/* INV = M^-1, INV, M are n by n matrices */
void matinv(double **INV, double **M, int n)
{
int *p, i, j;
double *col, *x;
p = ivector(n);
col = vector(n);
x = vector(n);
lupdcmp(M, n, p);
for (j = 0; j < n; j++) {
for (i = 0; i < n; i++) col[i]=0.0;
col[j] = 1.0;
lusolve(M, n, p, col, x);
for (i = 0; i < n; i++) INV[i][j]=x[i];
}
free_ivector(p);
free_vector(col);
free_vector(x);
}
/* creates matrices B and invB: BT = Power in the steady state.
* NOTE: EXTRA nodes: 4 heat spreader peripheral nodes, 4 heat
* sink inner peripheral nodes, 4 heat sink outer peripheral
* nodes(north, south, east and west) and 1 ambient node.
*/
void populate_R_model_block(block_model_t *model, flp_t *flp)
{
/* shortcuts */
double **b = model->b;
double *gx = model->gx, *gy = model->gy;
double *gx_int = model->gx_int, *gy_int = model->gy_int;
double *gx_sp = model->gx_sp, *gy_sp = model->gy_sp;
double *gx_hs = model->gx_hs, *gy_hs = model->gy_hs;
double *g_amb = model->g_amb;
double **len = model->len, **g = model->g, **lu = model->lu;
int **border = model->border;
int *p = model->p;
double t_chip = model->config.t_chip;
double r_convec = model->config.r_convec;
double s_sink = model->config.s_sink;
double t_sink = model->config.t_sink;
double s_spreader = model->config.s_spreader;
double t_spreader = model->config.t_spreader;
double t_interface = model->config.t_interface;
double k_chip = model->config.k_chip;
double k_sink = model->config.k_sink;
double k_spreader = model->config.k_spreader;
double k_interface = model->config.k_interface;
int i, j, n = flp->n_units;
double gn_sp=0, gs_sp=0, ge_sp=0, gw_sp=0;
double gn_hs=0, gs_hs=0, ge_hs=0, gw_hs=0;
double r_amb;
double w_chip = get_total_width (flp); /* x-axis */
double l_chip = get_total_height (flp); /* y-axis */
/* sanity check on floorplan sizes */
if (w_chip > s_sink || l_chip > s_sink ||
w_chip > s_spreader || l_chip > s_spreader) {
//print_flp(flp);
//print_flp_fig(flp);
//fatal("inordinate floorplan size!\n");
}
if(model->flp != flp || model->n_units != flp->n_units ||
model->n_nodes != NL * flp->n_units + EXTRA)
fatal("mismatch between the floorplan and the thermal model\n");
/* gx's and gy's of blocks */
for (i = 0; i < n; i++) {
/* at the silicon layer */
if (model->config.block_omit_lateral) {
gx[i] = gy[i] = 0;
}
else {
gx[i] = 1.0/getr(k_chip, flp->units[i].width / 2.0, flp->units[i].height * t_chip);
gy[i] = 1.0/getr(k_chip, flp->units[i].height / 2.0, flp->units[i].width * t_chip);
}
/* at the interface layer */
gx_int[i] = 1.0/getr(k_interface, flp->units[i].width / 2.0, flp->units[i].height * t_interface);
gy_int[i] = 1.0/getr(k_interface, flp->units[i].height / 2.0, flp->units[i].width * t_interface);
/* at the spreader layer */
gx_sp[i] = 1.0/getr(k_spreader, flp->units[i].width / 2.0, flp->units[i].height * t_spreader);
gy_sp[i] = 1.0/getr(k_spreader, flp->units[i].height / 2.0, flp->units[i].width * t_spreader);
/* at the heatsink layer */
gx_hs[i] = 1.0/getr(k_sink, flp->units[i].width / 2.0, flp->units[i].height * t_sink);
gy_hs[i] = 1.0/getr(k_sink, flp->units[i].height / 2.0, flp->units[i].width * t_sink);
}
/* shared lengths between blocks */
for (i = 0; i < n; i++)
for (j = i; j < n; j++)
len[i][j] = len[j][i] = get_shared_len(flp, i, j);
