Evolution of Computing Energy Efficiency: Koomey’s Law Revisited

E olu ion o compu ing ene gy e iciency: Koomey’s law e isi ed Albe o P ie o 1 •Bea iz P ie o 1 •Juan Jose ´Escoba 2 •Thomas Lampe 3 Recei ed: 23 May 2024 / Re ised: 10 July 2024 / Accep ed: 5 Augus 2024 The Au ho (s) 2024 Abs ac Fo in o ma ion and communica ion echnology powe consump ion o be sus ainable, he ene gy e iciency o compu ing sys ems mus g ow a leas as as as he demand o compu ing se ices. I is he e o e c ucial o unde s and how ene gy e iciency is e ol ing and how i will end in he u u e, in o de o ake app op ia e measu es whe e possible. This a icle analyses he e olu ion o his pa ame e by analysing high-pe o mance compu e s om 2008 o 2023, con as ing he esul s wi h hose om Koomey’s Law. I is concluded, a e compa ing he wo ha in he s udied pe iod and in he nea u u e, ene gy e iciency con inues o g ow exponen ially bu a a slowe a e han ha es ablished by Koomey’s Law (maximum ene gy e iciency doubles e e y 2.29 yea s ins ead o e e y 1.57 yea s). Ano he in e es ing esul is ha ene gy e iciency g ows a a slowe a e (doubling e e y 2.29 yea s) han pe o mance (doubling e e y 1.85 yea s). Keywo ds Koomey’s Law G een compu ing G een500 Ene gy e iciency High-pe o mance compu ing (HPC) 1 In oduc ion In he con ex o he en i onmen al implica ions and ele- ance o he inc easing ene gy consump ion o compu e sys ems, his pape p esen s a s udy on he e olu ion o he ene gy e iciency in such sys ems. I has o be conside ed ha he o e all ene gy consump ion o ICTs depends no only on he g owing numbe o de ices o di e en na u e (mobiles, PC, e c.) and he ema kable use made o hem due o he cons an inc ease o new applica ions, bu also on he ene gy e iciency o hese de ices. Clea ly, in o de o con ibu e o he sus ainabili y o he plane , he in e es o manu ac u e s and enginee s is no in educing he use o ICT, bu in inc easing he ene gy e iciency o de ices a leas as as as hei demand. In addi ion o educing g eenhouse gas emissions, inc easing ene gy e iciency is o in e es o dec ease powe supply cos s ( om la ge da a cen es o mobile de ices) and o ex end he li e o ba - e ies. The e o e, i is o g ea in e es o analyse he e o- lu ion o he ene gy e iciency o compu e sys ems and o make es ima es o he u u e, which is he objec i e o his pape . Koomey’s Law, c ea ed by analysing da a om di e en sys ems om 1946 o 2009, es ablished ha he ene gy e iciency o compu e s doubled e e y 1.57 yea s [1,2]. Howe e , o ecas s in he ICT ield need o be upda ed equen ly as echnological changes occu a a e y as a e. The aim o his pape is o upda e he Koomey esul s, using eal, public and e i ied da a such as hose p esen ed in he TOP and G een500 lis s [3,4] o high-pe o mance compu e s (HPC). I should be no ed ha also sys ems wi h much lowe compu ing pe o mances, such as pe sonal compu e s, ha e ene gy e iciencies o he same o de o magni ude [5], so he esul s ob ained a e easily gene al- isable o his ype o sys ems. The pape ocuses on Koomey’s Law, which is o g ea ele ance o enginee s and manu ac u e s. As E ik B yn- jol sson poin ed ou back in 2011 as a p o esso a MIT, in &Albe o P ie o [email p o ec ed] Bea iz P ie o [email p o ec ed] Juan Jose ´Escoba [email p o ec ed] Thomas Lampe [email p o ec ed] 1 Depa men o Compu e Enginee ing, Au oma ics and Robo ic, CITIC, Uni e si y o G anada, 18071 G anada, Spain 2 Depa men o So wa e Enginee ing, CITIC, Uni e si y o G anada, 18071 G anada, Spain 3 ICube, Uni e si y o S asbou g, 67081 S asbou g, F ance 123 Clus e Compu ing (2025) 28:42 h ps://doi.o g/10.1007/s10586-024-04767-y(0123456789().,- olV)(0123456789().,- olV) a ce ain sense his law may eclipse Moo e’s Law due o he impo ance ha use s inc easingly place on powe consump ion in many applica ions, as is he case, o example, in mobile applica ions [6–8]. Table 1summa ises he e minology and symbols used in his a icle o acili a e he eade s’ unde s anding. The es o his pape is o ganised as ollows. Fi s , in o de o ame he con ex o he pape and o p esen some basic concep s and e minology, a backg ound sec ion is in oduced (Sec . 2). The me hodology and da a used a e jus i ied in Sec . 3. The nume ical and g aphical esul s a e p o ided in Sec . 4. The analysis o he abo e esul s is p esen ed in Sec . 5, and inally, a discussion and he main conclusions a e summa ised in Sec . 6. 2 Backg ound Sec ion 2.1 desc ibes he implica ions and ele ance o he ole o ICT in ene gy consump ion. Sec ion 2.2 jus i ies he use o he da a p o ided by he TOP500 lis s, based on he Linpack benchma k, o ca ying ou he p esen s udy. Sec ion 2.3 b ie ly ou lines he con ibu ions o a ious wo ks ela ed o he opic p esen ed, and inally, Sec . 2.4 de ines a numbe o concep s necessa y o a p ope unde s anding o he es o his s udy. 2.1 ICT ene gy demand One o he majo challenges o oday’s socie y is o educe ene gy demand, and ICT is a ele an ield o elec ical ene gy consump ion, ha ing a majo impac on g eenhouse gas emissions [9,10]. Indeed, he US Semiconduc o Indus y Associa ion [11] s a es ha while global ene gy p oduc ion g ows linea ly, elec ici y demand om com- pu e s does so exponen ially. O he s udies indica e ha , in a wo s -case scena io, ICTs could con ibu e up o 23% o global g eenhouse gas emissions by 2030 [12]. I he end con inues, he elec ical ene gy consump ion o he as amoun o echnological equipmen will exceed he wo ld’s elec ical ene gy p oduc ion by 2040, which means ha he e would no be enough o powe all he compu e s in he wo ld [13]. The en i onmen al implica ions o ICTs a e o a di - e en na u e, no always ha m ul, and can be g ouped in o h ee ypes o e ec s [14–16]: 1. Di ec e ec . This is mainly due o he la ge p oli e - a ion and global inc ease in he numbe o elec onic de ices, communica ions ne wo ks and da a cen es connec ed o he In e ne . This e ec is also in luenced by he inc ease o applica ions ha a e cons an ly used bo h in ou ine asks (sma phones, e-mails, social ne wo ks, e c.) and in adi ional compu ing sys ems ( om PC o HPC applica ions). I is also necessa y o conside he eme gence o new applica ions, which, as in he case o he In e ne o he Things (IoT), equi e new de ices ha , al hough indi idually ha e a e y low consump ion, gi en hei eno mous quan i y, hei o e all con ibu ion o consump ion is e y signi ican . 2. Indi ec e ec . I is caused by ICT applica ions ha acili a e e iciency imp o emen s and he educ ion o p ima y ene gy consump ion in e y di e se sec o s such as: cons uc ion, indus y, anspo and com- me ce, by p o iding in elligen solu ions. I is good o he en i onmen as he inc ease in ICT consump ion comes la gely om i s educ ion in o he sec o s, mode a ing, on balance, o e all consump ion. Among he main sec o s bene i ing a e [17,18]: •E-Wo k •E-Heal h •Sma G id •Sma Ag icul u e •E-Lea ning Table 1 No a ions and symbols used Ac onym Meaning CE Compu ing e iciency E Ene gy (Wa s hou s o Joules) EE Ene gy e iciency GE Global ene gy GPU G aphics p ocessing uni FLOP Floa ing-poin ope a ions FLOPS Floa ing-poin ope a ions pe second HPC High-pe o mance compu ing HPL High-pe o mance Linpack ICT In o ma ion and communica ion echnology IT In o ma ion echnology NB Numbe o bi s NBI Numbe o bi s pe ins uc ion NC Numbe o compu a ions NPU Neu al p ocessing uni NS Numbe o s a es NI Numbe o ins uc ions P Powe (Wa s) PC Pe sonal compu e R Compu ing pe o mance Rmax Maximum pe o mance Rpeak Peak pe o mance 2 De e mina ion coe icien Time TPU Tenso p ocessing uni 42 Page 2 o 24 Clus e Compu ing (2025) 28:42 123 •Connec ed p i a e anspo •T a ic con ol and op imisa ion •E-Comme ce •E-Banking •Sma manu ac u ing •Sma logis ics 3. Rebound e ec . This is a phenomenon ha occu s as ICT se ices become mo e use ul, cheape and mo e ene gy e icien . This inc eases he digi al li es yle o he socie y, leading o a ebound e ec : ICT equipmen consumes less, bu is used much mo e. O e all, his has a nega i e consequence. Es ima es show ha possible ebound e ec s due o digi isa ion ange om 10 o 30% highe ene gy consump ion, a ying by sec o , echnology and end-use [18]. The p edominan ac o in he inc ease o ene gy con- sump ion in compu ing is o a la ge ex en de e mined by he inc easing amoun o ins uc ion p ocessing ha akes place. The esul s o some s udies’ o ecas s o ene gy consump ion pe ins uc ion o bi p ocessed a e no alid. This is because hey e oneously conside wi hou u he analysis ha exponen ially g owing compu ing demand ansla es in o exponen ially g owing ene gy equi emen s. The demand can be measu ed simply by he numbe o compu a ions pe o med (NC) bu , o alid s udies, i is necessa y o conside also he ene gy consumed by each o hem (EC). In sho , he global ene gy consump ion (GE) in compu a ion is a unc ion o bo h he p ocessing demand ( ep esen ed, o example, by he o al numbe o compu- a ions execu ed) and he a e age ene gy consumed pe compu a ion (EC), gi ing: GE ¼NC EC ð1Þ Compu a ions (NC) can e e o he numbe o ins uc- ions (NI) o bi s (NB) execu ed and ene gy can be exp essed in Joules o KWh. The ene gy e iciency o compu a ion, also called elec- ical e iciency, EE, is a pa ame e ep esen ing he numbe o execu able compu a ions (ins uc ions o bi s) pe uni o ene gy (Joule o KWh), such ha : EE ¼Numbe o compu a ions Ene gy consumed by hose compu a ions ¼NC Eð2Þ whe e E ep esen s he ene gy consumed in pe o ming he NC compu a ions (numbe o ins uc ions o bi s) indica ed in he nume a o . The ene gy consumed pe compu a ion (EC) will be: EC ¼E NC ¼1 EE ð3Þ Thus, subs i u ing he alue o EC in Eq. (1), he global consump ion (GE) can be exp essed as a unc ion o e iciency: GE ¼NC EE ð4Þ I is deduced om Eq. (4) ha , in o de o educe o e all consump ion (GE), ei he use demand o compu ing ( ep esen ed by NC) is educed o ene gy e iciency (EE) is imp o ed. In o he wo ds, in o de o p e en an o e all inc ease in compu ing ene gy consump ion, he denomi- na o o GE in Eq. (2) (e iciency) mus g ow a leas as as as he nume a o (demand). Many o ecas s o ene gy consump ion a e lawed by conside ing only es ima es o he inc ease in he nume a o wi hou conside ing he denomina o . Acco ding o he abo e easoning, and as s a ed in Sec . 