number(L,H,-1).
L = -2,
H = 0.

?- bounded_number(0,1r2,1).
false.

?- bounded_number(L,H,1.0Inf).
false.