/* package R's */
populate_package_R(&model->pack, &model->config, w_chip, l_chip);
/* short the R's from block centers to a particular chip edge */
for (i = 0; i < n; i++) {
if (eq(flp->units[i].bottomy + flp->units[i].height, l_chip)) {
gn_sp += gy_sp[i];
gn_hs += gy_hs[i];
border[i][2] = 1; /* block is on northern border */
} else
border[i][2] = 0;
if (eq(flp->units[i].bottomy, 0)) {
gs_sp += gy_sp[i];
gs_hs += gy_hs[i];
border[i][3] = 1; /* block is on southern border */
} else
border[i][3] = 0;
if (eq(flp->units[i].leftx + flp->units[i].width, w_chip)) {
ge_sp += gx_sp[i];
ge_hs += gx_hs[i];
border[i][1] = 1; /* block is on eastern border */
} else
border[i][1] = 0;
if (eq(flp->units[i].leftx, 0)) {
gw_sp += gx_sp[i];
gw_hs += gx_hs[i];
border[i][0] = 1; /* block is on western border */
} else
border[i][0] = 0;
}
/* initialize g */
zero_dmatrix(g, NL*n+EXTRA, NL*n+EXTRA);
zero_dvector(g_amb, n+EXTRA);
/* overall Rs between nodes */
for (i = 0; i < n; i++) {
double area = (flp->units[i].height * flp->units[i].width);
/* amongst functional units in the various layers */
for (j = 0; j < n; j++) {
double part = 0, part_int = 0, part_sp = 0, part_hs = 0;
if (is_horiz_adj(flp, i, j)) {
part = gx[i] / flp->units[i].height;
part_int = gx_int[i] / flp->units[i].height;
part_sp = gx_sp[i] / flp->units[i].height;
part_hs = gx_hs[i] / flp->units[i].height;
}
else if (is_vert_adj(flp, i,j)) {
part = gy[i] / flp->units[i].width;
part_int = gy_int[i] / flp->units[i].width;
part_sp = gy_sp[i] / flp->units[i].width;
part_hs = gy_hs[i] / flp->units[i].width;
}
g[i][j] = part * len[i][j];
g[IFACE*n+i][IFACE*n+j] = part_int * len[i][j];
g[HSP*n+i][HSP*n+j] = part_sp * len[i][j];
g[HSINK*n+i][HSINK*n+j] = part_hs * len[i][j];
}
/* the 2.0 factor in the following equations is
* explained during the calculation of the B matrix
*/
/* vertical g's in the silicon layer */
g[i][IFACE*n+i]=g[IFACE*n+i][i]=2.0/getr(k_chip, t_chip, area);
/* vertical g's in the interface layer */
g[IFACE*n+i][HSP*n+i]=g[HSP*n+i][IFACE*n+i]=2.0/getr(k_interface, t_interface, area);
/* vertical g's in the spreader layer */
g[HSP*n+i][HSINK*n+i]=g[HSINK*n+i][HSP*n+i]=2.0/getr(k_spreader, t_spreader, area);
/* vertical g's in the heatsink core layer */
/* vertical R to ambient: divide r_convec proportional to area */
r_amb = r_convec * (s_sink * s_sink) / area;
g_amb[i] = 1.0 / (getr(k_sink, t_sink, area) + r_amb);
/* lateral g's from block center (spreader layer) to peripheral (n,s,e,w) spreader nodes */
g[HSP*n+i][NL*n+SP_N]=g[NL*n+SP_N][HSP*n+i]=2.0*border[i][2] /
((1.0/gy_sp[i])+model->pack.r_sp1_y*gn_sp/gy_sp[i]);
g[HSP*n+i][NL*n+SP_S]=g[NL*n+SP_S][HSP*n+i]=2.0*border[i][3] /
((1.0/gy_sp[i])+model->pack.r_sp1_y*gs_sp/gy_sp[i]);
g[HSP*n+i][NL*n+SP_E]=g[NL*n+SP_E][HSP*n+i]=2.0*border[i][1] /
((1.0/gx_sp[i])+model->pack.r_sp1_x*ge_sp/gx_sp[i]);
g[HSP*n+i][NL*n+SP_W]=g[NL*n+SP_W][HSP*n+i]=2.0*border[i][0] /
((1.0/gx_sp[i])+model->pack.r_sp1_x*gw_sp/gx_sp[i]);
/* lateral g's from block center (heatsink layer) to peripheral (n,s,e,w) heatsink nodes */
g[HSINK*n+i][NL*n+SINK_C_N]=g[NL*n+SINK_C_N][HSINK*n+i]=2.0*border[i][2] /
((1.0/gy_hs[i])+model->pack.r_hs1_y*gn_hs/gy_hs[i]);
