Optimise EQ coef calculation routines for both speed and size. Move now unneeded fsqrt function to plugin fixed point library in case it'll be needed. Move all fixed point helper macros to dsp.h. Added FRACMUL_SHL macro to facilitate high-precision shifting of 64 bit multiplies and remove rounding from macsr in main thread to make this work as intended.

Tested quite thorougly, but as always, be careful with your ears.


git-svn-id: svn://svn.rockbox.org/rockbox/trunk@12203 a1c6a512-1295-4272-9138-f99709370657

1 files changed, 69 insertions, 114 deletions

diff --git a/apps/eq.c b/apps/eq.c
index bf562c73f2..588c23f89f 100644
--- a/apps/eq.c
+++ b/apps/eq.c
@@ -19,39 +19,9 @@
 
 #include <inttypes.h>
 #include "config.h"
+#include "dsp.h"
 #include "eq.h"
-
-/* Coef calculation taken from Audio-EQ-Cookbook.txt by Robert Bristow-Johnson.
-   Slightly faster calculation can be done by deriving forms which use tan()
-   instead of cos() and sin(), but the latter are far easier to use when doing
-   fixed point math, and performance is not a big point in the calculation part.
-   All the 'a' filter coefficients are negated so we can use only additions
-   in the filtering equation.
-   We realise the filters as a second order direct form 1 structure. Direct
-   form 1 was chosen because of better numerical properties for fixed point
-   implementations.
- */
-
-#define DIV64(x, y, z) (long)(((long long)(x) << (z))/(y))
-/* This macro requires the EMAC unit to be in fractional mode
-   when the coef generator routines are called. If this can't be guaranteed,
-   then add "&& 0" below. This will use a slower coef calculation on Coldfire.
- */
-#if defined(CPU_COLDFIRE) && !defined(SIMULATOR)
-#define FRACMUL(x, y) \
-({ \
-    long t; \
-    asm volatile ("mac.l    %[a], %[b], %%acc0\n\t" \
-                  "movclr.l %%acc0, %[t]\n\t" \
-                  : [t] "=r" (t) : [a] "r" (x), [b] "r" (y)); \
-    t; \
-})
-#else
-#define FRACMUL(x, y) ((long)(((((long long) (x)) * ((long long) (y))) >> 31)))
-#endif
-
-/* TODO: replaygain.c has some fixed point routines. perhaps we could reuse
-   them? */
+#include "replaygain.h"
 
 /* Inverse gain of circular cordic rotation in s0.31 format. */
 static const long cordic_circular_gain = 0xb2458939; /* 0.607252929 */
@@ -148,46 +118,8 @@ static long fsincos(unsigned long phase, long *cos) {
     return y;
 }
 
-/* Fixed point square root via Newton-Raphson.
- * Output is in same fixed point format as input. 
- * fracbits specifies number of fractional bits in argument.
- */
-static long fsqrt(long a, unsigned int fracbits)
-{
-    long b = a/2 + (1 << fracbits); /* initial approximation */
-    unsigned n;
-    const unsigned iterations = 4;
-    
-    for (n = 0; n < iterations; ++n)
-        b = (b + DIV64(a, b, fracbits))/2;
-
-    return b;
-}
-
-static const short dbtoatab[49] = {
-    2058, 2180, 2309, 2446, 2591, 2744, 2907, 3079, 3261, 3455, 3659, 3876,
-    4106, 4349, 4607, 4880, 5169, 5475, 5799, 6143, 6507, 6893, 7301, 7734,
-    8192, 8677, 9192, 9736, 10313, 10924, 11572, 12257, 12983, 13753, 14568,
-    15431, 16345, 17314, 18340, 19426, 20577, 21797, 23088, 24456, 25905, 27440,
-    29066, 30789, 32613
-};
-
-/* Function for converting dB to squared amplitude factor (A = 10^(dB/40)).
-   Range is -24 to 24 dB. If gain values outside of this is needed, the above
-   table needs to be extended.
-   Parameter format is s15.16 fixed point. Return format is s2.29 fixed point.
- */
-static long dbtoA(long db)
-{
-    const unsigned long bias = 24 << 16;
-    unsigned short frac = (db + bias) & 0x0000ffff;
-    unsigned short pos = (db + bias) >> 16;
-    short diff = dbtoatab[pos + 1] - dbtoatab[pos];
-    
-    return (dbtoatab[pos] << 16) + frac*diff;
-}
-
-/* Calculate first order shelving filter coefficients.
+/**
+ * Calculate first order shelving filter coefficients.
  * Note that the filter is not compatible with the eq_filter routine.
  * @param cutoff a value from 0 to 0x80000000, where 0 represents 0 Hz and
  * 0x80000000 represents the Nyquist frequency (samplerate/2).
@@ -205,8 +137,8 @@ void filter_bishelf_coefs(unsigned long cutoff, long ad, long an, int32_t *c)
     cs = one + (cs >> 4);
 
