// * jidctfst.c // * // * Copyright (C) 1994-1995, 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] | inptr[DCTSIZE*2] | inptr[DCTSIZE*3] | inptr[DCTSIZE*4] | inptr[DCTSIZE*5] | inptr[DCTSIZE*6] | 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] | wsptr[2] | wsptr[3] | wsptr[4] | wsptr[5] | wsptr[6] | 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