Freescale Semiconductor SC140 specifications Round Dalu, RndDa → Dn, RND Da,Dn

RND

RND	Round (DALU)
Operation	Assembler Syntax
Rnd(Da) → Dn	RND Da,Dn

RND

Description

RND Da,Dn

Rounds the 40-bit value in the source data register (Da) and stores the result in the destination data register (Dn). In the round function, the contribution of the least significant bits is rounded into the HP of the destination data register by adding a rounding constant RC to the LS bits of the source data register. The boundary between the LP and HP is determined by the scaling mode bits S0 and S1 in SR. The LSBs of the result are cleared. The number of LSBs cleared is determined by the scaling mode bits in SR. All bits to the right of (including the rounding position) are cleared in the result.

Two types of rounding can be used: convergent rounding (round to the nearest even number) or two’s complement rounding. The type of rounding is selected by the rounding mode bit (RM) in SR. The default mode is convergent rounding (SR[3] = 0).

In both rounding modes, a rounding constant (RC) is first added to the source data. The value of the rounding constant added is determined by the scaling mode bits S0 and S1 in SR. A 1 is positioned in the rounding constant aligned with the MSB of the scaled LP. The rounding constant weight is actually equal to half the weight of the scaled HP’s LSB.

For two’s complement rounding, the scaled LP bits are then truncated. Numbers with an original value of 1/2 in the scaled LP are rounded up, resulting in a small positive bias.

If convergent rounding is used, the result of the addition is tested. If all the bits of the result to the right of (including the rounding position) are cleared, then the bit to the left of the rounding position is cleared in the result, ensuring that the result is even. An even result eliminates the two’s complement bias where 1/2 is always rounded up.

See Section 2.2.2.6, “Rounding Modes,” on page 2-21 for more detailed information.

The following table shows the rounding position (LP MSB) and rounding constant (RC) as determined by the scaling mode bits:

			Rounding		Rounding Constant
						(RC) Bits
S1	S0	Scaling Mode	Position	39–17	16		15	14	13–0
0	0	No Scaling	15	0 . . . 0	0		1	0	0 . . . 0
0	1	Scale Down	16	0 . . . 0	1	0		0	0 . . . 0
1	0	Scale Up	14	0 . . . 0	0	0		1	0 . . . 0

SC140 DSP Core Reference Manual A-359