Thomas G. Lane | 2cbeb8a | 1991-10-07 00:00:00 +0000 | [diff] [blame] | 1 | /* |
| 2 | * jfwddct.c |
| 3 | * |
Thomas G. Lane | 4a6b730 | 1992-03-17 00:00:00 +0000 | [diff] [blame^] | 4 | * Copyright (C) 1991, 1992, Thomas G. Lane. |
Thomas G. Lane | 2cbeb8a | 1991-10-07 00:00:00 +0000 | [diff] [blame] | 5 | * This file is part of the Independent JPEG Group's software. |
| 6 | * For conditions of distribution and use, see the accompanying README file. |
| 7 | * |
| 8 | * This file contains the basic DCT (Discrete Cosine Transform) |
| 9 | * transformation subroutine. |
| 10 | * |
| 11 | * This implementation is based on Appendix A.2 of the book |
| 12 | * "Discrete Cosine Transform---Algorithms, Advantages, Applications" |
| 13 | * by K.R. Rao and P. Yip (Academic Press, Inc, London, 1990). |
| 14 | * It uses scaled fixed-point arithmetic instead of floating point. |
| 15 | */ |
| 16 | |
| 17 | #include "jinclude.h" |
| 18 | |
Thomas G. Lane | 4a6b730 | 1992-03-17 00:00:00 +0000 | [diff] [blame^] | 19 | /* |
| 20 | * This routine is specialized to the case DCTSIZE = 8. |
Thomas G. Lane | 2cbeb8a | 1991-10-07 00:00:00 +0000 | [diff] [blame] | 21 | */ |
| 22 | |
Thomas G. Lane | 4a6b730 | 1992-03-17 00:00:00 +0000 | [diff] [blame^] | 23 | #if DCTSIZE != 8 |
| 24 | Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ |
Thomas G. Lane | 2cbeb8a | 1991-10-07 00:00:00 +0000 | [diff] [blame] | 25 | #endif |
| 26 | |
Thomas G. Lane | bd543f0 | 1991-12-13 00:00:00 +0000 | [diff] [blame] | 27 | |
| 28 | /* The poop on this scaling stuff is as follows: |
| 29 | * |
| 30 | * We have to do addition and subtraction of the integer inputs, which |
| 31 | * is no problem, and multiplication by fractional constants, which is |
| 32 | * a problem to do in integer arithmetic. We multiply all the constants |
| 33 | * by DCT_SCALE and convert them to integer constants (thus retaining |
| 34 | * LG2_DCT_SCALE bits of precision in the constants). After doing a |
| 35 | * multiplication we have to divide the product by DCT_SCALE, with proper |
| 36 | * rounding, to produce the correct output. The division can be implemented |
| 37 | * cheaply as a right shift of LG2_DCT_SCALE bits. The DCT equations also |
| 38 | * specify an additional division by 2 on the final outputs; this can be |
| 39 | * folded into the right-shift by shifting one more bit (see UNFIXH). |
| 40 | * |
| 41 | * If you are planning to recode this in assembler, you might want to set |
| 42 | * LG2_DCT_SCALE to 15. This loses a bit of precision, but then all the |
| 43 | * multiplications are between 16-bit quantities (given 8-bit JSAMPLEs!) |
| 44 | * so you could use a signed 16x16=>32 bit multiply instruction instead of |
| 45 | * full 32x32 multiply. Unfortunately there's no way to describe such a |
| 46 | * multiply portably in C, so we've gone for the extra bit of accuracy here. |
| 47 | */ |