1, compu e a chi ec s and designe s should ocus on imp o ing (inc easing) ene gy e iciency. The p esen s udy add esses his by ocussing on he analysis o he e olu ion o e ime o his pa ame e by making as igo ous es ima es as possible o he u u e. 2.2 The TOP500 lis s and he Linpack benchma k The aim o his pape is o analyse he e olu ion o he ene gy e iciency (EE) o compu e s o e he las h ee decades. To do so, i is necessa y o s a om he knowledge o hei compu ing pe o mance (R), exp essed as he numbe o ins uc ions execu ed pe second, and he elec ical powe (P) consumed when execu ing hose ins uc ions. A p esen , i is p ac ically impossible o ha e access o compu e s om all he yea s included in his s udy o be able o ake app op ia e measu emen s. How- e e , such da a a e a ailable in he TOP500 and G een500 lis s [1], eleased wice a yea . These da a a e widely ec- ognized by he scien i ic communi y, since om 2020 o May 2024 mo e han 5,000 pape s ha make use o hem appea in he li e a u e. Indeed, he TOP500 compu e anking ollows a clea and anspa en me hodology, being alida ed and p esen ed o discussion in he open o ums o he In e na ional Supe compu e Con e ences on High Pe o mance (ISC HPC), and he In e na ional Con e ence o High Pe o mance Compu ing, Ne wo king, S o age, and Analysis (SC) [2,3]. Es ima ing he pe o mance o a compu e is a complex ask as i depends on many di e en in e ela ed ac o s. These ac o s, among o he s, include he compile ’s abili y o op imise he high-le el p og ams, he ope a ing sys em, he a chi ec u e and he ha dwa e cha ac e is ics o he compu e . The desi ed objec i e o he Linpack and he TOP500 is o know, wi h a single pa ame e , how as a compu e will pe o m when sol ing eal p oblems. Ne - e heless, he applica ions un on compu e s in gene al, and Clus e Compu ing (2025) 28:42 Page 3 o 24 42 123 high-pe o mance compu e s in pa icula , a e e y di e se. Finding a single pa ame e ha measu es he o e all pe - o mance o he compu e , is a complica ed issue since no single compu a ional ask can e lec he o e all pe o - mance o a compu e sys em unning a wide ange o p og ams. In o de o measu e he numbe o ins uc ions execu ed pe second, he maximum pe o mance (Rmax) is used as a me ic, bu i mus be conside ed ha no all ypes o ins uc ions consume he same ime, so i is necessa y o use benchma k p og ams o ob ain measu es o objec i ely compa e he pe o mance o di e en compu e s. These p og ams a e es ablished by he scien i ic o indus ial communi ies [4]. Some examples a e Whe s one [5,6], Dh ys one [7], Linpack [3] o SPEC [8–10]. Nume ous benchma ks and s anda ds exis o measu e o he cha ac- e is ics o compu e s in addi ion o compu ing pe o - mance [11]. The asks ha mo e closely ma ch a di e se and b oad se o impo an applica ions in he ield o high-pe o - mance compu ing (HPC) a e based on p imi i es such as ec o , ec o –ma ix and ma ix–ma ix ope a ions. These ope a ions a e undamen al in scien i ic applica ions (wea he and clima e p edic ion, o example), enginee ing, bio echnology, c yp oanalysis, g aphics applica ions and in a ious ields o A i icial In elligence (e.g. deep lea ning). In he case o Linpack benchma k, i ocuses on he abo e- men ioned ope a ions, as i consis s in sol ing a andom dense sys em o nlinea equa ions (A •x=b), in double p ecision a i hme ic (64 bi s), and de e mines he amoun o ime spen ac o ing and esol ing he sys em, using ha ime as a measu e o compu ing pe o mance [3]. Linpack is widely used and pe o mance alues a e a ailable o almos all ele an sys ems; o example, he TOP500 lis s [12] ha e used i as a benchma k since i s beginnings, as i i s easonably well in mos HPC appli- ca ion a eas. The TOP500 lis s a emp o selec and ank he 500 mos powe ul compu e s by es ima ing hei p o- cessing speed (Rmax). The G een500 anking, associa ed wi h he TOP500 since 2013, uses ene gy e iciency (EE) as a anking pa ame e , ins ead o maximum pe o mance as he TOP500 does. Bo h ankings include, o each compu e sys em, o he pa ame e s such as p ocesso model, o al numbe o co es, accele a o /co-p ocesso (numbe o co es and model), a chi ec u e (clus e o MPP), p ocesso speed (MHz), in e connec ion amily and loca ion si e. O e ime, se e al e sions o Linpack ha e been de eloped wi h di e en p oblem sizes. Ini ially (1977), he ma ices associa ed wi h he sys em o linea equa ions we e o he o de n= 100. La e (1986) i was ex ended o n= 1000, wi h an addi ional e sion o pa allel p ocess- ing. This e sion gi es g ea e e sa ili y o op imising Linpack implemen a ions as ha dwa e a chi ec u es began o include ma ix– ec o and ma ix–ma ix ope a ions. The ou h e sion (1991) was he Highly Pa allel Com- pu ing Benchma k, o HPLinpack, mo e app op ia e o es ing pa allel compu e s. In HPLinpack, he size n o he p oblem can be as la ge as necessa y o op imise he pe - o mance esul s o he machine. This was he e sion adop ed as a benchma k in he TOP500 in 1993 [1] and allows he use o scale he p oblem size and op imise he so wa e in o de o achie e he bes pe o mance o a gi en machine. A po able and eely a ailable imple- men a ion o HPLinpack w i en in C, called High-Pe - o mance Linpack (HPL) and o ien ed o dis ibu ed- memo y compu e s, was also de eloped and i is consid- e ed as a benchma k implemen a ion [3]. The HPL package p o ides a es ing and iming p og am o quan i y he accu acy o he ob ained solu ion as well as he ime aken o compu e i . The algo i hm, depending on he in e con- nec ion ne wo k, can be scalable in he sense ha i s pa - allel e iciency emains cons an wi h espec o he memo y usage pe p ocesso [13]. Imp o emen s and add-ons ha e been and a e cons an ly being in oduced in o de o use compu a ional and com- munica ion da a pa e ns ha mo e closely ma ch a di - e en and b oad se o applica ions. Among o he p ojec s highligh he High-Pe o mance Conjuga e G adien s (HPCG) Benchma k, which s esses he sys em’s main memo y bandwid h and i s in luence on he o e all pe - o mance o he sys em [14]. In addi ion, i includes a la ge se o asks o be execu ed han he ini ial e sion o he Linpack, including: spa se ma ix– ec o mul iplica- ion, ec o upda es, global do p oduc s and local sym- me ic Gauss–Seidel smoo he [15,16]. One o he undamen al cha ac e is ics ha dis inguishes HPL is ha i o e s ull eedom o implemen he es and can be op imised o each ype o compu e o a chi ec u e. Indeed, i allows hand op imisa ions o he p og am, so ha he p oblem size and i s implemen a ion can be adap ed and adjus ed o use mos o he a ailable ha dwa e esou ces and achie e he bes possible pe o mance when execu ing he benchma k. The me hodology used o imp o e he me ic esul s o a pa icula pla o m can subsequen ly be used o ob ain be e pe o mance in eal applica ions [17,18]. Also, he g ea e o s o ob ain he bes possible esul a e made because he inclusion o a compu e in leading posi ions in he TOP500, means g ea p es ige o he ins i u ion ha owns he compu e . One o he objec i es o hand op imisa ions is o use addi ional esou ces a ailable in he execu ion o he benchma k such as accele a o s, cop ocesso s, and specialised ha dwa e [19–22]. I should be no ed ha , in gene al, hese de ices a e specialised in ec o o ma ix p ocessing and can he e o e pe o m he basic ope a ions on which he Lin- pack ocuses. Thus, he la es edi ions o he TOP500 42 Page 4 o 24 Clus e Compu ing (2025) 28:42 123 implici ly e lec he pe o mance o sys ems wi h he e o- geneous compu ing esou ces, such as hose using mul iple GPUs (G aphics P ocessing Uni s), TPUs (Tenso P o- cessing Uni s) o o he specialised accele a o s. Table 2 includes a lis o he di e en models o p ocesso s used by he compu e s included in he TOP500 lis o No embe 2023. In Table 3, he co-p ocesso s o accele a o s ( ec o p ocesso s, ma ix p ocesso s, GPUs, TPUs, NPUs, e c.) a ailable in he sys ems o ha same edi ion a e e e enced. The op place in he TOP500 lis is aken by he F on ie exascale sys em, loca ed a he Oak Ridge Na ional Lab- o a o y in Tennessee, USA, which has a o al o 8,699,904 combined CPU and GPU co es, achie ing a pe o mance o Rmax = 1.194 EFLOPS, and an excellen powe e iciency o EE =52.59 GFLOPS/Wa [23]. As an example, in [24] a no el de ice-cen ic High- Pe o mance Linpack (HPL) app oach is p oposed and expe imen ally es ed o cu en main-s eam mul i Gen- e al-Pu pose G aphics P ocessing Uni (GPGPU) pla - o ms, whe e each p ocess can make ull use o he esou ces o a node, including accele a o s, CPU socke s, PCI-e buses and memo y/ne wo k bandwid h, e c. In his way, pa allel p ocessing can be achie ed by combining he Single Ins uc ion, Mul iple Da a (SIMD) echnique wi h mul i h eading, hus ob aining SIMT (Single Ins uc ion Mul iple Th ead) p ocessing. As a esul , he wo kload on he CPU-end and he in e -p ocess communica ion a e g ea ly enhanced due o highe sys em u ilisa ion, while he compu a ion on he de ice-end emains e icien . This app oach can se e as a compe i i e basis o op imisa ions on u u e he e ogeneous pla o ms. As wi h o he benchma king p og ams, i should be no ed ha he esul s ob ained by Linpack ha e limi a ions as i is no igo ous o measu e he execu ion ime o a single p og am o de e mine he compu a ional powe o a compu e sys em. Despi e i s limi a ions, as i only mea- su es how as a compu e will pe o m [6], oday Linpack is s ill conside ed he main e e ence ool used by scien- is s, enginee s, manu ac u e s and he In e ne communi y o compa e be ween he pe o mances o he di e en HPC sys ems [3]. Linpack is clea ly he s anda d o compa a i e s udies on he pe o mance o pa allel compu ing sys ems [3,22]. The se o 62 TOP500 lis s b ings oge he aluable Table 2 Families o models o p ocesso s o he TOP500 compu e s (No embe 2023 edi ion) P ocesso amily o ype # O sys ems ha con ain i In el Xeon Gold 164 Xeon Gold 62xx (Cascade Lake) 90 Xeon Gold (Skylake) 71 Xeon Gold (Sapphi e Rapids) 1 Xeon Gold 42xx (Cascade Lake) 1 Xeon Gold 63xx (Ice Lake) 1 AMD Zen 140 AMD Zen-2 (Rome) 69 AMD Zen-3 (Milan) 66 AMD Zen-4 (Genoa) 5 In el Xeon Pla inum 121 Xeon Pla inum (Sapphi e Rapids) 19 Xeon Pla inum (Skylake) 21 Xeon Pla inum 82xx (Cascade Lake) 40 Xeon Pla inum 83xx (Ice Lake) 35 Xeon Pla inum 92xx (Cascade Lake) 6 In el Xeon E5 37 In el Xeon E5 (B oadwell) 18 In el Xeon E5 (Haswell) 11 In el Xeon E5 (I yB idge) 7 In el Xeon E5 (SandyB idge) 1 Fuji su A64FX 8 IBM Powe 9 7 In el Xeon Phi 7 In el Xeon Max 5 Vec o Engine 5 Xeon Sil e (Skylake) 3 Hygon Dhyana 1 Sunway 1 Xeon 5600-se ies (Wes me e-EP) 1 To al 500 Table 3 Families and models o cop ocesso s o accele a o s o he TOP500 compu e s (No embe 2023 edi ion) Cop ocesso o accele a o # o sys ems ha con ain i NVIDIA Tesla V100 60 NVIDIA Tesla A100 47 NVIDIA A100 SXM4 30 AMD Ins inc MI 11 NVIDIA H100 10 NVIDIA Tesla K 6 NVIDIA Tesla P 6 NVIDIA Vol a 5 In el Da a Cen e GPU Max 4 In el Xeon Phi 2 Deep Compu ing P ocesso 1 Ma ix-2000 1 NVIDIA 2050 1 NVIDIA HGX A100 80 GB 500W 1 P e e id Ne wo ks MN-Co e 1 Clus e Compu ing (2025) 28:42 Page 5 o 24 42 123 in o ma ion on he e olu ion o supe compu e s o e he las 31 yea s (1993–2023). A sys ema ic, con olled and anspa en me hodology has been used o compile hese lis s. Mo eo e , his in o ma ion is unique, as he e is no o he esou ce ha p o ides such da a and allows s udies o be ca ied ou on such a la ge numbe o compu e sys ems. 2.3 Rela ed wo ks The e a e nume ous s udies on he e olu ion and p edic ion models o ene gy consump ion in he ield o ICT, some mo e pessimis ic han o he s, and among hem a e hose e e enced ch onologically below. In 2009, Feng and Scogland [25] analysed he i s h ee lis s o he G een500 (No embe 2007 o No embe 2008), compa ing he e olu ion in he maximum and a e age ene gy e iciency, he ene gy e iciency e sus speed (measu ed as he posi ion wi hin o he TOP500 ank), and he ela ionship be ween o al powe and ene gy e iciency. Among o he conclusions, hey indica e ha he o e all ene gy e iciency (on a e age) has imp o ed in a manne ha acks wi h Moo e’s Law, i.e., he a e age ene gy e iciency o he G een500 doubles e e y 18 mon hs. In 2009 and 2011 Koomey e al. p esen ed a s udy on he e olu ion o he ene gy e iciency o 80 gene al-pu pose compu e s (like main ames, minicompu e s and PCs) exis ing be ween he yea s 1946 o 2009. They concluded ha du ing ha pe iod o ime, he compu a ions pe KWh doubled e e y 1.57 yea s [26,27]. This ela ionship is known in he scien i ic and enginee ing communi ies as ‘‘Koomey’s Law’’. The de ails o his s udy, as well as o he s de i ed om i , will be analysed h oughou his a icle. Came on, in his 2010 a icle [28], analyses he e olu- ion, om No embe 2007 o May 2010, o he a e age alues o ene gy e iciency and elec ical powe o all compu e s, he i s 10 and he las 10 o each o he G een500 lis s. He concludes ha he op 10 supe com- pu e s a e abou h ee imes mo e e icien han he a e age sys em on each lis and, despi e his esul in ene gy e i- ciency, he o e all ene gy equi ed o mos sys ems on a e age is inc easing, al hough he a e o his inc ease is slowing. The 2011 a icle by Hin on e al. [29] shows ha he impo ance o he In e ne and ICT is con inually inc eas- ing bo h in e ms o economic g ow h and as a sou ce o g eenhouse gas p oduc ion. In his con ex , he au ho s p opose a ne wo k-based model o ene gy consump ion in In e ne in as uc u e. This model aims o iden i y he elemen s o he In e ne ha domina e i s ene gy con- sump ion as access inc eases o e ime. This knowledge is essen ial o de ine s a egies o imp o e he ene gy e i- ciency o he In e ne . They belie e ha he ene gy consump ion o da a cen es and con en deli e y ne wo ks is domina ed by he ene gy consump ion o da a s o age o in equen ly downloaded ma e ial and by da a anspo o equen ly downloaded ma e ial. Deng e al. [30], using da a om he TOP500 and G een500, ela e he ene gy e iciency o he Linpack e iciency in he yea 2012, and compa e hei e olu ion om 2007 o 2012 o hese pa ame e s conside ing a ious ypes o ne wo ks (Gigabi , In iniband, p op ie a y, and cus om/o he s), a chi ec u es (MPP, clus e ), leading en- do s, and p ocesso amilies. In 2013, he JASON g oup published a highly in e es - ing epo on he echnical challenges and echnological implica ions o supe compu ing om 1 PFLOPS (10 15 FLOPS) o 1 EFLOPS (10 18 FLOPS) [31]. This s udy analysed he e olu ion and ex apola ion o u u e yea s o a ious pa ame e s o high-pe o mance compu e s such as peak pe o mance (1993–2009), ene gy cos s o compu- a ional ope a ions (2012 and 2020), ela ionship be ween memo y bandwid h and ene gy, and ene gy consumed pe FLOP (1996–2024). They conclude ha , while a six- old educ ion in ene gy consump ion o loa ing-poin ope a- ions was achie ed by 2020, he imp o emen is mo e modes (hal as much) o on-chip communica ion. Finally, hey show ha he e is a la ge dispa i y be ween he ene gy cos o loa ing-poin compu ing and access o o -chip memo y. In 2012, a DRAM access, wi h 64-bi wo ds, equi ed 1.2 nJ, and in 2020 i is educed by a ac o o 4 ( o 320 pJ). Sub amaniam e al. [32] analyse he 2008 DARPA p ojec o build an exascale supe compu e (10 18 FLOPS) by 2020 wi h a maximum powe consump ion o 20 MW o make i economically easible [33]. They conclude ha , gi en he pa ame e s o he momen in which hey w o e hei a icle (2013), a 56.8- old imp o emen in compu a- ional pe o mance would be equi ed wi h only a 2.4- old inc ease in ene gy consump ion, which would be unachie able by 2020 i ene gy e iciency we e o be inc eased in line wi h Koomey’s Law. Using da a om he G een500 om 2007 o 2012, hey p ojec he end in HPC ene gy e iciency o 2020, concluding ha un o una ely i would be 7.2 imes below he e iciency needed o mee DARPA’s 20 MW EFLOPS a ge . Also, in hei pape hey showed ha he e ogeneous compu e s (i.e., sys ems using GPUs o o he co-p ocesso s) and cus om-buil sys- ems con inue o ha e a be e o e all ene gy e iciency han hei con en ional coun e pa s. Van Heddeghem e al., in a 2014 a icle [34], e alua ed how he elec ici y consump ion caused by he use o ICT e ol ed om 2007 o 2012. They analysed h ee main domains o ICT: communica ion ne wo ks, pe sonal com- pu e s and da a cen es. They p o ided a de ailed desc ip- ion o how hey ob ained he esul s o he e olu ion o 42 Page 6 o 24 Clus e Compu ing (2025) 28:42 123 elec ici y consump ion in each domain. Thei es ima es show ha he annual g ow h in each o he a eas (10%, 5% and 4%, espec i ely) was g ea e han he g ow h in global elec ici y consump ion in he same pe iod (3%). The el- a i e sha e o his subse o ICT p oduc s and se ices in o al global elec ici y consump ion inc eased om a ound 3.9% in 2007 o 4.6%in 2012. The con ibu ion o absolu e elec ici y consump ion o each o he a eas u ned ou o be app oxima ely he same. I ollows ha esea ch should be ca ied ou on inc easing ene gy e iciency in all hese a eas, ins ead o ocusing on jus one o hem. Vic o Zhi no and collabo a o s published a e y in e es ing wo k in 2014 [35], in which hey p esen a i- ous models o es ima e he minimum compu ing ene gy consump ion in compu e sys ems. They ob ain om hei models and using eal da a, he ene gy e iciency o di - e en bina y elemen s (logic de ices and memo y ele- men s) conside ing he e olu ion o he consump ion o indi idual ansis o s and mic op ocesso s o e ime and he dynamics o he physical p ocesses ha ake place in he di e en componen s (capaci i e and esis i e e ec s, e c.). They s a e ha while wo ld ene gy p oduc ion has g own linea ly, he demand o elec ici y om compu e s has g own exponen ially. In ypical si ua ions, he mini- mum amoun o ene gy equi ed pe bi is conside ed o be a ound 10 –14 J, wi h his igu e being used o lap ops and PCs as well as supe compu e s. Fu he mo e, Vic o Zhi - no in his a icle es ima es ha in p ac ice imp o emen s a e possible o each a p ac ical lowe bound o sys em- le el powe consump ion, o app oxima ely 10 –17 J/bi , which can be conside ed as a challenge o achie e. Ano he o he conclusions o he epo is ha , i he end con- inues upwa ds, he consump ion o all his huge echno- logical equipmen could exceed he wo ld’s elec ici y p oduc ion by yea 2040. The e o e, a adical imp o emen in he ene gy e iciency o he IT equipmen is needed. Zhi no ’s conclusions we e collec ed a yea la e (2015) in a epo published by he U.S. Semiconduc o Indus y Associa ion in collabo a ion wi h he Semiconduc o Resea ch Co po a ion (SRC) and he Na ional Science Founda ion [36]. In 2015 and 2019, And ae and Edle analysed and modelled he elec ic powe use o ICT, making o ecas s un il 2030. The 2015 s udy [37] conside s h ee di e en scena ios o he use and p oduc ion o consume de ices, communica ion ne wo ks and da a cen es: he bes , he expec ed, and he wo s . One o he conclusions o he s udy is ha , in he wo s case, ICT could consume up o 51% o elec ici y in 2030, gene a ing up o 23% o he g eenhouse gas emissions eleased wo ldwide ha yea . In he 2019 wo k [38], hey es ima ed ha consump ion om 2019 o 2030 has been lowe han he da a and expec a ions hey made in 2015. Al hough hese s udies p ojec ene gy consump ion o e 15 and 11 yea s and ob ain e y spec- acula igu es, hey do no su icien ly app ecia e he impo ance o imp o emen s in he ene gy e iciency o he de ices. Fu he mo e, gi en he changing na u e o com- pu e echnology, making p edic ions o e so many yea s is no