Commit 4a275d4d by Timothy B. Terriberry Committed by Jean-Marc Valin

### Accuracy improvements to the fixed-point celt_rsqrt().

parent a3bba38b
 ... ... @@ -190,15 +190,32 @@ static inline celt_word32 celt_rsqrt(celt_word32 x) { int k; celt_word16 n; celt_word16 r; celt_word16 r2; celt_word16 y; celt_word32 rt; const celt_word16 C[5] = {23126, -11496, 9812, -9097, 4100}; k = celt_ilog2(x)>>1; x = VSHR32(x, (k-7)<<1); /* Range of n is [-16384,32767] */ /* Range of n is [-16384,32767] ([-0.5,1) in Q15). */ n = x-32768; rt = ADD16(C[0], MULT16_16_Q15(n, ADD16(C[1], MULT16_16_Q15(n, ADD16(C[2], MULT16_16_Q15(n, ADD16(C[3], MULT16_16_Q15(n, (C[4]))))))))); rt = VSHR32(rt,k); /* Get a rough initial guess for the root. The optimal minimax quadratic approximation is r = 1.4288615575712422-n*(0.8452316405039975+n*0.4519141640876117). Coefficients here, and the final result r, are Q14.*/ r = ADD16(23410, MULT16_16_Q15(n, ADD16(-13848, MULT16_16_Q15(n, 7405)))); /* We want y = x*r*r-1 in Q15, but x is 32-bit Q16 and r is Q14. We can compute the result from n and r using Q15 multiplies with some adjustment, carefully done to avoid overflow. Range of y is [-2014,2362]. */ r2 = MULT16_16_Q15(r, r); y = SHL16(SUB16(ADD16(MULT16_16_Q15(r2, n), r2), 16384), 1); /* Apply a 2nd-order Householder iteration: r' = r*(1+y*(-0.5+y*0.375)). */ rt = ADD16(r, MULT16_16_Q15(r, MULT16_16_Q15(y, ADD16(-16384, MULT16_16_Q15(y, 12288))))); /* rt is now the Q14 reciprocal square root of the Q16 x, with a maximum error of 2.70970/16384 and a MSE of 0.587003/16384^2. */ /* Most of the error in this approximation comes from the following shift: */ rt = PSHR32(rt,k); return rt; } ... ...
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