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overte-HifiExperiments/libraries/audio/src/AudioHRTF.cpp
Ken Cooke fa55fc84f5 Optimized compute of distance filters using log-quantized lookup tables. 
Magnitude error < 0.25dB for entire parameter space.
2016-07-14 12:04:05 -07:00

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//
// AudioHRTF.cpp
// libraries/audio/src
//
// Created by Ken Cooke on 1/17/16.
// Copyright 2016 High Fidelity, Inc.
//
// Distributed under the Apache License, Version 2.0.
// See the accompanying file LICENSE or http://www.apache.org/licenses/LICENSE-2.0.html
//
#include <math.h>
#include <string.h>
#include <assert.h>
#include "AudioHRTF.h"
#include "AudioHRTFData.h"
#ifndef MAX
#define MAX(a,b) (((a) > (b)) ? (a) : (b))
#endif
#ifndef MIN
#define MIN(a,b) (((a) < (b)) ? (a) : (b))
#endif
//
// Equal-gain crossfade
//
// Cos(x)^2 window minimizes the modulation sidebands when a pure tone is panned.
// Transients in the time-varying Thiran allpass filter are eliminated by the initial delay.
// Valimaki, Laakso. "Elimination of Transients in Time-Varying Allpass Fractional Delay Filters"
//
static const float crossfadeTable[HRTF_BLOCK] = {
1.0000000000f, 1.0000000000f, 1.0000000000f, 1.0000000000f, 1.0000000000f, 0.9999611462f, 0.9998445910f, 0.9996503524f,
0.9993784606f, 0.9990289579f, 0.9986018986f, 0.9980973490f, 0.9975153877f, 0.9968561049f, 0.9961196033f, 0.9953059972f,
0.9944154131f, 0.9934479894f, 0.9924038765f, 0.9912832366f, 0.9900862439f, 0.9888130845f, 0.9874639561f, 0.9860390685f,
0.9845386431f, 0.9829629131f, 0.9813121235f, 0.9795865307f, 0.9777864029f, 0.9759120199f, 0.9739636731f, 0.9719416652f,
0.9698463104f, 0.9676779344f, 0.9654368743f, 0.9631234783f, 0.9607381059f, 0.9582811279f, 0.9557529262f, 0.9531538935f,
0.9504844340f, 0.9477449623f, 0.9449359044f, 0.9420576968f, 0.9391107867f, 0.9360956322f, 0.9330127019f, 0.9298624749f,
0.9266454408f, 0.9233620996f, 0.9200129616f, 0.9165985472f, 0.9131193872f, 0.9095760221f, 0.9059690029f, 0.9022988899f,
0.8985662536f, 0.8947716742f, 0.8909157412f, 0.8869990541f, 0.8830222216f, 0.8789858616f, 0.8748906015f, 0.8707370778f,
0.8665259359f, 0.8622578304f, 0.8579334246f, 0.8535533906f, 0.8491184090f, 0.8446291692f, 0.8400863689f, 0.8354907140f,
0.8308429188f, 0.8261437056f, 0.8213938048f, 0.8165939546f, 0.8117449009f, 0.8068473974f, 0.8019022052f, 0.7969100928f,
0.7918718361f, 0.7867882182f, 0.7816600290f, 0.7764880657f, 0.7712731319f, 0.7660160383f, 0.7607176017f, 0.7553786457f,
0.7500000000f, 0.7445825006f, 0.7391269893f, 0.7336343141f, 0.7281053287f, 0.7225408922f, 0.7169418696f, 0.7113091309f,
0.7056435516f, 0.6999460122f, 0.6942173981f, 0.6884585998f, 0.6826705122f, 0.6768540348f, 0.6710100717f, 0.6651395310f,
0.6592433251f, 0.6533223705f, 0.6473775872f, 0.6414098993f, 0.6354202341f, 0.6294095226f, 0.6233786988f, 0.6173287002f,
0.6112604670f, 0.6051749422f, 0.5990730716f, 0.5929558036f, 0.5868240888f, 0.5806788803f, 0.5745211331f, 0.5683518042f,
0.5621718523f, 0.5559822381f, 0.5497839233f, 0.5435778714f, 0.5373650468f, 0.5311464151f, 0.5249229428f, 0.5186955971f,
0.5124653459f, 0.5062331573f, 0.5000000000f, 0.4937668427f, 0.4875346541f, 0.4813044029f, 0.4750770572f, 0.4688535849f,
0.4626349532f, 0.4564221286f, 0.4502160767f, 0.4440177619f, 0.4378281477f, 0.4316481958f, 0.4254788669f, 0.4193211197f,
0.4131759112f, 0.4070441964f, 0.4009269284f, 0.3948250578f, 0.3887395330f, 0.3826712998f, 0.3766213012f, 0.3705904774f,
0.3645797659f, 0.3585901007f, 0.3526224128f, 0.3466776295f, 0.3407566749f, 0.3348604690f, 0.3289899283f, 0.3231459652f,
0.3173294878f, 0.3115414002f, 0.3057826019f, 0.3000539878f, 0.2943564484f, 0.2886908691f, 0.2830581304f, 0.2774591078f,
0.2718946713f, 0.2663656859f, 0.2608730107f, 0.2554174994f, 0.2500000000f, 0.2446213543f, 0.2392823983f, 0.2339839617f,
0.2287268681f, 0.2235119343f, 0.2183399710f, 0.2132117818f, 0.2081281639f, 0.2030899072f, 0.1980977948f, 0.1931526026f,
0.1882550991f, 0.1834060454f, 0.1786061952f, 0.1738562944f, 0.1691570812f, 0.1645092860f, 0.1599136311f, 0.1553708308f,
0.1508815910f, 0.1464466094f, 0.1420665754f, 0.1377421696f, 0.1334740641f, 0.1292629222f, 0.1251093985f, 0.1210141384f,
0.1169777784f, 0.1130009459f, 0.1090842588f, 0.1052283258f, 0.1014337464f, 0.0977011101f, 0.0940309971f, 0.0904239779f,
0.0868806128f, 0.0834014528f, 0.0799870384f, 0.0766379004f, 0.0733545592f, 0.0701375251f, 0.0669872981f, 0.0639043678f,
0.0608892133f, 0.0579423032f, 0.0550640956f, 0.0522550377f, 0.0495155660f, 0.0468461065f, 0.0442470738f, 0.0417188721f,
0.0392618941f, 0.0368765217f, 0.0345631257f, 0.0323220656f, 0.0301536896f, 0.0280583348f, 0.0260363269f, 0.0240879801f,
0.0222135971f, 0.0204134693f, 0.0186878765f, 0.0170370869f, 0.0154613569f, 0.0139609315f, 0.0125360439f, 0.0111869155f,
0.0099137561f, 0.0087167634f, 0.0075961235f, 0.0065520106f, 0.0055845869f, 0.0046940028f, 0.0038803967f, 0.0031438951f,
0.0024846123f, 0.0019026510f, 0.0013981014f, 0.0009710421f, 0.0006215394f, 0.0003496476f, 0.0001554090f, 0.0000388538f,
};
//
// Model the frequency-dependent attenuation of sound propogation in air.