easonable. Pang le in his 2015 wo k [39], wi h da a ob ained om he No embe 2014 lis o he G een500, ela es ene gy e iciency o compu ing pe o mance, and makes es ima es o he o al powe consumed by supe compu e s un il 2022. The conclusion is ha i will each app oxima ely 20 MW. Gao and Zhang in 2016 [40] p esen and analyse he co ela ions o he Linpack and powe e iciencies om 2011 o 2015 in he TOP500 and G een500 lis s. They g oup he supe compu e s on he lis s acco ding o hei a chi ec u e: homogeneous o he e ogeneous, depending on whe he hey use a single o a ious ype o p ocesso o co e, and including as a subse wi hin each class he ype o in e connec ion (In iniBand, Gigabi E he ne , and cus- om). Wi hin each g oup hey analyse he pe o mance and powe beha iou s. They conclude ha he e ogeneous sys- ems imp o e pe o mance o ene gy e iciency no by adding he same ype o p ocesso s, bu by adding di e en p ocesso s o cop ocesso s, which usually ha e specialised capabili ies o speed up massi e pa allel asks. Mos wo ks on he impac o ICT on he global p o- duc ion o g eenhouse gas emissions only e e o he elec ici y p oduced by he use o he de ices. Howe e , he wo k o Belkhi and Elmeligi [41] es ima es he ene gy necessa y o he manu ac u e o ICT componen s, ha is, he ene gy o he p oduc ion phase, which is a ixed alue pe de ice p oduced, and does no o e look he ene gy cos s o he use phase which is a a iable alue. The au ho s also analyse a hi d pa ame e consis ing o es i- ma ing he inc ease in ene gy consump ion caused by he sho ening o he use ul li e (li ecycle) o he de ices. Reducing his leads o mo e equen esales and, he e o e, mo e pu chases o new p oduc s, hus inc easing p oduc- ion ene gy consump ion occu s. These and o he e ec s a e analysed in ha wo k, whe e hey also make a o ecas o ICT oo p in as a pe cen age o global oo p in p o- jec ed o 2040 using bo h an exponen ial and linea i s. Mo ley e al. [42] make a con o e sial app oach by p oposing ha he g owing educ ion in elec ical con- sump ion caused by digi al in as uc u es, a he han he imp o emen o echnological e iciency (e icien se e s and cooling echnologies), equi es limi ing he g ow h o digi al a ic. Thei s udy ocuses on de e mining he maximum daily da a demand and, he e o e, he peak elec ici y consump ion o da a cen es. These peaks a e p ima ily due o he la ge olume o da a ans e o he ansmission o s eaming ideo and in e ac i e ideo, ha is, IP a ic om use s o da a cen es. Clus e Compu ing (2025) 28:42 Page 7 o 24 42 123 Hin emann and Hin e holze in 2019 [43] collec da a om a ious sou ces on ene gy consump ion o se e s and da a cen es wo ldwide and show how he a ious s udies p esen ed di e signi ican ly. They b ie ly analyse possible scena ios o consump ion o 2030, which gi e a ious esul s anging om, in he bes case, keeping ene gy consump ion cons an , o, in he wo s scena io, an inc ease by a ac o o 40 by 2030 (compa ed o 2015). Koo and Wijnho en [44] p esen ed a o ecas ing model o da a cen e elec ici y needs based on unde s anding usage g ow h. To make hei o ecas s, hey use da a om, among o he sou ces, Cisco Sys ems om 2010 o 2021 [45], de e mining he ene gy needs un il 2023 using hei model. The simula ion shows exponen ial g ow hs o da a cen e usage. Thei esul s a e compa ed wi h he p ojec- ions ob ained in 2020, independen ly by And ae [37] and Masane e al. [46] be ween 2016 and 2030. The conclusion o his a icle is ha u u e ene gy demands o global da a cen es emain cons an due o echnological inno a ions, e en as bo h consume and en e p ise wo kloads appea o g ow exponen ially o e he nex decade. Howe e , he end o Moo e’s law is likely o cause exponen ial g ow h in da a cen e elec ici y consump ion, while unce ain y in bo h echnological and beha iou al e olu ion explains he disc epancies ound in he cu en li e a u e. In 2022, Hadla and Se hi [47] de eloped an ICT con- sump ion model o 16 coun ies in eme ging economies ha uses, as basic da a, In e ne pene a ion and he numbe o mobile subsc ip ions in ela ion o CO 2 emissions pe pe son. They analysed he pe iod om 2000 o 2018 and conclude ha bo h he numbe o mobile phones and he use o he In e ne inc ease cons an ly. Ne e heless, he slope o g ow h o gas emissions is gen le . This indica es ha CO 2, in hese eme ging coun ies, inc eased a a slowe a e han he use o ICT. Ka al e al. in 2023 [48] w o e a su ey pape con- ce ning so wa e-based echnologies ha can be used o building g een da a cen es and ha include powe man- agemen a he so wa e le el. They desc ibe he exis ence o new g een cloud compu ing app oaches a he i uali- sa ion le el, ope a ing sys em le el and applica ion le el. They also ecommend he use o con aine echnology o educe ene gy consump ion and achie e he challenge o ob aining mo e sus ainable da a cen es. In he a icle by Fa ima e al. [49], he en i onmen al impac o da a cen es is e alua ed and he ac o s ha cause CO 2 emissions a e iden i ied. Common s a egies ha can help make da a cen es mo e sus ainable a e dis- cussed. They also analyse h ee da a cen es ha ha e claimed o be g een, o iden i y how hey achie e hei sus ainabili y goals. Fo example, educed ca bon emis- sions, ypes o ene gy esou ces used, and how hey es ained e-was e p oduc ion. They conclude by sugges ing a consump ion educ ion amewo k based on he concep s desc ibed. In a ecen a icle, Malmodin e al. [50] p esen ed a s udy in which hey es ima e, o he yea 2020, ha he o al elec ici y consump ion and g eenhouse gas emissions p oduced by he use o he ICT sec o di ided in o h ee pa s: use de ices including he in e ne o hings, ne - wo ks and da a cen es. They conclude ha globally he ICT sec o consumed a ound 4% o he wo ld’s elec ici y wi h he use o compu ing and digi al communica ions equipmen , accoun ing o a ound 1.4% o global g een- house gas emissions in 2020. In absolu e e ms, o al g eenhouse gas emissions we e 5% highe han in 2015. Acco ding o hese esul s, emissions om he ICT sec o ha e e ol ed in line wi h he es o he wo ld. Howe e , despi e he challenges o many companies, he ICT sec o did no educe i s emissions be ween 2015 and 2020 o mee he deca bonisa ion a ge s se by o ganisa ions such as he ITU, GSMA, GESI and SBTi, so e o s o educe ICT ene gy consump ion need o be scaled up and inc eased. The abo e-men ioned wo ks desc ibe he e olu ion o ene gy e iciency and elec ici y consump ion in ICT, bu changes a e cons an ly occu ing in his ield. They use di e en da a sou ces and co e e y di e se objec i es and app oaches such as consump ion o da a cen es, se - e s, in o ma ion a ic o e he In e ne o mobile phones. They also ocus on a ious aspec s such as he consump- ion o compu e subsys ems o how o limi e-was e p o- duc ion. In any case, conside ing he con inuous echnological ad ances in compu e a chi ec u e, hese analyses and p ojec ions need o be e iewed equen ly o be alid, so he ocus o his wo k is o achie e his. One o he cha ac e is ics o he p esen wo k is o use as a base da a ob ained om expe imen al measu emen s ha a e public and alida ed by he scien i ic communi y. Speci i- cally, hose ob ained om he G een500 and TOP500 lis s. The s udy ca ied ou uses a la ge amoun o da a, unlike he a icles e e enced abo e. These da a co e om June 2008 o No embe 2023 and includes a o al o 8364 compu e s, gi ing g ea alidi y o he esul s ob ained. Many o he compu e s appea epea ed in he lis s, edi ion by edi ion, bu , in gene al, hei con igu a ions and ea u es a e upda ed yea by yea . On he o he hand, he me hod- ology used o measu e he ene gy consumed by he sys ems used is uni o m and public [51] and conside s he ene gy consump ion o all he elemen s ha make up he compu e sys em and hose o he ins alla ion whe e i is loca ed (ai condi ioning, ene gy ans o ma ion, ligh ing, e c.). The ene gy consump ion o ICT is de e mined by he use o compu ing and elecommunica ions equipmen ( h ough he execu ion o applica ions) and he ene gy e iciency o said equipmen . F om a comme cial and 42 Page 8 o 24 Clus e Compu ing (2025) 28:42 123 echnological poin o iew, i does no make sense o limi he use o esou ces demanded by use s, so e o s should ocus on imp o ing ene gy e iciency, his being he pa ame e mainly analysed in his pape . 2.4 E iciency and pe o mance in compu ing As indica ed in Sec . 2.2, usually, and in pa icula wi h Linpack, he Rmax alue is conside ed as a measu e o pe o mance (p ocessing speed). This pa ame e indica es he maximal double p ecision (64 bi s) loa ing-poin ins uc ions p ocessed pe second (MFLOP/s, o , in sho , MFLOPS). The heo e ical peak pe o mance (Rpeak) is also used o measu e compu ing speed. The alue o his pa ame e is de e mined by he pa icula a chi ec u e o he compu e sys em as i depends on he o al numbe o co es ac ing in pa allel, he p ocesso speed (clock equency), and he numbe o addi ions and mul iplica ions in loa ing-poin ull p ecision ha can be pe o med in one clock cycle. A dis ibu ed sys em, in gene al, is s uc u ed in acks, each o which is composed o nodes, whe e in each node he e a e CPU socke s con aining mul iple co es (CPUs). In his way, he heo e ical peak pe o mance can be exp essed as [52]: Rpeak ¼ acks nodes ack socke s node co es socke cycles second FLOP ins uc ions cycle ð5Þ whe e FLOP ins uc ions/cycle ep esen s he a e age numbe o ins uc ions execu ed pe cycle in each o he co es, conside ing he implici ins uc ion-le el pa allelism. Ano he pa ame e o in e es is he compu ing e i- ciency (CE), which is de ined as he a io be ween he maximum measu ed pe o mance and he peak pe o mance: CE ¼Rmax Rpeak ð6Þ The compu ing e iciency measu es he u ilisa ion a e o sys em’s compu a ion esou ces du ing he execu ion o a p og am. This pa ame e ies o assess how he in e- g a ion and coo dina ion be ween all he elemen s o a compu e (co es, memo y s o age subsys em, in