nuclear@1: /* nuclear@1: * jidctfst.c nuclear@1: * nuclear@1: * Copyright (C) 1994-1998, Thomas G. Lane. nuclear@1: * This file is part of the Independent JPEG Group's software. nuclear@1: * For conditions of distribution and use, see the accompanying README file. nuclear@1: * nuclear@1: * This file contains a fast, not so accurate integer implementation of the nuclear@1: * inverse DCT (Discrete Cosine Transform). In the IJG code, this routine nuclear@1: * must also perform dequantization of the input coefficients. nuclear@1: * nuclear@1: * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT nuclear@1: * on each row (or vice versa, but it's more convenient to emit a row at nuclear@1: * a time). Direct algorithms are also available, but they are much more nuclear@1: * complex and seem not to be any faster when reduced to code. nuclear@1: * nuclear@1: * This implementation is based on Arai, Agui, and Nakajima's algorithm for nuclear@1: * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in nuclear@1: * Japanese, but the algorithm is described in the Pennebaker & Mitchell nuclear@1: * JPEG textbook (see REFERENCES section in file README). The following code nuclear@1: * is based directly on figure 4-8 in P&M. nuclear@1: * While an 8-point DCT cannot be done in less than 11 multiplies, it is nuclear@1: * possible to arrange the computation so that many of the multiplies are nuclear@1: * simple scalings of the final outputs. These multiplies can then be nuclear@1: * folded into the multiplications or divisions by the JPEG quantization nuclear@1: * table entries. The AA&N method leaves only 5 multiplies and 29 adds nuclear@1: * to be done in the DCT itself. nuclear@1: * The primary disadvantage of this method is that with fixed-point math, nuclear@1: * accuracy is lost due to imprecise representation of the scaled nuclear@1: * quantization values. The smaller the quantization table entry, the less nuclear@1: * precise the scaled value, so this implementation does worse with high- nuclear@1: * quality-setting files than with low-quality ones. nuclear@1: */ nuclear@1: nuclear@1: #define JPEG_INTERNALS nuclear@1: #include "jinclude.h" nuclear@1: #include "jpeglib.h" nuclear@1: #include "jdct.h" /* Private declarations for DCT subsystem */ nuclear@1: nuclear@1: #ifdef DCT_IFAST_SUPPORTED nuclear@1: nuclear@1: nuclear@1: /* nuclear@1: * This module is specialized to the case DCTSIZE = 8. nuclear@1: */ nuclear@1: nuclear@1: #if DCTSIZE != 8 nuclear@1: Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ nuclear@1: #endif nuclear@1: nuclear@1: nuclear@1: /* Scaling decisions are generally the same as in the LL&M algorithm; nuclear@1: * see jidctint.c for more details. However, we choose to descale nuclear@1: * (right shift) multiplication products as soon as they are formed, nuclear@1: * rather than carrying additional fractional bits into subsequent additions. nuclear@1: * This compromises accuracy slightly, but it lets us save a few shifts. nuclear@1: * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples) nuclear@1: * everywhere except in the multiplications proper; this saves a good deal nuclear@1: * of work on 16-bit-int machines. nuclear@1: * nuclear@1: * The dequantized coefficients