Should the argument is equal to 10n for integer n, then the result is n. The computed outcome needs to be in 1 ulp of the precise consequence. Success have to be semi-monotonic.

If a technique constantly has an mistake lower than 0.five ulps, the method normally returns the floating-place selection closest the exact consequence; this kind of a technique is correctly rounded. A correctly rounded method is generally the very best a floating-position approximation is usually; nevertheless, it can be impractical For numerous floating-position methods to be effectively rounded. As an alternative, for The maths course, a larger mistake sure of one or two ulps is permitted for particular methods. Informally, which has a 1 ulp error sure, when the exact result is a representable amount, the exact consequence need to be returned given that the computed end result; in any other case, both of the two floating-point values which bracket the precise consequence may very well be returned. For actual final results huge in magnitude, among the list of endpoints of your bracket could possibly be infinite. Apart from accuracy at unique arguments, sustaining appropriate relations between the method at diverse arguments can be vital. For that reason, most strategies with much more than 0.5 ulp glitches are necessary to be semi-monotonic: Each time the mathematical functionality is non-reducing, so is definitely the floating-position approximation, Similarly, whenever the mathematical operate is non-increasing, so is definitely the floating-position approximation. Not all approximations that have 1 ulp accuracy will routinely satisfy the monotonicity necessities.

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In the event the argument is NaN or its complete benefit is bigger than 1, then The end result is NaN. In the event the argument is zero, then the result is often a zero With all the same sign since the argument.

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Should the argument is infinite, then the result is undoubtedly an infinity While using the same indication since the argument. In the event the argument is zero, then The end result is often a zero Together with the very same sign as being the argument. The computed consequence need to be in just 2.5 ulps of the exact end result.

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