Thomas G. Lane | 36a4ccc | 1994-09-24 00:00:00 +0000 | [diff] [blame] | 1 | /* |
| 2 | * jfdctflt.c |
| 3 | * |
Thomas G. Lane | 489583f | 1996-02-07 00:00:00 +0000 | [diff] [blame] | 4 | * Copyright (C) 1994-1996, Thomas G. Lane. |
Thomas G. Lane | 36a4ccc | 1994-09-24 00:00:00 +0000 | [diff] [blame] | 5 | * This file is part of the Independent JPEG Group's software. |
DRC | 7e3acc0 | 2015-10-10 10:25:46 -0500 | [diff] [blame] | 6 | * For conditions of distribution and use, see the accompanying README.ijg |
| 7 | * file. |
Thomas G. Lane | 36a4ccc | 1994-09-24 00:00:00 +0000 | [diff] [blame] | 8 | * |
| 9 | * This file contains a floating-point implementation of the |
| 10 | * forward DCT (Discrete Cosine Transform). |
| 11 | * |
| 12 | * This implementation should be more accurate than either of the integer |
| 13 | * DCT implementations. However, it may not give the same results on all |
| 14 | * machines because of differences in roundoff behavior. Speed will depend |
| 15 | * on the hardware's floating point capacity. |
| 16 | * |
| 17 | * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT |
| 18 | * on each column. Direct algorithms are also available, but they are |
| 19 | * much more complex and seem not to be any faster when reduced to code. |
| 20 | * |
| 21 | * This implementation is based on Arai, Agui, and Nakajima's algorithm for |
| 22 | * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in |
| 23 | * Japanese, but the algorithm is described in the Pennebaker & Mitchell |
DRC | 7e3acc0 | 2015-10-10 10:25:46 -0500 | [diff] [blame] | 24 | * JPEG textbook (see REFERENCES section in file README.ijg). The following |
| 25 | * code is based directly on figure 4-8 in P&M. |
Thomas G. Lane | 36a4ccc | 1994-09-24 00:00:00 +0000 | [diff] [blame] | 26 | * While an 8-point DCT cannot be done in less than 11 multiplies, it is |
| 27 | * possible to arrange the computation so that many of the multiplies are |
| 28 | * simple scalings of the final outputs. These multiplies can then be |
| 29 | * folded into the multiplications or divisions by the JPEG quantization |
| 30 | * table entries. The AA&N method leaves only 5 multiplies and 29 adds |
| 31 | * to be done in the DCT itself. |
| 32 | * The primary disadvantage of this method is that with a fixed-point |
| 33 | * implementation, accuracy is lost due to imprecise representation of the |
| 34 | * scaled quantization values. However, that problem does not arise if |
| 35 | * we use floating point arithmetic. |
| 36 | */ |
| 37 | |
| 38 | #define JPEG_INTERNALS |
| 39 | #include "jinclude.h" |
| 40 | #include "jpeglib.h" |
DRC | e5eaf37 | 2014-05-09 18:00:32 +0000 | [diff] [blame] | 41 | #include "jdct.h" /* Private declarations for DCT subsystem */ |
Thomas G. Lane | 36a4ccc | 1994-09-24 00:00:00 +0000 | [diff] [blame] | 42 | |
| 43 | #ifdef DCT_FLOAT_SUPPORTED |
| 44 | |
| 45 | |
| 46 | /* |
| 47 | * This module is specialized to the case DCTSIZE = 8. |
| 48 | */ |
| 49 | |
| 50 | #if DCTSIZE != 8 |
| 51 | Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ |
| 52 | #endif |
| 53 | |
| 54 | |
| 55 | /* |
| 56 | * Perform the forward DCT on one block of samples. |
| 57 | */ |
| 58 | |
Thomas G. Lane | 489583f | 1996-02-07 00:00:00 +0000 | [diff] [blame] | 59 | GLOBAL(void) |
