Interpolation is a technique by which the sample rate is increased in order to extend the frequency range. Interpolation can be of any order but rely upon a common interpolation/decimation factor. In the case here it is simple because the interpolation is an order of 2 ie: 1:4 so a simple interpolation filter is all that is required!
// Generate 1:4 samples via interpolation
bit set MODE1 PEYEN;
nop;
r4=dm(_audio48k); // data at 48k
r0=0;
r1=0;
// jump =(loops-1)*2
m2=0x1e;
m3=2;
m10=2;
r5=_coeffs_interpolate;
i4=_history192k;
r8=r0+r1, r12=r0-r1, i12=r5;
// Save data in history[30],[31]
r9=r0+r1, r13=r0-r1, dm(m2,i4)=r4;
r10=r0+r1, r14=r0-r1, r2=dm(m3,i4);
r11=r0+r1, r15=r0-r1;
// Loop 16 times filter = 64 coefficients
lcntr=0x10, do lpr4 until lce; // Calculate the 4 data streams
dm(i4,m3)=r2, r4=pm(i12,m10);
f12=f2*f4, f8=f8+f12, r4=pm(i12,m10);
f13=f2*f4, f9=f9+f13, r4=pm(i12,m10);
f14=f2*f4, f10=f10+f14, r4=pm(i12,m10);
lpr4: f15=f2*f4, f11=f11+f15, r2=dm(m3,i4);
// Last sums to tidy up the loop runover
f8=f8+f12;
f9=f9+f13;
f10=f10+f14;
f11=f11+f15;
i4=_audio192k; // Save data in blocks of 4
dm(0x6,i4)=r8;
dm(0x4,i4)=r9;
dm(m3,i4)=r10;
dm(m5,i4)=r11;
bit clr MODE1 PEYEN;
nop;