# Decimal Floating Point - Floating Point Arithmetic Operations

Floating Point Arithmetic Operations

The usual rule for performing floating point arithmetic is that the exact mathematical value is calculated, and the result is then rounded to the nearest representable value in the specified precision. This is in fact the behavior mandated for IEEE-compliant computer hardware, under normal rounding behavior and in the absence of exceptional conditions.

For ease of presentation and understanding, 7 digit precision will be used in the examples. The fundamental principles are the same in any precision.

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You can’t have operations without screams. Pain and the knife—they’re inseparable.
—Jean Scott Rogers. Robert Day. Mr. Blount (Frank Pettingell)

I hope I may claim in the present work to have made it probable that the laws of arithmetic are analytic judgments and consequently a priori. Arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic, albeit a derivative one. To apply arithmetic in the physical sciences is to bring logic to bear on observed facts; calculation becomes deduction.
Gottlob Frege (1848–1925)

The man who, from the beginning of his life, has been bathed at length in the soft atmosphere of a woman, in the smell of her hands, of her bosom, of her knees, of her hair, of her supple and floating clothes, ... has contracted from this contact a tender skin and a distinct accent, a kind of androgyny without which the harshest and most masculine genius remains, as far as perfection in art is concerned, an incomplete being.
Charles Baudelaire (1821–1867)

Parents are led to believe that they must be consistent, that is, always respond to the same issue the same way. Consistency is good up to a point but your child also needs to understand context and subtlety . . . much of adult life is governed by context: what is appropriate in one setting is not appropriate in another; the way something is said may be more important than what is said. . . .
Stanley I. Greenspan (20th century)