298 lines
11 KiB
Plaintext
298 lines
11 KiB
Plaintext
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unit imjfdctint;
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{ This file contains a slow-but-accurate integer implementation of the
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forward DCT (Discrete Cosine Transform).
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A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
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on each column. Direct algorithms are also available, but they are
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much more complex and seem not to be any faster when reduced to code.
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This implementation is based on an algorithm described in
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C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
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Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
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Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
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The primary algorithm described there uses 11 multiplies and 29 adds.
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We use their alternate method with 12 multiplies and 32 adds.
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The advantage of this method is that no data path contains more than one
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multiplication; this allows a very simple and accurate implementation in
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scaled fixed-point arithmetic, with a minimal number of shifts. }
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{ Original : jfdctint.c ; Copyright (C) 1991-1996, Thomas G. Lane. }
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interface
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{$I imjconfig.inc}
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uses
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imjmorecfg,
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imjinclude,
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imjutils,
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imjpeglib,
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imjdct; { Private declarations for DCT subsystem }
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{ Perform the forward DCT on one block of samples. }
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{GLOBAL}
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procedure jpeg_fdct_islow (var data : array of DCTELEM);
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implementation
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{ This module is specialized to the case DCTSIZE = 8. }
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{$ifndef DCTSIZE_IS_8}
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Sorry, this code only copes with 8x8 DCTs. { deliberate syntax err }
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{$endif}
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{ The poop on this scaling stuff is as follows:
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Each 1-D DCT step produces outputs which are a factor of sqrt(N)
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larger than the true DCT outputs. The final outputs are therefore
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a factor of N larger than desired; since N=8 this can be cured by
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a simple right shift at the end of the algorithm. The advantage of
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this arrangement is that we save two multiplications per 1-D DCT,
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because the y0 and y4 outputs need not be divided by sqrt(N).
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In the IJG code, this factor of 8 is removed by the quantization step
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(in jcdctmgr.c), NOT in this module.
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We have to do addition and subtraction of the integer inputs, which
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is no problem, and multiplication by fractional constants, which is
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a problem to do in integer arithmetic. We multiply all the constants
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by CONST_SCALE and convert them to integer constants (thus retaining
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CONST_BITS bits of precision in the constants). After doing a
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multiplication we have to divide the product by CONST_SCALE, with proper
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rounding, to produce the correct output. This division can be done
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cheaply as a right shift of CONST_BITS bits. We postpone shifting
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as long as possible so that partial sums can be added together with
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full fractional precision.
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The outputs of the first pass are scaled up by PASS1_BITS bits so that
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they are represented to better-than-integral precision. These outputs
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require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
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with the recommended scaling. (For 12-bit sample data, the intermediate
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array is INT32 anyway.)
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To avoid overflow of the 32-bit intermediate results in pass 2, we must
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have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis
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shows that the values given below are the most effective. }
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{$ifdef BITS_IN_JSAMPLE_IS_8}
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const
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CONST_BITS = 13;
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PASS1_BITS = 2;
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{$else}
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const
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CONST_BITS = 13;
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PASS1_BITS = 1; { lose a little precision to avoid overflow }
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{$endif}
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const
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CONST_SCALE = (INT32(1) shl CONST_BITS);
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const
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FIX_0_298631336 = INT32(Round(CONST_SCALE * 0.298631336)); {2446}
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FIX_0_390180644 = INT32(Round(CONST_SCALE * 0.390180644)); {3196}
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FIX_0_541196100 = INT32(Round(CONST_SCALE * 0.541196100)); {4433}
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FIX_0_765366865 = INT32(Round(CONST_SCALE * 0.765366865)); {6270}
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FIX_0_899976223 = INT32(Round(CONST_SCALE * 0.899976223)); {7373}
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FIX_1_175875602 = INT32(Round(CONST_SCALE * 1.175875602)); {9633}
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FIX_1_501321110 = INT32(Round(CONST_SCALE * 1.501321110)); {12299}
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FIX_1_847759065 = INT32(Round(CONST_SCALE * 1.847759065)); {15137}
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FIX_1_961570560 = INT32(Round(CONST_SCALE * 1.961570560)); {16069}
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FIX_2_053119869 = INT32(Round(CONST_SCALE * 2.053119869)); {16819}
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FIX_2_562915447 = INT32(Round(CONST_SCALE * 2.562915447)); {20995}
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FIX_3_072711026 = INT32(Round(CONST_SCALE * 3.072711026)); {25172}
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{ Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
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For 8-bit samples with the recommended scaling, all the variable
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and constant values involved are no more than 16 bits wide, so a
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16x16->32 bit multiply can be used instead of a full 32x32 multiply.