| 48 | |
| 49 | #ifdef EIGHT_BIT_SAMPLES |
| 50 | #define LG2_DCT_SCALE 16 |
| 51 | #else |
| 52 | #define LG2_DCT_SCALE 15 /* lose a little precision to avoid overflow */ |
| 53 | #endif |
| 54 | |
| 55 | #define ONE ((INT32) 1) |
| 56 | |
Thomas G. Lane | 2cbeb8a | 1991-10-07 00:00:00 +0000 | [diff] [blame] | 57 | #define DCT_SCALE (ONE << LG2_DCT_SCALE) |
| 58 | |
Thomas G. Lane | bd543f0 | 1991-12-13 00:00:00 +0000 | [diff] [blame] | 59 | /* In some places we shift the inputs left by a couple more bits, */ |
| 60 | /* so that they can be added to fractional results without too much */ |
| 61 | /* loss of precision. */ |
Thomas G. Lane | 2cbeb8a | 1991-10-07 00:00:00 +0000 | [diff] [blame] | 62 | #define LG2_OVERSCALE 2 |
Thomas G. Lane | bd543f0 | 1991-12-13 00:00:00 +0000 | [diff] [blame] | 63 | #define OVERSCALE (ONE << LG2_OVERSCALE) |
| 64 | #define OVERSHIFT(x) ((x) <<= LG2_OVERSCALE) |
Thomas G. Lane | 2cbeb8a | 1991-10-07 00:00:00 +0000 | [diff] [blame] | 65 | |
Thomas G. Lane | bd543f0 | 1991-12-13 00:00:00 +0000 | [diff] [blame] | 66 | /* Scale a fractional constant by DCT_SCALE */ |
| 67 | #define FIX(x) ((INT32) ((x) * DCT_SCALE + 0.5)) |
| 68 | |
| 69 | /* Scale a fractional constant by DCT_SCALE/OVERSCALE */ |
| 70 | /* Such a constant can be multiplied with an overscaled input */ |
| 71 | /* to produce something that's scaled by DCT_SCALE */ |
Thomas G. Lane | 2cbeb8a | 1991-10-07 00:00:00 +0000 | [diff] [blame] | 72 | #define FIXO(x) ((INT32) ((x) * DCT_SCALE / OVERSCALE + 0.5)) |
Thomas G. Lane | 2cbeb8a | 1991-10-07 00:00:00 +0000 | [diff] [blame] | 73 | |
Thomas G. Lane | bd543f0 | 1991-12-13 00:00:00 +0000 | [diff] [blame] | 74 | /* Descale and correctly round a value that's scaled by DCT_SCALE */ |
| 75 | #define UNFIX(x) RIGHT_SHIFT((x) + (ONE << (LG2_DCT_SCALE-1)), LG2_DCT_SCALE) |
| 76 | |
| 77 | /* Same with an additional division by 2, ie, correctly rounded UNFIX(x/2) */ |
| 78 | #define UNFIXH(x) RIGHT_SHIFT((x) + (ONE << LG2_DCT_SCALE), LG2_DCT_SCALE+1) |
| 79 | |
| 80 | /* Take a value scaled by DCT_SCALE and round to integer scaled by OVERSCALE */ |
| 81 | #define UNFIXO(x) RIGHT_SHIFT((x) + (ONE << (LG2_DCT_SCALE-1-LG2_OVERSCALE)),\ |
| 82 | LG2_DCT_SCALE-LG2_OVERSCALE) |
| 83 | |
| 84 | /* Here are the constants we need */ |
| 85 | /* SIN_i_j is sine of i*pi/j, scaled by DCT_SCALE */ |
| 86 | /* COS_i_j is cosine of i*pi/j, scaled by DCT_SCALE */ |
| 87 | |
| 88 | #define SIN_1_4 FIX(0.707106781) |
Thomas G. Lane | 2cbeb8a | 1991-10-07 00:00:00 +0000 | [diff] [blame] | 89 | #define COS_1_4 SIN_1_4 |
| 90 | |
Thomas G. Lane | bd543f0 | 1991-12-13 00:00:00 +0000 | [diff] [blame] | 91 | #define SIN_1_8 FIX(0.382683432) |
| 92 | #define COS_1_8 FIX(0.923879533) |
Thomas G. Lane | 2cbeb8a | 1991-10-07 00:00:00 +0000 | [diff] [blame] | 93 | #define SIN_3_8 COS_1_8 |
| 94 | #define COS_3_8 SIN_1_8 |
| 95 | |
