Intel 80286 manual Inter Glossary of 80287 and FLOATING-POINT Terminology

inter GLOSSARY OF 80287 AND FLOATING-POINT TERMINOLOGY

Denormal: a special form of Floating-Point Number, produced when an Underflow occurs. On the 80287, a Denormal is defined as a number with a Biased Exponent that is zero. By providing a Signi- ficand with leading zeros, the range of possible negative Exponents can be extended by the number of bits in the Significand. Each leading zero is a bit of lost accuracy, so the extended Exponent range is obtained by reducing significance.

Double Extended: the Standard's term for the 80287 Temporary Real format, with more Exponent and Significand bits than the Double (Long Real) format, and an explicit Integer bit in the Significand.

Double Floating Point Number: the Standard's term for the 80287's 64-bit Long Real format.

Environment: the 14 bytes of 80287 registers affected by the FSTENV and FLDENV instructions. It encompasses the entire state of the 80287, except for the 8 Temporary Real numbers of the 80287 stack. Included are the Control Word, Status Word, Tag Word, and the instruction, opcode, and operand information provided by interrupts.

Exception: any of the six error conditions (I, D, 0, U, Z, P) signalled by the 80287.

Exponent: (1) any power that is raised by an exponential function. For example, the operand to the function mqerEXP is an Exponent. The Integer operand to mqerYI2 is an Exponent.

Exponent: (2) the field of a Floating-Point Number that indicates the magnitude of the number. This would fall under the above more general definition (1), except that a Bias sometimes needs to be subtracted to obtain the correct power.

Floating-Point Number: a sequence of data bytes that, when interpreted in a standardized way, repre- sents a Real number. Floating-Point Numbers are more versatile than Integer representations in two ways. First, they include fractions. Second, their Exponent parts allow a much wider range of magni-

tude than possible with fixed-length Integer representations. .

Gradual Underflow: a method of handling the Underflow error condition that minimizes the loss of accuracy in the result. If there is a Denormal number that represents the correct result, that Denormal is returned. Thus, digits are lost only to the extent of denormalization. Most computers return zero when Underflow occurs, losing all significant digits.

Implicit Integer Bit: a part of the Significand in the Short Real and Long Real formats that is not explicitly given. In these formats, the entire given Significand is considered to be to the right of the Binary Point. A single Implicit Integer Bit to the left of the Binary Point is always 1, except in one case. When the Exponent is the minimum (Biased Exponent is 0), the Implicit Integer Bit is O.

Indefinite: a special value that is returned by functions when the inputs are such that no other sensible answer is possible. For each Floating-Point format there exists one Nontrapping NaN that is designated as the IndetImte value. For binary Integer iormals, the negative number funnesl frum zt:ru is UlLt:1l considered the Indefinite value. For the 80287 Packed Decimal format, the Indefinite value contains all 1's in the sign byte and the uppermost digits byte.

Infinity: a value that has greater magnitude than any Integer or any Real number. The existence of Infinity is subject to heated philosophical debate. However, it is often useful to consider Infinity as another number, subject to special rules of arithmetic. All three Intel Floating-Point formats provide representations for +INFINITY and - INFINITY. They support two ways of dealing with Infinity: Projective (unsigned) and Affine (signed).

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