     /* For max A = 4 (24 dB) */
-    b0 = (FRACMUL(an, cs) << 4) + (FRACMUL(ad, s) << 4);
-    b1 = (FRACMUL(ad, s) << 4) - (FRACMUL(an, cs) << 4);
+    b0 = FRACMUL_SHL(an, cs, 4) + FRACMUL_SHL(ad, s, 4);
+    b1 = FRACMUL_SHL(ad, s, 4) - FRACMUL_SHL(an, cs, 4);
     a0 = s + cs;
     a1 = s - cs;
 
@@ -215,36 +147,48 @@ void filter_bishelf_coefs(unsigned long cutoff, long ad, long an, int32_t *c)
     c[2] = -DIV64(a1, a0, 31);
 }
 
+/* Coef calculation taken from Audio-EQ-Cookbook.txt by Robert Bristow-Johnson.
+ * Slightly faster calculation can be done by deriving forms which use tan()
+ * instead of cos() and sin(), but the latter are far easier to use when doing
+ * fixed point math, and performance is not a big point in the calculation part.
+ * All the 'a' filter coefficients are negated so we can use only additions
+ * in the filtering equation.
+ */
+
 /** 
  * Calculate second order section peaking filter coefficients.
  * @param cutoff a value from 0 to 0x80000000, where 0 represents 0 Hz and
  * 0x80000000 represents the Nyquist frequency (samplerate/2).
- * @param Q 16.16 fixed point value describing Q factor. Lower bound
- * is artificially set at 0.5.
- * @param db s15.16 fixed point value describing gain/attenuation at peak freq.
+ * @param Q Q factor value multiplied by ten. Lower bound is artificially set
+ * at 0.5.
+ * @param db decibel value multiplied by ten, describing gain/attenuation at
+ * peak freq.
  * @param c pointer to coefficient storage. Coefficients are s3.28 format.
  */
 void eq_pk_coefs(unsigned long cutoff, unsigned long Q, long db, int32_t *c)
 {
-    long cc;
+    long cs;
     const long one = 1 << 28; /* s3.28 */
-    const long A = dbtoA(db);
-    const long alpha = DIV64(fsincos(cutoff, &cc), 2*Q, 15); /* s1.30 */
+    const long A = get_replaygain_int(db*5) << 5; /* 10^(db/40), s2.29 */
+    const long alpha = fsincos(cutoff, &cs)/(2*Q)*10 >> 1; /* s1.30 */
     int32_t a0, a1, a2; /* these are all s3.28 format */
     int32_t b0, b1, b2;
+    const long alphadivA = DIV64(alpha, A, 27);
 
     /* possible numerical ranges are in comments by each coef */
     b0 = one + FRACMUL(alpha, A);     /* [1 .. 5] */
-    b1 = a1 = -2*(cc >> 3);           /* [-2 .. 2] */
+    b1 = a1 = -2*(cs >> 3);           /* [-2 .. 2] */
     b2 = one - FRACMUL(alpha, A);     /* [-3 .. 1] */
-    a0 = one + DIV64(alpha, A, 27);   /* [1 .. 5] */
-    a2 = one - DIV64(alpha, A, 27);   /* [-3 .. 1] */
-
-    c[0] = DIV64(b0, a0, 28);         /* [0.25 .. 4] */
-    c[1] = DIV64(b1, a0, 28);         /* [-2 .. 2] */
-    c[2] = DIV64(b2, a0, 28);         /* [-2.4 .. 1] */
-    c[3] = DIV64(-a1, a0, 28);        /* [-2 .. 2] */
-    c[4] = DIV64(-a2, a0, 28);        /* [-0.6 .. 1] */
+    a0 = one + alphadivA;             /* [1 .. 5] */
+    a2 = one - alphadivA;             /* [-3 .. 1] */
+
+    /* range of this is roughly [0.2 .. 1], but we'll never hit 1 completely */
+    const long rcp_a0 = DIV64(1, a0, 59); /* s0.31 */
+    *c++ = FRACMUL(b0, rcp_a0);         /* [0.25 .. 4] */
+    *c++ = FRACMUL(b1, rcp_a0);         /* [-2 .. 2] */
+    *c++ = FRACMUL(b2, rcp_a0);         /* [-2.4 .. 1] */
+    *c++ = FRACMUL(-a1, rcp_a0);        /* [-2 .. 2] */
+    *c++ = FRACMUL(-a2, rcp_a0);        /* [-0.6 .. 1] */
 }
 
