ARM Architecture Reference Manual ARMv7-A and ARMv7-R edition

Reciprocal square root
Application Level Programmers’ Model
The Advanced SIMD extension includes instructions that support Newton-Raphson calculation of the
reciprocal of the square root of a number.
The VRSQRTE instruction produces the initial estimate of the reciprocal of the square root. It uses the following
pseudocode functions:
// FPRSqrtEstimate()
// =================
bits(32) FPRSqrtEstimate(bits(32) operand)
(type,sign,value) = FPUnpack(operand, StandardFPSCRValue());
if type == FPType_SNaN || type == FPType_QNaN then
result = FPProcessNaN(type, operand, StandardFPSCRValue());
elsif type = FPType_Zero then
result = FPInfinity(sign, 32);
FPProcessException(FPExc_DivideByZero, StandardFPSCRValue());
elsif sign == ‘1’ then
result = FPDefaultNaN(32);
FPProcessException(FPExc_InvalidOp, StandardFPSCRValue());
elsif type = FPType_Infinity then
result = FPZero(‘0’, 32);
else
// Operand must be normalized, since denormalized numbers are flushed to zero. Scale to a
// double-precision value in the range 0.25