/******************************************************************************
*
* Copyright (C) 2014 The Android Open Source Project
* Copyright 2003 - 2004 Open Interface North America, Inc. All rights
* reserved.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at:
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
******************************************************************************/
/*******************************************************************************
$Revision: #1 $
******************************************************************************/
/** @file
@ingroup codec_internal
*/
/**@addgroup codec_internal*/
/**@{*/
/*
* Performs an 8-point Type-II scaled DCT using the Arai-Agui-Nakajima
* factorization. The scaling factors are folded into the windowing
* constants. 29 adds and 5 16x32 multiplies per 8 samples.
*/
#include "oi_codec_sbc_private.h"
#define AAN_C4_FIX (759250125) /* S1.30 759250125 0.707107*/
#define AAN_C6_FIX (410903207) /* S1.30 410903207 0.382683*/
#define AAN_Q0_FIX (581104888) /* S1.30 581104888 0.541196*/
#define AAN_Q1_FIX (1402911301) /* S1.30 1402911301 1.306563*/
/** Scales x by y bits to the right, adding a rounding factor.
*/
#ifndef SCALE
#define SCALE(x, y) (((x) + (1 << ((y)-1))) >> (y))
#endif
/**
* Default C language implementation of a 32x32->32 multiply. This function may
* be replaced by a platform-specific version for speed.
*
* @param u A signed 32-bit multiplicand
* @param v A signed 32-bit multiplier
* @return A signed 32-bit value corresponding to the 32 most significant bits
* of the 64-bit product of u and v.
*/
INLINE int32_t default_mul_32s_32s_hi(int32_t u, int32_t v) {
uint32_t u0, v0;
int32_t u1, v1, w1, w2, t;
u0 = u & 0xFFFF;
u1 = u >> 16;
v0 = v & 0xFFFF;
v1 = v >> 16;
t = u0 * v0;
t = u1 * v0 + ((uint32_t)t >> 16);
w1 = t & 0xFFFF;
w2 = t >> 16;
w1 = u0 * v1 + w1;
return u1 * v1 + w2 + (w1 >> 16);
}
#define MUL_32S_32S_HI(_x, _y) default_mul_32s_32s_hi(_x, _y)
#ifdef DEBUG_DCT
PRIVATE void float_dct2_8(float* RESTRICT out, int32_t const* RESTRICT in) {
#define FIX(x, bits) \
(((int)floor(0.5f + ((x) * ((float)(1 << bits))))) / ((float)(1 << bits)))
#define FLOAT_BUTTERFLY(x, y) \
x += y; \
y = x - (y * 2); \
OI_ASSERT(VALID_INT32(x)); \
OI_ASSERT(VALID_INT32(y));
#define FLOAT_MULT_DCT(K, sample) (FIX(K, 20) * sample)
#define FLOAT_SCALE(x, y) (((x) / (double)(1 << (y))))
double L00, L01, L02, L03, L04, L05, L06, L07;
double L25;
double in0, in1, in2, in3;
double in4, in5, in6, in7;
in0 = FLOAT_SCALE(in[0], DCTII_8_SHIFT_IN);
OI_ASSERT(VALID_INT32(in0));
in1 = FLOAT_SCALE(in[1], DCTII_8_SHIFT_IN);
OI_ASSERT(VALID_INT32(in1));
in2 = FLOAT_SCALE(in[2], DCTII_8_SHIFT_IN);
OI_ASSERT(VALID_INT32(in2));
in3 = FLOAT_SCALE(in[3], DCTII_8_SHIFT_IN);
OI_ASSERT(VALID_INT32(in3));
in4 = FLOAT_SCALE(in[4], DCTII_8_SHIFT_IN);
OI_ASSERT(VALID_INT32(in4));
in5 = FLOAT_SCALE(in[5], DCTII_8_SHIFT_IN);
OI_ASSERT(VALID_INT32(in5));
in6 = FLOAT_SCALE(in[6], DCTII_8_SHIFT_IN);
OI_ASSERT(VALID_INT32(in6));
in7 = FLOAT_SCALE(in[7], DCTII_8_SHIFT_IN);
OI_ASSERT(VALID_INT32(in7));
