[fjl] / idct.c

#include <math.h>

#include "idct.h"

void idct_reference(const int16_t* input, const uint32_t* quant_table, uint8_t* output)
{
        double temp[DCTSIZE2];

        for (unsigned y = 0; y < 8; ++y) {
                for (unsigned x = 0; x < 8; ++x) {
                        double acc = 0.0;
                        for (unsigned u = 0; u < 8; ++u) {
                                for (unsigned v = 0; v < 8; ++v) {
                                        double c_u = (u == 0) ? 1/sqrt(2.0) : 1.0;
                                        double c_v = (v == 0) ? 1/sqrt(2.0) : 1.0;
                                        acc += c_u * c_v
                                                * input[u * DCTSIZE + v] * quant_table[u * DCTSIZE + v]
                                                * cos((2 * x + 1) * v * M_PI / 16.0)
                                                * cos((2 * y + 1) * u * M_PI / 16.0);
                                }
                        }
                        temp[y * DCTSIZE + x] = 0.25 * acc;
                }
        }

        for (unsigned y = 0; y < 8; ++y) {
                for (unsigned x = 0; x < 8; ++x) {
                        double val = temp[y * DCTSIZE + x];
                        if (val < 0.0) {
                                output[y * DCTSIZE + x] = 0;
                        } else if (val >= 255.0) {
                                output[y * DCTSIZE + x] = 255;
                        } else {
                                output[y * DCTSIZE + x] = (uint8_t)(val + 0.5);
                        }
                }
        }
}

// AA&N (Arai, Agui and Nakajima) floating-point IDCT.
// This IDCT is based on the same DCT that libjpeg uses -- in fact, exactly the
// same figure from the same book ("JPEG: Still Image Data Compression Standard",
// page 52, figure 4-8). However, it is coded from scratch, and uses the
// transposition method for converting DCT -> IDCT suggested in the book.
// (libjpeg seems to use some other method that yields similar, but not
// the same, code.) 

// As this is generally meant as a reference and not useful code (we expect
// a SIMD fixed-point algorithm to be used in most cases), it has not been
// attempted significantly optimized. We assume the compiler will be smart
// enough to do all the variable propagation for us anyway.

// Scale factors; 1.0 / (sqrt(2.0) * cos(k * M_PI / 16.0)), except for the first which is 1.
static const double scalefac[] = {
        1.0, 0.7209598220069479, 0.765366864730180, 0.8504300947672564,
        1.0, 1.2727585805728336, 1.847759065022573, 3.6245097854115502
};

// 1D 8-point DCT.
static inline void idct1d_float(double y0, double y1, double y2, double y3, double y4, double y5, double y6, double y7, double *x)
{
        // constants
        static const double a1 = 0.7071067811865474;   // sqrt(2)
        static const double a2 = 0.5411961001461971;   // cos(3/8 pi) * sqrt(2)
        static const double a3 = a1;
        static const double a4 = 1.3065629648763766;   // cos(pi/8) * sqrt(2)
        static const double a5 = 0.5 * (a4 - a2);

        // phase 1
        const double p1_0 = y0 * scalefac[0];
        const double p1_1 = y4 * scalefac[4];
        const double p1_2 = y2 * scalefac[2];
        const double p1_3 = y6 * scalefac[6];
        const double p1_4 = y5 * scalefac[5];
        const double p1_5 = y1 * scalefac[1];
        const double p1_6 = y7 * scalefac[7];
        const double p1_7 = y3 * scalefac[3];

        // phase 2
        const double p2_0 = p1_0;
        const double p2_1 = p1_1;
        const double p2_2 = p1_2;
        const double p2_3 = p1_3;
        const double p2_4 = p1_4 - p1_7;
        const double p2_5 = p1_5 + p1_6;
        const double p2_6 = p1_5 - p1_6;
        const double p2_7 = p1_4 + p1_7;