e connec subsys em, e c.) a ec he o e all u ilisa ion o compu a- ion esou ces. To calcula e he alue o CE in he TOP500 lis s, Rmax is measu ed by execu ing he Linpack ool, so he pa ame e CE is o en e e ed o as Linpack e iciency. The ene gy e iciency (EE) alue de ined by Eq. (2), ha is, he numbe o execu able compu a ions pe uni o ene gy consumed, can also be ob ained as he quo ien be ween he sys em pe o mance (R) and he a e age powe (P) consumed by he sys em o deli e he measu ed pe o mance. Indeed, conside ing ha he numbe o compu a ions pe o med in a ime is NC =R and he ene gy consumed du ing i s execu ion is E=P , EE can be calcula ed as: EE ¼NC E¼R P ¼R P¼Pe o mance Powe !FLOPS Wa ð7Þ In o he wo ds, ene gy e iciency also ep esen s he pe o mances pe wa . I each compu a ion is conside ed o consis o he execu ion o a loa ing-poin ins uc ion (FLOP), he pe o mance will be exp essed in FLOPS and he ene gy e iciency in FLOPS/W. Knowing he ene gy e iciency in ins uc ions/W, i is possible o ob ain i in bi s/W by simply conside ing he a e age numbe o bi s pe ins uc ion. Indeed, he numbe o bi s (NB) can be exp essed as he numbe o ins uc ions (NI) mul iplied by he a e age numbe o da a bi s pe ins uc ion (NBI): NB ¼NI NBI ð8Þ In HPCs, i is common o ope a e wi h double p ecision da a so, in hese cases, NBI = 64 bi s. In o de o sum- ma ise he e olu ion o e ime o some pa ame e s, and o be able o easily make compa isons, he ime necessa y o achie e a ce ain objec i e, o example, doubling i s alue, is used. I y ep esen s he alue o he pa ame e and he ime, he slope o he cu e y= ( ) a each poin ep esen s he ins an aneous g ow h a e (m). I he unc ion y= ( ) we e exponen ial, i s loga i hmic ep esen a ion, ln(y) e sus , would co espond o a s aigh line, being he slope: m¼Dln yðÞ½ D ¼lnðy2Þlnðy1Þ 2 1 ¼ ln y2 y1  D ð9Þ To ind he ime in e al (D ) equi ed o he alue o he pa ame e y o double, simply subs i u e y 2 =2y 1 o he abo e equa ion, so ha : m¼ln 2ðÞ D !D ¼ln 2ðÞ m¼0:6931 mð10Þ Tha is, he ime equi ed o a doubling o he alue o y can be ob ained by di iding 0.6931 by he alue o he slope (m). 3 Me hodology and da a The p esen s udy is based on he o iginal da a om Koomey [26,27] and he TOP500 and G een500 lis s [1] eleased wice a yea . Clus e Compu ing (2025) 28:42 Page 9 o 24 42 123 ha each inc ease in pe o mance o 1 TFLOPS p oduces only an imp o emen o 1 MFLOPS/W in ene gy e iciency. As shown in Fig. 6, acco ding o he o ecas s made in his pape , he Landaue limi will be eached in app oxi- ma ely he yea 2090. This means ha , i he ene gy e i- ciency o i e e sible in o ma ion p ocessing ollows he end o he las 16 yea s, he limi will be eached a ound 2090. This is because, as desc ibed in Sec . 4.5, acco ding o he second p inciple o he modynamics, i is physically impossible o i e e sibly p ocess in o ma ion consuming less han &310 –21 J/bi o ene gy. The p ocessing o a bi is iden i ied as a logical swi ching o elemen a y compu- a ion. The e a e o he p edic ions, such as ha o Feyn- man, which assume a h ee-a om ansis o o calcula e his limi , se ing i a app oxima ely 2.010 –18 J/bi [66,68,69]. I should be no ed ha , in he case o e e - sible compu a ions (as occu s in he ield o quan um compu ing), he alue deduced by he Ma golus-Le i in Theo em should be used as he lowe limi o ene gy consump ion, which is &3.010 –34 J/bi [79]. Fo con en ional (non-quan um) compu ing, i he inc ease in pe o mance ollows he end o he las 15 yea s (doubling e e y 1.85 yea s, in line wi h Moo e’s Law) when he Landaue limi is eached, he pe o mance would be o he o de o Rmax &10 14 TFLOPS. Conce ning he posi ion occupied by he #1 G een500 compu e s in he TOP500 ables o he same edi ions (Fig. 7a), i is obse ed ha 19% o G een500 winne s occupy he i s qua ile o he TOP500; 24% he second qua ile; 33% he hi d qua ile and 24% he ou h qua ile. On he con a y, o he case o he posi ion occupied by he #1 TOP500 compu e s in he G een500 ables (Fig. 7b), i was concluded ha om 2013 o 2015 hey occupied posi ions anging om 30 o 90, g adually dec easing posi ions o he G een500, un il eaching posi ion 90. Howe e , om 2016 o 2023, he ene gy e iciency sub- s an ially imp o ed since he i s compu e in he TOP500 o each lis occupies posi ions anging be ween 1 and 26 o he G een500 (Fig. 7b). 6 Discussion and conclusions Rega ding he da a sou ce used in his wo k, i should be no ed ha clea p o ocols on he me hodology mus be ollowed o ake measu emen s o compu e s o be inclu- ded in he TOP500 and G een500 lis s. Howe e , he esul s a e p o ided by hose esponsible o he da a cen es hemsel es, wi h li le o no independen con ols o e i y hei au hen ici y. Indeed, hose esponsible o p epa ing he lis s, in addi ion o checking di e en sou ces o in o ma ion, limi hemsel es o andomly selec ing a s a is ical ep esen a i e sample o he i s 500 sys ems o hei da abase, pe o ming an audi on hem. Fo example, he me hodology o be ollowed in he G een500 mea- su emen s [51] es ablishes ha , o he calcula ion o ene gy e iciency, he elec ical consump ion o all com- pu a ional nodes, any in e connec ne wo k he applica ion uses, any head o con ol nodes, any s o age sys em he applica ion uses, all powe con e sion losses inside he compu e , and any in e nal cooling de ices (sel -con ained liquid cooling sys ems and ans), mus be included. Ne - e heless, no p ocedu es a e de ined o e i y ha his is done co ec ly. Ano he issue o in e es is o highligh ha Linpack is a benchma k aimed a measu ing compu ing powe in applica ions ha equi e in ensi e calcula ion (a lo o da a including ec o and ma ix ope a ions), bu i may no co ela e well wi h some eal wo kloads o cu en supe - compu e s o gene al-pu pose compu e s (which ollow o he objec i es and ends). In hese cases, Linpack would no e lec he ha dwa e imp o emen s designed o ob ain g ea e e iciency in o he pa icula ypes o wo kloads. (a) Compu ing pe o mance o he #1 G een500 compu e s in he TOP500 lis . (b) Ene gy e iciency o he #1 TOP500 compu e s in he G een500 lis . Fig. 7 Posi ion in he TOP500 and G een500 lis s o he i s G een500 and TOP500 compu e , espec i ely, wi hin he same edi ion 42 Page 16 o 24 Clus e Compu ing (2025) 28:42 123 No wi hs anding wha has been said in he p e ious pa ag aphs, he TOP500, oge he wi h he G een500, cons i u es an excep ional and open mee ing poin o sci- en is s and enginee s. In ac , hese wo ankings a e use ul o analyse he si ua ion and ends in he e olu ion o he cha ac e is ics o HPC sys ems, as well as compa ing di - e en equipmen (always conside ing he indica ed limi- a ions). Mo eo e , Linpack has been in use o decades and allows consis en compa isons o e ime and emains a e y use ul ool. This wo k has been ca ied ou based on Koomey da a co e ing he yea s 1946 o 2010 and he TOP and G een500 lis s om 2008 o June 2023. I has been p o en ha he ene gy e iciency o HPCs be ween he las abo e- men ioned yea s g ew exponen ially, doubling e e y 2.29 yea s. This conclusion has been ob ained h ough a eg ession analysis wi h coe icien o de e mina ion o 2 = 0.9916, conside ing a o al o 9,682 HPCs included in he 30 lis s used. I mus be no ed ha in successi e lis s many supe compu e s a e epea ed, al hough hei con ig- u a ions and cha ac e is ics a e gene ally upda ed lis by lis . The esul ob ained indica e ha he g ow h o ene gy e iciency is occu ing a a slowe a e han ha ob ained by Koomey in 2011 wi h da a be ween 1946 and 2009, which was doubling e e y 1.57 yea s wi h a coe icien o de e - mina ion o 2 = 0.983. Howe e , he esul has been ob ained using as ‘‘compu a ions double p ecision loa ing poin ins uc ions’’, and in he case o Koomey, as men- ioned in Sec . 5, he concep o ‘‘compu a ion’’ is based on he wo k o No dhaus [70]. This p esen wo k has ocused on analysing he e olu- ion o he ene gy e iciency o he mos powe ul supe compu e s in he wo ld compiled in he TOP500 lis s, ep esen ing he en i e y o each lis by hei a e age al- ues. I is wo h no ing ha many supe compu e s a e epea ed h oughou edi ions, bu gene ally hei s uc u es a e modi ied, ei he by simply adding mo e nodes and acks o by changing some o hem o mo e powe ul o ene gy- e icien compu ing uni s. These lis s e lec he eali y o he compu e s ha ope a e e e y yea . Ano he app oach o g ea in e es is he one ollowed by Koomey [80], which ies o e lec he imp o emen s o e ime o he cu en echnical abili y o c ea e new compu ing de ices. To do his, he conside s supe compu e s only in hei yea o i s ope a ion, so he does no e lec machines beyond his da e. In he indica ed wo k by Koomey, bo h compu ing powe and ene gy e iciency a e analysed. The ollowing con- clusions a e d awn wi h espec o ene gy e iciency in da a ha is cleaned o include only equipmen in i s i s yea o ope a ion: •The ene gy e iciency o he supe compu e sui e om 2009 o 2019 doubled e e y 2.14 yea s wi h 2 = 0.6. •The ene gy e iciency o he i s supe compu e om 2009 o 2019 doubled e e y 2.12 yea s wi h 2 = 0.86. •The ene gy e iciency o he op 10% o supe compu e s om 2009 o 2019 doubled e e y 2.11 yea s wi h 2 =0.7. These esul s a e summa ised in Table 5. I has also been shown ha , wi h he ends ob ained he e, he Landaue limi would be eached app oxima ely in he yea 2090, and he ene gy/bi equi alen o ha es ima ed by Feynman wi h 3-a om ansis o s in 2070. The e olu ion o o he pa ame e s has also been anal- ysed, such as compu ing pe o mance, which doubles e e y Table 5 Compa ison o esul s ob ained wi h hose o Koomey and Sub amaniam Re e ences Pa ame e Yea Da a sou ce Compu e s Analysed yea s Doubling yea s 2 Koomey EE 2009 Di e se Main ames, se e , gene al pu pose and PCs 1946–2009 1.57 0.983 Koomey EE 2009 Di e se PCs 1975–2010 1.52 0.970 Sub amaniam EE 2017 G een500 Top 100 o each lis 2007–2012 2,33 0.84 Koomey EE 2020 TOP500 TOP #1 (Lis s o compu e s in hei 1s yea