L00 = (in0 + in7);
OI_ASSERT(VALID_INT32(L00));
L01 = (in1 + in6);
OI_ASSERT(VALID_INT32(L01));
L02 = (in2 + in5);
OI_ASSERT(VALID_INT32(L02));
L03 = (in3 + in4);
OI_ASSERT(VALID_INT32(L03));
L04 = (in3 - in4);
OI_ASSERT(VALID_INT32(L04));
L05 = (in2 - in5);
OI_ASSERT(VALID_INT32(L05));
L06 = (in1 - in6);
OI_ASSERT(VALID_INT32(L06));
L07 = (in0 - in7);
OI_ASSERT(VALID_INT32(L07));
FLOAT_BUTTERFLY(L00, L03);
FLOAT_BUTTERFLY(L01, L02);
L02 += L03;
OI_ASSERT(VALID_INT32(L02));
L02 = FLOAT_MULT_DCT(AAN_C4_FLOAT, L02);
OI_ASSERT(VALID_INT32(L02));
FLOAT_BUTTERFLY(L00, L01);
out[0] = (float)FLOAT_SCALE(L00, DCTII_8_SHIFT_0);
OI_ASSERT(VALID_INT16(out[0]));
out[4] = (float)FLOAT_SCALE(L01, DCTII_8_SHIFT_4);
OI_ASSERT(VALID_INT16(out[4]));
FLOAT_BUTTERFLY(L03, L02);
out[6] = (float)FLOAT_SCALE(L02, DCTII_8_SHIFT_6);
OI_ASSERT(VALID_INT16(out[6]));
out[2] = (float)FLOAT_SCALE(L03, DCTII_8_SHIFT_2);
OI_ASSERT(VALID_INT16(out[2]));
L04 += L05;
OI_ASSERT(VALID_INT32(L04));
L05 += L06;
OI_ASSERT(VALID_INT32(L05));
L06 += L07;
OI_ASSERT(VALID_INT32(L06));
L04 /= 2;
L05 /= 2;
L06 /= 2;
L07 /= 2;
L05 = FLOAT_MULT_DCT(AAN_C4_FLOAT, L05);
OI_ASSERT(VALID_INT32(L05));
L25 = L06 - L04;
OI_ASSERT(VALID_INT32(L25));
L25 = FLOAT_MULT_DCT(AAN_C6_FLOAT, L25);
OI_ASSERT(VALID_INT32(L25));
L04 = FLOAT_MULT_DCT(AAN_Q0_FLOAT, L04);
OI_ASSERT(VALID_INT32(L04));
L04 -= L25;
OI_ASSERT(VALID_INT32(L04));
L06 = FLOAT_MULT_DCT(AAN_Q1_FLOAT, L06);
OI_ASSERT(VALID_INT32(L06));
L06 -= L25;
OI_ASSERT(VALID_INT32(L25));
FLOAT_BUTTERFLY(L07, L05);
FLOAT_BUTTERFLY(L05, L04);
out[3] = (float)(FLOAT_SCALE(L04, DCTII_8_SHIFT_3 - 1));
OI_ASSERT(VALID_INT16(out[3]));
out[5] = (float)(FLOAT_SCALE(L05, DCTII_8_SHIFT_5 - 1));
OI_ASSERT(VALID_INT16(out[5]));
FLOAT_BUTTERFLY(L07, L06);
out[7] = (float)(FLOAT_SCALE(L06, DCTII_8_SHIFT_7 - 1));
OI_ASSERT(VALID_INT16(out[7]));
out[1] = (float)(FLOAT_SCALE(L07, DCTII_8_SHIFT_1 - 1));
OI_ASSERT(VALID_INT16(out[1]));
}
#undef BUTTERFLY
#endif
/*
* This function calculates the AAN DCT. Its inputs are in S16.15 format, as
* returned by OI_SBC_Dequant. In practice, abs(in[x]) < 52429.0 / 1.38
* (1244918057 integer). The function it computes is an approximation to the
* array defined by:
*
* diag(aan_s) * AAN= C2
*
* or
*
* AAN = diag(1/aan_s) * C2
*
* where C2 is as it is defined in the comment at the head of this file, and
*
* aan_s[i] = aan_s = 1/(2*cos(i*pi/16)) with i = 1..7, aan_s[0] = 1;
*
* aan_s[i] = [ 1.000 0.510 0.541 0.601 0.707 0.900 1.307 2.563 ]
*
* The output ranges are shown as follows:
*
* Let Y[0..7] = AAN * X[0..7]
*
* Without loss of generality, assume the input vector X consists of elements
* between -1 and 1. The maximum possible value of a given output element occurs
* with some particular combination of input vector elements each of which is -1
* or 1. Consider the computation of Y[i]. Y[i] = sum t=0..7 of AAN[t,i]*X[i]. Y
* is maximized if the sign of X[i] matches the sign of AAN[t,i], ensuring a
* positive contribution to the sum. Equivalently, one may simply sum
* abs(AAN)[t,i] over t to get the maximum possible value of Y[i].