g[HSINK*n+i][NL*n+SINK_C_S]=g[NL*n+SINK_C_S][HSINK*n+i]=2.0*border[i][3] /
((1.0/gy_hs[i])+model->pack.r_hs1_y*gs_hs/gy_hs[i]);
g[HSINK*n+i][NL*n+SINK_C_E]=g[NL*n+SINK_C_E][HSINK*n+i]=2.0*border[i][1] /
((1.0/gx_hs[i])+model->pack.r_hs1_x*ge_hs/gx_hs[i]);
g[HSINK*n+i][NL*n+SINK_C_W]=g[NL*n+SINK_C_W][HSINK*n+i]=2.0*border[i][0] /
((1.0/gx_hs[i])+model->pack.r_hs1_x*gw_hs/gx_hs[i]);
}
/* g's from peripheral(n,s,e,w) nodes */
/* vertical g's between peripheral spreader nodes and center peripheral heatsink nodes */
g[NL*n+SP_N][NL*n+SINK_C_N]=g[NL*n+SINK_C_N][NL*n+SP_N]=2.0/model->pack.r_sp_per_y;
g[NL*n+SP_S][NL*n+SINK_C_S]=g[NL*n+SINK_C_S][NL*n+SP_S]=2.0/model->pack.r_sp_per_y;
g[NL*n+SP_E][NL*n+SINK_C_E]=g[NL*n+SINK_C_E][NL*n+SP_E]=2.0/model->pack.r_sp_per_x;
g[NL*n+SP_W][NL*n+SINK_C_W]=g[NL*n+SINK_C_W][NL*n+SP_W]=2.0/model->pack.r_sp_per_x;
/* lateral g's between peripheral outer sink nodes and center peripheral sink nodes */
g[NL*n+SINK_C_N][NL*n+SINK_N]=g[NL*n+SINK_N][NL*n+SINK_C_N]=2.0/(model->pack.r_hs + model->pack.r_hs2_y);
g[NL*n+SINK_C_S][NL*n+SINK_S]=g[NL*n+SINK_S][NL*n+SINK_C_S]=2.0/(model->pack.r_hs + model->pack.r_hs2_y);
g[NL*n+SINK_C_E][NL*n+SINK_E]=g[NL*n+SINK_E][NL*n+SINK_C_E]=2.0/(model->pack.r_hs + model->pack.r_hs2_x);
g[NL*n+SINK_C_W][NL*n+SINK_W]=g[NL*n+SINK_W][NL*n+SINK_C_W]=2.0/(model->pack.r_hs + model->pack.r_hs2_x);
/* vertical g's between inner peripheral sink nodes and ambient */
g_amb[n+SINK_C_N] = g_amb[n+SINK_C_S] = 1.0 / (model->pack.r_hs_c_per_y+model->pack.r_amb_c_per_y);
g_amb[n+SINK_C_E] = g_amb[n+SINK_C_W] = 1.0 / (model->pack.r_hs_c_per_x+model->pack.r_amb_c_per_x);
/* vertical g's between outer peripheral sink nodes and ambient */
g_amb[n+SINK_N] = g_amb[n+SINK_S] = g_amb[n+SINK_E] =
g_amb[n+SINK_W] = 1.0 / (model->pack.r_hs_per+model->pack.r_amb_per);
/* calculate matrix B such that BT = POWER in steady state */
/* non-diagonal elements */
for (i = 0; i < NL*n+EXTRA; i++)
for (j = 0; j < i; j++)
if ((g[i][j] == 0.0) || (g[j][i] == 0.0))
b[i][j] = b[j][i] = 0.0;
else
/* here is why the 2.0 factor comes when calculating g[][] */
b[i][j] = b[j][i] = -1.0/((1.0/g[i][j])+(1.0/g[j][i]));
/* diagonal elements */
for (i = 0; i < NL*n+EXTRA; i++) {
/* functional blocks in the heat sink layer */
if (i >= HSINK*n && i < NL*n)
b[i][i] = g_amb[i%n];
/* heat sink peripheral nodes */
else if (i >= NL*n+SINK_C_W)
b[i][i] = g_amb[n+i-NL*n];
/* all other nodes that are not connected to the ambient */
else
b[i][i] = 0.0;
/* sum up the conductances */
for(j=0; j < NL*n+EXTRA; j++)
if (i != j)
b[i][i] -= b[i][j];
}
/* compute the LUP decomposition of B and store it too */
copy_dmatrix(lu, b, NL*n+EXTRA, NL*n+EXTRA);
/*
* B is a symmetric positive definite matrix. It is
* symmetric because if a node A is connected to B,
* then B is also connected to A with the same R value.
* It is positive definite because of the following
* informal argument from Professor Lieven Vandenberghe's
* lecture slides for the spring 2004-2005 EE 103 class
* at UCLA: http://www.ee.ucla.edu/~vandenbe/103/chol.pdf
* x^T*B*x = voltage^T * (B*x) = voltage^T * current
* = total power dissipated in the resistors > 0
* for x != 0.
*/
lupdcmp(lu, NL*n+EXTRA, p, 1);
/* done */
model->flp = flp;
model->r_ready = TRUE;
}