o ope a ion) 2009–2019 2.12 0.86 Koomey EE 2020 TOP500 TOP 10% Lis s o compu e s in hei 1s yea o ope a ion 2009–2019 2,11 0,7 Koomey EE 2020 TOP500 Lis s o all compu e s in hei 1s yea o ope a ion 2009–2019 2.14 0.6 Koomey Rmax 2020 TOP500 Lis s o compu e s in hei 1s yea o ope a ion 2009–2019 1.66 0.73 P esen wo k EE 2024 G een500 A e age alue o each lis 2008–2023 2.29 0.99 P esen wo k EE 2024 G een 500 TOP #1 2008–2023 2.22 0.97 P esen wo k Rmax 2024 G een500 A e age alue o each lis 2008–2023 1.85 0.98 Clus e Compu ing (2025) 28:42 Page 17 o 24 42 123 1.85 yea s (in line wi h Moo e’s Law). I is assumed ha by inc easing compu ing pe o mance, he numbe o applica ions and use o compu e s will inc ease, so he numbe o compu a ions (NC) would inc ease. Unde his hypo hesis, i is wo ying ha ene gy e iciency is g owing a a slowe a e han pe o mance (doubling e e y 2.29 yea s compa ed o 1.85). Ano he un a ou able implica ion is ha he e migh be an e en ual nega i e end, al hough a he slow, in ene gy e iciency, i.e., i is possible ha i will dec ease u he in he u u e. Al hough he di e ence seems small, doubling ene gy e iciency e e y 1.85 yea s means inc easing i app oxima ely 43 imes in a decade, and doubling i e e y 2.29 yea s means inc easing i only abou 21 imes pe decade. The e o e, mo e needs o be done o ensu e ha ene gy e iciency g ows a leas as as as pe o mance. The esul s ob ained a e o in e es o esea che s, enginee s and manu ac u e s in o de o make o ecas s abou new p oduc s, ying o ensu e ha he e iciency inc ease exceeds ha o he demand o compu ing se ices. A common goal o ins i u ions owning HPC sys ems is o be included in he TOP500 lis , and wi hin i in leading posi ions. To his end, Linpack implemen a ions a e op i- mised o ake ull ad an age o he he e ogenei y in he sys ems and he di e en accele a o s, cop ocesso s, and specialised ha dwa e a ailable. In his way, he measu es p esen ed in he TOP500 a e cons an ly adap ed o e lec he imp o emen s in oduced by new concep s and ech- nologies in compu e a chi ec u e. Howe e , one mus be ca e ul wi h o ecas s, as new ideas and echnologies a e being esea ched. This is he case, o example, in he a ea o educing consump ion in se e s, s o age, ne wo ks, in e connec ions, powe con e sion and cooling sys ems, whe e he ollowing concep s, among o he s, can be ound [81]: •Changes in he de ices and in he in e nal a chi ec u e o he mic ochips [82–84]. •Managemen and planning o esou ce use, om low o high sys em le els, such as using he Dynamic Vol age and F equency Scaling (DVFS) echnique [85,86], Dynamic Powe Managemen (DPM) [86,87], o e en using powe capping p o ocols, es ablishing a ce ain powe h eshold o a de ice ha i canno exceed [88]. •Scale changes, in o de o plan and assign asks o he a ailable ha dwa e esou ces conside ing hei ene gy e iciency. Wi hin his a ea, i ualisa ion echnologies [48] ha e acqui ed g ea ele ance, which ha e been enhanced by he inc ease in scale o da a cen es h ough he me ge o ans o ma ion o medium-sized cen es o hype scale cen es (Google Cloud, Amazon Web Se ices, Mic oso Azu e, OVHCloud o Rack- space Open Cloud), whe e ene gy consump ion is be e managed [89–92]. An in e es ing aspec is ha he ul ima e objec i e is o educe he ene gy consumed in he execu ion o ou p o- g ams, a alue ha can be ob ained by applying Eq. (3), whe e in his case NC would be he numbe o ins uc ions execu ed by he p og am and EE he ene gy e iciency o he ha dwa e whe e hese ins uc ions a e execu ed. Con- sequen ly, o educe he ene gy consumed by he p og am, he ene gy e iciency o he ha dwa e de ices (EE) mus be inc eased and he numbe o ins uc ions (NC) mus be educed as much as possible, ha is, main aining he esponse imes and p ecision equi ed o he esul s. The e o e, om an ene gy poin o iew, i is ex emely impo an , no only o inc ease ene gy e iciency, as con- side ed in his wo k, bu also o use echniques o e icien algo i hm de elopmen : HW/SW codesign p ocedu es, compile s, and so wa e, in gene al, bo h o gene al-pu - pose compu e s and o speci ic applica ions. As Leise son [93] poin s ou , as minia u isa ion app oaches i s limi s, b inging an end o Moo e’s law, pe o mance imp o e- men s will ha e o come om wha migh be called he h ee ‘‘ op end’’ echnologies: so wa e, algo i hms and ha dwa e, o dis inguish hem om he adi ional ‘‘bo om end’’ echnologies (semiconduc o physics and silicon ab ica ion echnology). These h ee op echnologies ha e a key ole o play in educing he ene gy consump ion o ICT. Koomey and Masane indica e ha ‘‘IT changes so quickly ha mos da a cha ac e izing i a e obsole e in sho o de ’’ [94], so ha in his wo k we ha e ied o upda e some o he o ecas s made. Howe e , due o he g ea imp o emen s ha a e cons an ly being in oduced, i is ad isable ha he p ojec ions p esen ed should be only conside ed o a ew yea s. Appendix See Tables 6,7,8. 42 Page 18 o 24 Clus e Compu ing (2025) 28:42 123 Table 6 Da a om he compu e s wi h he highes ene gy e iciency, ex ac ed om TOP500 and GREEN500 lis s Sou ce G een500 edi ion TOP500 Rank Name Rmax (TFLOPS) Rpeak (TFLOPS Rmax/ Rpeak Powe (kW) Maximum ene gy e iciency (GFLOPS/ W) Peak ene gy e iciency (GFLOPS/W) TOP500 2008-06 324 BladeCen e QS22 Clus e 11.11 18.28 0.61 22.76 0.49 0.80 TOP500 2008-11 220 BladeCen e QS22 Clus e 18.57 30.46 0.61 34.63 0.54 0.88 TOP500 2009-06 422 BladeCen e QS22 Clus e 18.57 30.46 0.61 34.63 0.54 0.88 TOP500 2009-11 445 GRAPE-DR accele a o Clus e 21.96 84.48 0.26 51.20 1.65 1.65 TOP500 2010-06 131 QPACE SFB TR Clus e 44.50 55.71 0.80 57.54 0.77 0.97 TOP500 2010-11 115 NNSA/SC Blue Gene/Q 65.35 104.86 0.62 38.80 1.68 2.70 TOP500 2011-06 109 NNSA/SC Blue Gene/Q P o . 2 85.88 104.86 0.82 40.95 2.10 2.56 TOP500 2011-11 64 BlueGene/Q 172.49 209.72 0.82 85.12 2.03 2.46 TOP500 2012-06 252 BlueGene/Q 86.35 104.86 0.82 41.09 2.10 2.55 TOP500 2012-11 253 Beacon 110.50 157.55 0.70 45.11 2.45 3.49 G een500 2013-06 467 Eu o a 98.51 175.67 0.56 30.70 3.21 5.72 G een500 2013-11 311 TSUBAME- KFC 125.10 217.66 0.57 27.78 4.50 7.84 G een500 2014-06 439 TSUBAME- KFC 151.80 217.82 0.70 34.58 4.39 6.30 G een500 2014-11 168 L-CSC 301.30 593.60 0.51 57.15 5.27 10.39 G een500 2015-06 160 Shoubu 353.82 842.96 0.42 50.32 7.03 16.75 G een500 2015-11 133 Shoubu 353.82 1535.83 0.23 50.32 7.03 30.52 G een500 2016-06 94 Shoubu 1001.01 1533.46 0.65 149.99 6.67 10.22 G een500 2016-11 28 DGX Sa u nV 3307.00 4896.51 0.68 349.50 9.46 14.01 G een500 2017-06 61 TSUBAME3.0 1998.00 3207.63 0.62 141.60 14.11 22.65 G een500 2017-11 259 Shoubu sys em B 841.96 1127.68 0.75 49.50 17.01 22.78 G een500 2018-06 359 Shoubu sys em B 857.63 1127.68 0.76 46.60 18.40 24.20 G een500 2018-11 374 Shoubu sys em B 1063.31 1353.22 0.79 60.40 17.60 22.40 G een500 2019-06 469 DGX Sa u nV Vol a 1070.00 1819.75 0.59 97.00 15.11 18.76 G een500 2019-11 159 A64FX p o o ype 1999.50 2359.30 0.85 118.48 16.88 19.91 G een500 2020-06 393 MN-3 1621.10 3922.33 0.41 76.80 21.11 51.07 G een500 2020-11 170 NVIDIA DGX Supe POD 2356.00 2812.80 0.84 89.94 26.20 31.27 G een500 2021-06 336 MN-3 1822.40 3137.87 0.58 61.36 29.70 51.14 G een500 2021-11 301 MN-3 2181.20 3389.52 0.64 55.39 39.38 61.19 G een500 2022-06 29 F on ie TDS 19,200.00 23,105.54 0.83 308.68 62.68 74.85 G een500 2022-11 405 Hen i 2038.00 5417.34 0.38 31.31 65.09 173.02 G een500 2023-06 255 Hen i 2882.00 3579.13 0.81 44.07 65.40 81.21 G een500 2023-11 293 Hen i 2882.00 3579,13 0.81 44.07 65.40 81.21 Clus e Compu ing (2025) 28:42 Page 19 o 24 42 123 Table 7 A e age alues calcula ed in each TOP500 and G een500 lis Sou ce G een500 edi ion Rmax (TFLOPS) Rpeak (TFLOPS) Compu ing e iciency (Rmax/ Rpeak) Powe (kW) Numbe o sys ems wi h powe da a Maximum ene gy e iciency (GFLOPS/W) Peak ene gy e iciency (GFLOPS/W) TOP500 2008-06 29.57 44.03 0.63 253.41 247.00 0.12 0.19 TOP500 2008-11 44.70 30.46 0.62 359.83 253.00 0.13 0.21 TOP500 2009-06 57.98 84.14 0.63 387.30 238.00 0.15 0.24 TOP500 2009-11 69.50 98.33 0.66 401.53 238.00 0.27 0.27 TOP500 2010-06 72.75 99.90 0.67 398.42 257.00 0.20 0.28 TOP500 2010-11 110.24 160.56 0.71 476.50 263.00 0.24 0.35 TOP500 2011-06 151.46 211.30 0.68 545.92 274.00 0.25 0.38 TOP500 2011-11 188.52 271.22 0.66 592.86 283.00 0.33 0.54 TOP500 2012-06 343.50 463.35 0.68 667.37 293.00 0.50 0.74 TOP500 2012-11 445.74 613.24 0.70 684.78 281.00 0.63 0.93 G een500 2013-06 489.53 701.51 0.68 988.17 500.00 0.49 0.71 G een500 2013-11 497.77 729.11 0.69 1100.05 500.00 0.58 0.81 G een500 2014-06 546.04 807.00 0.68 1124.37 500.00 0.64 0.91 G een500 2014-11 615.73 907.01 0.69 1184.62 500.00 0.75 1.10 G een500 2015-06 723.21 1026.25 0.72 1222.06 500.00 0.92 1.29 G een500 2015-11 834.18 1277.91 0.68 1321.90 500.00 1.01 1.56 G een500 2016-06 1139.83 1698.32 0.67 1271.98 500.00 1.13 1.68 G een500 2016-11 1350.86 2038.37 0.67 1335.91 500.00 1.29 1.91 G een500 2017-06 1496.74 2264.48 0.66 1305.55 500.00 1.58 2.41 G een500 2017-11 1690.24 2678.68 0.64 1502.84 305.00 2.25 3.35 G een500 2018-06 2421.83 3843.33 0.64 1602.57 263.00 2.64 3.98 G een500 2018-11 2809.84 4396.78 0.64 1755.46 234.00 2.97 4.60 G een500 2019-06 3119.52 4934.48 0.63 1756.60 209.00 3.17 5.12 G een500 2019-11 3294.41 5496.72 0.64 1555.19 214.00 3.77 6.43 G een500 2020-06 4412.27 6957.84 0.64 1673.28 206.00 4.21 7.20 G een500 2020-11 4857.52 7692.07 0.62 1727.63 189.00 4.88 8.24 G een500 2021-06 5593.44 8854.21 0.63 1899.95 182.00 6.24 10.16 G een500 2021-11 6073.72 9577.79 0.62 1753.91 179.00 7.27 12.11 G een500 2022-06 8806.17 13,696.88 0.61 1782.65 191.00 8.74 13.71 G een500 2022-11 9728.77 15,081.39 0.60 1780.59 195.00 10.40 16.32 G een500 2023-06 10,478.05 15,651.84 0.61 1813.99 188.00 11.80 18.08 G een500 2023-11 14,063.68 21,319.25 0,66 2068.71 190.00 12.66 18.92 42 Page 20 o 24 Clus e Compu ing (2025) 28:42 123 Acknowledgemen s The au ho s app ecia e he coope a ion o Ch is ian Mo illas, Jesu ´s Gonza ´lez and F ancisco Ille as ( om he Depa men o Compu e Enginee ing, Au oma ics and Robo ic o he Uni e si y o G anada, Spain) on his wo k. Au ho con ibu ions All au ho s ha e con ibu ed o he s udy con- cep ion and de elopmen o his wo k. A.P. pe o med supe ision, concep ualiza ion and me hodology. B.P. pe o med o mal analysis and in es iga ion. B.P. and J.J.E. p epa ed da a collec ion and anal- ysis. J.J.E. and T.L. pe o med alida ion o esul s. B.P. and J.J.E. w o e he i s d a o he manusc ip . All au ho s e iewed and app o ed he inal e sion o manusc ip . Funding This wo k was pa ially suppo ed by G an PID2022- 137461NB-C31 unded by MICIU/AEI/10.13039/501100011033 and by ‘‘ERDF/EU’’, G an PID2022-137461NB-C32 unded by MICIU/ AEI/10.13039/501100011033 and by ‘‘ERDF/EU’’, and P ojec PPJIA2023-025 unded by he Uni e si y o G anada (Spain). Da a a ailabili y Da a is p o ided wi hin he manusc ip . The da a and esul s p esen ed in his a icle can be used eely, always s a ing i s sou ce. The sou ce da a can be consul ed eely a h ps://www. op500.o g/lis s/g een500 (G een500 lis ), and a h ps://www. op500. o g (TOP500 lis ). 