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A hardware floating-point number (an object of type hfloat) is represented internally in Maple as a 64-bit IEEE binary floating-point value.

The HFloat(M, E) command can be used to construct the hardware floating-point number M * base^E.

If the mantissa parameter M is of type imaginary, HFloat(M, E) returns I * HFloat(Im(M), E).

If the mantissa is of type nonreal, HFloat(M, E) returns HFloat(Re(M), E) + I * HFloat(Im(M), E).

Maple also has arbitrary-precision software floating-point numbers, of type sfloat (see type/sfloat ), which can be constructed using the SFloat or Float constructor.

The maximum number of digits in the mantissa of a hardware float, and the maximum and minimum allowable exponents, can be obtained from evalhf (see evalhf/constant ).

To obtain the mantissa and exponent fields of a hardware float, use SFloatMantissa and SFloatExponent , respectively.

A hardware float, H, can be converted to a software float using SFloat(H). Similarly, a software float, S, can be converted to a hardware float using HFloat(S).

The presence of a hardware floating-point number in an expression generally implies that the computation will use hardware floating-point evaluation, unless the settings of Digits and UseHardwareFloats specify otherwise (see UseHardwareFloats ).

An expression can be forced to evaluate entirely using hardware floating-point by enclosing it in a call to evalhf . However, some expressions, notably those involving data structures, cannot be evaluated by evalhf .

Entire procedures can be written to work using hardware floats without the restrictions imposed by evalhf by adding option hfloat to the procedure (see option_hfloat ).

The number of digits carried in the mantissa for hardware floating-point arithmetic is approximately 15. More digits are displayed to ensure a base 10 representation from which the underlying binary hardware floating-point value can be reliably reconstructed.

Maple includes a variety of numeric functions to use with both hardware and software floating-point numbers.

The behaviors of hardware floating-point infinities, undefined values (so called "Not a Number", or "NaN", in IEEE nomenclature), and zero, are analogous to the corresponding software floating-point concepts. For details, see Float .

$\mathrm{HFloat}\left(2.3\right)$

$2.30000000000000$

$\mathrm{HFloat}\left(2.\right)$

$2.$

$\mathrm{HFloat}\left(-0.3\right)$

$\mathrm{-0.300000000000000}$

$\mathrm{HFloat}\left(-23000.\right)$

$\mathrm{-23000.}$

$\cdot 120000.$

$\mathrm{-2.760000000}\times {10}^9$

$\mathrm{type}\left(\,\mathrm{hfloat}\right)$

$\mathrm{true}$