 /**
@@ -255,20 +199,21 @@ void eq_ls_coefs(unsigned long cutoff, unsigned long Q, long db, int32_t *c)
 {
     long cs;
     const long one = 1 << 25; /* s6.25 */
-    const long A = dbtoA(db);
-    const long alpha = DIV64(fsincos(cutoff, &cs), 2*Q, 15); /* s1.30 */
+    const long sqrtA = get_replaygain_int(db*5/2) << 2; /* 10^(db/80), s5.26 */
+    const long A = FRACMUL_SHL(sqrtA, sqrtA, 8); /* s2.29 */
+    const long alpha = fsincos(cutoff, &cs)/(2*Q)*10 >> 1; /* s1.30 */
     const long ap1 = (A >> 4) + one;
     const long am1 = (A >> 4) - one;
-    const long twosqrtalpha = 2*FRACMUL(fsqrt(A >> 3, 26), alpha);
+    const long twosqrtalpha = 2*FRACMUL(sqrtA, alpha);
     int32_t a0, a1, a2; /* these are all s6.25 format */
     int32_t b0, b1, b2;
     
     /* [0.1 .. 40] */
-    b0 = FRACMUL(A, ap1 - FRACMUL(am1, cs) + twosqrtalpha) << 2;
+    b0 = FRACMUL_SHL(A, ap1 - FRACMUL(am1, cs) + twosqrtalpha, 2);
     /* [-16 .. 63.4] */
-    b1 = FRACMUL(A, am1 - FRACMUL(ap1, cs)) << 3;
+    b1 = FRACMUL_SHL(A, am1 - FRACMUL(ap1, cs), 3);
     /* [0 .. 31.7] */
-    b2 = FRACMUL(A, ap1 - FRACMUL(am1, cs) - twosqrtalpha) << 2;
+    b2 = FRACMUL_SHL(A, ap1 - FRACMUL(am1, cs) - twosqrtalpha, 2);
     /* [0.5 .. 10] */
     a0 = ap1 + FRACMUL(am1, cs) + twosqrtalpha;
     /* [-16 .. 4] */
@@ -276,11 +221,13 @@ void eq_ls_coefs(unsigned long cutoff, unsigned long Q, long db, int32_t *c)
     /* [0 .. 8] */
     a2 = ap1 + FRACMUL(am1, cs) - twosqrtalpha;
 
-    c[0] = DIV64(b0, a0, 26);       /* [0.06 .. 15.9] */
-    c[1] = DIV64(b1, a0, 26);       /* [-2 .. 31.7] */
-    c[2] = DIV64(b2, a0, 26);       /* [0 .. 15.9] */
-    c[3] = DIV64(-a1, a0, 26);      /* [-2 .. 2] */
-    c[4] = DIV64(-a2, a0, 26);      /* [0 .. 1] */
+    /* [0.1 .. 1.99] */
+    const long rcp_a0 = DIV64(1, a0, 55); /* s1.30 */
+    *c++ = FRACMUL_SHL(b0, rcp_a0, 2);       /* [0.06 .. 15.9] */
+    *c++ = FRACMUL_SHL(b1, rcp_a0, 2);       /* [-2 .. 31.7] */
+    *c++ = FRACMUL_SHL(b2, rcp_a0, 2);       /* [0 .. 15.9] */
+    *c++ = FRACMUL_SHL(-a1, rcp_a0, 2);      /* [-2 .. 2] */
+    *c++ = FRACMUL_SHL(-a2, rcp_a0, 2);      /* [0 .. 1] */
 }
 