//
// Fit using linear regression to a log-log model of lowpass cutoff frequency vs distance,
// loosely based on data from Handbook of Acoustics. Only the onset of significant
// attenuation is modelled, not the filter slope.
//
// 1m -> -3dB @ 55kHz
// 10m -> -3dB @ 12kHz
// 100m -> -3dB @ 2.5kHz
// 1km -> -3dB @ 0.6kHz
// 10km -> -3dB @ 0.1kHz
//
static const int NLOWPASS = 64;
static const float lowpassTable[NLOWPASS][5] = { // { b0, b1, b2, a1, a2 }
// distance = 1
{ 0.999772371f, 1.399489756f, 0.454495527f, 1.399458985f, 0.454298669f },
{ 0.999631480f, 1.357609808f, 0.425210203f, 1.357549905f, 0.424901586f },
{ 0.999405154f, 1.311503050f, 0.394349994f, 1.311386830f, 0.393871368f },
{ 0.999042876f, 1.260674595f, 0.361869089f, 1.260450057f, 0.361136504f },
// distance = 2
{ 0.998465222f, 1.204646525f, 0.327757118f, 1.204214978f, 0.326653886f },
{ 0.997548106f, 1.143019308f, 0.292064663f, 1.142195387f, 0.290436690f },
{ 0.996099269f, 1.075569152f, 0.254941286f, 1.074009405f, 0.252600301f },
{ 0.993824292f, 1.002389610f, 0.216688640f, 0.999469185f, 0.213433357f },
// distance = 4
{ 0.990280170f, 0.924075266f, 0.177827150f, 0.918684864f, 0.173497723f },
{ 0.984818279f, 0.841917936f, 0.139164195f, 0.832151968f, 0.133748443f },
{ 0.976528670f, 0.758036513f, 0.101832398f, 0.740761682f, 0.095635899f },
{ 0.964216485f, 0.675305244f, 0.067243474f, 0.645654855f, 0.061110348f },
// distance = 8
{ 0.946463038f, 0.596943020f, 0.036899688f, 0.547879974f, 0.032425772f },
{ 0.921823868f, 0.525770189f, 0.012060451f, 0.447952111f, 0.011702396f },
{ 0.890470015f, 0.463334299f, -0.001227816f, 0.347276405f, 0.005300092f },
{ 0.851335343f, 0.407521164f, -0.009353968f, 0.241900234f, 0.007602305f },
// distance = 16
{ 0.804237360f, 0.358139558f, -0.014293332f, 0.130934213f, 0.017149373f },
{ 0.750073259f, 0.314581568f, -0.016625381f, 0.014505388f, 0.033524057f },
{ 0.690412072f, 0.275936128f, -0.017054561f, -0.106682490f, 0.055976129f },
{ 0.627245545f, 0.241342015f, -0.016246850f, -0.231302564f, 0.083643275f },
// distance = 32
{ 0.562700627f, 0.210158533f, -0.014740899f, -0.357562697f, 0.115680957f },
{ 0.498787849f, 0.181982455f, -0.012925406f, -0.483461730f, 0.151306628f },
{ 0.437224055f, 0.156585449f, -0.011055180f, -0.607042210f, 0.189796534f },
{ 0.379336998f, 0.133834032f, -0.009281617f, -0.726580065f, 0.230469477f },
// distance = 64
{ 0.326040627f, 0.113624970f, -0.007683443f, -0.840693542f, 0.272675696f },
{ 0.277861727f, 0.095845793f, -0.006291936f, -0.948380091f, 0.315795676f },
{ 0.234997480f, 0.080357656f, -0.005109519f, -1.049001190f, 0.359246807f },
{ 0.197386484f, 0.066993521f, -0.004122547f, -1.142236313f, 0.402493771f },
// distance = 128
{ 0.164780457f, 0.055564709f, -0.003309645f, -1.228023442f, 0.445058962f },
{ 0.136808677f, 0.045870650f, -0.002646850f, -1.306498037f, 0.486530514f },
{ 0.113031290f, 0.037708627f, -0.002110591f, -1.377937457f, 0.526566783f },
{ 0.092980475f, 0.030881892f, -0.001679255f, -1.442713983f, 0.564897095f },
// distance = 256
{ 0.076190239f, 0.025205585f, -0.001333863f, -1.501257246f, 0.601319206f },
{ 0.062216509f, 0.020510496f, -0.001058229f, -1.554025452f, 0.635694228f },
{ 0.050649464f, 0.016644994f, -0.000838826f, -1.601484205f, 0.667939837f },
{ 0.041120009f, 0.013475547f, -0.000664513f, -1.644091518f, 0.698022561f },
// distance = 512
{ 0.033302044f, 0.010886252f, -0.000526217f, -1.682287704f, 0.725949783f },
{ 0.026911868f, 0.008777712f, -0.000416605f, -1.716488979f, 0.751761953f },
{ 0.021705773f, 0.007065551f, -0.000329788f, -1.747083800f, 0.775525335f },
{ 0.017476603f, 0.005678758f, -0.000261057f, -1.774431204f, 0.797325509f },
// distance = 1024
{ 0.014049828f, 0.004558012f, -0.000206658f, -1.798860530f, 0.817261711f },
{ 0.011279504f, 0.003654067f, -0.000163610f, -1.820672082f, 0.835442043f },
