SPRUHX5I August 2014 – May 2024 TMS320F28374S , TMS320F28375S , TMS320F28375S-Q1 , TMS320F28376S , TMS320F28377S , TMS320F28377S-Q1 , TMS320F28378S , TMS320F28379S
32-Bit Floating-Point Square-Root Reciprocal Approximation
MRa | CLA floating-point destination register (MR0 to MR3) |
MRb | CLA floating-point source register (MR0 to MR3) |
LSW: 0000 0000 0000 bbaa
MSW: 0111 1110 0100 0000
This operation generates an estimate of 1/sqrt(X) in 32-bit floating-point format accurate to approximately 8 bits. This value can be used in a Newton-Raphson algorithm to get a more accurate answer. That is:
Ye = Estimate(1/sqrt(X));
Ye = Ye*(1.5 - Ye*Ye*X/2.0);
Ye = Ye*(1.5 - Ye*Ye*X/2.0);
After 2 iterations of the Newton-Raphson algorithm, you get an exact answer accurate to the 32-bit floating-point format. On each iteration, the mantissa bit accuracy approximately doubles. The MEISQRTF32 operation does not generate a negative zero, DeNorm, or NaN value.
MRa = Estimate of 1/sqrt (MRb);
This instruction modifies the following flags in the MSTF register:
Flag | TF | ZF | NF | LUF | LVF |
---|---|---|---|---|---|
Modified | No | No | No | Yes | Yes |
The MSTF register flags are modified as follows:
This is a single-cycle instruction.
; Y = sqrt(X)
; Ye = Estimate(1/sqrt(X));
; Ye = Ye*(1.5 - Ye*Ye*X*0.5)
; Ye = Ye*(1.5 - Ye*Ye*X*0.5)
; Y = X*Ye
;
_Cla1Task3:
MMOV32 MR0, @_x ; MR0 = X
MEISQRTF32 MR1, MR0 ; MR1 = Ye = Estimate(1/sqrt(X))
MMOV32 MR1, @_x, EQ ; if(X == 0.0) Ye = 0.0
MMPYF32 MR3, MR0, #0.5 ; MR3 = X*0.5
MMPYF32 MR2, MR1, MR3 ; MR2 = Ye*X*0.5
MMPYF32 MR2, MR1, MR2 ; MR2 = Ye*Ye*X*0.5
MSUBF32 MR2, #1.5, MR2 ; MR2 = 1.5 - Ye*Ye*X*0.5
MMPYF32 MR1, MR1, MR2 ; MR1 = Ye = Ye*(1.5 - Ye*Ye*X*0.5)
MMPYF32 MR2, MR1, MR3 ; MR2 = Ye*X*0.5
MMPYF32 MR2, MR1, MR2 ; MR2 = Ye*Ye*X*0.5
MSUBF32 MR2, #1.5, MR2 ; MR2 = 1.5 - Ye*Ye*X*0.5
MMPYF32 MR1, MR1, MR2 ; MR1 = Ye = Ye*(1.5 - Ye*Ye*X*0.5)
MMPYF32 MR0, MR1, MR0 ; MR0 = Y = Ye*X
MMOV32 @_y, MR0 ; Store Y = sqrt(X)
MSTOP ; end of task