Double-Precision Floating-Point Square-Root Reciprocal Approximation
RSQRDP
4-65
TMS320C67x Floating-Point Instruction Set
Syntax
RSQRDP (.unit)
src2, dst
.unit = .S1 or .S2
Opcode map field used...
For operand type...
Unit
src2
dst
dp
dp
.S1, .S2
Opcode
31
29 28 27
23 22
18 17
creg
z
dst
13 12
5
4
3
2
1
0
1 0 1 1 1 0
0
0
0
s
p
3
5
5
5
6
6
1
11
x
rsv
src2
Description
The 64-bit double-precision floating-point square-root reciprocal approxima-
tion 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 RSQRDP 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 square root to greater accuracy.
The Newton-Rhapson algorithm can further extend the mantissa’s precision:
x[n+1] = x[n](1.5 – (v/2)*x[n]*x[n])
where v = the number whose reciprocal square root is to be found.
x[0], the seed value for the algorithm is given by RSQRDP. For each iteration
the accuracy doubles. Thus, with one iteration, the 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)
sqrcp(
src2)
→
dst
else
nop