Double-Precision Floating-Point Reciprocal Approximation

 

RCPDP

 

 

 

Double-Precision Floating-Point Reciprocal Approximation

 

 

 

 

RCPDP

 

 

 

 

 

 

Syntax

 

 

 

 

RCPDP (.unit) src2, dst

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.unit = .S1 or .S2

 

 

 

 

 

 

 

 

 

 

 

Compatibility

 

 

C67x and C67x+ CPU

 

 

 

 

 

 

 

 

 

 

 

Opcode

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

31

29

28

27

23

22

18

17

13

12

11

6

5

4

3

2

1

0

creg

z

dst

src2

reserved

x

1 0 1 1 0 1 1

0

0 0 s p

3 155511 1

Opcode map field used...

For operand type...

Unit

 

 

 

src2

dp

.S1, .S2

dst

dp

 

 

 

 

Description

The 64-bit double-precision floating-point reciprocal approximation value of

 

src2 is placed in dst. The operand is read in one cycle by using the src1 port

 

for the 32 LSBs and the src2 port for the 32 MSBs.

 

The RCPDP instruction provides the correct exponent, and the mantissa is

 

accurate to the eighth binary position (therefore, mantissa error is less

 

than 2−8). This estimate can be used as a seed value for an algorithm to

 

compute the reciprocal to greater accuracy.

 

The Newton-Rhapson algorithm can further extend the mantissa’s precision:

 

x[n + 1] = x[n](2 − v x[n])

 

where v = the number whose reciprocal is to be found.

 

x[0], the seed value for the algorithm, is given by RCPDP. For each iteration,

 

the accuracy doubles. Thus, with one iteration, accuracy is 16 bits in the

 

mantissa; with the second iteration, the accuracy is 32 bits; with the third itera-

 

tion, the accuracy is the full 52 bits.

Execution

if (cond)

rcp(src2) dst

 

else

nop

SPRU733

Instruction Set

3-197

Page 257
Image 257
Texas Instruments TMS320C67X/C67X+ DSP manual Double-Precision Floating-Point Reciprocal Approximation, Rcpdp