/* DCT1D_02.c version mar jan 1 08:45:57 GMT 2002 whygee@f-cpu.org 1* 8-bin DCT for a "baseline" JPG compressor. originally cut and pasted from : sbcci_DCT2D.pdf "Pipelined Fast 2-D DCT Architecture for JPEG Image Compression" Luciano Volcan Agostini Ivan Saraiva Silva Sergio Bampi Table 2 : Bit width differences between the two 1-D DCT architectures Pipeline First 1-D DCT Second 1-D DCT Stage bit width bit width 1 9 13 2 10 14 3 11 15 4 11 15 5 12 15 6 12 15 => the data are in 1Q15 format and left-aligned at the beginning. m1 = cos(4pi/16) m2 = cos(6pi/16) m3 = cos(2pi/16) - cos(6pi/16) m4 = cos(2pi/16)+ cos(6pi/16) Optimisation : part 2 = first cleanup All the unnecessary temporary variables are removed. A census of the "nodes" is made. Since their number is below 64, the register allocation is straight-forward. Furthermore, the original code seems to be incredibly well optimised. First, the "minimal distance" between operations seems to be compatible with FC0. Second, it seems possible to use less than the original number of temporary variables : although the "clean" model defines 30 variables, it is "sliced" in such a way that maybe 16 working registers are necessary. Later we will even describe how they are reduced to 10. b2 bug corrected on Tue Dec 16 06:37:45 CET 2003 */ sample b0, b1, b2, b3, b4, b5, b6, b7, c0, c1, c2, c3, c4, c5, c6, d0, d1, d3, d4, e2, e3, e4, e6, e7, f2, f3, f4, f5, f6, f7; /* Step 1 */ b0 = a0 + a7; b1 = a1 + a6; b2 = a3 - a4; /* corrected */ b3 = a1 - a6; b4 = a2 + a5; b5 = a3 + a4; b6 = a2 - a5; b7 = a0 - a7; /***/ /* Step 2 */ c0 = b0 + b5; c1 = b1 - b4; c2 = b2 + b6; /***/ c3 = b1 + b4; c4 = b0 - b5; c5 = b3 + b7; /***/ c6 = b3 + b6; /***/ /* Step 3 */ d0 = c0 + c3; /***/ d1 = c0 - c3; /***/ d3 = c1 + c4; d4 = c2 - c5; /* Step 4 */ e2 = m3 * c2; /*c2*/ e3 = m1 * c6; /*c6*/ e4 = m4 * c5; /*c5*/ e6 = m1 * d3; e7 = m2 * d4; /* Step 5 */ f2 = c4 + e6; /*c4*/ f3 = c4 - e6; /*c4*/ f4 = e3 + b7; /*b7*/ f5 = b7 - e3; /*b7*/ f6 = e2 + e7; f7 = e4 + e7; /* Step 6 */ S0 = d0; /*d0*/ S1 = f4 + f7; S2 = f2; S3 = f5 - f6; S4 = d1; /*d1*/ S5 = f5 + f6; S6 = f3; S7 = f4 - f7;