michael@0: /* michael@0: * jfdctfst.c michael@0: * michael@0: * Copyright (C) 1994-1996, Thomas G. Lane. michael@0: * This file is part of the Independent JPEG Group's software. michael@0: * For conditions of distribution and use, see the accompanying README file. michael@0: * michael@0: * This file contains a fast, not so accurate integer implementation of the michael@0: * forward DCT (Discrete Cosine Transform). michael@0: * michael@0: * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT michael@0: * on each column. Direct algorithms are also available, but they are michael@0: * much more complex and seem not to be any faster when reduced to code. michael@0: * michael@0: * This implementation is based on Arai, Agui, and Nakajima's algorithm for michael@0: * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in michael@0: * Japanese, but the algorithm is described in the Pennebaker & Mitchell michael@0: * JPEG textbook (see REFERENCES section in file README). The following code michael@0: * is based directly on figure 4-8 in P&M. michael@0: * While an 8-point DCT cannot be done in less than 11 multiplies, it is michael@0: * possible to arrange the computation so that many of the multiplies are michael@0: * simple scalings of the final outputs. These multiplies can then be michael@0: * folded into the multiplications or divisions by the JPEG quantization michael@0: * table entries. The AA&N method leaves only 5 multiplies and 29 adds michael@0: * to be done in the DCT itself. michael@0: * The primary disadvantage of this method is that with fixed-point math, michael@0: * accuracy is lost due to imprecise representation of the scaled michael@0: * quantization values. The smaller the quantization table entry, the less michael@0: * precise the scaled value, so this implementation does worse with high- michael@0: * quality-setting files than with low-quality ones. michael@0: */ michael@0: michael@0: #define JPEG_INTERNALS michael@0: #include "jinclude.h" michael@0: #include "jpeglib.h" michael@0: #include "jdct.h" /* Private declarations for DCT subsystem */ michael@0: michael@0: #ifdef DCT_IFAST_SUPPORTED michael@0: michael@0: michael@0: /* michael@0: * This module is specialized to the case DCTSIZE = 8. michael@0: */ michael@0: michael@0: #if DCTSIZE != 8 michael@0: Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ michael@0: #endif michael@0: michael@0: michael@0: /* Scaling decisions are generally the same as in the LL&M algorithm; michael@0: * see jfdctint.c for more details. However, we choose to descale michael@0: * (right shift) multiplication products as soon as they are formed, michael@0: * rather than carrying additional fractional bits into subsequent additions. michael@0: * This compromises accuracy slightly, but it lets us save a few shifts. michael@0: * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples) michael@0: * everywhere except in the multiplications proper; this saves a good deal michael@0: * of work on 16-bit-int machines. michael@0: * michael@0: * Again to save a few shifts, the intermediate results between pass 1 and michael@0: * pass 2 are not upscaled, but are represented only to integral precision. michael@0: * michael@0: * A final compromise is to represent the multiplicative constants to only michael@0: * 8 fractional bits, rather than 13. This saves some shifting work on some michael@0: * machines, and may also reduce the cost of multiplication (since there michael@0: * are fewer one-bits in the constants). michael@0: */ michael@0: michael@0: #define CONST_BITS 8 michael@0: michael@0: michael@0: /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus michael@0: * causing a lot of useless floating-point operations at run time. michael@0: * To get around this we use the following pre-calculated constants. michael@0: * If you change CONST_BITS you may want to add appropriate values. michael@0: * (With a reasonable C compiler, you can just rely on the FIX() macro...) michael@0: */ michael@0: michael@0: #if CONST_BITS == 8 michael@0: #define FIX_0_382683433 ((INT32) 98) /* FIX(0.382683433) */ michael@0: #define FIX_0_541196100 ((INT32) 139) /* FIX(0.541196100) */ michael@0: #define FIX_0_707106781 ((INT32) 181) /* FIX(0.707106781) */ michael@0: #define FIX_1_306562965 ((INT32) 334) /* FIX(1.306562965) */ michael@0: #else michael@0: #define FIX_0_382683433 FIX(0.382683433) michael@0: #define FIX_0_541196100 FIX(0.541196100) michael@0: #define FIX_0_707106781 FIX(0.707106781) michael@0: #define FIX_1_306562965 FIX(1.306562965) michael@0: #endif michael@0: michael@0: michael@0: /* We can gain a little more speed, with a further compromise in accuracy, michael@0: * by omitting the addition in a descaling shift. This yields an incorrectly michael@0: * rounded result half the time... michael@0: */ michael@0: michael@0: #ifndef USE_ACCURATE_ROUNDING michael@0: #undef DESCALE michael@0: #define DESCALE(x,n) RIGHT_SHIFT(x, n) michael@0: #endif michael@0: michael@0: michael@0: /* Multiply a DCTELEM variable by an INT32 constant, and immediately michael@0: * descale to yield a DCTELEM result. michael@0: */ michael@0: michael@0: #define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS)) michael@0: michael@0: michael@0: /* michael@0: * Perform the forward DCT on one block of samples. michael@0: */ michael@0: michael@0: GLOBAL(void) michael@0: jpeg_fdct_ifast (DCTELEM * data) michael@0: { michael@0: DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; michael@0: DCTELEM tmp10, tmp11, tmp12, tmp13; michael@0: DCTELEM z1, z2, z3, z4, z5, z11, z13; michael@0: DCTELEM *dataptr; michael@0: int ctr; michael@0: SHIFT_TEMPS michael@0: michael@0: /* Pass 1: process rows. */ michael@0: michael@0: dataptr = data; michael@0: for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { michael@0: tmp0 = dataptr[0] + dataptr[7]; michael@0: tmp7 = dataptr[0] - dataptr[7]; michael@0: tmp1 = dataptr[1] + dataptr[6]; michael@0: tmp6 = dataptr[1] - dataptr[6]; michael@0: tmp2 = dataptr[2] + dataptr[5]; michael@0: tmp5 = dataptr[2] - dataptr[5]; michael@0: tmp3 = dataptr[3] + dataptr[4]; michael@0: tmp4 = dataptr[3] - dataptr[4]; michael@0: michael@0: /* Even part */ michael@0: michael@0: tmp10 = tmp0 + tmp3; /* phase 2 */ michael@0: tmp13 = tmp0 - tmp3; michael@0: tmp11 = tmp1 + tmp2; michael@0: tmp12 = tmp1 - tmp2; michael@0: michael@0: dataptr[0] = tmp10 + tmp11; /* phase 3 */ michael@0: dataptr[4] = tmp10 - tmp11; michael@0: michael@0: z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */ michael@0: dataptr[2] = tmp13 + z1; /* phase 5 */ michael@0: dataptr[6] = tmp13 - z1; michael@0: michael@0: /* Odd part */ michael@0: michael@0: tmp10 = tmp4 + tmp5; /* phase 2 */ michael@0: tmp11 = tmp5 + tmp6; michael@0: tmp12 = tmp6 + tmp7; michael@0: michael@0: /* The rotator is modified from fig 4-8 to avoid extra negations. */ michael@0: z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */ michael@0: z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */ michael@0: z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */ michael@0: z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */ michael@0: michael@0: z11 = tmp7 + z3; /* phase 5 */ michael@0: z13 = tmp7 - z3; michael@0: michael@0: dataptr[5] = z13 + z2; /* phase 6 */ michael@0: dataptr[3] = z13 - z2; michael@0: dataptr[1] = z11 + z4; michael@0: dataptr[7] = z11 - z4; michael@0: michael@0: dataptr += DCTSIZE; /* advance pointer to next row */ michael@0: } michael@0: michael@0: /* Pass 2: process columns. */ michael@0: michael@0: dataptr = data; michael@0: for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { michael@0: tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7]; michael@0: tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7]; michael@0: tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6]; michael@0: tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6]; michael@0: tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5]; michael@0: tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5]; michael@0: tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4]; michael@0: tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4]; michael@0: michael@0: /* Even part */ michael@0: michael@0: tmp10 = tmp0 + tmp3; /* phase 2 */ michael@0: tmp13 = tmp0 - tmp3; michael@0: tmp11 = tmp1 + tmp2; michael@0: tmp12 = tmp1 - tmp2; michael@0: michael@0: dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */ michael@0: dataptr[DCTSIZE*4] = tmp10 - tmp11; michael@0: michael@0: z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */ michael@0: dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */ michael@0: dataptr[DCTSIZE*6] = tmp13 - z1; michael@0: michael@0: /* Odd part */ michael@0: michael@0: tmp10 = tmp4 + tmp5; /* phase 2 */ michael@0: tmp11 = tmp5 + tmp6; michael@0: tmp12 = tmp6 + tmp7; michael@0: michael@0: /* The rotator is modified from fig 4-8 to avoid extra negations. */ michael@0: z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */ michael@0: z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */ michael@0: z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */ michael@0: z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */ michael@0: michael@0: z11 = tmp7 + z3; /* phase 5 */ michael@0: z13 = tmp7 - z3; michael@0: michael@0: dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */ michael@0: dataptr[DCTSIZE*3] = z13 - z2; michael@0: dataptr[DCTSIZE*1] = z11 + z4; michael@0: dataptr[DCTSIZE*7] = z11 - z4; michael@0: michael@0: dataptr++; /* advance pointer to next column */ michael@0: } michael@0: } michael@0: michael@0: #endif /* DCT_IFAST_SUPPORTED */