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To iew a copy o his licence, isi h p://c ea i ecommons.o g/licenses/by-nc-nd/4. 0/. Re e ences 1. Koomey, J.G., Be a d, S., Sanchez, M., Wong, H.: Assessing ends in he elec ical e iciency o compu a ion o e ime. - IEEE Ann. His . Compu . 17 (2009) 2. Koomey, J., Be a d, S., Sanchez, M., Wong, H.: Implica ions o his o ical ends in he elec ical e iciency o compu ing. IEEE Ann. His . Compu . 33(3), 46–54 (2011) 3. TOP500 The lis . h ps://www. op500.o g/. 4. G een500 lis , h ps://www. op500.o g/lis s/g een500/ 5. P ie o, B., Escoba , J.J., Go ´mez-Lo ´pez, J.C., Dı ´az, A.F., Lam- pe , T.: Ene gy e iciency o pe sonal compu e s: a compa a i e analysis. Sus ainabili y 14(19), 12829 (2022) 6. B ynjol sson, E.: Is Koomey’s Law eclipsing Moo e’s Law?. Economics o In o ma ion Blog. MIT (2011) 7. G eene, K.: A new and imp o ed Moo e’s law. MIT Technol- ogy Re , 12. (2011) www. echnology e iew.com/2011/09/12/ 191382/a-new-and-imp o ed-moo es-law/ 8. Zhang, N.: Moo e’s Law is dead, long li e Moo e’s Law!. (2022) a Xi p ep in a Xi :2205.15011. 9. Malmodin, J., Lunde ´n, D.: The ene gy and ca bon oo p in o he global ICT and E&M sec o s 2010–2015. Sus ainabili y 10(9), 3027 (2018) 10. F ei ag, C., Be ne s-Lee, M., Widdicks, K., Knowles, B., Blai , G.S., F iday, A.: The eal clima e and ans o ma i e impac o ICT: A c i ique o es ima es, ends, and egula ions. Pa e ns, 2(9), (2021) 11. Semiconduc o Indus y Associa ion and he Semiconduc o Resea ch Co po a ion.: Reboo ing he IT Re olu ion: A call o he ac ion. (2015) h ps://www.semiconduc o s.o g/ esou ces/ eboo ing- he-i - e olu ion-a-call- o-ac ion-2/. 12. And ae, A.S., Edle , T.: On global elec ici y usage o com- munica ion echnology: ends o 2030. Challenges 6(1), 117–157 (2015) 13. Bu gess, A., B own, T.: By 2040, The e may no be enough powe o all ou compu e s. HENNIK RESEARCH, 17 (2016) 14. Halda , A., Se hi, N.: En i onmen al e ec s o In o ma ion and communica ion echnology-explo ing he oles o enewable ene gy, inno a ion, ade and inancial de elopmen . Renew. Sus ain. Ene gy Re . 153, 111754 (2022) 15. Li, X., Zhang, C., Zhu, H.: E ec o in o ma ion and commu- nica ion echnology on CO2 emissions: an analysis based on coun y he e ogenei y pe spec i e. Technol. Fo ecas . Soc. Chang. 192, 122599 (2023) 16. Oo, K.T., Jonah, K.A.Z.O.R.A., Thin, M.M.Z.: A sys ema ic e iew o he p os and cons o digi al pollu ion and i s impac on he en i onmen . J. Sus ain. En i on. Manage. 2(1), 61–73 (2023) 17. Global e-Sus ainabili y Ini ia i e. Accen u e S a egy (2015)# SMARTe 2030-ICT Solu ions o 21s Cen u y Table 8 Posi ion in he G een500 lis s o he #1 o he TOP500 Edi ion Posi ion in G een500 2013-06 32 2013-11 40 2014-06 49 2014-11 64 2015-06 83 2015-11 90 2016-06 3 2016-11 4 2017-06 17 2017-11 20 2018-06 5 2018-11 3 2019-06 2 2019-11 5 2020-06 9 2020-11 10 2021-06 20 2021-11 26 2022-06 1 2022-11 6 2023-06 2 2023-11 8 Clus e Compu ing (2025) 28:42 Page 21 o 24 42 123 Challenges. B ussels: Global e-Sus ainabili y Ini ia i e (GeSI) and Accen u eS a egy. 18. Global e-Sus ainabili y Ini ia i e.: A ailable online: h p://gesi. o g/asse s/js/lib/ inymce/jsc ip s/ iny_mce/plugins/ajax ilemana ge /uploaded/SMARTe 2020 - The Role o ICT in D i ing a Sus ainable Fu u e - Decembe 2012._2.pd . (2012) 19. S ohmaie , E., Meue , H.W., Donga a, J., Simon, H.D.: The TOP500 lis and p og ess in high-pe o mance compu ing. Compu e 48(11), 42–49 (2015) 20. Donga a, J.J., Luszczek, P., Pe i e , A.: The LINPACK benchma k: pas , p esen and u u e. Concu . Compu . ion 15(9), 803–820 (2003) 21. Da ies, I.N., Ike, A.V.: O e iew o Common Pa allel Bench- ma k Applica ions and Sui es. J. Appl. Compu . Sci. Ma h. 16(34) (2022) 22. Cu now, H.J., Wichmann, B.A.: A syn he ic benchma k. Com- pu . J. 19(1), 43–49 (1976) 23. F eibu ge , D.: Compu e benchma ks: 50 yea s ago and now. ACM SIGHPC Connec 11(2), 5–7 (2023) 24. Weicke , R.P.: Dh ys one: a syn he ic sys ems p og amming benchma k. Commun. ACM 27(10), 1013–1030 (1984) 25. Dixi , K.M.: O e iew o he SPEC Benchma ks. The Bench- ma k Handbook, 7. (1993) 26. Bucek, J., Lange, K. D., Kis owski, J.: SPEC CPU2017: Nex - gene a ion compu e benchma k. In Companion o he 2018 ACM/SPEC In e na ional Con e ence on Pe o mance Engi- nee ing, pp. 41–42. (2018) 27. B uns , H., Za ala, M.: Fi s expe iences in pe o mance benchma king wi h he new SPEChpc 2021 sui es. In 22nd IEEE In e na ional Symposium on Clus e , Cloud and In e ne Compu ing (CCG id), pp. 675–684 (2022) 28. Aslanpou , M.S., Gill, S.S., Toosi, A.N.: Pe o mance e alua- ion me ics o cloud, og and edge compu ing: a e iew, ax- onomy, benchma ks and s anda ds o u u e esea ch. In e ne o Things 12, 100273 (2020) 29. TOP500. The Linpack Benchma k. h ps://www. op500.o g/p o jec /linpack/ 30. Pe i e , A.: HPL-a po able implemen a ion o he high-pe o - mance Linpack benchma k o dis ibu ed-memo y compu e s. (2004) h ps://www.ne lib.o g/benchma k/hpl/ 31. He oux, M.A., Donga a, J.: Towa d a new me ic o anking high pe o mance compu ing sys ems (No. SAND2013-4744). Sandia Na ional Lab.(SNL-NM), Albuque que, NM (Uni ed S a es); Uni e si y o Tennessee,, Knox ille, TN (2013) 32. Donga a, J., He oux, M.A., Luszczek, P.: A new me ic o anking high-pe o mance compu ing sys ems. Na l. Sci. Re . 3(1), 30–35 (2016) 33. Donga a, J., He oux, M.A.: Towa d a new me ic o anking high pe o mance compu ing sys ems. Sandia Repo , SAND2013-4744, 312, 150 (2013) 34. Ba e , R.F., Chan, T.H.F., D’Aze edo, E.F., Jaege , E.F., Wong, K., Wong, R.Y.: Complex e sion o high pe o mance compu ing LINPACK benchma k (HPL). Concu . Compu . P ac . Exp. 22(5), 573–587 (2010) 35. Heinecke, A., Dubey, P.: Design and implemen a ion o he linpack benchma k o single and mul i-node sys ems based on in el xeon phi cop ocesso . In IEEE 27 h In e na ional Sympo- sium on Pa allel and Dis ibu ed P oceedings, pp. 126–137 (2013) 36. Roh , D., Lindens u h, V.: A load-dis ibu ed linpack imple- men a ion o he e ogeneous clus e s. In 2015 IEEE 17 h In e na ional Con e ence on Embedded So wa e and Sys, pp. 436–443. IEEE (2015) 37. In el.: Dis ibu ion o LINPACK and he In el Op imized HPL- AI benchma ks. (2023) h ps://www.in el.com/con en /www/us/ en/docs/onemkl/de elope -guide-windows/2023-2/in el-dis ibu ion- o -linpack-benchma k-con en s.h ml 38. Chalme s, N., Bauman, P.: Op imizing high-pe o mance lin- pack o exascale accele a ed a chi ec u es. In P oceedings o he In e na ional Con e ence o High Pe o mance Compu ing, pp. 1–12 (2023) 39. Kim, J., Kwon, H., Kang, J., Pa k, J., Lee, S., Lee, J.: SnuHPL: high pe o mance LINPACK o he e ogeneous GPUs. In P o- ceedings o he 36 h ACM In e na ional Con e ence on Supe - compu ing, pp. 1–12 (2022) 40. TOP500 The Lis . No emb e 2023. h ps://www. op500.o g/ lis s/ op500/2023/11/ 41. Sun, Q., Ma, W., Sun, J., Li, H.: E ol ing he HPL benchma k owa ds mul i-GPGPU clus e s. CCF T ans. High Pe o m. Compu . 5(1), 84–96 (2023) 42. Feng, W.C., Scogland, T.: The g een500 lis : Yea one. In 2009 IEEE In e na ional Symposium on Pa allel & Dis ibu ed P o- cessing, pp. 1–7. IEEE (2009) 43. Came on, K.W.: A ale o wo g een lis s. Compu e 43(09), 86–88 (2010) 44. Hin on, K., Baliga, J., Feng, M., Ay e, R., Tucke , R.S.: Powe consump ion and ene gy e iciency in he in e ne . IEEE Ne w. 25(2), 6–12 (2011) 45. Deng, Y., Zhang, P., Ma ques, C., Powell, R., Zhang, L.: Analysis o Linpack and powe e iciencies o he wo ld’s TOP500 supe compu e s. Pa allel Compu . 39(6–7), 271–279 (2013) 46. JASON: Technical challenges o exascale compu ing. MITRE Co po a ion, McLean, VI, USA (2013) 47. Sub amaniam, B., Saunde s, W., Feng, W.C.: T ends in ene gy- e icien compu ing: A pe spec i e om he G een500. In 2013 In e na ional G een Compu ing Con e ence P oceedings, pp. 1–8. IEEE (2013) 48. Be gman, K., Bo ka S., Yelick, K.: Exascale compu ing s udy: Technology challenges in achie ing exascale sys ems. De ense Ad anced Resea ch P ojec s Agency In o ma ion P ocessing Techniques O ice (DARPA IPTO), Tech. Rep., 15, 181 (2008) 49. Van Heddeghem, W., Lambe , S., Lannoo, B., Colle, D., Picka e , M., Demees e , P.: T ends in wo ldwide ICT elec- ici y consump ion om 2007 o 2012. Compu . Commun. 