Bottleneck At Heaven's Gates (Part Eight)

[August Highland]

Bottleneck At Heaven's Gates (Part Eight)



eT rick 
is to q 
uan tify the 
ad van 
tag e o f a pro 
pos ed 
enh anc em ent 
F00 30 
CS /EE 
58 10 
CS /EE 
68 10 
Am dah l's L 
aw 
Qu ant ific atio 
n o f th e d imi nis hin g re 
tur n p 
rin cip 
le 
eD efin es spe 
edu p g ain ed fro m a 
pa rtic ula r fe atu re 
eN ote XE Q-t ime 
is 1/p erf orm 
anc e 
eD epe nds on 2 f act ors 
kF rac tion 
of ori gin 
al c 
om put atio 
n ti me tha 
t ca n ta k a dva 
nta ge of 
the en han 
cem 
ent 
kL eve l of im pro 
vem 
ent of the en han 
cem 
ent 
Exe cut ion tim 
e w itho 
ut u sin g th 
e e nha 
nce me nt 
Exe cut ion tim 
e u sin g th 
e e nha 
nce me nt 
Sp eed 
up = 
Pag e 6 
F00 31 
CS /EE 
58 10 
CS /EE 
68 10 
Am dah l's L 
aw 
ExT ime 
new = E 
xTi me 
old x 
(1 - F rac tion 
enh anc ed) 
+ F 
rac tion 
enh anc ed 
Sp eed 
up 
ove rall = 
ExT ime 
old 
ExT ime 
new 
Sp eed 
up 
enh anc ed 
= 1 
(1 - Fr act 
ion 
enh anc ed) 
+ F 
rac tion 
enh anc ed 
Sp eed 
up 
enh anc ed 
F00 32 
CS /EE 
58 10 
CS /EE 
68 10 
Sim ple Exa mpl e 
Be wa re, 
Am dah 
l's law 
sa ys not 
hin g a bou 
t co st 
eF or one 
ap plic 
atio n: 
kF P in 
str uct 
ion s a cco 
unt for 50 % o 
f in stru 
ctio ns 
kF PS QR 
T is 
20 % 
kO the r 30 
% 
eD esi gne 
rs s ay the se are 
po ssi ble (at the 
sa me 
cos t) 
kI mp 
rov e F PS QR 
T b y 4 0x 
ki mp 
rov e a ll F P b y 2 x 
kI mp 
rov e o the r (n on sqr t) F P b y 8 x 
eW hic h o ne sho 
uld yo u d o? 
F00 33 
CS /EE 
58 10 
CS /EE 
68 10 
And the ans 
wer is... 
eF PS QR T 
eF P 
eO 
TH ER 
1 
(1-0 .2) + 
0.2 40 
= 1 .24 2 
= 
1 
(1-0 .5) + 
0.5 2 
= 1 .33 3 
= 
1 
(1-0 .3) + 
0.3 8 
= 1 .35 6 
= 
F00 34 
CS /EE 
58 10 
CS /EE 
68 10 
Ano ther Am dah l's E 
xam ple 
eS upp 
ose ap plic 
atio n is "a lmo 
st a ll" par 
alle l: 9 0% 
kW hat is the sp eed 
up usi ng 10, 10 0, a 
nd 100 
0 p roc ess ors ? 
# o f pr 
oce sso rs = P 
Fra ctio 
n 
enh 
anc ed = 
0.9 
Sp eed 
up 
p = 
1 
0.9 P 
0.1 + 
Sp eed 
up 
10 = 
1 0. 
9 10 
0.1 + 
1 0.19 
= 
= 5 .3 
Sp eed 
up 
100 = 
1 0.9 100 
0.1 + 
1 0.10 



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