Thomas G. Lane | bd543f0 | 1991-12-13 00:00:00 +0000 | [diff] [blame] | 96 | #define SIN_1_16 FIX(0.195090322) |
| 97 | #define COS_1_16 FIX(0.980785280) |
Thomas G. Lane | 2cbeb8a | 1991-10-07 00:00:00 +0000 | [diff] [blame] | 98 | #define SIN_7_16 COS_1_16 |
| 99 | #define COS_7_16 SIN_1_16 |
| 100 | |
Thomas G. Lane | bd543f0 | 1991-12-13 00:00:00 +0000 | [diff] [blame] | 101 | #define SIN_3_16 FIX(0.555570233) |
| 102 | #define COS_3_16 FIX(0.831469612) |
Thomas G. Lane | 2cbeb8a | 1991-10-07 00:00:00 +0000 | [diff] [blame] | 103 | #define SIN_5_16 COS_3_16 |
| 104 | #define COS_5_16 SIN_3_16 |
| 105 | |
Thomas G. Lane | bd543f0 | 1991-12-13 00:00:00 +0000 | [diff] [blame] | 106 | /* OSIN_i_j is sine of i*pi/j, scaled by DCT_SCALE/OVERSCALE */ |
| 107 | /* OCOS_i_j is cosine of i*pi/j, scaled by DCT_SCALE/OVERSCALE */ |
| 108 | |
| 109 | #define OSIN_1_4 FIXO(0.707106781) |
Thomas G. Lane | 2cbeb8a | 1991-10-07 00:00:00 +0000 | [diff] [blame] | 110 | #define OCOS_1_4 OSIN_1_4 |
| 111 | |
Thomas G. Lane | bd543f0 | 1991-12-13 00:00:00 +0000 | [diff] [blame] | 112 | #define OSIN_1_8 FIXO(0.382683432) |
| 113 | #define OCOS_1_8 FIXO(0.923879533) |
Thomas G. Lane | 2cbeb8a | 1991-10-07 00:00:00 +0000 | [diff] [blame] | 114 | #define OSIN_3_8 OCOS_1_8 |
| 115 | #define OCOS_3_8 OSIN_1_8 |
| 116 | |
Thomas G. Lane | bd543f0 | 1991-12-13 00:00:00 +0000 | [diff] [blame] | 117 | #define OSIN_1_16 FIXO(0.195090322) |
| 118 | #define OCOS_1_16 FIXO(0.980785280) |
Thomas G. Lane | 2cbeb8a | 1991-10-07 00:00:00 +0000 | [diff] [blame] | 119 | #define OSIN_7_16 OCOS_1_16 |
| 120 | #define OCOS_7_16 OSIN_1_16 |
| 121 | |
Thomas G. Lane | bd543f0 | 1991-12-13 00:00:00 +0000 | [diff] [blame] | 122 | #define OSIN_3_16 FIXO(0.555570233) |
| 123 | #define OCOS_3_16 FIXO(0.831469612) |
Thomas G. Lane | 2cbeb8a | 1991-10-07 00:00:00 +0000 | [diff] [blame] | 124 | #define OSIN_5_16 OCOS_3_16 |
| 125 | #define OCOS_5_16 OSIN_3_16 |
| 126 | |
| 127 | |
Thomas G. Lane | bd543f0 | 1991-12-13 00:00:00 +0000 | [diff] [blame] | 128 | /* |
Thomas G. Lane | 2cbeb8a | 1991-10-07 00:00:00 +0000 | [diff] [blame] | 129 | * Perform the forward DCT on one block of samples. |
| 130 | * |
Thomas G. Lane | bd543f0 | 1991-12-13 00:00:00 +0000 | [diff] [blame] | 131 | * A 2-D DCT can be done by 1-D DCT on each row |
| 132 | * followed by 1-D DCT on each column. |
Thomas G. Lane | 2cbeb8a | 1991-10-07 00:00:00 +0000 | [diff] [blame] | 133 | */ |
| 134 | |
| 135 | GLOBAL void |
| 136 | j_fwd_dct (DCTBLOCK data) |
| 137 | { |
Thomas G. Lane | 4a6b730 | 1992-03-17 00:00:00 +0000 | [diff] [blame^] | 138 | int pass, rowctr; |
| 139 | register DCTELEM *inptr, *outptr; |
| 140 | DCTBLOCK workspace; |
Thomas G. Lane | 2cbeb8a | 1991-10-07 00:00:00 +0000 | [diff] [blame] | 141 | |
Thomas G. Lane | 4a6b730 | 1992-03-17 00:00:00 +0000 | [diff] [blame^] | 142 | /* Each iteration of the inner loop performs one 8-point 1-D DCT. |