{ 0.009044384f, 0.002926264f, -0.000129544f, -1.840138412f, 0.851979516f },
{ 0.007244289f, 0.002341194f, -0.000102586f, -1.857505967f, 0.866988864f },
// distance = 2048
{ 0.005796846f, 0.001871515f, -0.000081250f, -1.872996926f, 0.880584038f },
{ 0.004634607f, 0.001494933f, -0.000064362f, -1.886811124f, 0.892876302f },
{ 0.003702543f, 0.001193324f, -0.000050993f, -1.899127955f, 0.903972829f },
{ 0.002955900f, 0.000951996f, -0.000040407f, -1.910108223f, 0.913975712f },
// distance = 4096
{ 0.002358382f, 0.000759068f, -0.000032024f, -1.919895894f, 0.922981321f },
{ 0.001880626f, 0.000604950f, -0.000025383f, -1.928619738f, 0.931079931f },
{ 0.001498926f, 0.000481920f, -0.000020123f, -1.936394836f, 0.938355560f },
{ 0.001194182f, 0.000383767f, -0.000015954f, -1.943323983f, 0.944885977f },
// distance = 8192
{ 0.000951028f, 0.000305502f, -0.000012651f, -1.949498943f, 0.950742822f },
{ 0.000757125f, 0.000243126f, -0.000010033f, -1.955001608f, 0.955991826f },
{ 0.000602572f, 0.000193434f, -0.000007957f, -1.959905036f, 0.960693085f },
{ 0.000479438f, 0.000153861f, -0.000006312f, -1.964274383f, 0.964901371f },
// distance = 16384
{ 0.000381374f, 0.000122359f, -0.000005007f, -1.968167752f, 0.968666478f },
{ 0.000303302f, 0.000097288f, -0.000003972f, -1.971636944f, 0.972033562f },
{ 0.000241166f, 0.000077342f, -0.000003151f, -1.974728138f, 0.975043493f },
{ 0.000191726f, 0.000061475f, -0.000002500f, -1.977482493f, 0.977733194f },
// distance = 32768
{ 0.000152399f, 0.000048857f, -0.000001984f, -1.979936697f, 0.980135969f },
{ 0.000121122f, 0.000038825f, -0.000001574f, -1.982123446f, 0.982281818f },
{ 0.000096252f, 0.000030849f, -0.000001249f, -1.984071877f, 0.984197728f },
{ 0.000076480f, 0.000024509f, -0.000000991f, -1.985807957f, 0.985907955f },
};
static const float TWOPI = 6.283185307f;
//
// on x86 architecture, assume that SSE2 is present
//
#if defined(_M_IX86) || defined(_M_X64) || defined(__i386__) || defined(__x86_64__)
#include <emmintrin.h>
// 1 channel input, 4 channel output
static void FIR_1x4_SSE(float* src, float* dst0, float* dst1, float* dst2, float* dst3, float coef[4][HRTF_TAPS], int numFrames) {
float* coef0 = coef[0] + HRTF_TAPS - 1; // process backwards
float* coef1 = coef[1] + HRTF_TAPS - 1;
float* coef2 = coef[2] + HRTF_TAPS - 1;
float* coef3 = coef[3] + HRTF_TAPS - 1;
assert(numFrames % 4 == 0);
for (int i = 0; i < numFrames; i += 4) {
__m128 acc0 = _mm_setzero_ps();
__m128 acc1 = _mm_setzero_ps();
__m128 acc2 = _mm_setzero_ps();
__m128 acc3 = _mm_setzero_ps();
float* ps = &src[i - HRTF_TAPS + 1]; // process forwards
assert(HRTF_TAPS % 4 == 0);
for (int k = 0; k < HRTF_TAPS; k += 4) {
acc0 = _mm_add_ps(acc0, _mm_mul_ps(_mm_load1_ps(&coef0[-k-0]), _mm_loadu_ps(&ps[k+0])));
acc1 = _mm_add_ps(acc1, _mm_mul_ps(_mm_load1_ps(&coef1[-k-0]), _mm_loadu_ps(&ps[k+0])));
acc2 = _mm_add_ps(acc2, _mm_mul_ps(_mm_load1_ps(&coef2[-k-0]), _mm_loadu_ps(&ps[k+0])));
acc3 = _mm_add_ps(acc3, _mm_mul_ps(_mm_load1_ps(&coef3[-k-0]), _mm_loadu_ps(&ps[k+0])));
acc0 = _mm_add_ps(acc0, _mm_mul_ps(_mm_load1_ps(&coef0[-k-1]), _mm_loadu_ps(&ps[k+1])));
acc1 = _mm_add_ps(acc1, _mm_mul_ps(_mm_load1_ps(&coef1[-k-1]), _mm_loadu_ps(&ps[k+1])));
acc2 = _mm_add_ps(acc2, _mm_mul_ps(_mm_load1_ps(&coef2[-k-1]), _mm_loadu_ps(&ps[k+1])));
acc3 = _mm_add_ps(acc3, _mm_mul_ps(_mm_load1_ps(&coef3[-k-1]), _mm_loadu_ps(&ps[k+1])));
acc0 = _mm_add_ps(acc0, _mm_mul_ps(_mm_load1_ps(&coef0[-k-2]), _mm_loadu_ps(&ps[k+2])));
acc1 = _mm_add_ps(acc1, _mm_mul_ps(_mm_load1_ps(&coef1[-k-2]), _mm_loadu_ps(&ps[k+2])));
acc2 = _mm_add_ps(acc2, _mm_mul_ps(_mm_load1_ps(&coef2[-k-2]), _mm_loadu_ps(&ps[k+2])));
acc3 = _mm_add_ps(acc3, _mm_mul_ps(_mm_load1_ps(&coef3[-k-2]), _mm_loadu_ps(&ps[k+2])));
acc0 = _mm_add_ps(acc0, _mm_mul_ps(_mm_load1_ps(&coef0[-k-3]), _mm_loadu_ps(&ps[k+3])));