*
* This yields approximately:
* [8.00 10.05 9.66 8.52 8.00 5.70 4.00 2.00]
*
* Given the maximum magnitude sensible input value of +/-37992, this yields the
* following vector of maximum output magnitudes:
*
* [ 303936 381820 367003 323692 303936 216555 151968 75984 ]
*
* Ultimately, these values must fit into 16 bit signed integers, so they must
* be scaled. A non-uniform scaling helps maximize the kept precision. The
* relative number of extra bits of precision maintainable with respect to the
* largest value is given here:
*
* [ 0 0 0 0 0 0 1 2 ]
*
*/
PRIVATE void dct2_8(SBC_BUFFER_T* RESTRICT out, int32_t const* RESTRICT in) {
#define BUTTERFLY(x, y) \
x += (y); \
(y) = (x) - ((y) << 1);
#define FIX_MULT_DCT(K, x) (MUL_32S_32S_HI(K, x) << 2)
int32_t L00, L01, L02, L03, L04, L05, L06, L07;
int32_t L25;
int32_t in0, in1, in2, in3;
int32_t in4, in5, in6, in7;
#if DCTII_8_SHIFT_IN != 0
in0 = SCALE(in[0], DCTII_8_SHIFT_IN);
in1 = SCALE(in[1], DCTII_8_SHIFT_IN);
in2 = SCALE(in[2], DCTII_8_SHIFT_IN);
in3 = SCALE(in[3], DCTII_8_SHIFT_IN);
in4 = SCALE(in[4], DCTII_8_SHIFT_IN);
in5 = SCALE(in[5], DCTII_8_SHIFT_IN);
in6 = SCALE(in[6], DCTII_8_SHIFT_IN);
in7 = SCALE(in[7], DCTII_8_SHIFT_IN);
#else
in0 = in[0];
in1 = in[1];
in2 = in[2];
in3 = in[3];
in4 = in[4];
in5 = in[5];
in6 = in[6];
in7 = in[7];
#endif
L00 = in0 + in7;
L01 = in1 + in6;
L02 = in2 + in5;
L03 = in3 + in4;
L04 = in3 - in4;
L05 = in2 - in5;
L06 = in1 - in6;
L07 = in0 - in7;
BUTTERFLY(L00, L03);
BUTTERFLY(L01, L02);
L02 += L03;
L02 = FIX_MULT_DCT(AAN_C4_FIX, L02);
BUTTERFLY(L00, L01);
out[0] = (int16_t)SCALE(L00, DCTII_8_SHIFT_0);
out[4] = (int16_t)SCALE(L01, DCTII_8_SHIFT_4);
BUTTERFLY(L03, L02);
out[6] = (int16_t)SCALE(L02, DCTII_8_SHIFT_6);
out[2] = (int16_t)SCALE(L03, DCTII_8_SHIFT_2);
L04 += L05;
L05 += L06;
L06 += L07;
L04 /= 2;
L05 /= 2;
L06 /= 2;
L07 /= 2;
L05 = FIX_MULT_DCT(AAN_C4_FIX, L05);
L25 = L06 - L04;
L25 = FIX_MULT_DCT(AAN_C6_FIX, L25);
L04 = FIX_MULT_DCT(AAN_Q0_FIX, L04);
L04 -= L25;
L06 = FIX_MULT_DCT(AAN_Q1_FIX, L06);
L06 -= L25;
BUTTERFLY(L07, L05);
BUTTERFLY(L05, L04);
out[3] = (int16_t)SCALE(L04, DCTII_8_SHIFT_3 - 1);
out[5] = (int16_t)SCALE(L05, DCTII_8_SHIFT_5 - 1);
BUTTERFLY(L07, L06);
out[7] = (int16_t)SCALE(L06, DCTII_8_SHIFT_7 - 1);
out[1] = (int16_t)SCALE(L07, DCTII_8_SHIFT_1 - 1);
#undef BUTTERFLY
#ifdef DEBUG_DCT
{
float float_out[8];
float_dct2_8(float_out, in);
}
#endif
}
/**@}*/