50, 64–76 (2014) 50. Zhi no , V., Ca in, R., Gammai oni, L.: Minimum ene gy o compu ing, undamen al conside a ions. In ICT-Ene gy-Con- cep s Towa ds Ze o-Powe In o ma ion and Communica ion Technology. In echOpen (2014) 51. And ae, A.S.: Compa ison o se e al simplis ic high-le el app oaches o es ima ing he global ene gy and elec ici y use o ICT ne wo ks and da a cen e s. In . J. 5, 51 (2019) 52. Pang le, B.: News on ene gy-e icien la ge-scale compu ing. In CHIPS 2020 VOL. 2: New Vis as in Nanoelec onics, pp. 165–170. Sp inge In e na ional Publishing, Cham (2015) 53. Gao, Y., Zhang, P.: A su ey o homogeneous and he e oge- neous sys em a chi ec u es in high pe o mance compu ing. In 2016 IEEE In e na ional Con e ence on Sma Cloud (Sma Cloud), pp. 170–175. IEEE (2016) 54. Belkhi , L., Elmeligi, A.: Assessing ICT global emissions oo p in : T ends o 2040 & ecommenda ions. J. Clean. P od. 177, 448–463 (2018) 55. Mo ley, J., Widdicks, K., Hazas, M.: Digi alisa ion, ene gy and da a demand: The impac o In e ne a ic on o e all and peak elec ici y consump ion. Ene gy Res. Soc. Sci. 38, 128–137 (2018) 56. Hin emann, R., Hin e holze , S.: Ene gy consump ion o da a cen e s wo ldwide. Business, Compu e Science (ICT4S) (2019) 42 Page 22 o 24 Clus e Compu ing (2025) 28:42 123 57. Koo , M., Wijnho en, F.: Usage impac on da a cen e elec ici y needs: A sys em dynamic o ecas ing model. Appl. Ene gy 291, 116798 (2021) 58. Cisco Sys ems.: Fo ecas and Me hodology, 2012–2017; (2013) h ps://d2s 9p9 571 z.cloud on .ne /upload/images/10_2013/ 131028130134.pd 59. Masane , E., Shehabi, A., Lei, N., Smi h, S., Koomey, J.: Recalib a ing global da a cen e ene gy-use es ima es. Science 367(6481), 984–986 (2020) 60. Ka al, A., Dahiya, S., Choudhu y, T.: Ene gy e iciency in cloud compu ing da a cen e s: a su ey on so wa e echnologies. Clus . Compu . 26(3), 1845–1875 (2023) 61. Fa ima, E., Ehsan, S.: Da a cen e s sus ainabili y: app oaches o g een da a cen e s. In 2023 In e na ional Con e ence on Com- munica ion Technologies (ComTech), pp. 105–110. IEEE (2023) 62. Malmodin, J., Lo ¨ ehagen, N., Be gma k, P., Lunde ´n, D.: ICT sec o elec ici y consump ion and g eenhouse gas emissions– 2020 ou come. Telecommun. Policy 48(3), 102701 (2024) 63. Tomic ´, D., Imamagic ´, E., Gjene o, L.: Towa ds new ene gy e iciency limi s o High Pe o mance Clus e s. In P oceedings o he ITI 2013 35 h In e na ional Con e ence on In o ma ion Technology In e aces, pp. 89–93. IEEE (2013) 64. Moo e, G.: Moo e’s law. Elec on. Mag. 38(8), 114 (1965) 65. Schalle , R.R.: Moo e’s law: pas , p esen and u u e. IEEE Spec . 34(6), 52–59 (1997) 66. Mollick, E.: Es ablishing Moo e’s law. IEEE Ann. His . Com- pu . 28(3), 62–75 (2006) 67. Koomey, J., Na zige , S.: Moo e’s Law migh be slowing down, bu no ene gy e iciency. IEEE Spec . 52(4), 35 (2015) 68. Donga a, J.J., Mole , C.B., Bunch, J.R., S ewa , G.W. LIN- PACK use s’ guide. Socie y o Indus ial and Applied Ma he- ma ics (1979) 69. Sha ma, S., Hsu, C.H., Feng, W.C.: Making a case o a G een500 lis . In P oceedings 20 h IEEE In e na ional Pa allel & Dis ibu ed P ocessing Symposium, p 8. IEEE (2006) 70. Ge, R., Feng, X., Pyla, H., Came on, K., Feng, W. Powe measu emen u o ial o he G een500 lis . The G een500 Lis : En i onmen ally Responsible Supe compu ing (2007) 71. WG, EEHPC.: Ene gy E icien High Pe o mance Compu ing Powe Measu emen Me hodology. ( e sion 2.0 RC 1.0), p. 33, (2015) h ps://www. op500.o g/s a ic/media/uploads/me hodol ogy-2.0 c1.pd 72. Landaue , R.: I e e sibili y and hea gene a ion in he com- pu ing p ocess. IBM J. Res. De . 5(3), 183–191 (1961) 73. Landaue , R.: Dissipa ion and noise immuni y in compu a ion and communica ion. Na u e 335(6193), 779–784 (1988) 74. Lloyd, S.: Ul ima e physical limi s o compu a ion. Na u e 406(6799), 1047–1054 (2000) 75. Be ´ u , A., A akelyan, A., Lu z, E.: Expe imen al e i ica ion o Landaue ’s p inciple linking in o ma ion and he modynamics. Na u e 483(7388), 187–189 (2012) 76. Ma ko , I.L.: Limi s on undamen al limi s o compu a ion. Na u e 512(7513), 147–154 (2014) 77. Koomey, J.G., Sco Ma hews, H., Williams, E.: Sma e e y- hing: Will in elligen sys ems educe esou ce use? Annu. Re . En i on. Resou . 38(1), 311–343 (2013) 78. Feynman, R.P.: The compu ing machines in he u u e. In: The pleasu e o inding hings ou : The bes sho wo ks o Richa d P. Feynman. Basic Books. Pe seus Books (2005) 79. Feynman, R.P.: The compu ing machines in he u u e. Lec . No es Phys. 746, 99–113 (2008). h ps://doi.o g/10.1007/978-4- 431-77056-5 80. No dhaus, W.D.: Two cen u ies o p oduc i i y g ow h in compu ing. J. Econ. His . 67(1), 128–159 (2007) 81. Baboulin, M., Tomo , S.: Accele a ing scien i ic compu a ions wi h mixed p ecision algo i hms. Comp. Phys. Comm. 180(12), 2526–2533 (2009) 82. Do ¨ ich, M., Fan, M., Kis , A.M.: Impac o Mixed p ecision echniques on aining and in e ence e iciency o deep neu al ne wo ks. IEEE Access (2023) 83. NVIDIA.: T ain wi h Mixed P ecision. Use ´s guide. (2023) h ps://docs.n idia.com/deeplea ning/pe o mance/pd /T aining- Mixed-P ecision-Use -Guide.pd 84. Kahle , S.: Tenso Flow 2.12, In el. (2023) h ps://communi y. in el.com/ 5/Blogs/Tech-Inno a ion/A i icial-In elligence-AI/ AMX-Suppo - o -Mixed-p ecision-T aining-and-In e ence- Now/pos /1484953. 85. NVIDIA.: H100 Tenso Co e GP, Da a shee . (2023) h ps:// esou ces.n idia.com/en-us- enso -co e/n idia- enso -co e-gpu- da ashee 86. HPL-MxP.: HPL-MxP Mixed-P ecision benchma k. (2023) h ps://hpl-mxp.o g/ 87. Lin, R., Yuan, X., Wang, F.: 5 ExaFlop/s HPL-MxP Benchma k wi h Linea Scalabili y. In P oceedings o he In e na ional Con e ence o High Pe o mance Compu ing, Ne wo king, S o age and Analysis, pp. 1–13 (2023) 88. Koomey, J.G.: A p ime on he ene gy e iciency o compu ing. Phys. Sus ain. Ene gy III PSE III Using Ene gy. E ic. P od. Renew. 1652(1), 82–89 (2015) 89. Ma golus, N., Le i in, L.B.: The maximum speed o dynamical e olu ion. Physica D 120(1–2), 188–195 (1998) 90. Koomey, J., Schmid , Z., Na zige , S.: Supe compu ing pe - o mance and e iciency: an explo a ion o ecen his o y and nea - e m p ojec ions. Bu lingame, CA: Koomey Analy ics, o AMD (2020) 91. Bha any, S., Sha ma, S., Khala , O.I., Abdulsahib, G.M., Al Humaimeedy, A.S., Aldhyani, T.H., Alkah ani, H.: A sys ema ic su ey on ene gy-e icien echniques in sus ainable cloud compu ing. Sus ainabili y 14(10), 6256 (2022) 92. Zhang, J., Gao, F., Hu, P.: A e ical ansis o wi h a sub-1-nm channel. Na u e Elec on. 4(5), 325–325 (2021) 93. Bush, S.: IBM bea s inFETs wi h e ical CMOS a IEDM. Elec onics Weekly.com (2021) 94. Va na a, C.: Chips cool o wi h in eg a ed mic o luidics. Na - u e Elec on. 3(10), 583–583 (2020) 95. He be , S., Ma culescu, D.: Analysis o dynamic ol age/ e- quency scaling in chip-mul ip ocesso s. In P oceedings o he 2007 In e na ional Symposium on Low Powe Elec onics and Design, pp. 38–43 (2007) 96. Koco , B., Cza nul, P., P o icz, J.: Ene gy-awa e scheduling o high-pe o mance compu ing sys ems: a su ey. Ene gies 16(2), 890 (2023) 97. Doughe y, B., Whi e, J., Schmid , D.C.: Model-d i en au o- scaling o g een cloud compu ing in as uc u e. Fu u . Gene . Compu . Sys . 28(2), 371–378 (2012) 98. Benini, L., Bogliolo, A., De Micheli, G.: A su ey o design echniques o sys em-le el dynamic powe managemen . IEEE. T ans. Ve y La ge Scale In eg . (VLSI) Sys . 8, 299–316 (2000) 99. P ojec Na ick Phase 2.: h ps://na ick. esea ch.mic oso .com/ 100. Roach, J.: Mic oso inds unde wa e da acen e s a e eliable, p ac ical and use ene gy sus ainably. Mic oso Inno . S o- ies, 14 (2020) 101. Zhang, Y., Shan, K., Li, X., Li, H., Wang, S.: Resea ch and Technologies o nex -gene a ion high- empe a u e da a cen e s. Renew. Sus ain. Ene gy Re . 171, 112991 (2023) 102. Capozzoli, A., P imice i, G.: Cooling sys ems in da a cen e s: s a e o a and eme ging echnologies. Ene gy P oc. 83, 484–493 (2015) 103. Leise son, C.E., Thompson, N.C., Eme , J.S., Kuszmaul, B.C., Lampson, B.W., Sanchez, D., Scha dl, T.B.: The e’s plen y o Clus e Compu ing (2025) 28:42 Page 23 o 24 42 123 oom a he Top: Wha will d i e compu e pe o mance a e Moo e’s law? Science 368(6495), eaam9744 (2020) 104. Koomey, J., Masane , E.: Does no compu e: A oiding pi alls assessing he In e ne ’s ene gy and ca bon impac s. Joule 5(7), 1625–1628 (2021) Publishe ’s No e Sp inge Na u e emains neu al wi h ega d o ju isdic ional claims in published maps and ins i u ional a ilia ions. Albe o P ie o ecei ed he M.Sc. and Ph.D. deg ees in Physics (elec onics) om Uni e si y Complu ense de Mad id (1968) and he Uni e - si y o G anada (1976), espec- i ely. He is a P o esso Eme i us in he Depa men o Compu e Enginee ing, Au o- ma ic Con ol and Robo ics o he Uni e si y o G anada. His esea ch in e es s include com- pu e enginee ing, a i icial neu al ne wo ks and in elligen sys ems, and mos ecen ly g een compu ing. Bea iz P ie o ecei ed he M.Sc. and Ph.D. in Elec onic Enginee ing om he Uni e si y o G anada. She is Associa e P o esso a he Depa men o Depa men o Compu e Engi- nee ing, Au oma ic Con ol and Robo ics o he Uni e si y o G anada. He esea ch in e es s a e ocused in he ields o in elligen sys ems o signal p ocessing applied o biomedi- cal applica ions, and ecen ly, g een compu ing. Juan Jose ´Escoba ecei ed he M.Sc. and Ph.D. deg ees in Compu e Enginee ing om Uni e si y o G anada, Spain, in 2014 and 2020, espec i ely. He is a Pe manen Lec u e a he Depa men o So wa e Engi- nee ing o Uni e si y o G an- ada. His esea ch in e es s include code op imiza ion, ene gy-e icien pa allel com- pu ing, and wo kload balancing s a egies on he e ogeneous and dis ibu ed sys ems, especially in issues ela ed o e olu iona y algo i hms and mul i-objec i e ea u e selec ion p oblems. Thomas Lampe has Ph.D. in Compu e Sciences om he Uni e si y o Yo k. He ha e held a ious esea ch posi ions a he Uni e si y o Yo k and he Uni e si y o S asbou g, whe e he is now he Chai o Da a Science and A i icial In elligence. His esea ch in e - es s a e in he ield o A i icial In elligence, and mo e speci i- cally in Machine Lea ning and Image and Time-Se ies Analy- sis in a ious ields o applica- ion (mos ecen ly in medical imaging and emo e sensing). 42 Page 24 o 24 Clus e Compu ing (2025) 28:42 123