acc1 = _mm_add_ps(acc1, _mm_mul_ps(_mm_load1_ps(&coef1[-k-3]), _mm_loadu_ps(&ps[k+3])));
acc2 = _mm_add_ps(acc2, _mm_mul_ps(_mm_load1_ps(&coef2[-k-3]), _mm_loadu_ps(&ps[k+3])));
acc3 = _mm_add_ps(acc3, _mm_mul_ps(_mm_load1_ps(&coef3[-k-3]), _mm_loadu_ps(&ps[k+3])));
}
_mm_storeu_ps(&dst0[i], acc0);
_mm_storeu_ps(&dst1[i], acc1);
_mm_storeu_ps(&dst2[i], acc2);
_mm_storeu_ps(&dst3[i], acc3);
}
}
//
// Runtime CPU dispatch
//
#include "CPUDetect.h"
void FIR_1x4_AVX(float* src, float* dst0, float* dst1, float* dst2, float* dst3, float coef[4][HRTF_TAPS], int numFrames);
static void FIR_1x4(float* src, float* dst0, float* dst1, float* dst2, float* dst3, float coef[4][HRTF_TAPS], int numFrames) {
static auto f = cpuSupportsAVX() ? FIR_1x4_AVX : FIR_1x4_SSE;
(*f)(src, dst0, dst1, dst2, dst3, coef, numFrames); // dispatch
}
// 4 channel planar to interleaved
static void interleave_4x4(float* src0, float* src1, float* src2, float* src3, float* dst, int numFrames) {
assert(numFrames % 4 == 0);
for (int i = 0; i < numFrames; i += 4) {
__m128 x0 = _mm_loadu_ps(&src0[i]);
__m128 x1 = _mm_loadu_ps(&src1[i]);
__m128 x2 = _mm_loadu_ps(&src2[i]);
__m128 x3 = _mm_loadu_ps(&src3[i]);
// interleave (4x4 matrix transpose)
__m128 t0 = _mm_unpacklo_ps(x0, x1);
__m128 t2 = _mm_unpacklo_ps(x2, x3);
__m128 t1 = _mm_unpackhi_ps(x0, x1);
__m128 t3 = _mm_unpackhi_ps(x2, x3);
x0 = _mm_movelh_ps(t0, t2);
x1 = _mm_movehl_ps(t2, t0);
x2 = _mm_movelh_ps(t1, t3);
x3 = _mm_movehl_ps(t3, t1);
_mm_storeu_ps(&dst[4*i+0], x0);
_mm_storeu_ps(&dst[4*i+4], x1);
_mm_storeu_ps(&dst[4*i+8], x2);
_mm_storeu_ps(&dst[4*i+12], x3);
}
}
// process 2 cascaded biquads on 4 channels (interleaved)
// biquads computed in parallel, by adding one sample of delay
static void biquad2_4x4(float* src, float* dst, float coef[5][8], float state[3][8], int numFrames) {
// enable flush-to-zero mode to prevent denormals
unsigned int ftz = _MM_GET_FLUSH_ZERO_MODE();
_MM_SET_FLUSH_ZERO_MODE(_MM_FLUSH_ZERO_ON);
// restore state
__m128 y00 = _mm_loadu_ps(&state[0][0]);
__m128 w10 = _mm_loadu_ps(&state[1][0]);
__m128 w20 = _mm_loadu_ps(&state[2][0]);
__m128 y01;
__m128 w11 = _mm_loadu_ps(&state[1][4]);
__m128 w21 = _mm_loadu_ps(&state[2][4]);
// first biquad coefs
__m128 b00 = _mm_loadu_ps(&coef[0][0]);
__m128 b10 = _mm_loadu_ps(&coef[1][0]);
__m128 b20 = _mm_loadu_ps(&coef[2][0]);
__m128 a10 = _mm_loadu_ps(&coef[3][0]);
__m128 a20 = _mm_loadu_ps(&coef[4][0]);
// second biquad coefs
__m128 b01 = _mm_loadu_ps(&coef[0][4]);
__m128 b11 = _mm_loadu_ps(&coef[1][4]);
__m128 b21 = _mm_loadu_ps(&coef[2][4]);
__m128 a11 = _mm_loadu_ps(&coef[3][4]);
__m128 a21 = _mm_loadu_ps(&coef[4][4]);
for (int i = 0; i < numFrames; i++) {
__m128 x00 = _mm_loadu_ps(&src[4*i]);
__m128 x01 = y00; // first biquad output
// transposed Direct Form II
y00 = _mm_add_ps(w10, _mm_mul_ps(x00, b00));
y01 = _mm_add_ps(w11, _mm_mul_ps(x01, b01));
w10 = _mm_add_ps(w20, _mm_mul_ps(x00, b10));
w11 = _mm_add_ps(w21, _mm_mul_ps(x01, b11));
w20 = _mm_mul_ps(x00, b20);
w21 = _mm_mul_ps(x01, b21);
w10 = _mm_sub_ps(w10, _mm_mul_ps(y00, a10));
w11 = _mm_sub_ps(w11, _mm_mul_ps(y01, a11));
w20 = _mm_sub_ps(w20, _mm_mul_ps(y00, a20));
w21 = _mm_sub_ps(w21, _mm_mul_ps(y01, a21));
_mm_storeu_ps(&dst[4*i], y01); // second biquad output
}
// save state
_mm_storeu_ps(&state[0][0], y00);
_mm_storeu_ps(&state[1][0], w10);
_mm_storeu_ps(&state[2][0], w20);
_mm_storeu_ps(&state[1][4], w11);
_mm_storeu_ps(&state[2][4], w21);
_MM_SET_FLUSH_ZERO_MODE(ftz);
}
// crossfade 4 inputs into 2 outputs with accumulation (interleaved)
static void crossfade_4x2(float* src, float* dst, const float* win, int numFrames) {
assert(numFrames % 4 == 0);
for (int i = 0; i < numFrames; i += 4) {
