/* * jidctflt.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 floating-point implementation of the * inverse DCT (Discrete Cosine Transform). In the IJG code, this routine * must also perform dequantization of the input coefficients. * * This implementation should be more accurate than either of the integer * IDCT implementations. However, it may not give the same results on all * machines because of differences in roundoff behavior. Speed will depend * on the hardware's floating point capacity. * * 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 a fixed-point * implementation, accuracy is lost due to imprecise representation of the * scaled quantization values. However, that problem does not arise if * we use floating point arithmetic. */ #define JPEG_INTERNALS #include "jinclude.h" #include "jpeglib.h" #include "jdct.h" /* Private declarations for DCT subsystem */ #ifdef DCT_FLOAT_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 /* Dequantize a coefficient by multiplying it by the multiplier-table * entry; produce a float result. */ #define DEQUANTIZE(coef,quantval) (((FAST_FLOAT) (coef)) * (quantval)) /* * Perform dequantization and inverse DCT on one block of coefficients. */ GLOBAL(void) jpeg_idct_float (j_decompress_ptr cinfo, jpeg_component_info * compptr, JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col) { FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; FAST_FLOAT tmp10, tmp11, tmp12, tmp13; FAST_FLOAT z5, z10, z11, z12, z13; JCOEFPTR inptr; FLOAT_MULT_TYPE * quantptr; FAST_FLOAT * wsptr; JSAMPROW outptr; JSAMPLE *range_limit = IDCT_range_limit(cinfo); int ctr; FAST_FLOAT workspace[DCTSIZE2]; /* buffers data between passes */ SHIFT_TEMPS /* Pass 1: process columns from input, store into work array. */ inptr = coef_block; quantptr = (FLOAT_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 */ FAST_FLOAT dcval = 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 = (tmp1 - tmp3) * ((FAST_FLOAT) 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 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); /* 2*c4 */ z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */ tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */ tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */ tmp6 = tmp12 - tmp7; /* phase 2 */ tmp5 = tmp11 - tmp6; tmp4 = tmp10 + tmp5; wsptr[DCTSIZE*0] = tmp0 + tmp7; wsptr[DCTSIZE*7] = tmp0 - tmp7; wsptr[DCTSIZE*1] = tmp1 + tmp6; wsptr[DCTSIZE*6] = tmp1 - tmp6; wsptr[DCTSIZE*2] = tmp2 + tmp5; wsptr[DCTSIZE*5] = tmp2 - tmp5; wsptr[DCTSIZE*4] = tmp3 + tmp4; wsptr[DCTSIZE*3] = 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. */ 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). * And testing floats for zero is relatively expensive, so we don't bother. */ /* Even part */ tmp10 = wsptr[0] + wsptr[4]; tmp11 = wsptr[0] - wsptr[4]; tmp13 = wsptr[2] + wsptr[6]; tmp12 = (wsptr[2] - wsptr[6]) * ((FAST_FLOAT) 1.414213562) - tmp13; tmp0 = tmp10 + tmp13; tmp3 = tmp10 - tmp13; tmp1 = tmp11 + tmp12; tmp2 = tmp11 - tmp12; /* Odd part */ z13 = wsptr[5] + wsptr[3]; z10 = wsptr[5] - wsptr[3]; z11 = wsptr[1] + wsptr[7]; z12 = wsptr[1] - wsptr[7]; tmp7 = z11 + z13; tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */ tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */ tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */ tmp6 = tmp12 - tmp7; tmp5 = tmp11 - tmp6; tmp4 = tmp10 + tmp5; /* Final output stage: scale down by a factor of 8 and range-limit */ outptr[0] = range_limit[(int) DESCALE((INT32) (tmp0 + tmp7), 3) & RANGE_MASK]; outptr[7] = range_limit[(int) DESCALE((INT32) (tmp0 - tmp7), 3) & RANGE_MASK]; outptr[1] = range_limit[(int) DESCALE((INT32) (tmp1 + tmp6), 3) & RANGE_MASK]; outptr[6] = range_limit[(int) DESCALE((INT32) (tmp1 - tmp6), 3) & RANGE_MASK]; outptr[2] = range_limit[(int) DESCALE((INT32) (tmp2 + tmp5), 3) & RANGE_MASK]; outptr[5] = range_limit[(int) DESCALE((INT32) (tmp2 - tmp5), 3) & RANGE_MASK]; outptr[4] = range_limit[(int) DESCALE((INT32) (tmp3 + tmp4), 3) & RANGE_MASK]; outptr[3] = range_limit[(int) DESCALE((INT32) (tmp3 - tmp4), 3) & RANGE_MASK]; wsptr += DCTSIZE; /* advance pointer to next row */ } } #endif /* DCT_FLOAT_SUPPORTED */

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