 /**
@@ -290,21 +237,22 @@ void eq_ls_coefs(unsigned long cutoff, unsigned long Q, long db, int32_t *c)
 void eq_hs_coefs(unsigned long cutoff, unsigned long Q, long db, int32_t *c)
 {
     long cs;
-    const int one = 1 << 25; /* s6.25 */
-    const int A = dbtoA(db);
-    const int alpha = DIV64(fsincos(cutoff, &cs), 2*Q, 15); /* s1.30 */
-    const int ap1 = (A >> 4) + one;
-    const int am1 = (A >> 4) - one;
-    const int twosqrtalpha = 2*FRACMUL(fsqrt(A >> 3, 26), alpha);
+    const long one = 1 << 25; /* s6.25 */
+    const long sqrtA = get_replaygain_int(db*5/2) << 2; /* 10^(db/80), s5.26 */
+    const long A = FRACMUL_SHL(sqrtA, sqrtA, 8); /* s2.29 */
+    const long alpha = fsincos(cutoff, &cs)/(2*Q)*10 >> 1; /* s1.30 */
+    const long ap1 = (A >> 4) + one;
+    const long am1 = (A >> 4) - one;
+    const long twosqrtalpha = 2*FRACMUL(sqrtA, alpha);
     int32_t a0, a1, a2; /* these are all s6.25 format */
     int32_t b0, b1, b2;
 
     /* [0.1 .. 40] */
-    b0 = FRACMUL(A, ap1 + FRACMUL(am1, cs) + twosqrtalpha) << 2;
+    b0 = FRACMUL_SHL(A, ap1 + FRACMUL(am1, cs) + twosqrtalpha, 2);
     /* [-63.5 .. 16] */
-    b1 = -FRACMUL(A, am1 + FRACMUL(ap1, cs)) << 3;
+    b1 = -FRACMUL_SHL(A, am1 + FRACMUL(ap1, cs), 3);
     /* [0 .. 32] */
-    b2 = FRACMUL(A, ap1 + FRACMUL(am1, cs) - twosqrtalpha) << 2;
+    b2 = FRACMUL_SHL(A, ap1 + FRACMUL(am1, cs) - twosqrtalpha, 2);
     /* [0.5 .. 10] */
     a0 = ap1 - FRACMUL(am1, cs) + twosqrtalpha;
     /* [-4 .. 16] */
@@ -312,13 +260,20 @@ void eq_hs_coefs(unsigned long cutoff, unsigned long Q, long db, int32_t *c)
     /* [0 .. 8] */
     a2 = ap1 - FRACMUL(am1, cs) - twosqrtalpha;
 
-    c[0] = DIV64(b0, a0, 26);       /* [0 .. 16] */
-    c[1] = DIV64(b1, a0, 26);       /* [-31.7 .. 2] */
-    c[2] = DIV64(b2, a0, 26);       /* [0 .. 16] */
-    c[3] = DIV64(-a1, a0, 26);      /* [-2 .. 2] */
-    c[4] = DIV64(-a2, a0, 26);      /* [0 .. 1] */
+    /* [0.1 .. 1.99] */
+    const long rcp_a0 = DIV64(1, a0, 55); /* s1.30 */
+    *c++ = FRACMUL_SHL(b0, rcp_a0, 2);       /* [0 .. 16] */
+    *c++ = FRACMUL_SHL(b1, rcp_a0, 2);       /* [-31.7 .. 2] */
+    *c++ = FRACMUL_SHL(b2, rcp_a0, 2);       /* [0 .. 16] */
+    *c++ = FRACMUL_SHL(-a1, rcp_a0, 2);      /* [-2 .. 2] */
+    *c++ = FRACMUL_SHL(-a2, rcp_a0, 2);      /* [0 .. 1] */
 }
 
+/* We realise the filters as a second order direct form 1 structure. Direct
+ * form 1 was chosen because of better numerical properties for fixed point
+ * implementations.
+ */
+
 #if (!defined(CPU_COLDFIRE) && !defined(CPU_ARM)) || defined(SIMULATOR)
 void eq_filter(int32_t **x, struct eqfilter *f, unsigned num,
                unsigned channels, unsigned shift)