__m128 f0 = _mm_loadu_ps(&win[i]);
__m128 x0 = _mm_loadu_ps(&src[4*i+0]);
__m128 x1 = _mm_loadu_ps(&src[4*i+4]);
__m128 x2 = _mm_loadu_ps(&src[4*i+8]);
__m128 x3 = _mm_loadu_ps(&src[4*i+12]);
__m128 y0 = _mm_loadu_ps(&dst[2*i+0]);
__m128 y1 = _mm_loadu_ps(&dst[2*i+4]);
// deinterleave (4x4 matrix transpose)
__m128 t0 = _mm_unpacklo_ps(x0, x1);
__m128 t2 = _mm_unpacklo_ps(x2, x3);
__m128 t1 = _mm_unpackhi_ps(x0, x1);
__m128 t3 = _mm_unpackhi_ps(x2, x3);
x0 = _mm_movelh_ps(t0, t2);
x1 = _mm_movehl_ps(t2, t0);
x2 = _mm_movelh_ps(t1, t3);
x3 = _mm_movehl_ps(t3, t1);
// crossfade
x0 = _mm_sub_ps(x0, x2);
x1 = _mm_sub_ps(x1, x3);
x2 = _mm_add_ps(x2, _mm_mul_ps(f0, x0));
x3 = _mm_add_ps(x3, _mm_mul_ps(f0, x1));
// interleave
x0 = _mm_unpacklo_ps(x2, x3);
x1 = _mm_unpackhi_ps(x2, x3);
// accumulate
y0 = _mm_add_ps(y0, x0);
y1 = _mm_add_ps(y1, x1);
_mm_storeu_ps(&dst[2*i+0], y0);
_mm_storeu_ps(&dst[2*i+4], y1);
}
}
// linear interpolation with gain
static void interpolate(float* dst, const float* src0, const float* src1, float frac, float gain) {
__m128 f0 = _mm_set1_ps(HRTF_GAIN * gain * (1.0f - frac));
__m128 f1 = _mm_set1_ps(HRTF_GAIN * gain * frac);
assert(HRTF_TAPS % 4 == 0);
for (int k = 0; k < HRTF_TAPS; k += 4) {
__m128 x0 = _mm_loadu_ps(&src0[k]);
__m128 x1 = _mm_loadu_ps(&src1[k]);
x0 = _mm_add_ps(_mm_mul_ps(f0, x0), _mm_mul_ps(f1, x1));
_mm_storeu_ps(&dst[k], x0);
}
}
#else // portable reference code
// 1 channel input, 4 channel output
static void FIR_1x4(float* src, float* dst0, float* dst1, float* dst2, float* dst3, float coef[4][HRTF_TAPS], int numFrames) {
float* coef0 = coef[0] + HRTF_TAPS - 1; // process backwards
float* coef1 = coef[1] + HRTF_TAPS - 1;
float* coef2 = coef[2] + HRTF_TAPS - 1;
float* coef3 = coef[3] + HRTF_TAPS - 1;
assert(numFrames % 4 == 0);
for (int i = 0; i < numFrames; i += 4) {
dst0[i+0] = 0.0f;
dst0[i+1] = 0.0f;
dst0[i+2] = 0.0f;
dst0[i+3] = 0.0f;
dst1[i+0] = 0.0f;
dst1[i+1] = 0.0f;
dst1[i+2] = 0.0f;
dst1[i+3] = 0.0f;
dst2[i+0] = 0.0f;
dst2[i+1] = 0.0f;
dst2[i+2] = 0.0f;
dst2[i+3] = 0.0f;
dst3[i+0] = 0.0f;
dst3[i+1] = 0.0f;
dst3[i+2] = 0.0f;
dst3[i+3] = 0.0f;
float* ps = &src[i - HRTF_TAPS + 1]; // process forwards
assert(HRTF_TAPS % 4 == 0);
for (int k = 0; k < HRTF_TAPS; k += 4) {
// channel 0
dst0[i+0] += coef0[-k-0] * ps[k+0] + coef0[-k-1] * ps[k+1] + coef0[-k-2] * ps[k+2] + coef0[-k-3] * ps[k+3];
dst0[i+1] += coef0[-k-0] * ps[k+1] + coef0[-k-1] * ps[k+2] + coef0[-k-2] * ps[k+3] + coef0[-k-3] * ps[k+4];
dst0[i+2] += coef0[-k-0] * ps[k+2] + coef0[-k-1] * ps[k+3] + coef0[-k-2] * ps[k+4] + coef0[-k-3] * ps[k+5];
dst0[i+3] += coef0[-k-0] * ps[k+3] + coef0[-k-1] * ps[k+4] + coef0[-k-2] * ps[k+5] + coef0[-k-3] * ps[k+6];
// channel 1
dst1[i+0] += coef1[-k-0] * ps[k+0] + coef1[-k-1] * ps[k+1] + coef1[-k-2] * ps[k+2] + coef1[-k-3] * ps[k+3];
dst1[i+1] += coef1[-k-0] * ps[k+1] + coef1[-k-1] * ps[k+2] + coef1[-k-2] * ps[k+3] + coef1[-k-3] * ps[k+4];
dst1[i+2] += coef1[-k-0] * ps[k+2] + coef1[-k-1] * ps[k+3] + coef1[-k-2] * ps[k+4] + coef1[-k-3] * ps[k+5];
dst1[i+3] += coef1[-k-0] * ps[k+3] + coef1[-k-1] * ps[k+4] + coef1[-k-2] * ps[k+5] + coef1[-k-3] * ps[k+6];
// channel 2
dst2[i+0] += coef2[-k-0] * ps[k+0] + coef2[-k-1] * ps[k+1] + coef2[-k-2] * ps[k+2] + coef2[-k-3] * ps[k+3];
dst2[i+1] += coef2[-k-0] * ps[k+1] + coef2[-k-1] * ps[k+2] + coef2[-k-2] * ps[k+3] + coef2[-k-3] * ps[k+4];
dst2[i+2] += coef2[-k-0] * ps[k+2] + coef2[-k-1] * ps[k+3] + coef2[-k-2] * ps[k+4] + coef2[-k-3] * ps[k+5];
dst2[i+3] += coef2[-k-0] * ps[k+3] + coef2[-k-1] * ps[k+4] + coef2[-k-2] * ps[k+5] + coef2[-k-3] * ps[k+6];
// channel 3
dst3[i+0] += coef3[-k-0] * ps[k+0] + coef3[-k-1] * ps[k+1] + coef3[-k-2] * ps[k+2] + coef3[-k-3] * ps[k+3];
dst3[i+1] += coef3[-k-0] * ps[k+1] + coef3[-k-1] * ps[k+2] + coef3[-k-2] * ps[k+3] + coef3[-k-3] * ps[k+4];
dst3[i+2] += coef3[-k-0] * ps[k+2] + coef3[-k-1] * ps[k+3] + coef3[-k-2] * ps[k+4] + coef3[-k-3] * ps[k+5];
