| /* |
| * jfwddct.c |
| * |
| * Copyright (C) 1991, 1992, 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 the basic DCT (Discrete Cosine Transform) |
| * transformation subroutine. |
| * |
| * This implementation is based on Appendix A.2 of the book |
| * "Discrete Cosine Transform---Algorithms, Advantages, Applications" |
| * by K.R. Rao and P. Yip (Academic Press, Inc, London, 1990). |
| * It uses scaled fixed-point arithmetic instead of floating point. |
| */ |
| |
| #include "jinclude.h" |
| |
| /* |
| * This routine is specialized to the case DCTSIZE = 8. |
| */ |
| |
| #if DCTSIZE != 8 |
| Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ |
| #endif |
| |
| |
| /* The poop on this scaling stuff is as follows: |
| * |
| * We have to do addition and subtraction of the integer inputs, which |
| * is no problem, and multiplication by fractional constants, which is |
| * a problem to do in integer arithmetic. We multiply all the constants |
| * by DCT_SCALE and convert them to integer constants (thus retaining |
| * LG2_DCT_SCALE bits of precision in the constants). After doing a |
| * multiplication we have to divide the product by DCT_SCALE, with proper |
| * rounding, to produce the correct output. The division can be implemented |
| * cheaply as a right shift of LG2_DCT_SCALE bits. The DCT equations also |
| * specify an additional division by 2 on the final outputs; this can be |
| * folded into the right-shift by shifting one more bit (see UNFIXH). |
| * |
| * If you are planning to recode this in assembler, you might want to set |
| * LG2_DCT_SCALE to 15. This loses a bit of precision, but then all the |
| * multiplications are between 16-bit quantities (given 8-bit JSAMPLEs!) |
| * so you could use a signed 16x16=>32 bit multiply instruction instead of |
| * full 32x32 multiply. Unfortunately there's no way to describe such a |
| * multiply portably in C, so we've gone for the extra bit of accuracy here. |
| */ |
| |
| #ifdef EIGHT_BIT_SAMPLES |
| #define LG2_DCT_SCALE 16 |
| #else |
| #define LG2_DCT_SCALE 15 /* lose a little precision to avoid overflow */ |
| #endif |
| |
| #define ONE ((INT32) 1) |
| |
| #define DCT_SCALE (ONE << LG2_DCT_SCALE) |
| |
| /* In some places we shift the inputs left by a couple more bits, */ |
| /* so that they can be added to fractional results without too much */ |
| /* loss of precision. */ |
| #define LG2_OVERSCALE 2 |
| #define OVERSCALE (ONE << LG2_OVERSCALE) |
| #define OVERSHIFT(x) ((x) <<= LG2_OVERSCALE) |
| |
| /* Scale a fractional constant by DCT_SCALE */ |
| #define FIX(x) ((INT32) ((x) * DCT_SCALE + 0.5)) |
| |
| /* Scale a fractional constant by DCT_SCALE/OVERSCALE */ |
| /* Such a constant can be multiplied with an overscaled input */ |
| /* to produce something that's scaled by DCT_SCALE */ |
| #define FIXO(x) ((INT32) ((x) * DCT_SCALE / OVERSCALE + 0.5)) |
| |
| /* Descale and correctly round a value that's scaled by DCT_SCALE */ |
| #define UNFIX(x) RIGHT_SHIFT((x) + (ONE << (LG2_DCT_SCALE-1)), LG2_DCT_SCALE) |
| |
| /* Same with an additional division by 2, ie, correctly rounded UNFIX(x/2) */ |
| #define UNFIXH(x) RIGHT_SHIFT((x) + (ONE << LG2_DCT_SCALE), LG2_DCT_SCALE+1) |
| |
| /* Take a value scaled by DCT_SCALE and round to integer scaled by OVERSCALE */ |
| #define UNFIXO(x) RIGHT_SHIFT((x) + (ONE << (LG2_DCT_SCALE-1-LG2_OVERSCALE)),\ |
| LG2_DCT_SCALE-LG2_OVERSCALE) |
| |
| /* Here are the constants we need */ |
| /* SIN_i_j is sine of i*pi/j, scaled by DCT_SCALE */ |
| /* COS_i_j is cosine of i*pi/j, scaled by DCT_SCALE */ |
| |
| #define SIN_1_4 FIX(0.707106781) |
| #define COS_1_4 SIN_1_4 |
| |
| #define SIN_1_8 FIX(0.382683432) |
| #define COS_1_8 FIX(0.923879533) |
| #define SIN_3_8 COS_1_8 |
