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.
Read more about this topic: Decimal Floating Point
Famous quotes containing the words floating, point, arithmetic and/or operations:
“I know, it must have been my imagination, but it makes me realize how desperately alone the Earth is. Hanging in space like a speck of food floating in the ocean. Sooner or later to be swallowed up by some creature floating by.... Time will tell, Dr. Mason. We can only wait and wonder. Wonder how, wonder when.”
—Tom Graeff. Young astronomer, Teenagers from Outer Space, after just seeing the invading spaceship through his telescope, and dismissing it (1959)
“I stand here tonight to say that we have never known defeat; we have never been vanquished. We have not always reached the goal toward which we have striven, but in the hour of our greatest disappointment we could always point to our battlefield and say: “There we fought our good fight, there we defended the principles for which our ancestors and yours laid down their lives; there is our battlefield for justice, equality and freedom. Where is yours?””
—Anna Howard Shaw (1847–1919)
“Under the dominion of an idea, which possesses the minds of multitudes, as civil freedom, or the religious sentiment, the power of persons are no longer subjects of calculation. A nation of men unanimously bent on freedom, or conquest, can easily confound the arithmetic of statists, and achieve extravagant actions, out of all proportion to their means; as, the Greeks, the Saracens, the Swiss, the Americans, and the French have done.”
—Ralph Waldo Emerson (1803–1882)
“There is a patent office at the seat of government of the universe, whose managers are as much interested in the dispersion of seeds as anybody at Washington can be, and their operations are infinitely more extensive and regular.”
—Henry David Thoreau (1817–1862)