dst3[i+3] += coef3[-k-0] * ps[k+3] + coef3[-k-1] * ps[k+4] + coef3[-k-2] * ps[k+5] + coef3[-k-3] * ps[k+6];
}
}
}
// 4 channel planar to interleaved
static void interleave_4x4(float* src0, float* src1, float* src2, float* src3, float* dst, int numFrames) {
for (int i = 0; i < numFrames; i++) {
dst[4*i+0] = src0[i];
dst[4*i+1] = src1[i];
dst[4*i+2] = src2[i];
dst[4*i+3] = src3[i];
}
}
// process 2 cascaded biquads on 4 channels (interleaved)
// biquads are computed in parallel, by adding one sample of delay
static void biquad2_4x4(float* src, float* dst, float coef[5][8], float state[3][8], int numFrames) {
// restore state
float y00 = state[0][0];
float w10 = state[1][0];
float w20 = state[2][0];
float y01 = state[0][1];
float w11 = state[1][1];
float w21 = state[2][1];
float y02 = state[0][2];
float w12 = state[1][2];
float w22 = state[2][2];
float y03 = state[0][3];
float w13 = state[1][3];
float w23 = state[2][3];
float y04;
float w14 = state[1][4];
float w24 = state[2][4];
float y05;
float w15 = state[1][5];
float w25 = state[2][5];
float y06;
float w16 = state[1][6];
float w26 = state[2][6];
float y07;
float w17 = state[1][7];
float w27 = state[2][7];
// first biquad coefs
float b00 = coef[0][0];
float b10 = coef[1][0];
float b20 = coef[2][0];
float a10 = coef[3][0];
float a20 = coef[4][0];
float b01 = coef[0][1];
float b11 = coef[1][1];
float b21 = coef[2][1];
float a11 = coef[3][1];
float a21 = coef[4][1];
float b02 = coef[0][2];
float b12 = coef[1][2];
float b22 = coef[2][2];
float a12 = coef[3][2];
float a22 = coef[4][2];
float b03 = coef[0][3];
float b13 = coef[1][3];
float b23 = coef[2][3];
float a13 = coef[3][3];
float a23 = coef[4][3];
// second biquad coefs
float b04 = coef[0][4];
float b14 = coef[1][4];
float b24 = coef[2][4];
float a14 = coef[3][4];
float a24 = coef[4][4];
float b05 = coef[0][5];
float b15 = coef[1][5];
float b25 = coef[2][5];
float a15 = coef[3][5];
float a25 = coef[4][5];
float b06 = coef[0][6];
float b16 = coef[1][6];
float b26 = coef[2][6];
float a16 = coef[3][6];
float a26 = coef[4][6];
float b07 = coef[0][7];
float b17 = coef[1][7];
float b27 = coef[2][7];
float a17 = coef[3][7];
float a27 = coef[4][7];
for (int i = 0; i < numFrames; i++) {
// first biquad input
float x00 = src[4*i+0] + 1.0e-20f; // prevent denormals
float x01 = src[4*i+1] + 1.0e-20f;
float x02 = src[4*i+2] + 1.0e-20f;
float x03 = src[4*i+3] + 1.0e-20f;
// second biquad input is previous output
float x04 = y00;
float x05 = y01;
float x06 = y02;
float x07 = y03;
// transposed Direct Form II
y00 = b00 * x00 + w10;
w10 = b10 * x00 - a10 * y00 + w20;
w20 = b20 * x00 - a20 * y00;
y01 = b01 * x01 + w11;
w11 = b11 * x01 - a11 * y01 + w21;
w21 = b21 * x01 - a21 * y01;
y02 = b02 * x02 + w12;
w12 = b12 * x02 - a12 * y02 + w22;
w22 = b22 * x02 - a22 * y02;
y03 = b03 * x03 + w13;
w13 = b13 * x03 - a13 * y03 + w23;
w23 = b23 * x03 - a23 * y03;
// transposed Direct Form II
y04 = b04 * x04 + w14;
w14 = b14 * x04 - a14 * y04 + w24;
w24 = b24 * x04 - a24 * y04;
y05 = b05 * x05 + w15;
w15 = b15 * x05 - a15 * y05 + w25;
w25 = b25 * x05 - a25 * y05;
y06 = b06 * x06 + w16;
w16 = b16 * x06 - a16 * y06 + w26;
w26 = b26 * x06 - a26 * y06;
y07 = b07 * x07 + w17;
w17 = b17 * x07 - a17 * y07 + w27;
w27 = b27 * x07 - a27 * y07;
dst[4*i+0] = y04; // second biquad output
dst[4*i+1] = y05;
dst[4*i+2] = y06;
dst[4*i+3] = y07;
}
// save state
state[0][0] = y00;
state[1][0] = w10;
state[2][0] = w20;
state[0][1] = y01;
state[1][1] = w11;
state[2][1] = w21;
state[0][2] = y02;
state[1][2] = w12;
state[2][2] = w22;
state[0][3] = y03;
state[1][3] = w13;
state[2][3] = w23;
state[1][4] = w14;
state[2][4] = w24;
state[1][5] = w15;
state[2][5] = w25;
state[1][6] = w16;
state[2][6] = w26;
state[1][7] = w17;
state[2][7] = w27;
