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Single-Precision Floating-Point Square-Root Reciprocal Approximation RSQRSP
3-203 Instruction SetSPRU733
Single-Precision Floating-Point Square-Root Reciprocal Approximation
RSQRSP
Syntax RSQRSP (.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 1 0 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 square-root reciprocal approximation value
of src2 is placed in dst.
The RSQRSP 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 RSQRSP. 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) sqrcp(src2) → dst
else nop