/* * jidctfst.c * * Copyright (C) 1994-1996, Thomas G. Lane. * This file is part of the Independent JPEG Group's software. * For conditions of distribution and use, see the accompanying README file. * * This file contains a fast, not so accurate integer implementation of the * inverse DCT (Discrete Cosine Transform). In the IJG code, this routine * must also perform dequantization of the input coefficients. * * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT * on each row (or vice versa, but it's more convenient to emit a row at * a time). 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 Arai, Agui, and Nakajima's algorithm for * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in * Japanese, but the algorithm is described in the Pennebaker & Mitchell * JPEG textbook (see REFERENCES section in file README). The following code * is based directly on figure 4-8 in P&M. * While an 8-point DCT cannot be done in less than 11 multiplies, it is * possible to arrange the computation so that many of the multiplies are * simple scalings of the final outputs. These multiplies can then be * folded into the multiplications or divisions by the JPEG quantization * table entries. The AA&N method leaves only 5 multiplies and 29 adds * to be done in the DCT itself. * The primary disadvantage of this method is that with fixed-point math, * accuracy is lost due to imprecise representation of the scaled * quantization values. The smaller the quantization table entry, the less * precise the scaled value, so this implementation does worse with high- * quality-setting files than with low-quality ones. */ /* * This module is specialized to the case DCTSIZE = 8. */ /* Scaling decisions are generally the same as in the LL&M algorithm; * see jidctint.c for more details. However, we choose to descale * (right shift) multiplication products as soon as they are formed, * rather than carrying additional fractional bits into subsequent additions. * This compromises accuracy slightly, but it lets us save a few shifts. * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples) * everywhere except in the multiplications proper; this saves a good deal * of work on 16-bit-int machines. * * The dequantized coefficients are not integers because the AA&N scaling * factors have been incorporated. We represent them scaled up by PASS1_BITS, * so that the first and second IDCT rounds have the same input scaling. * For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to * avoid a descaling shift; this compromises accuracy rather drastically * for small quantization table entries, but it saves a lot of shifts. * For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway, * so we use a much larger scaling factor to preserve accuracy. * * A final compromise is to represent the multiplicative constants to only * 8 fractional bits, rather than 13. This saves some shifting work on some * machines, and may also reduce the cost of multiplication (since there * are fewer one-bits in the constants). */ #define BITS_IN_JSAMPLE 8 #if BITS_IN_JSAMPLE == 8 #define CONST_BITS 8 #define PASS1_BITS 2 #else #define CONST_BITS 8 #define PASS1_BITS 1 /* lose a little precision to avoid overflow */ #endif /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus * causing a lot of useless floating-point operations at run time. * To get around this we use the following pre-calculated constants. * If you change CONST_BITS you may want to add appropriate values. * (With a reasonable C compiler, you can just rely on the FIX() macro...) */ #if CONST_BITS == 8 #define FIX_1_082392200 (277) /* FIX(1.082392200) */ #define FIX_1_414213562 (362) /* FIX(1.414213562) */ #define FIX_1_847759065 (473) /* FIX(1.847759065) */ #define FIX_2_613125930 (669) /* FIX(2.613125930) */ #else #define FIX_1_082392200 FIX(1.082392200) #define FIX_1_414213562 FIX(1.414213562) #define FIX_1_847759065 FIX(1.847759065) #define FIX_2_613125930 FIX(2.613125930) #endif /* 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... */ /* Multiply a DCTELEM variable by an INT32 constant, and immediately * descale to yield a DCTELEM result. */ #define MULTIPLY(var,const) (DESCALE((var) * (const), CONST_BITS)) /* Dequantize a coefficient by multiplying it by the multiplier-table * entry; produce a DCTELEM result. For 8-bit data a 16x16->16 * multiplication will do. For 12-bit data, the multiplier table is * declared INT32, so a 32-bit multiply will be used. */ #if BITS_IN_JSAMPLE == 8 #define DEQUANTIZE(coef,quantval) (coef) #else #define