}
// crossfade 4 inputs into 2 outputs with accumulation (interleaved)
static void crossfade_4x2(float* src, float* dst, const float* win, int numFrames) {
for (int i = 0; i < numFrames; i++) {
float frac = win[i];
dst[2*i+0] += src[4*i+2] + frac * (src[4*i+0] - src[4*i+2]);
dst[2*i+1] += src[4*i+3] + frac * (src[4*i+1] - src[4*i+3]);
}
}
// linear interpolation with gain
static void interpolate(float* dst, const float* src0, const float* src1, float frac, float gain) {
float f0 = HRTF_GAIN * gain * (1.0f - frac);
float f1 = HRTF_GAIN * gain * frac;
for (int k = 0; k < HRTF_TAPS; k++) {
dst[k] = f0 * src0[k] + f1 * src1[k];
}
}
#endif
// design a 2nd order Thiran allpass
static void ThiranBiquad(float f, float& b0, float& b1, float& b2, float& a1, float& a2) {
a1 = -2.0f * (f - 2.0f) / (f + 1.0f);
a2 = ((f - 1.0f) * (f - 2.0f)) / ((f + 1.0f) * (f + 2.0f));
b0 = a2;
b1 = a1;
b2 = 1.0f;
}
// split x into exponent and fraction (0.0f to 1.0f)
static void splitf(float x, int& expn, float& frac) {
union { float f; int i; } mant, bits = { x };
const int IEEE754_MANT_BITS = 23;
const int IEEE754_EXPN_BIAS = 127;
mant.i = bits.i & ((1 << IEEE754_MANT_BITS) - 1);
mant.i |= (IEEE754_EXPN_BIAS << IEEE754_MANT_BITS);
frac = mant.f - 1.0f;
expn = (bits.i >> IEEE754_MANT_BITS) - IEEE754_EXPN_BIAS;
}
static void distanceBiquad(float distance, float& b0, float& b1, float& b2, float& a1, float& a2) {
//
// Computed from a lookup table quantized to distance = 2^(N/4)
// and reconstructed by piecewise linear interpolation.
// Approximation error < 0.25dB
//
float x = distance;
x = MIN(MAX(x, 1.0f), 1<<30);
x *= x;
x *= x; // x = distance^4
// split x into e and frac, such that x = 2^(e+0) + frac * (2^(e+1) - 2^(e+0))
int e;
float frac;
splitf(x, e, frac);
// clamp to table limits
if (e < 0) {
e = 0;
frac = 0.0f;
}
if (e > NLOWPASS-2) {
e = NLOWPASS-2;
frac = 1.0f;
}
assert(frac >= 0.0f);
assert(frac <= 1.0f);
assert(e+0 >= 0);
assert(e+1 < NLOWPASS);
// piecewise linear interpolation
b0 = lowpassTable[e+0][0] + frac * (lowpassTable[e+1][0] - lowpassTable[e+0][0]);
b1 = lowpassTable[e+0][1] + frac * (lowpassTable[e+1][1] - lowpassTable[e+0][1]);
b2 = lowpassTable[e+0][2] + frac * (lowpassTable[e+1][2] - lowpassTable[e+0][2]);
a1 = lowpassTable[e+0][3] + frac * (lowpassTable[e+1][3] - lowpassTable[e+0][3]);
a2 = lowpassTable[e+0][4] + frac * (lowpassTable[e+1][4] - lowpassTable[e+0][4]);
}
// compute new filters for a given azimuth, distance and gain
static void setFilters(float firCoef[4][HRTF_TAPS], float bqCoef[5][8], int delay[4],
int index, float azimuth, float distance, float gain, int channel) {
// convert from radians to table units
azimuth *= HRTF_AZIMUTHS / TWOPI;
// wrap to principle value
while (azimuth < 0.0f) {
azimuth += HRTF_AZIMUTHS;
}
while (azimuth >= HRTF_AZIMUTHS) {
azimuth -= HRTF_AZIMUTHS;
}
// table parameters
int az0 = (int)azimuth;
int az1 = (az0 + 1) % HRTF_AZIMUTHS;
float frac = azimuth - (float)az0;
assert((az0 >= 0) && (az0 < HRTF_AZIMUTHS));
assert((az1 >= 0) && (az1 < HRTF_AZIMUTHS));
assert((frac >= 0.0f) && (frac < 1.0f));
// interpolate FIR
interpolate(firCoef[channel+0], ir_table_table[index][az0][0], ir_table_table[index][az1][0], frac, gain);
interpolate(firCoef[channel+1], ir_table_table[index][az0][1], ir_table_table[index][az1][1], frac, gain);
// interpolate ITD
float itd = (1.0f - frac) * itd_table_table[index][az0] + frac * itd_table_table[index][az1];
// split ITD into integer and fractional delay
int itdi = (int)fabsf(itd);
float itdf = fabsf(itd) - (float)itdi;
assert(itdi <= HRTF_DELAY);
assert(itdf <= 1.0f);
//
// Compute a 2nd-order Thiran allpass for the fractional delay.
// With nominal delay of 2, the active range of [2.0, 3.0] results
// in group delay flat to 1.5KHz and fast transient settling time.