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For 12-bit samples, a full 32-bit multiplication will be needed. }
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{$ifdef BITS_IN_JSAMPLE_IS_8}
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{MULTIPLY16C16(var,const)}
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function Multiply(X, Y: int): INT32;
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begin
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Multiply := int(X) * INT32(Y);
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end;
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{$else}
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function Multiply(X, Y: INT32): INT32;
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begin
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Multiply := X * Y;
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end;
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{$endif}
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{ Descale and correctly round an INT32 value that's scaled by N bits.
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We assume RIGHT_SHIFT rounds towards minus infinity, so adding
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the fudge factor is correct for either sign of X. }
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function DESCALE(x : INT32; n : int) : INT32;
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var
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shift_temp : INT32;
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begin
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{$ifdef RIGHT_SHIFT_IS_UNSIGNED}
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shift_temp := x + (INT32(1) shl (n-1));
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if shift_temp < 0 then
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Descale := (shift_temp shr n) or ((not INT32(0)) shl (32-n))
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else
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Descale := (shift_temp shr n);
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{$else}
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Descale := (x + (INT32(1) shl (n-1)) shr n;
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{$endif}
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end;
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{ Perform the forward DCT on one block of samples. }
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{GLOBAL}
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procedure jpeg_fdct_islow (var data : array of DCTELEM);
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type
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PWorkspace = ^TWorkspace;
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TWorkspace = array [0..DCTSIZE2-1] of DCTELEM;
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var
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tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7 : INT32;
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tmp10, tmp11, tmp12, tmp13 : INT32;
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z1, z2, z3, z4, z5 : INT32;
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dataptr : PWorkspace;
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ctr : int;
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{SHIFT_TEMPS}
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begin
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{ Pass 1: process rows. }
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{ Note results are scaled up by sqrt(8) compared to a true DCT; }
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{ furthermore, we scale the results by 2**PASS1_BITS. }
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dataptr := PWorkspace(@data);
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for ctr := DCTSIZE-1 downto 0 do
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begin
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tmp0 := dataptr^[0] + dataptr^[7];
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tmp7 := dataptr^[0] - dataptr^[7];
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tmp1 := dataptr^[1] + dataptr^[6];
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tmp6 := dataptr^[1] - dataptr^[6];
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tmp2 := dataptr^[2] + dataptr^[5];
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tmp5 := dataptr^[2] - dataptr^[5];
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tmp3 := dataptr^[3] + dataptr^[4];
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tmp4 := dataptr^[3] - dataptr^[4];
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{ Even part per LL&M figure 1 --- note that published figure is faulty;
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rotator "sqrt(2)*c1" should be "sqrt(2)*c6". }
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tmp10 := tmp0 + tmp3;
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tmp13 := tmp0 - tmp3;
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tmp11 := tmp1 + tmp2;
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tmp12 := tmp1 - tmp2;
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dataptr^[0] := DCTELEM ((tmp10 + tmp11) shl PASS1_BITS);
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dataptr^[4] := DCTELEM ((tmp10 - tmp11) shl PASS1_BITS);
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z1 := MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
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dataptr^[2] := DCTELEM (DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
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CONST_BITS-PASS1_BITS));
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dataptr^[6] := DCTELEM (DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
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CONST_BITS-PASS1_BITS));
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{ Odd part per figure 8 --- note paper omits factor of sqrt(2).
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cK represents cos(K*pi/16).
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i0..i3 in the paper are tmp4..tmp7 here. }
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z1 := tmp4 + tmp7;
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z2 := tmp5 + tmp6;
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z3 := tmp4 + tmp6;
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z4 := tmp5 + tmp7;
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z5 := MULTIPLY(z3 + z4, FIX_1_175875602); { sqrt(2) * c3 }
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tmp4 := MULTIPLY(tmp4, FIX_0_298631336); { sqrt(2) * (-c1+c3+c5-c7) }
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tmp5 := MULTIPLY(tmp5, FIX_2_053119869); { sqrt(2) * ( c1+c3-c5+c7) }
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tmp6 := MULTIPLY(tmp6, FIX_3_072711026); { sqrt(2) * ( c1+c3+c5-c7) }
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tmp7 := MULTIPLY(tmp7, FIX_1_501321110); { sqrt(2) * ( c1+c3-c5-c7) }
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z1 := MULTIPLY(z1, - FIX_0_899976223); { sqrt(2) * (c7-c3) }
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z2 := MULTIPLY(z2, - FIX_2_562915447); { sqrt(2) * (-c1-c3) }
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z3 := MULTIPLY(z3, - FIX_1_961570560); { sqrt(2) * (-c3-c5) }
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z4 := MULTIPLY(z4, - FIX_0_390180644); { sqrt(2) * (c5-c3) }
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Inc(z3, z5);
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Inc(z4, z5);
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dataptr^[7] := DCTELEM(DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS));
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dataptr^[5] := DCTELEM(DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS));
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dataptr^[3] := DCTELEM(DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS));
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dataptr^[1] := DCTELEM(DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS));
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Inc(DCTELEMPTR(dataptr), DCTSIZE); { advance pointer to next row }
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end;
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{ Pass 2: process columns.