DEQUANTIZE(coef,quantval) \ DESCALE((coef), IFAST_SCALE_BITS-PASS1_BITS) #endif /* Like DESCALE, but applies to a DCTELEM and produces an int. * We assume that int right shift is unsigned if INT32 right shift is. */ #define DESCALE(x,n) ((x)>>(n)) #define RANGE(n) (n) #define BLOCK int /* * Perform dequantization and inverse DCT on one block of coefficients. */ #define DCTSIZE 8 #define DCTSIZE2 64 static void IDCT1(BLOCK *block) { int val = RANGE(DESCALE(block[0], PASS1_BITS+3)); int i; for(i=0;i<DCTSIZE2;i++) block[i]=val; } void IDCT(BLOCK *block,int k) { int tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; int z5, z10, z11, z12, z13; BLOCK *ptr; int i; /* Pass 1: process columns from input, store into work array. */ switch(k){ case 1:IDCT1(block); return; } ptr = block; for (i = 0; i< DCTSIZE; i++,ptr++) { /* Due to quantization, we will usually find that many of the input * coefficients are zero, especially the AC terms. We can exploit this * by short-circuiting the IDCT calculation for any column in which all * the AC terms are zero. In that case each output is equal to the * DC coefficient (with scale factor as needed). * With typical images and quantization tables, half or more of the * column DCT calculations can be simplified this way. */ if ((ptr[DCTSIZE*1] | ptr[DCTSIZE*2] | ptr[DCTSIZE*3] | ptr[DCTSIZE*4] | ptr[DCTSIZE*5] | ptr[DCTSIZE*6] | ptr[DCTSIZE*7]) == 0) { /* AC terms all zero */ ptr[DCTSIZE*0] = ptr[DCTSIZE*1] = ptr[DCTSIZE*2] = ptr[DCTSIZE*3] = ptr[DCTSIZE*4] = ptr[DCTSIZE*5] = ptr[DCTSIZE*6] = ptr[DCTSIZE*7] = ptr[DCTSIZE*0]; continue; } /* Even part */ z10 = ptr[DCTSIZE*0] + ptr[DCTSIZE*4]; /* phase 3 */ z11 = ptr[DCTSIZE*0] - ptr[DCTSIZE*4]; z13 = ptr[DCTSIZE*2] + ptr[DCTSIZE*6]; /* phases 5-3 */ z12 = MULTIPLY(ptr[DCTSIZE*2] - ptr[DCTSIZE*6], FIX_1_414213562) - z13; /* 2*c4 */ tmp0 = z10 + z13; /* phase 2 */ tmp3 = z10 - z13; tmp1 = z11 + z12; tmp2 = z11 - z12; /* Odd part */ z13 = ptr[DCTSIZE*3] + ptr[DCTSIZE*5]; /* phase 6 */ z10 = ptr[DCTSIZE*3] - ptr[DCTSIZE*5]; z11 = ptr[DCTSIZE*1] + ptr[DCTSIZE*7]; z12 = ptr[DCTSIZE*1] - ptr[DCTSIZE*7]; z5 = MULTIPLY(z12 - z10, FIX_1_847759065); tmp7 = z11 + z13; /* phase 5 */ tmp6 = MULTIPLY(z10, FIX_2_613125930) + z5 - tmp7; /* phase 2 */ tmp5 = MULTIPLY(z11 - z13, FIX_1_414213562) - tmp6; tmp4 = MULTIPLY(z12, FIX_1_082392200) - z5 + tmp5; ptr[DCTSIZE*0] = (tmp0 + tmp7); ptr[DCTSIZE*7] = (tmp0 - tmp7); ptr[DCTSIZE*1] = (tmp1 + tmp6); ptr[DCTSIZE*6] = (tmp1 - tmp6); ptr[DCTSIZE*2] = (tmp2 + tmp5); ptr[DCTSIZE*5] = (tmp2 - tmp5); ptr[DCTSIZE*4] = (tmp3 + tmp4); ptr[DCTSIZE*3] = (tmp3 - tmp4); } /* Pass 2: process rows from work array, store into output array. */ /* Note that we must descale the results by a factor of 8 == 2**3, */ /* and also undo the PASS1_BITS scaling. */ ptr = block; for (i = 0; i < DCTSIZE; i++ ,ptr+=DCTSIZE) { /* Rows of zeroes can be exploited in the same way as we did with columns. * However, the column calculation has created many nonzero AC terms, so * the simplification applies less often (typically 5% to 10% of the time). * On machines with very fast multiplication, it's possible that the * test takes more time than it's worth. In that case this section * may be commented out. */ #ifndef NO_ZERO_ROW_TEST if ((ptr[1] | ptr[2] | ptr[3] | ptr[4] | ptr[5] | ptr[6] | ptr[7]) == 0) { /* AC terms all zero */ ptr[0] = ptr[1] = ptr[2] = ptr[3] = ptr[4] = ptr[5] = ptr[6] = ptr[7] = RANGE(DESCALE(ptr[0], PASS1_BITS+3));; continue; } #endif /* Even part */ z10 = ptr[0] + ptr[4]; z11 = ptr[0] - ptr[4]; z13 = ptr[2] + ptr[6]; z12 = MULTIPLY(ptr[2] - ptr[6], FIX_1_414213562) - z13; tmp0 = z10 + z13; tmp3 = z10 - z13; tmp1 = z11 + z12; tmp2 = z11 - z12; /* Odd part */ z13 = ptr[3] + ptr[5]; z10 = ptr[3] - ptr[5]; z11 = ptr[1] + ptr[7]; z12 = ptr[1] - ptr[7]; z5 = MULTIPLY(z12 - z10, FIX_1_847759065); tmp7 = z11 + z13; /* phase 5 */ tmp6 = MULTIPLY(z10, FIX_2_613125930) + z5 - tmp7; /* phase 2 */ tmp5 = MULTIPLY(z11 - z13, FIX_1_414213562) - tmp6; tmp4 = MULTIPLY(z12, FIX_1_082392200) - z5 + tmp5; /* Final output stage: scale down by a factor of 8 and range-limit */ ptr[0] = RANGE(DESCALE(tmp0 + tmp7, PASS1_BITS+3));; ptr[7] = RANGE(DESCALE(tmp0 - tmp7, PASS1_BITS+3));; ptr[1] = RANGE(DESCALE(tmp1 + tmp6, PASS1_BITS+3));; ptr[6] = RANGE(DESCALE(tmp1 - tmp6, PASS1_BITS+3));; ptr[2] = RANGE(DESCALE(tmp2 + tmp5, PASS1_BITS+3));; ptr[5] = RANGE(DESCALE(tmp2 - tmp5, PASS1_BITS+3));; ptr[4] = RANGE(DESCALE(tmp3 + tmp4, PASS1_BITS+3));; ptr[3] = RANGE(DESCALE(tmp3 - tmp4, PASS1_BITS+3));; } }