Page 379 - ARM 64 Bit Assembly Language

Advanced SIMD instructions 369

10.7.6 Reciprocal step

These instructions are used to perform one Newton-Raphson step for improving the reciprocal
estimates:
frecps Reciprocal Step, and
frsqrts Reciprocal Square Root Step.

For each element in the vector, the following equation can be used to improve the estimates of
the reciprocals:

x n+1 = x n (2 − dx n ).
Where x n is the estimated reciprocal from the previous step, and d is the number for which
the reciprocal is desired. This equation converges to 1 if x 0 is obtained using vrecpe on d.
d
The vrecps instruction computes
x n+1 = 2 − dx n ,

so one additional multiplication is required to complete the update step. The initial estimate
x 0 must be obtained using the vrecpe instruction.
For each element in the vector, the following equation can be used to improve the estimates of
the reciprocals of the square roots:

3 − dx n 2
x n+1 = x n .
2
Where x n is the estimated reciprocal from the previous step, and d is the number for which
1
the reciprocal is desired. This equation converges to √ if x 0 is obtained using vrsqrte on d.
d
The vrsqrts instruction computes
3 − dx n
x n+1 = ,
2
so two additional multiplications are required to complete the update step. The initial estimate
x 0 must be obtained using the vrsqrte instruction.

10.7.6.1 Syntax

f<op> Vd.T, Vn.T, Vm.T
f<op> Fd, Fn, Fm

• <op> is either recps or rsqrts.
• T must be 2s, 4s,or 2d.
• F is s or d.