section 7 - Index of

RND Round Accumulator RNDConvergent rounding differs from "standard" rounding in that convergent roundingattempts to remove the aforementioned positive bias by equally distributing the round-offerror. The convergent rounding technique initially performs "standard" rounding as previouslydescribed. Again, the rounding constant depends on the scaling mode being used.Once "standard" rounding has been done, the convergent rounding method tests theresult to determine if all bits Including and to the right of the rounding position arezero. If, and only if, this special condition is true, the convergent rounding method willclear the bit immediately to the left of the rounding position. When this special conditionis true, numbers which have a "1" in the bit immediately to the left of the rounding positionare rounded up; numbers with a "0" in the bit immediately to the left of the roundingposition are rounded down. Thus, these numbers are rounded up half the time androunded down the rest of the time. Therefore, the roundoff error averages out to zero.The LS bits of the convergently rounded result are then cleared so that the roundedresult may be immediately used by the next instruction.Example:RND A #$123456,X1 B,Y1;round A accumulator into A 1, zero AOBefore ExecutionAfter ExecutionCase I: A 1 .....__$_00_:1_23_4_56_:7_89_AB_C __ AI $00: 123456 :000000Case II: A 1-1__ $0_0:_12_34_5_6:8_0_00_00 __ AI $00:123456:000000Case III: A 1 .....__$0_0:_12_34_5_6:8_0_00_00 __ AI $00:123456:000000Explanation of Example: Prior to execution, the 56-bit A accumulator contains thevalue $00:123456:789ABC for Case I, the value $00:123456:800000 for Case II, and thevalue $00:123455:800000 for Case III. The execution of the RND A instruction roundsthe value in the A accumulator into the MSP portion of the A accumulator (A1), usingconvergent rounding, and then zeros the. LSP portion of the A accumulator (AO). Notethat Case II is the special case that distinguishes convergent rounding from standard orbiased rounding.-