| #define COS_3_8 SIN_1_8 |
| |
| #define SIN_1_16 FIX(0.195090322) |
| #define COS_1_16 FIX(0.980785280) |
| #define SIN_7_16 COS_1_16 |
| #define COS_7_16 SIN_1_16 |
| |
| #define SIN_3_16 FIX(0.555570233) |
| #define COS_3_16 FIX(0.831469612) |
| #define SIN_5_16 COS_3_16 |
| #define COS_5_16 SIN_3_16 |
| |
| /* OSIN_i_j is sine of i*pi/j, scaled by DCT_SCALE/OVERSCALE */ |
| /* OCOS_i_j is cosine of i*pi/j, scaled by DCT_SCALE/OVERSCALE */ |
| |
| #define OSIN_1_4 FIXO(0.707106781) |
| #define OCOS_1_4 OSIN_1_4 |
| |
| #define OSIN_1_8 FIXO(0.382683432) |
| #define OCOS_1_8 FIXO(0.923879533) |
| #define OSIN_3_8 OCOS_1_8 |
| #define OCOS_3_8 OSIN_1_8 |
| |
| #define OSIN_1_16 FIXO(0.195090322) |
| #define OCOS_1_16 FIXO(0.980785280) |
| #define OSIN_7_16 OCOS_1_16 |
| #define OCOS_7_16 OSIN_1_16 |
| |
| #define OSIN_3_16 FIXO(0.555570233) |
| #define OCOS_3_16 FIXO(0.831469612) |
| #define OSIN_5_16 OCOS_3_16 |
| #define OCOS_5_16 OSIN_3_16 |
| |
| |
| /* |
| * Perform the forward DCT on one block of samples. |
| * |
| * A 2-D DCT can be done by 1-D DCT on each row |
| * followed by 1-D DCT on each column. |
| */ |
| |
| GLOBAL void |
| j_fwd_dct (DCTBLOCK data) |
| { |
| int pass, rowctr; |
| register DCTELEM *inptr, *outptr; |
| DCTBLOCK workspace; |
| |
| /* Each iteration of the inner loop performs one 8-point 1-D DCT. |
| * It reads from a *row* of the input matrix and stores into a *column* |
| * of the output matrix. In the first pass, we read from the data[] array |
| * and store into the local workspace[]. In the second pass, we read from |
| * the workspace[] array and store into data[], thus performing the |
| * equivalent of a columnar DCT pass with no variable array indexing. |
| */ |
| |
| inptr = data; /* initialize pointers for first pass */ |
| outptr = workspace; |
| for (pass = 1; pass >= 0; pass--) { |
| for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--) { |
| /* many tmps have nonoverlapping lifetime -- flashy register colourers |
| * should be able to do this lot very well |
| */ |
| INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; |
| INT32 tmp10, tmp11, tmp12, tmp13; |
| INT32 tmp14, tmp15, tmp16, tmp17; |
| INT32 tmp25, tmp26; |
| SHIFT_TEMPS |
| |
| tmp0 = inptr[7] + inptr[0]; |
| tmp1 = inptr[6] + inptr[1]; |
| tmp2 = inptr[5] + inptr[2]; |
| tmp3 = inptr[4] + inptr[3]; |
| tmp4 = inptr[3] - inptr[4]; |
| tmp5 = inptr[2] - inptr[5]; |
| tmp6 = inptr[1] - inptr[6]; |
| tmp7 = inptr[0] - inptr[7]; |
| |
| tmp10 = tmp3 + tmp0; |
| tmp11 = tmp2 + tmp1; |
| tmp12 = tmp1 - tmp2; |
| tmp13 = tmp0 - tmp3; |
| |
| outptr[ 0] = (DCTELEM) UNFIXH((tmp10 + tmp11) * SIN_1_4); |
| outptr[DCTSIZE*4] = (DCTELEM) UNFIXH((tmp10 - tmp11) * COS_1_4); |
| |
| outptr[DCTSIZE*2] = (DCTELEM) UNFIXH(tmp13*COS_1_8 + tmp12*SIN_1_8); |
| outptr[DCTSIZE*6] = (DCTELEM) UNFIXH(tmp13*SIN_1_8 - tmp12*COS_1_8); |
| |
| tmp16 = UNFIXO((tmp6 + tmp5) * SIN_1_4); |
| tmp15 = UNFIXO((tmp6 - tmp5) * COS_1_4); |
| |
| OVERSHIFT(tmp4); |
| OVERSHIFT(tmp7); |
| |
| /* tmp4, tmp7, tmp15, tmp16 are overscaled by OVERSCALE */ |
| |
| tmp14 = tmp4 + tmp15; |
| tmp25 = tmp4 - tmp15; |
| tmp26 = tmp7 - tmp16; |
| tmp17 = tmp7 + tmp16; |
| |
| outptr[DCTSIZE ] = (DCTELEM) UNFIXH(tmp17*OCOS_1_16 + tmp14*OSIN_1_16); |
| outptr[DCTSIZE*7] = (DCTELEM) UNFIXH(tmp17*OCOS_7_16 - tmp14*OSIN_7_16); |
| outptr[DCTSIZE*5] = (DCTELEM) UNFIXH(tmp26*OCOS_5_16 + tmp25*OSIN_5_16); |
| outptr[DCTSIZE*3] = (DCTELEM) UNFIXH(tmp26*OCOS_3_16 - tmp25*OSIN_3_16); |
| |
| inptr += DCTSIZE; /* advance inptr to next row */ |
| outptr++; /* advance outptr to next column */ |
| } |
| /* end of pass; in case it was pass 1, set up for pass 2 */ |
| inptr = workspace; |
| outptr = data; |
| } |
| } |