/* This routine is a slow-but-accurate integer implementation of the * forward DCT (Discrete Cosine Transform). Taken from the IJG software * * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT * on each column.  Direct algorithms are also available, but they are * much more complex and seem not to be any faster when reduced to code. * * This implementation is based on an algorithm described in *   C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT *   Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics, *   Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991. * The primary algorithm described there uses 11 multiplies and 29 adds. * We use their alternate method with 12 multiplies and 32 adds. * The advantage of this method is that no data path contains more than one * multiplication; this allows a very simple and accurate implementation in * scaled fixed-point arithmetic, with a minimal number of shifts. * * The poop on this scaling stuff is as follows: * * Each 1-D DCT step produces outputs which are a factor of sqrt(N) * larger than the true DCT outputs.  The final outputs are therefore * a factor of N larger than desired; since N=8 this can be cured by * a simple right shift at the end of the algorithm.  The advantage of * this arrangement is that we save two multiplications per 1-D DCT, * because the y0 and y4 outputs need not be divided by sqrt(N). * In the IJG code, this factor of 8 is removed by the quantization step * (in jcdctmgr.c), here it is removed. * * We have to do addition and subtraction of the integer inputs, which * is no problem, and multiplication by fractional constants, which is * a problem to do in integer arithmetic.  We multiply all the constants * by CONST_SCALE and convert them to integer constants (thus retaining * CONST_BITS bits of precision in the constants).  After doing a * multiplication we have to divide the product by CONST_SCALE, with proper * rounding, to produce the correct output.  This division can be done * cheaply as a right shift of CONST_BITS bits.  We postpone shifting * as long as possible so that partial sums can be added together with * full fractional precision. * * The outputs of the first pass are scaled up by PASS1_BITS bits so that * they are represented to better-than-integral precision.  These outputs * require 8 + PASS1_BITS + 3 bits; this fits in a 16-bit word * with the recommended scaling.  (For 12-bit sample data, the intermediate * array is INT32 anyway.) * * To avoid overflow of the 32-bit intermediate results in pass 2, we must * have 8 + CONST_BITS + PASS1_BITS <= 26.  Error analysis * shows that the values given below are the most effective. * * We can gain a little more speed, with a further compromise in accuracy, * by omitting the addition in a descaling shift.  This yields an incorrectly * rounded result half the time... *///#include "fdct_xvid.h"#define USE_ACCURATE_ROUNDING#define RIGHT_SHIFT(x, shft)  ((x) >> (shft))#ifdef USE_ACCURATE_ROUNDING#define ONE ((int) 1)#define DESCALE(x, n)  RIGHT_SHIFT((x) + (ONE << ((n) - 1)), n)#else#define DESCALE(x, n)  RIGHT_SHIFT(x, n)#endif#define CONST_BITS  13#define PASS1_BITS  2// *8192#define FIX_0_298631336  ((int)  2446)	/* FIX(0.298631336) */#define FIX_0_390180644  ((int)  3196)	/* FIX(0.390180644) */#define FIX_0_541196100  ((int)  4433)	/* FIX(0.541196100) */#define FIX_0_765366865  ((int)  6270)	/* FIX(0.765366865) */#define FIX_0_899976223  ((int)  7373)	/* FIX(0.899976223) */#define FIX_1_175875602  ((int)  9633)	/* FIX(1.175875602) */#define FIX_1_501321110  ((int) 12299)	/* FIX(1.501321110) */#define FIX_1_847759065  ((int) 15137)	/* FIX(1.847759065) */#define FIX_1_961570560  ((int) 16069)	/* FIX(1.961570560) */#define FIX_2_053119869  ((int) 16819)	/* FIX(2.053119869) */#define FIX_2_562915447  ((int) 20995)	/* FIX(2.562915447) */#define FIX_3_072711026  ((int) 25172)	/* FIX(3.072711026) *//* * Perform an integer forward DCT on one block of samples. */voidfdct_int32(short *const block){	int tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;	int tmp10, tmp11, tmp12, tmp13;	int z1, z2, z3, z4, z5;	short *blkptr;	int *dataptr;	int data[64];	int i;	/* Pass 1: process rows. */	/* Note results are scaled up by sqrt(8) compared to a true DCT; */	/* furthermore, we scale the results by 2**PASS1_BITS. */	dataptr = data;	blkptr = block;	for (i = 0; i < 8; i++) {		tmp0 = blkptr[0] + blkptr[7];		tmp7 = blkptr[0] - blkptr[7];		tmp1 = blkptr[1] + blkptr[6];		tmp6 = blkptr[1] - blkptr[6];		tmp2 = blkptr[2] + blkptr[5];		tmp5 = blkptr[2] - blkptr[5];		tmp3 = blkptr[3] + blkptr[4];		tmp4 = blkptr[3] - blkptr[4];		/* Even part per LL&M figure 1 --- note that published figure is faulty;		 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".		 */		tmp10 = tmp0 + tmp3;		tmp13 = tmp0 - tmp3;		tmp11 = tmp1 + tmp2;		tmp12 = tmp1 - tmp2;		dataptr[0] = (tmp10 + tmp11) << PASS1_BITS;		dataptr[4] = (tmp10 - tmp11) << PASS1_BITS;		z1 = (tmp12 + tmp13) * FIX_0_541196100;		dataptr[2] =			DESCALE(z1 + tmp13 * FIX_0_765366865, CONST_BITS - PASS1_BITS);		dataptr[6] =			DESCALE(z1 + tmp12 * (-FIX_1_847759065), CONST_BITS - PASS1_BITS);		/* Odd part per figure 8 --- note paper omits factor of sqrt(2).		 * cK represents cos(K*pi/16).		 * i0..i3 in the paper are tmp4..tmp7 here.		 */		z1 = tmp4 + tmp7;		z2 = tmp5 + tmp6;		z3 = tmp4 + tmp6;		z4 = tmp5 + tmp7;		z5 = (z3 + z4) * FIX_1_175875602;	/* sqrt(2) * c3 */		tmp4 *= FIX_0_298631336;	/* sqrt(2) * (-c1+c3+c5-c7) */		tmp5 *= FIX_2_053119869;	/* sqrt(2) * ( c1+c3-c5+c7) */		tmp6 *= FIX_3_072711026;	/* sqrt(2) * ( c1+c3+c5-c7) */		tmp7 *= FIX_1_501321110;	/* sqrt(2) * ( c1+c3-c5-c7) */		z1 *= -FIX_0_899976223;	/* sqrt(2) * (c7-c3) */		z2 *= -FIX_2_562915447;	/* sqrt(2) * (-c1-c3) */		z3 *= -FIX_1_961570560;	/* sqrt(2) * (-c3-c5) */		z4 *= -FIX_0_390180644;	/* sqrt(2) * (c5-c3) */		z3 += z5;		z4 += z5;		dataptr[7] = DESCALE(tmp4 + z1 + z3, CONST_BITS - PASS1_BITS);		dataptr[5] = DESCALE(tmp5 + z2 + z4, CONST_BITS - PASS1_BITS);		dataptr[3] = DESCALE(tmp6 + z2 + z3, CONST_BITS - PASS1_BITS);		dataptr[1] = DESCALE(tmp7 + z1 + z4, CONST_BITS - PASS1_BITS);		dataptr += 8;			/* advance pointer to next row */		blkptr += 8;	}	/* Pass 2: process columns.	 * We remove the PASS1_BITS scaling, but leave the results scaled up	 * by an overall factor of 8.	 */	dataptr = data;	for (i = 0; i < 8; i++) {		tmp0 = dataptr[0] + dataptr[56];		tmp7 = dataptr[0] - dataptr[56];		tmp1 = dataptr[8] + dataptr[48];		tmp6 = dataptr[8] - dataptr[48];		tmp2 = dataptr[16] + dataptr[40];		tmp5 = dataptr[16] - dataptr[40];		tmp3 = dataptr[24] + dataptr[32];		tmp4 = dataptr[24] - dataptr[32];		/* Even part per LL&M figure 1 --- note that published figure is faulty;		 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".		 */		tmp10 = tmp0 + tmp3;		tmp13 = tmp0 - tmp3;		tmp11 = tmp1 + tmp2;		tmp12 = tmp1 - tmp2;		dataptr[0] = DESCALE(tmp10 + tmp11, PASS1_BITS);		dataptr[32] = DESCALE(tmp10 - tmp11, PASS1_BITS);		z1 = (tmp12 + tmp13) * FIX_0_541196100;		dataptr[16] =			DESCALE(z1 + tmp13 * FIX_0_765366865, CONST_BITS + PASS1_BITS);		dataptr[48] =			DESCALE(z1 + tmp12 * (-FIX_1_847759065), CONST_BITS + PASS1_BITS);		/* Odd part per figure 8 --- note paper omits factor of sqrt(2).		 * cK represents cos(K*pi/16).		 * i0..i3 in the paper are tmp4..tmp7 here.		 */		z1 = tmp4 + tmp7;		z2 = tmp5 + tmp6;		z3 = tmp4 + tmp6;		z4 = tmp5 + tmp7;		z5 = (z3 + z4) * FIX_1_175875602;	/* sqrt(2) * c3 */		tmp4 *= FIX_0_298631336;	/* sqrt(2) * (-c1+c3+c5-c7) */		tmp5 *= FIX_2_053119869;	/* sqrt(2) * ( c1+c3-c5+c7) */		tmp6 *= FIX_3_072711026;	/* sqrt(2) * ( c1+c3+c5-c7) */		tmp7 *= FIX_1_501321110;	/* sqrt(2) * ( c1+c3-c5-c7) */		z1 *= -FIX_0_899976223;	/* sqrt(2) * (c7-c3) */		z2 *= -FIX_2_562915447;	/* sqrt(2) * (-c1-c3) */		z3 *= -FIX_1_961570560;	/* sqrt(2) * (-c3-c5) */		z4 *= -FIX_0_390180644;	/* sqrt(2) * (c5-c3) */		z3 += z5;		z4 += z5;		dataptr[56] = DESCALE(tmp4 + z1 + z3, CONST_BITS + PASS1_BITS);		dataptr[40] = DESCALE(tmp5 + z2 + z4, CONST_BITS + PASS1_BITS);		dataptr[24] = DESCALE(tmp6 + z2 + z3, CONST_BITS + PASS1_BITS);		dataptr[8] = DESCALE(tmp7 + z1 + z4, CONST_BITS + PASS1_BITS);		dataptr++;				/* advance pointer to next column */	}	/* descale */	for (i = 0; i < 64; i++)		block[i] = (short int) DESCALE(data[i], 3);}