/* * jidctfst.c * * Copyright (C) 1994-1998, 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. */ #define JPEG_INTERNALS #include "jinclude.h" #include "jpeglib.h" #include "jdct.h" /* Private declarations for DCT subsystem */ #ifdef DCT_IFAST_SUPPORTED /* * This module is specialized to the case DCTSIZE = 8. */ #if DCTSIZE != 8 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ #endif /* 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). */ #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 ((INT32) 277) /* FIX(1.082392200) */ #define FIX_1_414213562 ((INT32) 362) /* FIX(1.414213562) */ #define FIX_1_847759065 ((INT32) 473) /* FIX(1.847759065) */ #define FIX_2_613125930 ((INT32) 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... */ #ifndef USE_ACCURATE_ROUNDING #undef DESCALE #define DESCALE(x,n) RIGHT_SHIFT(x, n) #endif /* Multiply a DCTELEM variable by an INT32 constant, and immediately * descale to yield a DCTELEM result. */ #define MULTIPLY(var,const) ((DCTELEM) 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) (((IFAST_MULT_TYPE) (coef)) * (quantval)) #else #define DEQUANTIZE(coef,quantval) \ DESCALE((coef)*(quantval), 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. */ #ifdef RIGHT_SHIFT_IS_UNSIGNED #define ISHIFT_TEMPS DCTELEM ishift_temp; #if BITS_IN_JSAMPLE == 8 #define DCTELEMBITS 16 /* DCTELEM may be 16 or 32 bits */ #else #define DCTELEMBITS 32 /* DCTELEM must be 32 bits */ #endif #define IRIGHT_SHIFT(x,shft) \ ((ishift_temp = (x)) < 0 ? \ (ishift_temp >> (shft)) | ((~((DCTELEM) 0)) << (DCTELEMBITS-(shft))) : \ (ishift_temp >> (shft))) #else #define ISHIFT_TEMPS #define IRIGHT_SHIFT(x,shft) ((x) >> (shft)) #endif #ifdef USE_ACCURATE_ROUNDING #define IDESCALE(x,n) ((int) IRIGHT_SHIFT((x) + (1 << ((n)-1)), n)) #else #define IDESCALE(x,n) ((int) IRIGHT_SHIFT(x, n)) #endif /* * Perform dequantization and inverse DCT on one block of coefficients. */ GLOBAL(void) jpeg_idct_ifast (j_decompress_ptr cinfo, jpeg_component_info * compptr, JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col) { DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; DCTELEM tmp10, tmp11, tmp12, tmp13; DCTELEM z5, z10, z11, z12, z13; JCOEFPTR inptr; IFAST_MULT_TYPE * quantptr; int * wsptr; JSAMPROW outptr; JSAMPLE *range_limit = IDCT_range_limit(cinfo); int ctr; int workspace[DCTSIZE2]; /* buffers data between passes */ SHIFT_TEMPS /* for DESCALE */ ISHIFT_TEMPS /* for IDESCALE */ /* Pass 1: process columns from input, store into work array. */ inptr = coef_block; quantptr = (IFAST_MULT_TYPE *) compptr->dct_table; wsptr = workspace; for (ctr = DCTSIZE; ctr > 0; ctr--) { /* 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 (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 && inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 && inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 && inptr[DCTSIZE*7] == 0) { /* AC terms all zero */ int dcval = (int) DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); wsptr[DCTSIZE*0] = dcval; wsptr[DCTSIZE*1] = dcval; wsptr[DCTSIZE*2] = dcval; wsptr[DCTSIZE*3] = dcval; wsptr[DCTSIZE*4] = dcval; wsptr[DCTSIZE*5] = dcval; wsptr[DCTSIZE*6] = dcval; wsptr[DCTSIZE*7] = dcval; inptr++; /* advance pointers to next column */ quantptr++; wsptr++; continue; } /* Even part */ tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]); tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]); tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]); tmp10 = tmp0 + tmp2; /* phase 3 */ tmp11 = tmp0 - tmp2; tmp13 = tmp1 + tmp3; /* phases 5-3 */ tmp12 = MULTIPLY(tmp1 - tmp3, FIX_1_414213562) - tmp13; /* 2*c4 */ tmp0 = tmp10 + tmp13; /* phase 2 */ tmp3 = tmp10 - tmp13; tmp1 = tmp11 + tmp12; tmp2 = tmp11 - tmp12; /* Odd part */ tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]); tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]); tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]); tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]); z13 = tmp6 + tmp5; /* phase 6 */ z10 = tmp6 - tmp5; z11 = tmp4 + tmp7; z12 = tmp4 - tmp7; tmp7 = z11 + z13; /* phase 5 */ tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */ z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */ tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */ tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */ tmp6 = tmp12 - tmp7; /* phase 2 */ tmp5 = tmp11 - tmp6; tmp4 = tmp10 + tmp5; wsptr[DCTSIZE*0] = (int) (tmp0 + tmp7); wsptr[DCTSIZE*7] = (int) (tmp0 - tmp7); wsptr[DCTSIZE*1] = (int) (tmp1 + tmp6); wsptr[DCTSIZE*6] = (int) (tmp1 - tmp6); wsptr[DCTSIZE*2] = (int) (tmp2 + tmp5); wsptr[DCTSIZE*5] = (int) (tmp2 - tmp5); wsptr[DCTSIZE*4] = (int) (tmp3 + tmp4); wsptr[DCTSIZE*3] = (int) (tmp3 - tmp4); inptr++; /* advance pointers to next column */ quantptr++; wsptr++; } /* 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. */ wsptr = workspace; for (ctr = 0; ctr < DCTSIZE; ctr++) { outptr = output_buf[ctr] + output_col; /* 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 (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 && wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) { /* AC terms all zero */ JSAMPLE dcval = range_limit[IDESCALE(wsptr[0], PASS1_BITS+3) & RANGE_MASK]; outptr[0] = dcval; outptr[1] = dcval; outptr[2] = dcval; outptr[3] = dcval; outptr[4] = dcval; outptr[5] = dcval; outptr[6] = dcval; outptr[7] = dcval; wsptr += DCTSIZE; /* advance pointer to next row */ continue; } #endif /* Even part */ tmp10 = ((DCTELEM) wsptr[0] + (DCTELEM) wsptr[4]); tmp11 = ((DCTELEM) wsptr[0] - (DCTELEM) wsptr[4]); tmp13 = ((DCTELEM) wsptr[2] + (DCTELEM) wsptr[6]); tmp12 = MULTIPLY((DCTELEM) wsptr[2] - (DCTELEM) wsptr[6], FIX_1_414213562) - tmp13; tmp0 = tmp10 + tmp13; tmp3 = tmp10 - tmp13; tmp1 = tmp11 + tmp12; tmp2 = tmp11 - tmp12; /* Odd part */ z13 = (DCTELEM) wsptr[5] + (DCTELEM) wsptr[3]; z10 = (DCTELEM) wsptr[5] - (DCTELEM) wsptr[3]; z11 = (DCTELEM) wsptr[1] + (DCTELEM) wsptr[7]; z12 = (DCTELEM) wsptr[1] - (DCTELEM) wsptr[7]; tmp7 = z11 + z13; /* phase 5 */ tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */ z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */ tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */ tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */ tmp6 = tmp12 - tmp7; /* phase 2 */ tmp5 = tmp11 - tmp6; tmp4 = tmp10 + tmp5; /* Final output stage: scale down by a factor of 8 and range-limit */ outptr[0] = range_limit[IDESCALE(tmp0 + tmp7, PASS1_BITS+3) & RANGE_MASK]; outptr[7] = range_limit[IDESCALE(tmp0 - tmp7, PASS1_BITS+3) & RANGE_MASK]; outptr[1] = range_limit[IDESCALE(tmp1 + tmp6, PASS1_BITS+3) & RANGE_MASK]; outptr[6] = range_limit[IDESCALE(tmp1 - tmp6, PASS1_BITS+3) & RANGE_MASK]; outptr[2] = range_limit[IDESCALE(tmp2 + tmp5, PASS1_BITS+3) & RANGE_MASK]; outptr[5] = range_limit[IDESCALE(tmp2 - tmp5, PASS1_BITS+3) & RANGE_MASK]; outptr[4] = range_limit[IDESCALE(tmp3 + tmp4, PASS1_BITS+3) & RANGE_MASK]; outptr[3] = range_limit[IDESCALE(tmp3 - tmp4, PASS1_BITS+3) & RANGE_MASK]; wsptr += DCTSIZE; /* advance pointer to next row */ } } #endif /* DCT_IFAST_SUPPORTED */

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