are not integers because the AA&N scaling nuclear@1: * factors have been incorporated. We represent them scaled up by PASS1_BITS, nuclear@1: * so that the first and second IDCT rounds have the same input scaling. nuclear@1: * For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to nuclear@1: * avoid a descaling shift; this compromises accuracy rather drastically nuclear@1: * for small quantization table entries, but it saves a lot of shifts. nuclear@1: * For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway, nuclear@1: * so we use a much larger scaling factor to preserve accuracy. nuclear@1: * nuclear@1: * A final compromise is to represent the multiplicative constants to only nuclear@1: * 8 fractional bits, rather than 13. This saves some shifting work on some nuclear@1: * machines, and may also reduce the cost of multiplication (since there nuclear@1: * are fewer one-bits in the constants). nuclear@1: */ nuclear@1: nuclear@1: #if BITS_IN_JSAMPLE == 8 nuclear@1: #define CONST_BITS 8 nuclear@1: #define PASS1_BITS 2 nuclear@1: #else nuclear@1: #define CONST_BITS 8 nuclear@1: #define PASS1_BITS 1 /* lose a little precision to avoid overflow */ nuclear@1: #endif nuclear@1: nuclear@1: /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus nuclear@1: * causing a lot of useless floating-point operations at run time. nuclear@1: * To get around this we use the following pre-calculated constants. nuclear@1: * If you change CONST_BITS you may want to add appropriate values. nuclear@1: * (With a reasonable C compiler, you can just rely on the FIX() macro...) nuclear@1: */ nuclear@1: nuclear@1: #if CONST_BITS == 8 nuclear@1: #define FIX_1_082392200 ((INT32) 277) /* FIX(1.082392200) */ nuclear@1: #define FIX_1_414213562 ((INT32) 362) /* FIX(1.414213562) */ nuclear@1: #define FIX_1_847759065 ((INT32) 473) /* FIX(1.847759065) */ nuclear@1: #define FIX_2_613125930 ((INT32) 669) /* FIX(2.613125930) */ nuclear@1: #else nuclear@1: #define FIX_1_082392200 FIX(1.082392200) nuclear@1: #define FIX_1_414213562 FIX(1.414213562) nuclear@1: #define FIX_1_847759065 FIX(1.847759065) nuclear@1: #define FIX_2_613125930 FIX(2.613125930) nuclear@1: #endif nuclear@1: nuclear@1: nuclear@1: /* We can gain a little more speed, with a further compromise in accuracy, nuclear@1: * by omitting the addition in a descaling shift. This yields an incorrectly nuclear@1: * rounded result half the time... nuclear@1: */ nuclear@1: nuclear@1: #ifndef USE_ACCURATE_ROUNDING nuclear@1: #undef DESCALE nuclear@1: #define DESCALE(x,n) RIGHT_SHIFT(x, n) nuclear@1: #endif nuclear@1: nuclear@1: nuclear@1: /* Multiply a DCTELEM variable by an INT32 constant, and immediately nuclear@1: * descale to yield a DCTELEM result. nuclear@1: */ nuclear@1: nuclear@1: #define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS)) nuclear@1: nuclear@1: nuclear@1: /* Dequantize a coefficient by multiplying it by the multiplier-table nuclear@1: * entry; produce a DCTELEM result. For 8-bit data a 16x16->16 nuclear@1: * multiplication will do. For 12-bit data, the multiplier table is nuclear@1: * declared INT32, so a 32-bit multiply will be used. nuclear@1: */ nuclear@1: nuclear@1: #if BITS_IN_JSAMPLE == 8 nuclear@1: #define