| 1 | /*
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| 2 | * jfdctfst.c
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| 3 | *
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| 4 | * Copyright (C) 1994-1996, Thomas G. Lane.
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| 5 | * This file is part of the Independent JPEG Group's software.
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| 6 | * For conditions of distribution and use, see the accompanying README file.
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| 7 | *
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| 8 | * This file contains a fast, not so accurate integer implementation of the
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| 9 | * forward DCT (Discrete Cosine Transform).
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| 10 | *
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| 11 | * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
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| 12 | * on each column. Direct algorithms are also available, but they are
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| 13 | * much more complex and seem not to be any faster when reduced to code.
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| 14 | *
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| 15 | * This implementation is based on Arai, Agui, and Nakajima's algorithm for
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| 16 | * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
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| 17 | * Japanese, but the algorithm is described in the Pennebaker & Mitchell
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| 18 | * JPEG textbook (see REFERENCES section in file README). The following code
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| 19 | * is based directly on figure 4-8 in P&M.
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| 20 | * While an 8-point DCT cannot be done in less than 11 multiplies, it is
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| 21 | * possible to arrange the computation so that many of the multiplies are
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| 22 | * simple scalings of the final outputs. These multiplies can then be
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| 23 | * folded into the multiplications or divisions by the JPEG quantization
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| 24 | * table entries. The AA&N method leaves only 5 multiplies and 29 adds
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| 25 | * to be done in the DCT itself.
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| 26 | * The primary disadvantage of this method is that with fixed-point math,
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| 27 | * accuracy is lost due to imprecise representation of the scaled
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| 28 | * quantization values. The smaller the quantization table entry, the less
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| 29 | * precise the scaled value, so this implementation does worse with high-
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| 30 | * quality-setting files than with low-quality ones.
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| 31 | */
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| 32 |
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| 33 | #define JPEG_INTERNALS
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| 34 | #include "jinclude.h"
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| 35 | #include "jpeglib.h"
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| 36 | #include "jdct.h" /* Private declarations for DCT subsystem */
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| 37 |
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| 38 | #ifdef DCT_IFAST_SUPPORTED
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| 39 |
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| 40 |
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| 41 | /*
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| 42 | * This module is specialized to the case DCTSIZE = 8.
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| 43 | */
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| 44 |
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| 45 | #if DCTSIZE != 8
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| 46 | Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
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| 47 | #endif
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| 48 |
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| 49 |
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| 50 | /* Scaling decisions are generally the same as in the LL&M algorithm;
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| 51 | * see jfdctint.c for more details. However, we choose to descale
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| 52 | * (right shift) multiplication products as soon as they are formed,
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| 53 | * rather than carrying additional fractional bits into subsequent additions.
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| 54 | * This compromises accuracy slightly, but it lets us save a few shifts.
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| 55 | * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
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| 56 | * everywhere except in the multiplications proper; this saves a good deal
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| 57 | * of work on 16-bit-int machines.
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| 58 | *
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| 59 | * Again to save a few shifts, the intermediate results between pass 1 and
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| 60 | * pass 2 are not upscaled, but are represented only to integral precision.
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| 61 | *
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| 62 | * A final compromise is to represent the multiplicative constants to only
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| 63 | * 8 fractional bits, rather than 13. This saves some shifting work on some
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| 64 | * machines, and may also reduce the cost of multiplication (since there
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| 65 | * are fewer one-bits in the constants).
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