Can the value of Tau be approximated to a static value?

I have this little macro:

I have this little macro:

#define EIGENROTATE(a,i,j,k,l) g=a.n*;h=a.n;a.n**=g-s*(h+g*tau);\*

a.n=h+s*(g-h*tau);

I want to translate it to asm.. 'a' is a 3x3 matrix, 's' is a REAL4 variable..

I want to translate it to asm.. 'a' is a 3x3 matrix, 's' is a REAL4 variable..

*
*OK check this out..

Tau is a mathematical oddity, and contains several mathematical oddities in itself.

Even though Tau is a series, its value can be estimated as a hard value of fixed precision, in a way it is mathematically related to Pi.

I have not checked the following code, and I foresee a potential collision problem if the values of i,j and k,l are the same, but I PRESUME this never happens...

Tau is a mathematical oddity, and contains several mathematical oddities in itself.

Even though Tau is a series, its value can be estimated as a hard value of fixed precision, in a way it is mathematically related to Pi.

I have not checked the following code, and I foresee a potential collision problem if the values of i,j and k,l are the same, but I PRESUME this never happens...

.data

Tau REAL8 1.7579327566180045 ;Anyone got Tau to more than 16 decimal places?

.code

EIGENROTATE macro a,i,j,k,l

;Where a = Mat33, s = (given) REAL4

; g=a.n*;*

mov eax,12

mul j

mov ebx,i

shl ebx,2

add eax,ebx

mov ebx,eax

add ebx,a

; h=a.n;

mov eax,12

mul l

mov edx,k

shl edx,2

add eax,edx

add eax,a

; a.n*=g-s*(h+g*tau);*

fld REAL4 ptr

fld REAL4 ptr

fmul Tau

fadd REAL4 ptr

fmul s

fsub

fstp REAL4 ptr

; a.n=h+s*(g-h*tau);

fld REAL4 ptr

fld REAL4 ptr

fld REAL4 ptr

fmul Tau

fsub

fmul s

fadd

fstp REAL4 ptr

endm

*
*What's tau? I have never heard of it before.

Google it, really interesting, only recently bumped into it during my journey into dynamic physics equations, via the 'Jacobian rotation method of solving an Eigen Vector equation'.

I have never heard of a mathematically symbol called tau - i don't seem to be finding up much on it on google. I only encounter this term in physics where is it used to represent torque. Maybe they are related? I don't really know.

Tau if I recall correctly also is a "unit" (calculated for each specific) of discharge of a capacitor, where normally 5*tau is when you can consider that a capacitor is discharged... or some like that...

Tau is a greek letter, and thus has at least a couple of different meanings - math and physics. Considering that Homer is talking about rigid body physics, I doubt capacitor discharge has any relevance here :)

A bit improved the int part of the code:

EIGENROTATE2 macro a,i,j,k,l

;Where a = Mat33, s = (given) REAL4

; g=a.n*; *

; h=a.n;

mov ebx,j

mov eax,l

lea ebx,

lea eax,

add ebx,i

add eax,k

shl ebx,2

shl eax,2

add ebx,a

add eax,a

; a.n*=g-s*(h+g*tau);*

fld REAL4 ptr

fld ST

fmul Tau

fadd REAL4 ptr

fmul s

fsub

fstp REAL4 ptr

; a.n=h+s*(g-h*tau);

fld REAL4 ptr

fld REAL4 ptr

fld REAL4 ptr

fmul Tau

fsub

fmul s

fadd

fstp REAL4 ptr

endm

*
*In laymans terms, Tau is the sum of the roots of integers incrementing usually from 1:

eg Tau = sqrt (1+sqrt(2+sqrt(3+sqrt(N))))

The value produced by this infinite series is nevertheless a fixed value, just its precision increases, which is why I mentioned pi in a previous posting.

Tau is indeed related to Pi, and also to the Golden Mean.

Funny thing : the procedure which uses the EIGENROTATE macro I posted earlier actually calculates its own values for Tau, and I didn't need to research Tau after all :)

eg Tau = sqrt (1+sqrt(2+sqrt(3+sqrt(N))))

The value produced by this infinite series is nevertheless a fixed value, just its precision increases, which is why I mentioned pi in a previous posting.

Tau is indeed related to Pi, and also to the Golden Mean.

Funny thing : the procedure which uses the EIGENROTATE macro I posted earlier actually calculates its own values for Tau, and I didn't need to research Tau after all :)

That doesn't look like a series to me :P

Yeah I too find it hard to believe thats a real series, it doesn't converge as N ? ? :) .

http://www.hermetic.ch/misc/tau/tau.htm

Looks like it converges to me :P

Looks like it converges to me :P

tau=1.7579327566180045

Give us a strict mathematical attestation without computer.

regards

Give us a strict mathematical attestation without computer.

regards

Ok, let's be clear, that value is only valid when the series begins with 1.

If we start our series at any given value other than 1, we produce a different but equally finite value.

That's why the code I'm playing with generates values for tau rather than use that hardcoded value.

I find it infinitely interesting that one of the tau series generates the golden mean :)

If we start our series at any given value other than 1, we produce a different but equally finite value.

That's why the code I'm playing with generates values for tau rather than use that hardcoded value.

I find it infinitely interesting that one of the tau series generates the golden mean :)

A or B ?

regards

regards

Yes, it converges, but it's not a series, because it's not a sum. But a series doesn't have to converge either.