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unit imjidctflt;
{ 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. }
{ Original: jidctflt.c ; Copyright (C) 1994-1996, Thomas G. Lane. }
interface
{$I imjconfig.inc}
uses imjmorecfg, imjinclude, imjpeglib, imjdct; { Private declarations for DCT subsystem }
{ Perform dequantization and inverse DCT on one block of coefficients. }
{GLOBAL}procedure jpeg_idct_float (cinfo : j_decompress_ptr; compptr : jpeg_component_info_ptr; coef_block : JCOEFPTR; output_buf : JSAMPARRAY; output_col : JDIMENSION);
implementation
{ This module is specialized to the case DCTSIZE = 8. }
{$ifndef DCTSIZE_IS_8} Sorry, this code only copes with 8x8 DCTs. { deliberate syntax err }{$endif}
{ Dequantize a coefficient by multiplying it by the multiplier-table entry; produce a float result. }
function DEQUANTIZE(coef : int; quantval : FAST_FLOAT) : FAST_FLOAT;begin Dequantize := ( (coef) * quantval);end;
{ Descale and correctly round an INT32 value that's scaled by N bits. We assume RIGHT_SHIFT rounds towards minus infinity, so adding the fudge factor is correct for either sign of X. }
function DESCALE(x : INT32; n : int) : INT32;var shift_temp : INT32;begin{$ifdef RIGHT_SHIFT_IS_UNSIGNED} shift_temp := x + (INT32(1) shl (n-1)); if shift_temp < 0 then Descale := (shift_temp shr n) or ((not INT32(0)) shl (32-n)) else Descale := (shift_temp shr n);{$else} Descale := (x + (INT32(1) shl (n-1)) shr n;{$endif}end;
{ Perform dequantization and inverse DCT on one block of coefficients. }
{GLOBAL}procedure jpeg_idct_float (cinfo : j_decompress_ptr; compptr : jpeg_component_info_ptr; coef_block : JCOEFPTR; output_buf : JSAMPARRAY; output_col : JDIMENSION);type PWorkspace = ^TWorkspace; TWorkspace = array[0..DCTSIZE2-1] of FAST_FLOAT;var tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7 : FAST_FLOAT; tmp10, tmp11, tmp12, tmp13 : FAST_FLOAT; z5, z10, z11, z12, z13 : FAST_FLOAT; inptr : JCOEFPTR; quantptr : FLOAT_MULT_TYPE_FIELD_PTR; wsptr : PWorkSpace; outptr : JSAMPROW; range_limit : JSAMPROW; ctr : int; workspace : TWorkspace; { buffers data between passes } {SHIFT_TEMPS}var dcval : FAST_FLOAT;begin{ Each IDCT routine is responsible for range-limiting its results and converting them to unsigned form (0..MAXJSAMPLE). The raw outputs could be quite far out of range if the input data is corrupt, so a bulletproof range-limiting step is required. We use a mask-and-table-lookup method to do the combined operations quickly. See the comments with prepare_range_limit_table (in jdmaster.c) for more info. }
range_limit := JSAMPROW(@(cinfo^.sample_range_limit^[CENTERJSAMPLE]));
{ Pass 1: process columns from input, store into work array. }
inptr := coef_block; quantptr := FLOAT_MULT_TYPE_FIELD_PTR (compptr^.dct_table); wsptr := @workspace; for ctr := pred(DCTSIZE) downto 0 do begin { 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) and (inptr^[DCTSIZE*2]=0) and (inptr^[DCTSIZE*3]=0) and (inptr^[DCTSIZE*4]=0) and (inptr^[DCTSIZE*5]=0) and (inptr^[DCTSIZE*6]=0) and (inptr^[DCTSIZE*7]=0) then begin { 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;
Inc(JCOEF_PTR(inptr)); { advance pointers to next column } Inc(FLOAT_MULT_TYPE_PTR(quantptr)); Inc(FAST_FLOAT_PTR(wsptr)); continue; end;
{ 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;
Inc(JCOEF_PTR(inptr)); { advance pointers to next column } Inc(FLOAT_MULT_TYPE_PTR(quantptr)); Inc(FAST_FLOAT_PTR(wsptr)); end;
{ 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 to pred(DCTSIZE) do begin outptr := JSAMPROW(@(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(Round((tmp0 + tmp7))), 3)) and RANGE_MASK]; outptr^[7] := range_limit^[ int(DESCALE( INT32(Round((tmp0 - tmp7))), 3)) and RANGE_MASK]; outptr^[1] := range_limit^[ int(DESCALE( INT32(Round((tmp1 + tmp6))), 3)) and RANGE_MASK]; outptr^[6] := range_limit^[ int(DESCALE( INT32(Round((tmp1 - tmp6))), 3)) and RANGE_MASK]; outptr^[2] := range_limit^[ int(DESCALE( INT32(Round((tmp2 + tmp5))), 3)) and RANGE_MASK]; outptr^[5] := range_limit^[ int(DESCALE( INT32(Round((tmp2 - tmp5))), 3)) and RANGE_MASK]; outptr^[4] := range_limit^[ int(DESCALE( INT32(Round((tmp3 + tmp4))), 3)) and RANGE_MASK]; outptr^[3] := range_limit^[ int(DESCALE( INT32(Round((tmp3 - tmp4))), 3)) and RANGE_MASK];
Inc(FAST_FLOAT_PTR(wsptr), DCTSIZE); { advance pointer to next row } end;end;
end.
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