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imdct.go
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imdct.go
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package vorbis
import "math"
type imdctLookup struct {
A, B, C []float32
}
func generateIMDCTLookup(n int, l *imdctLookup) {
l.A = make([]float32, n/2)
l.B = make([]float32, n/2)
l.C = make([]float32, n/4)
fn := float64(n)
for k := 0; k < n/4; k++ {
fk := float64(k)
l.A[2*k] = float32(math.Cos(4 * fk * math.Pi / fn))
l.A[2*k+1] = float32(-math.Sin(4 * fk * math.Pi / fn))
l.B[2*k] = float32(math.Cos((2*fk + 1) * math.Pi / fn / 2))
l.B[2*k+1] = float32(math.Sin((2*fk + 1) * math.Pi / fn / 2))
}
for k := 0; k < n/8; k++ {
fk := float64(k)
l.C[2*k] = float32(math.Cos(2 * (2*fk + 1) * math.Pi / fn))
l.C[2*k+1] = float32(-math.Sin(2 * (2*fk + 1) * math.Pi / fn))
}
}
// "inverse modified discrete cosine transform"
func imdct(t *imdctLookup, in, out []float32) {
n := len(in) * 2
n2, n4, n8 := n/2, n/4, n/8
n3_4 := n - n4
// more of these steps could be done in place, but we need two arrays anyway
for j := 0; j < n8; j++ {
a0 := t.A[n2-2*j-1]
a1 := t.A[n2-2*j-2]
a2 := t.A[n4-2*j-1]
a3 := t.A[n4-2*j-2]
a4 := t.A[n2-4-4*j]
a5 := t.A[n2-3-4*j]
v0 := (-in[4*j+3])*a0 + (-in[4*j+1])*a1
v1 := (-in[4*j+3])*a1 - (-in[4*j+1])*a0
v2 := (in[n2-4*j-4])*a2 + (in[n2-4*j-2])*a3
v3 := (in[n2-4*j-4])*a3 - (in[n2-4*j-2])*a2
out[n4+2*j+1] = v3 + v1
out[n4+2*j] = v2 + v0
out[2*j+1] = (v3-v1)*a4 - (v2-v0)*a5
out[2*j] = (v2-v0)*a4 + (v3-v1)*a5
}
ld := int(ilog(n) - 1)
for l := 0; l < ld-3; l++ {
k0 := n >> uint(l+3)
k1 := 1 << uint(l+3)
rlim := n >> uint(l+4)
s2lim := 1 << uint(l+2)
for r := 0; r < rlim; r++ {
a0 := t.A[r*k1]
a1 := t.A[r*k1+1]
i0 := n2 - 1 - 2*r
i1 := n2 - 2 - 2*r
i2 := n2 - 1 - k0 - 2*r
i3 := n2 - 2 - k0 - 2*r
for s2 := 0; s2 < s2lim; s2 += 2 {
v0, v1 := out[i0], out[i1]
v2, v3 := out[i2], out[i3]
out[i0] = v0 + v2
out[i1] = v1 + v3
out[i2] = (v0-v2)*a0 - (v1-v3)*a1
out[i3] = (v1-v3)*a0 + (v0-v2)*a1
i0 -= 2 * k0
i1 -= 2 * k0
i2 -= 2 * k0
i3 -= 2 * k0
}
}
}
for i := 0; i < n8; i++ {
j := int(bitReverse(uint32(i)) >> uint(32-ld+3))
if i < j {
out[4*j], out[4*i] = out[4*i], out[4*j]
out[4*j+1], out[4*i+1] = out[4*i+1], out[4*j+1]
out[4*j+2], out[4*i+2] = out[4*i+2], out[4*j+2]
out[4*j+3], out[4*i+3] = out[4*i+3], out[4*j+3]
}
}
for k := 0; k < n8; k++ {
in[n2-1-2*k] = out[4*k]
in[n2-2-2*k] = out[4*k+1]
in[n4-1-2*k] = out[4*k+2]
in[n4-2-2*k] = out[4*k+3]
}
i0 := 0
i1 := 1
i2 := n2 - 2
i3 := n2 - 1
for k := 0; k < n8; k++ {
v0, v1 := in[i0], in[i1]
v2, v3 := in[i2], in[i3]
c0 := t.C[i0]
c1 := t.C[i1]
out[i0] = (v0 + v2 + c1*(v0-v2) + c0*(v1+v3)) / 2
