Algorithm to find positive real solutions to quartic equations? - c

Question

I am using these algorithms on a microcontroller:
float32_t cubic(float32_t b,float32_t c,float32_t d)
{
float32_t p=c-b*b/3.0f;
float32_t q=2.0f*b*b*b/27.0f-b*c/3.0f+d;
if(fabsf(p)==0.0f) return powf(q,1.0f/3.0f);
if(fabsf(q)==0.0f){
PRINTF(INFO, "q=0 %f", p);
return 0.0f; // TODO
}
float32_t t=sqrtf(fabsf(p)/3.0f);
float32_t g=1.5f*q/(p*t);
if(p>0.0f)
return -2.0f*t*sinhf(asinhf(g)/3.0f)-b/3.0f;
if(4.0f*p*p*p+27.0f*q*q<0.0f)
return 2.0f*t*cosf(acosf(g)/3.0f)-b/3.0f;
if(q>0.0f)
return -2.0f*t*coshf(acoshf(-g)/3.0f)-b/3.0f;
return 2.0f*t*coshf(acoshf(g)/3.0f)-b/3.0f;
}
int quartic(float32_t b,float32_t c,float32_t d,float32_t e,float32_t* ans)
{
float32_t p=c-0.375f*b*b;
float32_t q=0.125f*b*b*b-0.5f*b*c+d;
float32_t m=cubic(p,0.25f*p*p+0.01171875f*b*b*b*b-e+0.25f*b*d-0.0625f*b*b*c,-0.125f*q*q);
if(fabsf(q)==0.0f)
{
if(m<0.0f) return 0;
int nroots=0;
float32_t sqrt_2m=sqrtf(2.0f*m);
if(-m-p>0.0f)
{
float32_t delta=sqrtf(2.0f*(-m-p));
ans[nroots++]=-0.25f*b+0.5f*(sqrt_2m-delta);
ans[nroots++]=-0.25f*b-0.5f*(sqrt_2m-delta);
ans[nroots++]=-0.25f*b+0.5f*(sqrt_2m+delta);
ans[nroots++]=-0.25f*b-0.5f*(sqrt_2m+delta);
}
if(fabsf(-m-p)==0.0f)
{
ans[nroots++]=-0.25f*b-0.5f*sqrt_2m;
ans[nroots++]=-0.25f*b+0.5f*sqrt_2m;
}
return nroots;
}
if(m<0.0f) return 0;
float32_t sqrt_2m=sqrtf(2.0f*m);
int nroots=0;
if(fabsf(-m-p+q/sqrt_2m)>=0.0f)
{
float32_t delta=sqrtf(2.0f*(-m-p+q/sqrt_2m));
ans[nroots++]=0.5f*(-sqrt_2m+delta)-0.25f*b;
ans[nroots++]=0.5f*(-sqrt_2m-delta)-0.25f*b;
}
if(fabsf(-m-p-q/sqrt_2m)>=0.0f)
{
float32_t delta=sqrtf(2.0f*(-m-p-q/sqrt_2m));
ans[nroots++]=0.5f*(sqrt_2m+delta)-0.25f*b;
ans[nroots++]=0.5f*(sqrt_2m-delta)-0.25f*b;
}
return nroots;
}
From: Specialised algorithm to find positive real solutions to quartic equations? (I can't comment on this thread because I haven't enough Stackoverflow privileges)
Is the same but with single precision instead of doubles.
With doubles it seems that works.
With singles, i have some points in which q=0 in the cubic function, so it returns m=0 for the quartic function and the result is not a real root. I get zeros.
I need to implement Matlab root method for real positive roots.
This point gives problems with the above code but has solution with roots in Matlab.
C1=53.3456154
C2=1729.59448
C3=54973.8164
C4=56.3456192
C5=1729.5946
C6=54973.8242
ans=single(roots([C5 (-C1+2*C4-C6) (3*C2-3*C5) (C1-2*C3+C6) -C2]))
r=r(r==conj(r));
r=r(r>0)
In Matlab the result is ok
ans =
31.7814 + 0i
-0.0000 + 1.0001i
-0.0000 - 1.0001i
-0.0315 + 0i
r = 31.7814