Top web site - 4.2.1 SINGLE-PRECISION CALCULATIONS 201 N4. Scale right Nl.
4.2.1 SINGLE-PRECISION CALCULATIONS 201 N4. Scale right Nl. underflow N7. Pack Fig. 3. Normalization of (e, f). base-b digits to the right of the radix point. If such a large accumulator is not available, it is possible to shorten the requirement to p + 2 or p + 3 places if proper precautions are taken; the details are given in exercise 5.1 A6. [Add.] Set fw +- fU + fV. A7. [Normalize.] (At this point (G,,, fiu) represents the sum of u and 21, but lfwj may have more than p digits, and it may be greater than unity or less than l/b.) Perform Algorithm N below, to normalize and round (ezu, jiu) into the final answer. 1 Algorithm N (Normalization). A raw exponent e and a raw fraction f are converted to normalized form, rounding if necessary to p digits. This algorithm assumes that ]f 1 < b. Nl. [Test f .] If If] 2 1 ( fraction overflow ), go to step N4. If f = 0, set e to its lowest possible value and go to step N7. N2. [Is f normalized?] If ] f ] 2 l/b, go to step N5. N3. [Scale left.] Shift f to the left by one digit position (i.e., multiply it by b), and decrease e by 1. Return to step N2. N4. [Scale right.] Shift f to the right by one digit position (i.e., divide it by b), and increase e by 1. N5. [Round.] Round f to p places. (We take this to mean that f is changed to the nearest multiple of b-p. It is possible that (bpf)modl = f so that there are two nearest multiples; if b is even, we choose the one that makes bPf + $b odd. Further discussion of rounding appears in Section 4.2.2.) It is important to note that this rounding operation can make If] = 1 ( rounding overflow ); in such a case, return to step N4. N6. [Check e.] If e is too large, i.e., larger than its allowed range, an exponent overflow condition is sensed. If e is too small, an exponent underflow condition is sensed. (See the discussion below; since the result cannot