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Fix wrong residues for FP32+M61 and M31+M61 FFTs at low BPW (i96 sloppy carry word)… #351

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Fix wrong residues for FP32+M61 and M31+M61 FFTs at low BPW (i96 sloppy carry word)… #351

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7 changes: 6 additions & 1 deletion src/cl/carryutil.cl
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Expand Up @@ -681,7 +681,12 @@ Word OVERLOAD carryStepSignedSloppy(i96 x, i64 *outCarry, bool isBigWord) {
// i64 xhi = i96_hi64(x) + xmid_topbit;
// *outCarry = xhi >> (nBits - 32);
// return as_long((int2)(i96_lo32(x), whi));
#elif EXP / NWORDS == 31 || SLOPPY_MAXBPW >= 3200 // nBits = 31 or 32, bigwordBits = 32 (or allowed to create 32-bit word for better performance)
// Like the i64/i32 variant below, the sloppy 32-bit word fails when BPW is low. With 32-bit words the convolution digits
// reach ~2^63, and the carry that carryFinal then computes into its i32 tmpCarry (carryStep(i64, i32*) -> xtract32) needs
// about 63 - 2*nBits bits, i.e. more than 31 once nBits <= 15: the high bits are dropped and the residue is wrong.
// Observed with the FP32+M61 and M31+M61 FFTs (the i96 users) at 11.5-13.4 BPW (measured 39.5/36.2/33.9 bits needed;
// 29.5 at 14.5 BPW works); M3021377 reported composite, -prp Gerbicz errors. Same BPW guard as the i64 variant below.
#elif EXP / NWORDS == 31 || (EXP / NWORDS >= 23 && SLOPPY_MAXBPW >= 3200) // nBits = 31 or 32, bigwordBits = 32 (or allowed to create 32-bit word for better performance)
i32 w = i96_lo32(x); // lowBits(x, bigwordBits = 32);
*outCarry = (i96_hi64(x) + (w < 0)) << (32 - nBits);
return w;
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