Sep 22, 2019
08:33 AM

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Sep 22, 2019
08:33 AM

Hello Everyone,

I have a problem about the fast sqrt in the 3.1 of

the docment said:Yn+1 = Yn * (1.5 – (X*2)* Yn^2), I don't know why it is like this.

I know the fast alg of sqrt with div is like that: Yn+1=0.5*(Yn+X/Yn), it is implemented with div, so, it is not fast.

furthermor, I kown the fast alg of invSqrt is:Yn+1=Yn * (1.5 – (X*0.5)* Yn^2), it avoid div, so, it is fast. and it is very similar to infineion's fast sqrt.

I really don't know how to conclude formula of infineion's fast sqrt, Is there anyone would like to tell me?or, tell me how to find the reference papers?

I have a problem about the fast sqrt in the 3.1 of

the docment said:Yn+1 = Yn * (1.5 – (X*2)* Yn^2), I don't know why it is like this.

I know the fast alg of sqrt with div is like that: Yn+1=0.5*(Yn+X/Yn), it is implemented with div, so, it is not fast.

furthermor, I kown the fast alg of invSqrt is:Yn+1=Yn * (1.5 – (X*0.5)* Yn^2), it avoid div, so, it is fast. and it is very similar to infineion's fast sqrt.

I really don't know how to conclude formula of infineion's fast sqrt, Is there anyone would like to tell me?or, tell me how to find the reference papers?

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4 Replies

Sep 24, 2019
08:11 PM

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Sep 24, 2019
08:11 PM

it's so pity, nobody tell me how to do

Sep 26, 2019
12:20 PM

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Sep 26, 2019
12:20 PM

Sep 26, 2019
06:06 PM

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Sep 26, 2019
06:06 PM

I just want to know how to conclude the formula, so, I think the compiler is not the key for my question

Oct 03, 2019
12:55 AM

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Oct 03, 2019
12:55 AM

Hi Shaquille,

This one had me confused for a while as well. The confusion starts with the formula (ignore the

*PHP Code*prefix):

[PHP]

Yn1 = Yn*(1.5–(2*sX)*Yn^2)

[/PHP]

Whereas you would expect the following inverse square root formula instead:

[PHP]

Yn1 = Yn*(1.5–(sX/2)*Yn^2)

[/PHP]

So initially it appears to make no sense. Let's start with a breakdown of the formula:

[PHP]

Yn1 = Yn*(1.5–(2*sX)*Yn^2)

[/PHP]

This was unlucky steno perhaps. What is being referred to is this assembly statement:

MOV sK,sX

And particularly the comment behind it that says that

*sK*is implicitly being scaled to twice the size of

*sX*because it will be used in

*Q2.14*calculations. This is what the factor 2 is referring to. But even then the formula still doesn't seem to make sense. How can half

*sX*be scaled upwards by a factor 4 while at the same time constant 1.5 is unchanged? That is mathematically impossible. Yet still, when you code this bit of assembly, it rings true every time.

I think the mistake lies in some of the comments, in this snippet of assembly:

MULR.Q tmp,sY u,sY u,#1

SH tmp,tmp,#-1

MSUBRS.Q tmp,d8,tmp u,sK u,#1

For the first line of code the comment says it will be formatted in

*Q1.15*. This is probably not the case. It - the result of the calculation - must be

*Q3.13*which is then scaled to

*Q4.12*in the next statement. The third statement uses

*Q3.13*has its outcome. The multiplication itself presumes its members are in

*Q2.14*. This was the reason why

*sX*was implicitly scaled upwards by a factor 2. For the same reason

*Yn^2*

*must therefore be scaled down by a factor 4. So what is in fact being calculated in the third statement (*

[PHP]

0.5–(2*X)*((Yn^2)/4)

0.5–(sX/2)*Yn^2)

[/PHP]

And then it is starting to make sense. After the iterations complete, the exit-format is in

The exit formula (the last three assembly statements) is this one:

[PHP]

SQRT(sX) = ((2*sX-1)/(2*SQRT(sX))) + 1/(2*SQRT(sX))

= (2*sX - 1 + 1)/(2*SQRT(sX))

= sX/SQRT(sX)

[/PHP]

I therefore think it could also simply have been this single statement instead:

*Q3.13*) is this:[PHP]

0.5–(2*X)*((Yn^2)/4)

0.5–(sX/2)*Yn^2)

[/PHP]

And then it is starting to make sense. After the iterations complete, the exit-format is in

*Q2.14*. By then the loop will have converged to*1/2z*. The scaling by 1/2 is because prior to exit*Q3.13*is scaled to*Q2.14*.The exit formula (the last three assembly statements) is this one:

[PHP]

SQRT(sX) = ((2*sX-1)/(2*SQRT(sX))) + 1/(2*SQRT(sX))

= (2*sX - 1 + 1)/(2*SQRT(sX))

= sX/SQRT(sX)

[/PHP]

I therefore think it could also simply have been this single statement instead:

MULR.Q %d3,%sYu,%sKu,1

As this calculates the following in one go:

[PHP]

SQRT(sX) = (2*sX)/(2*SQRT(sX))) = sX/SQRT(sX)

[/PHP]

Best regards,

Henk-Piet Glas

Principal Technical Specialist

Embedded Software

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