Texas Instruments TMS320C67X/C67X+ DSP - Manual (Page 259)

Single-Precision Floating-Point Reciprocal Approximation RCPSP
3-199 Instruction Set SPRU733
Single-Precision Floating-Point Reciprocal Approximation RCPSP
Syntax RCPSP (.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 0 0 0 0 0 x 1 1 1 1 0 1 1 0 0 0 s p
3 1 5 5 1 1 1
Opcode map field used... For operand type... Unit
src2
dst xsp
sp .S1, .S2
Description The single-precision floating-point reciprocal approximation value of src2 is
placed in dst.
The RCPSP 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 RCPSP. For each iteration,
the accuracy doubles. Thus, with one iteration, accuracy is 16 bits in the
mantissa; with the second iteration, the accuracy is the full 23 bits.
Execution if (cond) rcp(src2) → dst
else nop