//
float b0, b1, b2, a1, a2;
ThiranBiquad(2.0f + itdf, b0, b1, b2, a1, a2);
// positive ITD means left channel is delayed
if (itd >= 0.0f) {
// left (contralateral) = 2 + itdi + itdf
bqCoef[0][channel+0] = b0;
bqCoef[1][channel+0] = b1;
bqCoef[2][channel+0] = b2;
bqCoef[3][channel+0] = a1;
bqCoef[4][channel+0] = a2;
delay[channel+0] = itdi;
// right (ipsilateral) = 2
bqCoef[0][channel+1] = 0.0f;
bqCoef[1][channel+1] = 0.0f;
bqCoef[2][channel+1] = 1.0f;
bqCoef[3][channel+1] = 0.0f;
bqCoef[4][channel+1] = 0.0f;
delay[channel+1] = 0;
} else {
// left (ipsilateral) = 2
bqCoef[0][channel+0] = 0.0f;
bqCoef[1][channel+0] = 0.0f;
bqCoef[2][channel+0] = 1.0f;
bqCoef[3][channel+0] = 0.0f;
bqCoef[4][channel+0] = 0.0f;
delay[channel+0] = 0;
// right (contralateral) = 2 + itdi + itdf
bqCoef[0][channel+1] = b0;
bqCoef[1][channel+1] = b1;
bqCoef[2][channel+1] = b2;
bqCoef[3][channel+1] = a1;
bqCoef[4][channel+1] = a2;
delay[channel+1] = itdi;
}
//
// Second biquad implements the distance filter.
//
distanceBiquad(distance, b0, b1, b2, a1, a2);
bqCoef[0][channel+4] = b0;
bqCoef[1][channel+4] = b1;
bqCoef[2][channel+4] = b2;
bqCoef[3][channel+4] = a1;
bqCoef[4][channel+4] = a2;
bqCoef[0][channel+5] = b0;
bqCoef[1][channel+5] = b1;
bqCoef[2][channel+5] = b2;
bqCoef[3][channel+5] = a1;
bqCoef[4][channel+5] = a2;
}
void AudioHRTF::render(int16_t* input, float* output, int index, float azimuth, float distance, float gain, int numFrames) {
assert(index >= 0);
assert(index < HRTF_TABLES);
assert(numFrames == HRTF_BLOCK);
float in[HRTF_TAPS + HRTF_BLOCK]; // mono
float firCoef[4][HRTF_TAPS]; // 4-channel
float firBuffer[4][HRTF_DELAY + HRTF_BLOCK]; // 4-channel
float bqCoef[5][8]; // 4-channel (interleaved)
float bqBuffer[4 * HRTF_BLOCK]; // 4-channel (interleaved)
int delay[4]; // 4-channel (interleaved)
// to avoid polluting the cache, old filters are recomputed instead of stored
setFilters(firCoef, bqCoef, delay, index, _azimuthState, _distanceState, _gainState, L0);
// compute new filters
setFilters(firCoef, bqCoef, delay, index, azimuth, distance, gain, L1);
// new parameters become old
_azimuthState = azimuth;
_distanceState = distance;
_gainState = gain;
// convert mono input to float
for (int i = 0; i < HRTF_BLOCK; i++) {
in[HRTF_TAPS+i] = (float)input[i] * (1/32768.0f);
}
// FIR state update
memcpy(in, _firState, HRTF_TAPS * sizeof(float));
memcpy(_firState, &in[HRTF_BLOCK], HRTF_TAPS * sizeof(float));
// process old/new FIR
FIR_1x4(&in[HRTF_TAPS],
&firBuffer[L0][HRTF_DELAY],
&firBuffer[R0][HRTF_DELAY],
&firBuffer[L1][HRTF_DELAY],
&firBuffer[R1][HRTF_DELAY],
firCoef, HRTF_BLOCK);
// delay state update
memcpy(firBuffer[L0], _delayState[L0], HRTF_DELAY * sizeof(float));
memcpy(firBuffer[R0], _delayState[R0], HRTF_DELAY * sizeof(float));
memcpy(firBuffer[L1], _delayState[L1], HRTF_DELAY * sizeof(float));
memcpy(firBuffer[R1], _delayState[R1], HRTF_DELAY * sizeof(float));
memcpy(_delayState[L0], &firBuffer[L1][HRTF_BLOCK], HRTF_DELAY * sizeof(float)); // new state becomes old
memcpy(_delayState[R0], &firBuffer[R1][HRTF_BLOCK], HRTF_DELAY * sizeof(float)); // new state becomes old
memcpy(_delayState[L1], &firBuffer[L1][HRTF_BLOCK], HRTF_DELAY * sizeof(float));
memcpy(_delayState[R1], &firBuffer[R1][HRTF_BLOCK], HRTF_DELAY * sizeof(float));
// interleave with old/new integer delay
interleave_4x4(&firBuffer[L0][HRTF_DELAY] - delay[L0],
&firBuffer[R0][HRTF_DELAY] - delay[R0],
&firBuffer[L1][HRTF_DELAY] - delay[L1],
&firBuffer[R1][HRTF_DELAY] - delay[R1],
bqBuffer, HRTF_BLOCK);
// process old/new biquads
biquad2_4x4(bqBuffer, bqBuffer, bqCoef, _bqState, HRTF_BLOCK);
// new state becomes old
_bqState[0][L0] = _bqState[0][L1];
_bqState[1][L0] = _bqState[1][L1];
_bqState[2][L0] = _bqState[2][L1];
_bqState[0][R0] = _bqState[0][R1];
_bqState[1][R0] = _bqState[1][R1];
_bqState[2][R0] = _bqState[2][R1];
_bqState[0][L2] = _bqState[0][L3];
_bqState[1][L2] = _bqState[1][L3];
_bqState[2][L2] = _bqState[2][L3];
_bqState[0][R2] = _bqState[0][R3];
_bqState[1][R2] = _bqState[1][R3];
_bqState[2][R2] = _bqState[2][R3];
// crossfade old/new output and accumulate
crossfade_4x2(bqBuffer, output, crossfadeTable, HRTF_BLOCK);
_silentState = false;
}
void AudioHRTF::renderSilent(int16_t* input, float* output, int index, float azimuth, float distance, float gain, int numFrames) {
// process the first silent block, to flush internal state
if (!_silentState) {
render(input, output, index, azimuth, distance, gain, numFrames);
}
// new parameters become old
_azimuthState = azimuth;
_distanceState = distance;
_gainState = gain;
_silentState = true;
}
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