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We remove the PASS1_BITS scaling, but leave the results scaled up
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by an overall factor of 8. }
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dataptr := PWorkspace(@data);
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for ctr := DCTSIZE-1 downto 0 do
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begin
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tmp0 := dataptr^[DCTSIZE*0] + dataptr^[DCTSIZE*7];
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tmp7 := dataptr^[DCTSIZE*0] - dataptr^[DCTSIZE*7];
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tmp1 := dataptr^[DCTSIZE*1] + dataptr^[DCTSIZE*6];
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tmp6 := dataptr^[DCTSIZE*1] - dataptr^[DCTSIZE*6];
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tmp2 := dataptr^[DCTSIZE*2] + dataptr^[DCTSIZE*5];
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tmp5 := dataptr^[DCTSIZE*2] - dataptr^[DCTSIZE*5];
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tmp3 := dataptr^[DCTSIZE*3] + dataptr^[DCTSIZE*4];
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tmp4 := dataptr^[DCTSIZE*3] - dataptr^[DCTSIZE*4];
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{ Even part per LL&M figure 1 --- note that published figure is faulty;
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rotator "sqrt(2)*c1" should be "sqrt(2)*c6". }
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tmp10 := tmp0 + tmp3;
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tmp13 := tmp0 - tmp3;
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tmp11 := tmp1 + tmp2;
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tmp12 := tmp1 - tmp2;
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dataptr^[DCTSIZE*0] := DCTELEM (DESCALE(tmp10 + tmp11, PASS1_BITS));
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dataptr^[DCTSIZE*4] := DCTELEM (DESCALE(tmp10 - tmp11, PASS1_BITS));
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z1 := MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
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dataptr^[DCTSIZE*2] := DCTELEM (DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
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CONST_BITS+PASS1_BITS));
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dataptr^[DCTSIZE*6] := DCTELEM (DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
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CONST_BITS+PASS1_BITS));
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{ Odd part per figure 8 --- note paper omits factor of sqrt(2).
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cK represents cos(K*pi/16).
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i0..i3 in the paper are tmp4..tmp7 here. }
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z1 := tmp4 + tmp7;
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z2 := tmp5 + tmp6;
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z3 := tmp4 + tmp6;
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z4 := tmp5 + tmp7;
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z5 := MULTIPLY(z3 + z4, FIX_1_175875602); { sqrt(2) * c3 }
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tmp4 := MULTIPLY(tmp4, FIX_0_298631336); { sqrt(2) * (-c1+c3+c5-c7) }
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tmp5 := MULTIPLY(tmp5, FIX_2_053119869); { sqrt(2) * ( c1+c3-c5+c7) }
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tmp6 := MULTIPLY(tmp6, FIX_3_072711026); { sqrt(2) * ( c1+c3+c5-c7) }
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tmp7 := MULTIPLY(tmp7, FIX_1_501321110); { sqrt(2) * ( c1+c3-c5-c7) }
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z1 := MULTIPLY(z1, - FIX_0_899976223); { sqrt(2) * (c7-c3) }
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z2 := MULTIPLY(z2, - FIX_2_562915447); { sqrt(2) * (-c1-c3) }
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z3 := MULTIPLY(z3, - FIX_1_961570560); { sqrt(2) * (-c3-c5) }
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z4 := MULTIPLY(z4, - FIX_0_390180644); { sqrt(2) * (c5-c3) }
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Inc(z3, z5);
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Inc(z4, z5);
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dataptr^[DCTSIZE*7] := DCTELEM (DESCALE(tmp4 + z1 + z3,
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CONST_BITS+PASS1_BITS));
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dataptr^[DCTSIZE*5] := DCTELEM (DESCALE(tmp5 + z2 + z4,
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CONST_BITS+PASS1_BITS));
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dataptr^[DCTSIZE*3] := DCTELEM (DESCALE(tmp6 + z2 + z3,
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CONST_BITS+PASS1_BITS));
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dataptr^[DCTSIZE*1] := DCTELEM (DESCALE(tmp7 + z1 + z4,
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CONST_BITS+PASS1_BITS));
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Inc(DCTELEMPTR(dataptr)); { advance pointer to next column }
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end;
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end;
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end.
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