| 143 | * It reads from a *row* of the input matrix and stores into a *column* |
| 144 | * of the output matrix. In the first pass, we read from the data[] array |
| 145 | * and store into the local workspace[]. In the second pass, we read from |
| 146 | * the workspace[] array and store into data[], thus performing the |
| 147 | * equivalent of a columnar DCT pass with no variable array indexing. |
| 148 | */ |
| 149 | |
| 150 | inptr = data; /* initialize pointers for first pass */ |
| 151 | outptr = workspace; |
| 152 | for (pass = 1; pass >= 0; pass--) { |
| 153 | for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--) { |
| 154 | /* many tmps have nonoverlapping lifetime -- flashy register colourers |
| 155 | * should be able to do this lot very well |
| 156 | */ |
| 157 | INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; |
| 158 | INT32 tmp10, tmp11, tmp12, tmp13; |
| 159 | INT32 tmp14, tmp15, tmp16, tmp17; |
| 160 | INT32 tmp25, tmp26; |
| 161 | SHIFT_TEMPS |
| 162 | |
| 163 | tmp0 = inptr[7] + inptr[0]; |
| 164 | tmp1 = inptr[6] + inptr[1]; |
| 165 | tmp2 = inptr[5] + inptr[2]; |
| 166 | tmp3 = inptr[4] + inptr[3]; |
| 167 | tmp4 = inptr[3] - inptr[4]; |
| 168 | tmp5 = inptr[2] - inptr[5]; |
| 169 | tmp6 = inptr[1] - inptr[6]; |
| 170 | tmp7 = inptr[0] - inptr[7]; |
| 171 | |
| 172 | tmp10 = tmp3 + tmp0; |
| 173 | tmp11 = tmp2 + tmp1; |
| 174 | tmp12 = tmp1 - tmp2; |
| 175 | tmp13 = tmp0 - tmp3; |
| 176 | |
| 177 | outptr[ 0] = (DCTELEM) UNFIXH((tmp10 + tmp11) * SIN_1_4); |
| 178 | outptr[DCTSIZE*4] = (DCTELEM) UNFIXH((tmp10 - tmp11) * COS_1_4); |
| 179 | |
| 180 | outptr[DCTSIZE*2] = (DCTELEM) UNFIXH(tmp13*COS_1_8 + tmp12*SIN_1_8); |
| 181 | outptr[DCTSIZE*6] = (DCTELEM) UNFIXH(tmp13*SIN_1_8 - tmp12*COS_1_8); |
| 182 | |
| 183 | tmp16 = UNFIXO((tmp6 + tmp5) * SIN_1_4); |
| 184 | tmp15 = UNFIXO((tmp6 - tmp5) * COS_1_4); |
| 185 | |
| 186 | OVERSHIFT(tmp4); |
| 187 | OVERSHIFT(tmp7); |
| 188 | |
| 189 | /* tmp4, tmp7, tmp15, tmp16 are overscaled by OVERSCALE */ |
| 190 | |
| 191 | tmp14 = tmp4 + tmp15; |
| 192 | tmp25 = tmp4 - tmp15; |
| 193 | tmp26 = tmp7 - tmp16; |
| 194 | tmp17 = tmp7 + tmp16; |
| 195 | |
| 196 | outptr[DCTSIZE ] = (DCTELEM) UNFIXH(tmp17*OCOS_1_16 + tmp14*OSIN_1_16); |
| 197 | outptr[DCTSIZE*7] = (DCTELEM) UNFIXH(tmp17*OCOS_7_16 - tmp14*OSIN_7_16); |
| 198 | outptr[DCTSIZE*5] = (DCTELEM) UNFIXH(tmp26*OCOS_5_16 + tmp25*OSIN_5_16); |
| 199 | outptr[DCTSIZE*3] = (DCTELEM) UNFIXH(tmp26*OCOS_3_16 - tmp25*OSIN_3_16); |
| 200 | |
| 201 | inptr += DCTSIZE; /* advance inptr to next row */ |
| 202 | outptr++; /* advance outptr to next column */ |
| 203 | } |
| 204 | /* end of pass; in case it was pass 1, set up for pass 2 */ |
| 205 | inptr = workspace; |
| 206 | outptr = data; |
| 207 | } |
Thomas G. Lane | 2cbeb8a | 1991-10-07 00:00:00 +0000 | [diff] [blame] | 208 | } |