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Expose the normalized range for reciprocal square roots in fixed-point mode. This allows subsequnt calculations to use the full precision of the result.

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Timothy Terriberry 2009-10-31 10:19:06 -07:00 • committed by Jean-Marc Valin
parent 630ee44aaa
commit 8c7bb4c9c7
3 changed files with 42 additions and 20 deletions
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29
libcelt/mathops.h
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@ -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) */