DRC | bd49803 | 2016-02-19 08:53:33 -0600 | [diff] [blame] | 60 | jpeg_fdct_float (FAST_FLOAT *data) |
Thomas G. Lane | 36a4ccc | 1994-09-24 00:00:00 +0000 | [diff] [blame] | 61 | { |
| 62 | FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; |
| 63 | FAST_FLOAT tmp10, tmp11, tmp12, tmp13; |
| 64 | FAST_FLOAT z1, z2, z3, z4, z5, z11, z13; |
| 65 | FAST_FLOAT *dataptr; |
| 66 | int ctr; |
| 67 | |
| 68 | /* Pass 1: process rows. */ |
| 69 | |
| 70 | dataptr = data; |
| 71 | for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { |
| 72 | tmp0 = dataptr[0] + dataptr[7]; |
| 73 | tmp7 = dataptr[0] - dataptr[7]; |
| 74 | tmp1 = dataptr[1] + dataptr[6]; |
| 75 | tmp6 = dataptr[1] - dataptr[6]; |
| 76 | tmp2 = dataptr[2] + dataptr[5]; |
| 77 | tmp5 = dataptr[2] - dataptr[5]; |
| 78 | tmp3 = dataptr[3] + dataptr[4]; |
| 79 | tmp4 = dataptr[3] - dataptr[4]; |
DRC | e5eaf37 | 2014-05-09 18:00:32 +0000 | [diff] [blame] | 80 | |
Thomas G. Lane | 36a4ccc | 1994-09-24 00:00:00 +0000 | [diff] [blame] | 81 | /* Even part */ |
DRC | e5eaf37 | 2014-05-09 18:00:32 +0000 | [diff] [blame] | 82 | |
| 83 | tmp10 = tmp0 + tmp3; /* phase 2 */ |
Thomas G. Lane | 36a4ccc | 1994-09-24 00:00:00 +0000 | [diff] [blame] | 84 | tmp13 = tmp0 - tmp3; |
| 85 | tmp11 = tmp1 + tmp2; |
| 86 | tmp12 = tmp1 - tmp2; |
DRC | e5eaf37 | 2014-05-09 18:00:32 +0000 | [diff] [blame] | 87 | |
Thomas G. Lane | 36a4ccc | 1994-09-24 00:00:00 +0000 | [diff] [blame] | 88 | dataptr[0] = tmp10 + tmp11; /* phase 3 */ |
| 89 | dataptr[4] = tmp10 - tmp11; |
DRC | e5eaf37 | 2014-05-09 18:00:32 +0000 | [diff] [blame] | 90 | |
Thomas G. Lane | 36a4ccc | 1994-09-24 00:00:00 +0000 | [diff] [blame] | 91 | z1 = (tmp12 + tmp13) * ((FAST_FLOAT) 0.707106781); /* c4 */ |
DRC | e5eaf37 | 2014-05-09 18:00:32 +0000 | [diff] [blame] | 92 | dataptr[2] = tmp13 + z1; /* phase 5 */ |
Thomas G. Lane | 36a4ccc | 1994-09-24 00:00:00 +0000 | [diff] [blame] | 93 | dataptr[6] = tmp13 - z1; |
DRC | e5eaf37 | 2014-05-09 18:00:32 +0000 | [diff] [blame] | 94 | |
Thomas G. Lane | 36a4ccc | 1994-09-24 00:00:00 +0000 | [diff] [blame] | 95 | /* Odd part */ |
| 96 | |
DRC | e5eaf37 | 2014-05-09 18:00:32 +0000 | [diff] [blame] | 97 | tmp10 = tmp4 + tmp5; /* phase 2 */ |
Thomas G. Lane | 36a4ccc | 1994-09-24 00:00:00 +0000 | [diff] [blame] | 98 | tmp11 = tmp5 + tmp6; |
| 99 | tmp12 = tmp6 + tmp7; |
| 100 | |
| 101 | /* The rotator is modified from fig 4-8 to avoid extra negations. */ |
| 102 | z5 = (tmp10 - tmp12) * ((FAST_FLOAT) 0.382683433); /* c6 */ |
| 103 | z2 = ((FAST_FLOAT) 0.541196100) * tmp10 + z5; /* c2-c6 */ |
| 104 | z4 = ((FAST_FLOAT) 1.306562965) * tmp12 + z5; /* c2+c6 */ |
| 105 | z3 = tmp11 * ((FAST_FLOAT) 0.707106781); /* c4 */ |
| 106 | |
DRC | e5eaf37 | 2014-05-09 18:00:32 +0000 | [diff] [blame] | 107 | z11 = tmp7 + z3; /* phase 5 */ |
Thomas G. Lane | 36a4ccc | 1994-09-24 00:00:00 +0000 | [diff] [blame] | 108 | z13 = tmp7 - z3; |
| 109 | |
DRC | e5eaf37 | 2014-05-09 18:00:32 +0000 | [diff] [blame] | 110 | dataptr[5] = z13 + z2; /* phase 6 */ |
Thomas G. Lane | 36a4ccc | 1994-09-24 00:00:00 +0000 | [diff] [blame] | 111 | dataptr[3] = z13 - z2; |
| 112 | dataptr[1] = z11 + z4; |
| 113 | dataptr[7] = z11 - z4; |
| 114 | |
DRC | e5eaf37 | 2014-05-09 18:00:32 +0000 | [diff] [blame] | 115 | dataptr += DCTSIZE; /* advance pointer to next row */ |