out[i2] = (v0 + v2 - c1*(v0-v2) - c0*(v1+v3)) / 2
out[i1] = (v1 - v3 + c1*(v1+v3) - c0*(v0-v2)) / 2
out[i3] = (-v1 + v3 + c1*(v1+v3) - c0*(v0-v2)) / 2
i0 += 2
i1 += 2
i2 -= 2
i3 -= 2
}
for k := 0; k < n4; k++ {
b0 := t.B[2*k]
b1 := t.B[2*k+1]
v0 := out[2*k]
v1 := out[2*k+1]
in[k] = v0*b0 + v1*b1
in[n2-1-k] = v0*b1 - v1*b0
}
for i := 0; i < n4; i++ {
out[i] = in[i+n4]
out[n-i-1] = -in[n-i-n3_4-1]
}
for i := n4; i < n3_4; i++ {
out[i] = -in[n3_4-i-1]
}
}
func bitReverse(n uint32) uint32 {
n = ((n & 0xAAAAAAAA) >> 1) | ((n & 0x55555555) << 1)
n = ((n & 0xCCCCCCCC) >> 2) | ((n & 0x33333333) << 2)
n = ((n & 0xF0F0F0F0) >> 4) | ((n & 0x0F0F0F0F) << 4)
n = ((n & 0xFF00FF00) >> 8) | ((n & 0x00FF00FF) << 8)
return (n >> 16) | (n << 16)
}
// original c code from stb_vorbis
/*
// this is the original version of the above code, if you want to optimize it from scratch
void inverse_mdct_naive(float *buffer, int n)
{
float s;
float A[1 << 12], B[1 << 12], C[1 << 11];
int i,k,k2,k4, n2 = n >> 1, n4 = n >> 2, n8 = n >> 3, l;
int n3_4 = n - n4, ld;
// how can they claim this only uses N words?!
// oh, because they're only used sparsely, whoops
float u[1 << 13], X[1 << 13], v[1 << 13], w[1 << 13];
// set up twiddle factors
for (k=k2=0; k < n4; ++k,k2+=2) {
A[k2 ] = (float) cos(4*k*M_PI/n);
A[k2+1] = (float) -sin(4*k*M_PI/n);
B[k2 ] = (float) cos((k2+1)*M_PI/n/2);
B[k2+1] = (float) sin((k2+1)*M_PI/n/2);
}
for (k=k2=0; k < n8; ++k,k2+=2) {
C[k2 ] = (float) cos(2*(k2+1)*M_PI/n);
C[k2+1] = (float) -sin(2*(k2+1)*M_PI/n);
}
// IMDCT algorithm from "The use of multirate filter banks for coding of high quality digital audio"
// Note there are bugs in that pseudocode, presumably due to them attempting
// to rename the arrays nicely rather than representing the way their actual
// implementation bounces buffers back and forth. As a result, even in the
// "some formulars corrected" version, a direct implementation fails. These
// are noted below as "paper bug".
// copy and reflect spectral data
for (k=0; k < n2; ++k) u[k] = buffer[k];
for ( ; k < n ; ++k) u[k] = -buffer[n - k - 1];
// kernel from paper
// step 1
for (k=k2=k4=0; k < n4; k+=1, k2+=2, k4+=4) {
v[n-k4-1] = (u[k4] - u[n-k4-1]) * A[k2] - (u[k4+2] - u[n-k4-3])*A[k2+1];
v[n-k4-3] = (u[k4] - u[n-k4-1]) * A[k2+1] + (u[k4+2] - u[n-k4-3])*A[k2];
}
// step 2
for (k=k4=0; k < n8; k+=1, k4+=4) {
w[n2+3+k4] = v[n2+3+k4] + v[k4+3];
w[n2+1+k4] = v[n2+1+k4] + v[k4+1];
w[k4+3] = (v[n2+3+k4] - v[k4+3])*A[n2-4-k4] - (v[n2+1+k4]-v[k4+1])*A[n2-3-k4];
w[k4+1] = (v[n2+1+k4] - v[k4+1])*A[n2-4-k4] + (v[n2+3+k4]-v[k4+3])*A[n2-3-k4];
}
// step 3
ld = ilog(n) - 1; // ilog is off-by-one from normal definitions
