Commit 8c7bb4c9 by Timothy Terriberry Committed by Jean-Marc Valin

### Expose the normalized range for reciprocal square roots in fixed-point mode....

`Expose the normalized range for reciprocal square roots in fixed-point mode. This allows subsequnt calculations to use the full precision of the result.`
parent 630ee44a
 ... ... @@ -106,6 +106,7 @@ static inline celt_int16 bitexact_cos(celt_int16 x) #define celt_sqrt(x) ((float)sqrt(x)) #define celt_psqrt(x) ((float)sqrt(x)) #define celt_rsqrt(x) (1.f/celt_sqrt(x)) #define celt_rsqrt_norm(x) (celt_rsqrt(x)) #define celt_acos acos #define celt_exp exp #define celt_cos_norm(x) (cos((.5f*M_PI)*(x))) ... ... @@ -186,17 +187,13 @@ static inline celt_int16 celt_zlog2(celt_word32 x) return x <= 0 ? 0 : celt_ilog2(x); } /** Reciprocal sqrt approximation (Q30 input, Q0 output or equivalent) */ static inline celt_word32 celt_rsqrt(celt_word32 x) /** Reciprocal sqrt approximation in the range [0.25,1) (Q16 in, Q14 out) */ static inline celt_word16 celt_rsqrt_norm(celt_word32 x) { int k; celt_word16 n; celt_word16 r; celt_word16 r2; celt_word16 y; celt_word32 rt; k = celt_ilog2(x)>>1; x = VSHR32(x, (k-7)<<1); /* Range of n is [-16384,32767] ([-0.5,1) in Q15). */ n = x-32768; /* Get a rough initial guess for the root. ... ... @@ -210,15 +207,21 @@ static inline celt_word32 celt_rsqrt(celt_word32 x) Range of y is [-1564,1594]. */ 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*y*(y*0.375-0.5). */ rt = ADD16(r, MULT16_16_Q15(r, MULT16_16_Q15(y, SUB16(MULT16_16_Q15(y, 12288), 16384)))); /* rt is now the Q14 reciprocal square root of the Q16 x, with a maximum /* Apply a 2nd-order Householder iteration: r += r*y*(y*0.375-0.5). This yields the Q14 reciprocal square root of the Q16 x, with a maximum relative error of 1.04956E-4, a (relative) RMSE of 2.80979E-5, and a peak absolute error of 2.26591/16384. */ /* Most of the error in this function comes from the following shift: */ rt = PSHR32(rt,k); return rt; return ADD16(r, MULT16_16_Q15(r, MULT16_16_Q15(y, SUB16(MULT16_16_Q15(y, 12288), 16384)))); } /** Reciprocal sqrt approximation (Q30 input, Q0 output or equivalent) */ static inline celt_word32 celt_rsqrt(celt_word32 x) { int k; k = celt_ilog2(x)>>1; x = VSHR32(x, (k-7)<<1); return PSHR32(celt_rsqrt_norm(x), k); } /** Sqrt approximation (QX input, QX/2 output) */ ... ...
 ... ... @@ -215,10 +215,21 @@ void find_spectral_pitch(const CELTMode *m, kiss_fftr_cfg fft, const struct PsyD Xr = MULT16_16_16(n, Xr); Xi = MULT16_16_16(n, Xi); #else n = celt_rsqrt(EPSILON+curve[i]); /* Pre-multiply X by n, so we can keep everything in 16 bits */ Xr = EXTRACT16(SHR32(MULT16_16(n, Xr),3)); Xi = EXTRACT16(SHR32(MULT16_16(n, Xi),3)); { celt_word32 t; #ifdef FIXED_POINT int k; #endif t = EPSILON+curve[i]; #ifdef FIXED_POINT k = celt_ilog2(t)>>1; #endif t = VSHR32(t, (k-7)<<1); n = celt_rsqrt_norm(t); /* Pre-multiply X by n, so we can keep everything in 16 bits */ Xr = EXTRACT16(PSHR32(MULT16_16(n, Xr),3+k)); Xi = EXTRACT16(PSHR32(MULT16_16(n, Xi),3+k)); } #endif /* Cross-spectrum between X and conj(Y) */ *Xptr++ = ADD16(MULT16_16_Q15(Xr, Yptr[0]), MULT16_16_Q15(Xi,Yptr[1])); ... ...
 ... ... @@ -103,13 +103,21 @@ static void exp_rotation(celt_norm *X, int len, int dir, int stride, int K) static void normalise_residual(int * restrict iy, celt_norm * restrict X, int N, int K, celt_word32 Ryy) { int i; celt_word32 g; #ifdef FIXED_POINT int k; #endif celt_word32 t; celt_word16 g; g = celt_rsqrt(Ryy); #ifdef FIXED_POINT k = celt_ilog2(Ryy)>>1; #endif t = VSHR32(Ryy, (k-7)<<1); g = celt_rsqrt_norm(t); i=0; do X[i] = EXTRACT16(SHR32(MULT16_16(g, iy[i]),1)); X[i] = EXTRACT16(PSHR32(MULT16_16(g, iy[i]), k+1)); while (++i < N); } ... ...
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