Thomas G. Lane | 36a4ccc | 1994-09-24 00:00:00 +0000 | [diff] [blame] | 116 | } |
| 117 | |
| 118 | /* Pass 2: process columns. */ |
| 119 | |
| 120 | dataptr = data; |
| 121 | for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { |
| 122 | tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7]; |
| 123 | tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7]; |
| 124 | tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6]; |
| 125 | tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6]; |
| 126 | tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5]; |
| 127 | tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5]; |
| 128 | tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4]; |
| 129 | tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4]; |
DRC | e5eaf37 | 2014-05-09 18:00:32 +0000 | [diff] [blame] | 130 | |
Thomas G. Lane | 36a4ccc | 1994-09-24 00:00:00 +0000 | [diff] [blame] | 131 | /* Even part */ |
DRC | e5eaf37 | 2014-05-09 18:00:32 +0000 | [diff] [blame] | 132 | |
| 133 | tmp10 = tmp0 + tmp3; /* phase 2 */ |
Thomas G. Lane | 36a4ccc | 1994-09-24 00:00:00 +0000 | [diff] [blame] | 134 | tmp13 = tmp0 - tmp3; |
| 135 | tmp11 = tmp1 + tmp2; |
| 136 | tmp12 = tmp1 - tmp2; |
DRC | e5eaf37 | 2014-05-09 18:00:32 +0000 | [diff] [blame] | 137 | |
Thomas G. Lane | 36a4ccc | 1994-09-24 00:00:00 +0000 | [diff] [blame] | 138 | dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */ |
| 139 | dataptr[DCTSIZE*4] = tmp10 - tmp11; |
DRC | e5eaf37 | 2014-05-09 18:00:32 +0000 | [diff] [blame] | 140 | |
Thomas G. Lane | 36a4ccc | 1994-09-24 00:00:00 +0000 | [diff] [blame] | 141 | z1 = (tmp12 + tmp13) * ((FAST_FLOAT) 0.707106781); /* c4 */ |
| 142 | dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */ |
| 143 | dataptr[DCTSIZE*6] = tmp13 - z1; |
DRC | e5eaf37 | 2014-05-09 18:00:32 +0000 | [diff] [blame] | 144 | |
Thomas G. Lane | 36a4ccc | 1994-09-24 00:00:00 +0000 | [diff] [blame] | 145 | /* Odd part */ |
| 146 | |
DRC | e5eaf37 | 2014-05-09 18:00:32 +0000 | [diff] [blame] | 147 | tmp10 = tmp4 + tmp5; /* phase 2 */ |
Thomas G. Lane | 36a4ccc | 1994-09-24 00:00:00 +0000 | [diff] [blame] | 148 | tmp11 = tmp5 + tmp6; |
| 149 | tmp12 = tmp6 + tmp7; |
| 150 | |
| 151 | /* The rotator is modified from fig 4-8 to avoid extra negations. */ |
| 152 | z5 = (tmp10 - tmp12) * ((FAST_FLOAT) 0.382683433); /* c6 */ |
| 153 | z2 = ((FAST_FLOAT) 0.541196100) * tmp10 + z5; /* c2-c6 */ |
| 154 | z4 = ((FAST_FLOAT) 1.306562965) * tmp12 + z5; /* c2+c6 */ |
| 155 | z3 = tmp11 * ((FAST_FLOAT) 0.707106781); /* c4 */ |
| 156 | |
DRC | e5eaf37 | 2014-05-09 18:00:32 +0000 | [diff] [blame] | 157 | z11 = tmp7 + z3; /* phase 5 */ |
Thomas G. Lane | 36a4ccc | 1994-09-24 00:00:00 +0000 | [diff] [blame] | 158 | z13 = tmp7 - z3; |
| 159 | |
| 160 | dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */ |
| 161 | dataptr[DCTSIZE*3] = z13 - z2; |
| 162 | dataptr[DCTSIZE*1] = z11 + z4; |
| 163 | dataptr[DCTSIZE*7] = z11 - z4; |
| 164 | |
DRC | e5eaf37 | 2014-05-09 18:00:32 +0000 | [diff] [blame] | 165 | dataptr++; /* advance pointer to next column */ |
Thomas G. Lane | 36a4ccc | 1994-09-24 00:00:00 +0000 | [diff] [blame] | 166 | } |
| 167 | } |
| 168 | |
| 169 | #endif /* DCT_FLOAT_SUPPORTED */ |