for (l=0; l < ld-3; ++l) {
int k0 = n >> (l+2), k1 = 1 << (l+3);
int rlim = n >> (l+4), r4, r;
int s2lim = 1 << (l+2), s2;
for (r=r4=0; r < rlim; r4+=4,++r) {
for (s2=0; s2 < s2lim; s2+=2) {
u[n-1-k0*s2-r4] = w[n-1-k0*s2-r4] + w[n-1-k0*(s2+1)-r4];
u[n-3-k0*s2-r4] = w[n-3-k0*s2-r4] + w[n-3-k0*(s2+1)-r4];
u[n-1-k0*(s2+1)-r4] = (w[n-1-k0*s2-r4] - w[n-1-k0*(s2+1)-r4]) * A[r*k1]
- (w[n-3-k0*s2-r4] - w[n-3-k0*(s2+1)-r4]) * A[r*k1+1];
u[n-3-k0*(s2+1)-r4] = (w[n-3-k0*s2-r4] - w[n-3-k0*(s2+1)-r4]) * A[r*k1]
+ (w[n-1-k0*s2-r4] - w[n-1-k0*(s2+1)-r4]) * A[r*k1+1];
}
}
if (l+1 < ld-3) {
// paper bug: ping-ponging of u&w here is omitted
memcpy(w, u, sizeof(u));
}
}
// step 4
for (i=0; i < n8; ++i) {
int j = bit_reverse(i) >> (32-ld+3);
assert(j < n8);
if (i == j) {
// paper bug: original code probably swapped in place; if copying,
// need to directly copy in this case
int i8 = i << 3;
v[i8+1] = u[i8+1];
v[i8+3] = u[i8+3];
v[i8+5] = u[i8+5];
v[i8+7] = u[i8+7];
} else if (i < j) {
int i8 = i << 3, j8 = j << 3;
v[j8+1] = u[i8+1], v[i8+1] = u[j8 + 1];
v[j8+3] = u[i8+3], v[i8+3] = u[j8 + 3];
v[j8+5] = u[i8+5], v[i8+5] = u[j8 + 5];
v[j8+7] = u[i8+7], v[i8+7] = u[j8 + 7];
}
}
// step 5
for (k=0; k < n2; ++k) {
w[k] = v[k*2+1];
}
// step 6
for (k=k2=k4=0; k < n8; ++k, k2 += 2, k4 += 4) {
u[n-1-k2] = w[k4];
u[n-2-k2] = w[k4+1];
u[n3_4 - 1 - k2] = w[k4+2];
u[n3_4 - 2 - k2] = w[k4+3];
}
// step 7
for (k=k2=0; k < n8; ++k, k2 += 2) {
v[n2 + k2 ] = ( u[n2 + k2] + u[n-2-k2] + C[k2+1]*(u[n2+k2]-u[n-2-k2]) + C[k2]*(u[n2+k2+1]+u[n-2-k2+1]))/2;
v[n-2 - k2] = ( u[n2 + k2] + u[n-2-k2] - C[k2+1]*(u[n2+k2]-u[n-2-k2]) - C[k2]*(u[n2+k2+1]+u[n-2-k2+1]))/2;
v[n2+1+ k2] = ( u[n2+1+k2] - u[n-1-k2] + C[k2+1]*(u[n2+1+k2]+u[n-1-k2]) - C[k2]*(u[n2+k2]-u[n-2-k2]))/2;
v[n-1 - k2] = (-u[n2+1+k2] + u[n-1-k2] + C[k2+1]*(u[n2+1+k2]+u[n-1-k2]) - C[k2]*(u[n2+k2]-u[n-2-k2]))/2;
}
// step 8
for (k=k2=0; k < n4; ++k,k2 += 2) {
X[k] = v[k2+n2]*B[k2 ] + v[k2+1+n2]*B[k2+1];
X[n2-1-k] = v[k2+n2]*B[k2+1] - v[k2+1+n2]*B[k2 ];
}
// decode kernel to output
// determined the following value experimentally
// (by first figuring out what made inverse_mdct_slow work); then matching that here
// (probably vorbis encoder premultiplies by n or n/2, to save it on the decoder?)
s = 0.5; // theoretically would be n4
// [[[ note! the s value of 0.5 is compensated for by the B[] in the current code,
// so it needs to use the "old" B values to behave correctly, or else
// set s to 1.0 ]]]
for (i=0; i < n4 ; ++i) buffer[i] = s * X[i+n4];
for ( ; i < n3_4; ++i) buffer[i] = -s * X[n3_4 - i - 1];
for ( ; i < n ; ++i) buffer[i] = -s * X[i - n3_4];
}
*/