Hermite Interpolator (x86 ASM)

Type : Hermite interpolator in x86 assembly (for MS VC++)
References : Posted by robert[DOT]bielik[AT]rbcaudio[DOT]com
Notes :
An "assemblified" variant of Laurent de Soras hermite interpolator. I tried to do calculations as parallell as I could muster, but there is almost certainly room for improvements. Right now, it works about 5.3 times (!) faster, not bad to start with...

Parameter explanation:
frac_pos: fractional value [0.0f - 1.0f] to interpolator
pntr: pointer to float array where:
pntr[0] = previous sample (idx = -1)
pntr[1] = current sample (idx = 0)
pntr[2] = next sample (idx = +1)
pntr[3] = after next sample (idx = +2)

The interpolation takes place between pntr[1] and pntr[2].

/Robert Bielik
RBC Audio

Code :
const float c_half = 0.5f;

__declspec(naked) float __hermite(float frac_pos, const float* pntr)
        push    ecx;        
        mov        ecx, dword ptr[esp + 12]; //////////////////////////////////////////////////////////////////////////////////////////////////
        add        ecx, 0x04;            //    ST(0)        ST(1)        ST(2)        ST(3)        ST(4)        ST(5)        ST(6)        ST(7)        
        fld        dword ptr [ecx+4];    //    x1
        fsub    dword ptr [ecx-4];    //    x1-xm1
        fld        dword ptr [ecx];    //    x0            x1-xm1
        fsub    dword ptr [ecx+4];    //    v            x1-xm1
        fld        dword ptr [ecx+8];    //    x2            v            x1-xm1
        fsub    dword ptr [ecx];    //    x2-x0        v            x1-xm1
        fxch    st(2);                //    x1-m1        v            x2-x0
        fmul    c_half;                //    c            v            x2-x0
        fxch    st(2);                //    x2-x0        v            c
        fmul    c_half;                //    0.5*(x2-x0)    v            c
        fxch    st(2);                //    c            v            0.5*(x2-x0)
        fst        st(3);                //    c            v            0.5*(x2-x0)    c
        fadd    st(0), st(1);        //    w            v            0.5*(x2-x0)    c
        fxch    st(2);                //    0.5*(x2-x0)    v            w            c    
        faddp    st(1), st(0);        //  v+.5(x2-x0)    w            c    
        fadd    st(0), st(1);        //    a            w            c
        fadd    st(1), st(0);        //    a            b_neg        c
        fmul    dword ptr [esp+8];    //    a*frac        b_neg        c
        fsubp    st(1), st(0);        //    a*f-b        c
        fmul    dword ptr [esp+8];    //    (a*f-b)*f    c
        faddp    st(1), st(0);        //    res-x0/f
        fmul    dword ptr [esp+8];    //    res-x0
        fadd    dword ptr [ecx];    //    res
        pop        ecx;

from : dmi[at]smartelectronix
comment : This code produces a nasty buzzing sound. I think there might be a bug somwhere but I haven't found it yet.

from : hplus-musicdsp[at]mindcontrol[DOT]org
comment : I agree; the output, when plotted, looks like it has overlaid rectangular shapes on it.

from : robert[DOT]bielik[AT]rbcaudio[DOT]com
comment : AHH! True! A bug has sneaked in! Change the row that says: fsubp st(1), st(0); // a*f-b c to: fsubrp st(1), st(0); // a*f-b c and it should be much better. Although I noticed that a good optimization by the compiler generates nearly as fast a code, but only nearly. This is still about 10% faster.

from : dwerner[AT]experimentalscene[DOT]com
comment : I have tested the four hermite interpolation algorithms posted to musicdsp.org plus the assemblified version of Laurent de Soras' code by Robert Bielik and found that on a Pentium 4 with full optimization (targeting the Pentium 4 and above, but not using code that won't work on older processors) with MS VC++ 7 that the second function is the fastest. Function Percent Total Time Return Value hermite1: 18.90%, 375ms, 0.52500004f hermite2: 16.53%, 328ms, 0.52500004f hermite3: 17.34%, 344ms, 0.52500004f hermite4: 19.66%, 390ms, 0.52500004f hermite5: 27.57%, 547ms, 0.52500004f - Daniel Werner http://experimentalscene.com/