S_XY += (X[i] - avg_X) * (Y[i] - avg_Y)
return (S_XY / n)
-##----------------------------------
+##---------------------------------------------------------------------
## variance : variance
## param X data vector ( ..x_i.. )
## (S_X)^2 = (Sum ( x_i - avg(x) )^2 ) / n
-##----------------------------------
+##---------------------------------------------------------------------
def variance (X):
n = len(X)
avg_X = avg (X)
S_X2 += (X[i] - avg_X) ** 2
return (S_X2 / n)
+##---------------------------------------------------------------------
+## calibrate : output correction factors, c_lat on latency, c_bw on bw
+## such that bandwidth * c_bw = bw_regr, latency * c_lat = lat_regr
+## where bw_regr and lat_regr are the values approximating experimental
+## observations.
+##
+## param links number of links traversed during ping-pong
+## param latency as specified on command line, in s
+## param bandwidth as specified on command line, in Byte/s
+## param sizes vector of data sizes, in Bytes
+## param timings vector of time taken: timings[i] for sizes[i], in us
+##---------------------------------------------------------------------
def calibrate (links, latency, bandwidth, sizes, timings):
assert len(sizes) == len(timings)
if len(sizes) < 2:
return None
+ # compute linear regression : find an affine form time = a*size+b
S_XY = cov(sizes, timings)
S_X2 = variance(sizes)
a = S_XY / S_X2
b = avg(timings) - a * avg(sizes)
- return (b * 1e-6) / (latency * links), 1e6 / (a * bandwidth)
+ # corresponding bandwith, in byte/s (was in byte/us in skampi dat)
+ bw_regr = 1e6 / a
+ # corresponding latency, in s (was in us in skampi dat)
+ lat_regr = b*1e-6
+ print("\nregression: {0} * x + {1}".format(a,b))
+ print("corr_bw = bw_regr/bandwidth= {0}/{1}={2} lat_regr/(lat_xml*links)={3}/({4}*{5}))".format(bw_regr,bandwidth,bw_regr/bandwidth,lat_regr,latency,links))
+ # return linear regression result and corresponding correction factors c_bw,c_lat
+ return a,b, bw_regr/bandwidth, lat_regr/(latency*links)
+
+
+##---------------------------------------------------------------------
+## outputs a C formatted conditional return value for factor
+##
+## param lb lower bound
+## param ub upper bound
+## param lb_included boolean to tell if bound is included (<=) or exclude (<)
+## param ub_included boolean to tell if bound is included (<=) or exclude (<)
+##---------------------------------------------------------------------
+def c_code_print (lb,ub, retval, lb_included, ub_included):
+ lb_cmp = ub_cmp = "<"
+ if lb_included:
+ lb_cmp ="<="
+ if ub_included:
+ ub_cmp ="<="
+
+ ub_kib=ub/1024.
+ lb_kib=lb/1024.
+ print("\t /* case {0:.1f} KiB {1} size {2} {3:.1f} KiB */".format(lb_kib,lb_cmp,ub_cmp,ub_kib))
+ print("\t if ({0:d} {1} size && size {2} {3:d}) ".format(lb,lb_cmp,ub_cmp,ub))
+ print("\t return({0});" . format(retval))
+
##-----------------------------------------------------------------------------------------------
## main
## ---------------
#count= 8388608 8388608 144916.1 7.6 32 144916.1 143262.0
#("%s %d %d %f %f %d %f %f\n" % (countlbl, count, countn, time, stddev, iter, mini, maxi)
- readdata.append( (int(l[1]),float(l[3]) / 2 ) ); # divide by 2 because of ping-pong measured
+ readdata.append( (int(l[1]),float(l[3]) / 2) ); # divide by 2 because of ping-pong measured
## These may not be sorted so sort it by message size before processing.
sorteddata = sorted( readdata, key=lambda pair: pair[0])
-sizes,timings = zip(*sorteddata);
+sizes,timings= zip(*sorteddata)
## adds message sizes of interest: if values are specified starting from the 6th command line arg
limits += [idx for idx in range(len(sizes)) if sizes[idx] == int(sys.argv[i])]
limits.append(len(sizes) - 1)
+factors = []
low = 0
for lim in limits:
correc = calibrate(links, latency, bandwidth, sizes[low:lim + 1], timings[low:lim + 1])
if correc:
- print("Segment [%d:%d] -- Latency factor=%g -- Bandwidth factor=%g" % (sizes[low], sizes[lim], correc[0], correc[1]))
+ # save interval [lb,ub] correction, regression line direction and origin
+ # and corresponding correction factors for bw and lat resp.
+ (dircoef,origin,factor_bw,factor_lat) = correc
+ factors.append( (sizes[low],sizes[lim], dircoef, origin, factor_bw,factor_lat) )
+ print("Segment [%d:%d] --Bandwidth factor=%g --Latency factor=%g " % (sizes[low], sizes[lim], factor_bw,factor_lat))
low = lim + 1
+
+# now computes joining lines between segments
+joinseg=[]
+
+print("\n/**\n *------------------ <copy/paste C code snippet in surf/network.c> ----------------------")
+print(" *\n * produced by: {0}\n *".format(' '.join(sys.argv)))
+print(" *---------------------------------------------------------------------------------------\n **/")
+
+# print correction factor for bandwidth for each segment
+print("static double smpi_bandwidth_factor(double size)\n{")
+for (lb,ub,a,b,factor_bw,factor_lat) in factors:
+ c_code_print(lb,ub,factor_bw,True,True)
+
+ # save ends and starts of segments
+ if lb != sizes[0]:
+ joinseg.append( (lb,timings[sizes.index(lb)]) )
+ if ub != sizes[-1]:
+ joinseg.append( (ub,timings[sizes.index(ub)]) )
+
+# print correction factor for bandwidth between segments
+joinseg.reverse()
+print("\n\t /* ..:: inter-segment corrections ::.. */");
+inx=len(joinseg)-1
+while inx>=1:
+ (x0,y0) = joinseg[inx]
+ inx = inx -1
+ (x1,y1) = joinseg[inx]
+ inx = inx -1
+ # line eq. is y = (y1-y0)/(x0-x1) * x + (y0 x1 - y1 x0)/(x1-x0)
+ a = (y1-y0) / (x1-x0)
+ bw_join = 1e6 / a
+ factor_join_bw = bw_join / bandwidth
+ #print("Joining points (%f,%f) -> (%f,%f) : line dir : a=%g\n" % (x0,y0,x1,y1,a))
+ c_code_print(x0,x1,factor_join_bw,False,False)
+
+print("}\n")
+
+# print correction factor for latency for each segment
+print("static double smpi_latency_factor(double size)\n{")
+for (lb,ub,a,b,factor_bw,factor_lat) in factors:
+ c_code_print(lb,ub,factor_lat,True,True)
+
+print("\n\t /* ..:: inter-segment corrections ::.. */");
+while joinseg:
+ (x0,y0) = joinseg.pop()
+ (x1,y1) = joinseg.pop()
+ # line eq. is y = (y0-y1)/(x0-x1) * x + (y0 x1 - y1 x0)/(x1-x0)
+ #print("(%f,%f) -> (%f,%f)\n" % (x0,y0,x1,y1))
+ b = 1e-6 * (y0*x1-y1*x0) / (x1-x0)
+ factor_join_lat = b / (latency*links)
+ c_code_print(x0,x1,factor_join_lat,False,False)
+
+print("\n/**\n *------------------ <copy/paste C code snippet in surf/network.c> ----------------------\n **/")