DEQUANTIZE(coef,quantval) (((IFAST_MULT_TYPE) (coef)) * (quantval)) nuclear@1: #else nuclear@1: #define DEQUANTIZE(coef,quantval) \ nuclear@1: DESCALE((coef)*(quantval), IFAST_SCALE_BITS-PASS1_BITS) nuclear@1: #endif nuclear@1: nuclear@1: nuclear@1: /* Like DESCALE, but applies to a DCTELEM and produces an int. nuclear@1: * We assume that int right shift is unsigned if INT32 right shift is. nuclear@1: */ nuclear@1: nuclear@1: #ifdef RIGHT_SHIFT_IS_UNSIGNED nuclear@1: #define ISHIFT_TEMPS DCTELEM ishift_temp; nuclear@1: #if BITS_IN_JSAMPLE == 8 nuclear@1: #define DCTELEMBITS 16 /* DCTELEM may be 16 or 32 bits */ nuclear@1: #else nuclear@1: #define DCTELEMBITS 32 /* DCTELEM must be 32 bits */ nuclear@1: #endif nuclear@1: #define IRIGHT_SHIFT(x,shft) \ nuclear@1: ((ishift_temp = (x)) < 0 ? \ nuclear@1: (ishift_temp >> (shft)) | ((~((DCTELEM) 0)) << (DCTELEMBITS-(shft))) : \ nuclear@1: (ishift_temp >> (shft))) nuclear@1: #else nuclear@1: #define ISHIFT_TEMPS nuclear@1: #define IRIGHT_SHIFT(x,shft) ((x) >> (shft)) nuclear@1: #endif nuclear@1: nuclear@1: #ifdef USE_ACCURATE_ROUNDING nuclear@1: #define IDESCALE(x,n) ((int) IRIGHT_SHIFT((x) + (1 << ((n)-1)), n)) nuclear@1: #else nuclear@1: #define IDESCALE(x,n) ((int) IRIGHT_SHIFT(x, n)) nuclear@1: #endif nuclear@1: nuclear@1: nuclear@1: /* nuclear@1: * Perform dequantization and inverse DCT on one block of coefficients. nuclear@1: */ nuclear@1: nuclear@1: GLOBAL(void) nuclear@1: jpeg_idct_ifast (j_decompress_ptr cinfo, jpeg_component_info * compptr, nuclear@1: JCOEFPTR coef_block, nuclear@1: JSAMPARRAY output_buf, JDIMENSION output_col) nuclear@1: { nuclear@1: DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; nuclear@1: DCTELEM tmp10, tmp11, tmp12, tmp13; nuclear@1: DCTELEM z5, z10, z11, z12, z13; nuclear@1: JCOEFPTR inptr; nuclear@1: IFAST_MULT_TYPE * quantptr; nuclear@1: int * wsptr; nuclear@1: JSAMPROW outptr; nuclear@1: JSAMPLE *range_limit = IDCT_range_limit(cinfo); nuclear@1: int ctr; nuclear@1: int workspace[DCTSIZE2]; /* buffers data between passes */ nuclear@1: SHIFT_TEMPS /* for DESCALE */ nuclear@1: ISHIFT_TEMPS /* for IDESCALE */ nuclear@1: nuclear@1: /* Pass 1: process columns from input, store into work array. */ nuclear@1: nuclear@1: inptr = coef_block; nuclear@1: quantptr = (IFAST_MULT_TYPE *) compptr->dct_table; nuclear@1: wsptr = workspace; nuclear@1: for (ctr = DCTSIZE; ctr > 0; ctr--) { nuclear@1: /* Due to quantization, we will usually find that many of the input nuclear@1: * coefficients are zero, especially the AC terms. We can exploit this nuclear@1: * by short-circuiting the IDCT calculation for any column in which all nuclear@1: * the AC terms are zero. In that case each output is equal to the nuclear@1: * DC coefficient (with scale factor as needed). nuclear@1: * With typical images and quantization tables, half or more of the nuclear@1: * column DCT calculations can be simplified this way. nuclear@1: */ nuclear@1: nuclear@1: if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 && nuclear@1: inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 && nuclear@1: inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 && nuclear@1: inptr[DCTSIZE*7] == 0) { nuclear@1: /* AC terms all zero */ nuclear@1: int dcval = (int) DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); nuclear@1: nuclear@1: wsptr[DCTSIZE*0] = dcval; nuclear@1: wsptr[DCTSIZE*1] = dcval; nuclear@1: wsptr[DCTSIZE*2] = dcval; nuclear@1: wsptr[DCTSIZE*3] = dcval; nuclear@1: wsptr[DCTSIZE*4] = dcval; nuclear@1: wsptr[DCTSIZE*5] = dcval; nuclear@1: wsptr[DCTSIZE*6] = dcval; nuclear@1: wsptr[DCTSIZE*7] = dcval; nuclear@1: nuclear@1: inptr++; /* advance pointers to next column */ nuclear@1: quantptr++; nuclear@1: wsptr++; nuclear@1: continue; nuclear@1: } nuclear@1: nuclear@1: /* Even part */ nuclear@1: nuclear@1: tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); nuclear@1: tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]); nuclear@1: tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]); nuclear@1: tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]); nuclear@1: nuclear@1: tmp10 = tmp0 + tmp2; /* phase 3 */ nuclear@1: tmp11 = tmp0 - tmp2; nuclear@1: nuclear@1: tmp13 = tmp1 + tmp3; /* phases 5-3 */ nuclear@1: tmp12 = MULTIPLY(tmp1 - tmp3, FIX_1_414213562) - tmp13; /* 2*c4 */ nuclear@1: nuclear@1: tmp0 = tmp10 + tmp13; /* phase 2 */ nuclear@1: tmp3 = tmp10 - tmp13; nuclear@1: tmp1 = tmp11 + tmp12; nuclear@1: tmp2 = tmp11 - tmp12; nuclear@1: nuclear@1: /* Odd part */ nuclear@1: nuclear@1: tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]); nuclear@1: tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]); nuclear@1: tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]); nuclear@1: tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]); nuclear@1: nuclear@1: z13 = tmp6 + tmp5; /* phase 6 */ nuclear@1: z10 = tmp6 - tmp5; nuclear@1: z11 = tmp4 + tmp7; nuclear@1: z12 = tmp4 - tmp7; nuclear@1: nuclear@1: tmp7 = z11 + z13; /* phase 5 */ nuclear@1: tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */ nuclear@1: nuclear@1: z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */ nuclear@1: tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */ nuclear@1: tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */ nuclear@1: nuclear@1: tmp6 = tmp12 - tmp7; /* phase 2 */ nuclear@1: tmp5 = tmp11 - tmp6; nuclear@1: tmp4 = tmp10 + tmp5; nuclear@1: nuclear@1: wsptr[DCTSIZE*0] = (int) (tmp0 + tmp7); nuclear@1: wsptr[DCTSIZE*7] = (int) (tmp0 - tmp7); nuclear@1: wsptr[DCTSIZE*1] = (int) (tmp1 + tmp6); nuclear@1: wsptr[DCTSIZE*6] = (int) (tmp1 - tmp6); nuclear@1: wsptr[DCTSIZE*2] = (int) (tmp2 + tmp5); nuclear@1: wsptr[DCTSIZE*5] = (int) (tmp2 - tmp5); nuclear@1: wsptr[DCTSIZE*4] = (int) (tmp3 + tmp4); nuclear@1: wsptr[DCTSIZE*3] = (int) (tmp3 - tmp4); nuclear@1: nuclear@1: inptr++; /* advance pointers to next column */ nuclear@1: quantptr++; nuclear@1: wsptr++; nuclear@1: } nuclear@1: nuclear@1: /* Pass 2: process rows from work array, store into output array. */ nuclear@1: /* Note that we must descale the results by a factor of 8 == 2**3, */ nuclear@1: /* and also undo the PASS1_BITS scaling. */ nuclear@1: nuclear@1: wsptr = workspace; nuclear@1: for (ctr = 0; ctr < DCTSIZE; ctr++) { nuclear@1: outptr = output_buf[ctr] + output_col; nuclear@1: /* Rows of zeroes can be exploited in the same way as we did with columns. nuclear@1: * However, the column calculation has created many nonzero AC terms, so nuclear@1: * the simplification applies less often (typically 5% to 10% of the time). nuclear@1: * On machines with very fast multiplication, it's possible that the nuclear@1: * test takes more time than it's worth. In that case this section nuclear@1: * may be commented out. nuclear@1: */ nuclear@1: nuclear@1: #ifndef NO_ZERO_ROW_TEST nuclear@1: if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 && nuclear@1: wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) { nuclear@1: /* AC terms all zero */ nuclear@1: JSAMPLE dcval = range_limit[IDESCALE(wsptr[0], PASS1_BITS+3) nuclear@1: & RANGE_MASK]; nuclear@1: nuclear@1: outptr[0] = dcval; nuclear@1: outptr[1] = dcval; nuclear@1: outptr[2] = dcval; nuclear@1: outptr[3] = dcval; nuclear@1: outptr[4] = dcval; nuclear@1: outptr[5] = dcval; nuclear@1: outptr[6] = dcval; nuclear@1: outptr[7] = dcval; nuclear@1: nuclear@1: wsptr += DCTSIZE; /* advance pointer to next row */ nuclear@1: continue; nuclear@1: } nuclear@1: #endif nuclear@1: nuclear@1: /* Even part */ nuclear@1: nuclear@1: tmp10 = ((DCTELEM) wsptr[0] + (DCTELEM) wsptr[4]); nuclear@1: tmp11 = ((DCTELEM) wsptr[0] - (DCTELEM) wsptr[4]); nuclear@1: nuclear@1: tmp13 = ((DCTELEM) wsptr[2] + (DCTELEM) wsptr[6]); nuclear@1: tmp12 = MULTIPLY((DCTELEM) wsptr[2] - (DCTELEM) wsptr[6], FIX_1_414213562) nuclear@1: - tmp13; nuclear@1: nuclear@1: tmp0 = tmp10 + tmp13; nuclear@1: tmp3 = tmp10 - tmp13; nuclear@1: tmp1 = tmp11 + tmp12; nuclear@1: tmp2 = tmp11 - tmp12; nuclear@1: nuclear@1: /* Odd part */ nuclear@1: nuclear@1: z13 = (DCTELEM) wsptr[5] + (DCTELEM) wsptr[3]; nuclear@1: z10 = (DCTELEM) wsptr[5] - (DCTELEM) wsptr[3]; nuclear@1: z11 = (DCTELEM) wsptr[1] + (DCTELEM) wsptr[7]; nuclear@1: z12 = (DCTELEM) wsptr[1] - (DCTELEM) wsptr[7]; nuclear@1: nuclear@1: tmp7 = z11 + z13; /* phase 5 */ nuclear@1: tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */ nuclear@1: nuclear@1: z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */ nuclear@1: tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */ nuclear@1: tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */ nuclear@1: nuclear@1: tmp6 = tmp12 - tmp7; /* phase 2 */ nuclear@1: tmp5 = tmp11 - tmp6; nuclear@1: tmp4 = tmp10 + tmp5; nuclear@1: nuclear@1: /* Final output stage: scale down by a factor of 8 and range-limit */ nuclear@1: nuclear@1: outptr[0] = range_limit[IDESCALE(tmp0 + tmp7, PASS1_BITS+3) nuclear@1: & RANGE_MASK]; nuclear@1: outptr[7] = range_limit[IDESCALE(tmp0 - tmp7, PASS1_BITS+3) nuclear@1: & RANGE_MASK]; nuclear@1: outptr[1] = range_limit[IDESCALE(tmp1 + tmp6, PASS1_BITS+3) nuclear@1: & RANGE_MASK]; nuclear@1: outptr[6] = range_limit[IDESCALE(tmp1 - tmp6, PASS1_BITS+3) nuclear@1: & RANGE_MASK]; nuclear@1: outptr[2] = range_limit[IDESCALE(tmp2 + tmp5, PASS1_BITS+3) nuclear@1: & RANGE_MASK]; nuclear@1: outptr[5] = range_limit[IDESCALE(tmp2 - tmp5, PASS1_BITS+3) nuclear@1: & RANGE_MASK]; nuclear@1: outptr[4] = range_limit[IDESCALE(tmp3 + tmp4, PASS1_BITS+3) nuclear@1: & RANGE_MASK]; nuclear@1: outptr[3] = range_limit[IDESCALE(tmp3 - tmp4, PASS1_BITS+3) nuclear@1: & RANGE_MASK]; nuclear@1: nuclear@1: wsptr += DCTSIZE; /* advance pointer to next row */ nuclear@1: } nuclear@1: } nuclear@1: nuclear@1: #endif /* DCT_IFAST_SUPPORTED */