        // phase 3
        const double p3_0 = p2_0;
        const double p3_1 = p2_1;
        const double p3_2 = p2_2 - p2_3;
        const double p3_3 = p2_2 + p2_3;
        const double p3_4 = p2_4;
        const double p3_5 = p2_5 - p2_7;
        const double p3_6 = p2_6;
        const double p3_7 = p2_5 + p2_7;
        
        // phase 4
        const double p4_0 = p3_0;
        const double p4_1 = p3_1;
        const double p4_2 = a1 * p3_2;
        const double p4_3 = p3_3;
        const double p4_4 = p3_4 * -a2 + (p3_4 + p3_6) * -a5;
        const double p4_5 = a3 * p3_5;
        const double p4_6 = p3_6 * a4 + (p3_4 + p3_6) * -a5;
        const double p4_7 = p3_7;

        // phase 5
        const double p5_0 = p4_0 + p4_1;
        const double p5_1 = p4_0 - p4_1;
        const double p5_2 = p4_2;
        const double p5_3 = p4_2 + p4_3;
        const double p5_4 = p4_4;
        const double p5_5 = p4_5;
        const double p5_6 = p4_6;
        const double p5_7 = p4_7;

        // phase 6
        const double p6_0 = p5_0 + p5_3;
        const double p6_1 = p5_1 + p5_2;
        const double p6_2 = p5_1 - p5_2;
        const double p6_3 = p5_0 - p5_3;
        const double p6_4 = -p5_4;
        const double p6_5 = p5_5 - p5_4;
        const double p6_6 = p5_5 + p5_6;
        const double p6_7 = p5_6 + p5_7;

        // phase 7
        x[0] = p6_0 + p6_7;
        x[1] = p6_1 + p6_6;
        x[2] = p6_2 + p6_5;
        x[3] = p6_3 + p6_4;
        x[4] = p6_3 - p6_4;
        x[5] = p6_2 - p6_5;
        x[6] = p6_1 - p6_6;
        x[7] = p6_0 - p6_7;
}

void idct_float(const int16_t* input, const uint32_t* quant_table, uint8_t* output)
{
        double temp[DCTSIZE2];

        // IDCT columns.
        for (unsigned x = 0; x < DCTSIZE; ++x) {
                idct1d_float(input[DCTSIZE * 0 + x] * (int32_t)quant_table[DCTSIZE * 0 + x],
                             input[DCTSIZE * 1 + x] * (int32_t)quant_table[DCTSIZE * 1 + x],
                             input[DCTSIZE * 2 + x] * (int32_t)quant_table[DCTSIZE * 2 + x],
                             input[DCTSIZE * 3 + x] * (int32_t)quant_table[DCTSIZE * 3 + x],
                             input[DCTSIZE * 4 + x] * (int32_t)quant_table[DCTSIZE * 4 + x],
                             input[DCTSIZE * 5 + x] * (int32_t)quant_table[DCTSIZE * 5 + x],
                             input[DCTSIZE * 6 + x] * (int32_t)quant_table[DCTSIZE * 6 + x],
                             input[DCTSIZE * 7 + x] * (int32_t)quant_table[DCTSIZE * 7 + x],
                             temp + x * DCTSIZE);
        }
        
        // IDCT rows.
        for (unsigned y = 0; y < DCTSIZE; ++y) {
                double temp2[DCTSIZE];
                idct1d_float(temp[DCTSIZE * 0 + y],
                             temp[DCTSIZE * 1 + y],
                             temp[DCTSIZE * 2 + y],
                             temp[DCTSIZE * 3 + y],
                             temp[DCTSIZE * 4 + y],
                             temp[DCTSIZE * 5 + y],
                             temp[DCTSIZE * 6 + y],
                             temp[DCTSIZE * 7 + y],
                             temp2);
                for (unsigned x = 0; x < DCTSIZE; ++x) {
                        double val = (1.0/8.0) * temp2[x];
                        if (val < 0.0) {
                                output[y * DCTSIZE + x] = 0;
                        } else if (val >= 255.0) {
                                output[y * DCTSIZE + x] = 255;
                        } else {
                                output[y * DCTSIZE + x] = (uint8_t)(val + 0.5);
                        }
                }
        }
}