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Von Neumann's First Computer Program

DONALD E. KNUTH

Stanford University,* Stanford, California

An analysis of the two earliest sets of instruction codes planned for stored

program computers, and the earliest extant program for such a computer, gives

insight into the thoughts of John yon Neumann, the man who designed the

instruction sets and wrote the program, and shows how several important aspects

of computing have evolved. The paper is based on previously unpubhshed

documents from the files of Herman H. Goldstine.

Key words and phrases:

electronic computers, computer history, stored program

computers, machine organization and architecture, sorting, latency time, ENIAC,

EDVAC, order code, programming techniques

CR categories:

1.2, 6.0

INTRODUCTION

A handwritten document now in the posses-

sion of Dr. Herman H. Goldstine contains

what is probably the earliest extant program

for a stored program digital computer. Its

author, the remarkably talented mathema-

tician John von Neumann (1903-1957), was

in the process of refining the stored program

concept as he was writing this code; so his

program represents a significant step in the

evolution of computer organization as well

as of programming techniques. In this paper

we will therefore investigate the contents of

yon Neumann's manuscript in some detail,

attempting to relate its ideas to other de-

velopments in the early history of high

speed computing.

The program we will study is not what we

might expect an "ordinary" mathematician

to have written; it does not solve a partial

differential equation! Instead, it deals with

what was considered at that time to be the

principal example of a nonnumeric applica-

tion for computers, namely, the problem of

sorting data into nondecreasing order.

Von Neumann chose this application for

good reason. He had sketched out an order

* Computer Science Department

code for a stored program computer, with

numerical applications uppermost in his

mind; there was no question that his pro-

posed device could do the requisite arith-

metic operations. The key question was

whether or not the proposed instruction set

provided a satisfactory means of logical

control for complex processes, and so he felt

that a sorting program would be a most

instructive test case. Furthermore, the

existence of IBM's special purpose machines

for sorting gave him a standard against

which he could measure the proposed com-

puter's speed.

Before we start to study yon Neumann's

program, a few disclaimers are

order. In

the first place, he probably never intended to

have this program published and subjected

to such scrutiny; although his manuscript

is carefully documented, he probably wanted

only to circulate it among a few interested

colleagues. So when we find a few errors and

a few instances of clumsy coding, we should

realize that it was an early effort that was

not supposed to represent a polished product.

Second, we should realize that the histori-

cal interest of this program is in great

measure due to its connection with the de-

velopment of instruction codes for stored

Computing Surveys, Vol. 2, No. 4, December 1970

248

• D. E. Knuth

CONTENTS

Introduction 247-249

The Early

EDVAC

249-251

The Next EDVAC 252-253

The Sorting Program 253-257

Storage Allocation and Timing 257-258

The Sequel 258-259

References 259-260

Computing Surveys, Vol. 2, No. 4, December 1970

program computers; it is not the earliest in-

stance of a computer program. We have

Lady Lovelace's description of a program for

calculating Bernoulli numbers that Babbage

wrote for his Analytical Engine [1, Note G];

A. M. Turing's construction [16] of his

abstract Universal Machine, which involves

many important programming concepts;

Eckert and Mauchly's first sample program

for the ENIAC [4]; and a collection of

numerical programs, dating from 1944,

written by H. H. Aiken, G. M. Hopper,

R. V. D. Campbell, R. M. Bloch, B. J. Lock-

hart, and others, for the Harvard Mark I

[10, Chs. 4, 6].

A third precaution: The notation used in

this paper differs considerably from that

used by von Neumann, so that modern

readers can more easily understand what he

did. Where he would write, for instance,

15) c -}- (m' -- 1)(p ~- 1) ~-~ 14 [ p ~- 2,

we will use an equivalent assembly-like

language form,

MOVEIN PIK p~- 1, BUFFER, [YPTR].

This new notation isn't completely trans-

parent, but it seems to be an improvement

which doesn't go so far that the machine is

obscured. (For further information about

yon Neumann's original notation, see the

section on Storage Allocation and Timing.)

To set the stage for our story, let us con-

sider briefly the developments prior to 1945

when yon Neumann wrote his sorting pro-

gram. Several electromechanical calculators

were essentially operational in the late 1930s

and early 1940s: those of Stibitz [15] and

Aiken [10] in America, and Zuse [3] in

Germany. Another machine, which had

electronic circuitry for arithmetic although

it was slowed down by mechanical memory

elements, was also developed in the late

1930s at Iowa State College, by John V.

Atanasoff and Clifford E. Berry [see 12];

this machine was designed to solve sets of

simultaneous linear equations.

In August 1942, John W. Mauchly of the

Moore School of Electrical Engineering in

Philadelphia wrote a memorandum to his

colleagues summarizing briefly the ad-

Von Neumann's First Computer Program * 249

vantages which could be expected from an

electronic high speed computer such as he

felt could reasonably be developed. He was

familiar with previous American develop-

ments in computing, and he was also aware

of the extensive calculations needed by the

Ballistic Research Laboratory (BRL) in

connection with World War II; many of

these calculations were currently being done

on a Differential Analyzer at the Moore

School. It was by no means obvious that a

useful electronic computer could be built;

but Mauchly and a young electrical engineer

named J. P. Eckert, Jr., drew up a tentative

technical outline of a suitable machine, and

Prof. J. G. Brainerd decided it was worth the

risk of committing the Moore School to a

major effort in this direction. A technical

proposal was submitted to Col. Leslie E.

Simon, Col. Paul N. Gillon, and Lt. Herman

H. Goldstine of the BRL in the spring of

1943, and in a remarkably short time the US

government entered into a contract with the

Moore School for research and development

of high speed electronic calculating devices,

beginning July 1, 1943. The project, super-

vised by Brainerd, had Eckert as chief

engineer, Mauchly as principal consultant,

and Goldstine in charge of technical liaison

with BRL. A first machine, the ENIAC

(Electronic Numerical Integrator And Com-

puter), was soon designed, and its design was

frozen at an early stage so that future efforts

could be concentrated on its production and

testing; it was dedicated on February 15,

1946. (For further details about the develop-

ment of the ENIAC, see [6].)

The ENIAC was a highly parallel com-

puter; weighing over 30 tons, it involved

over 19,000 vacuum tubes, 1500 relays, etc.

Because of its electronic circuitry, it was

considerably faster than any computing

machine previously built. But it had only 20

words of internal memory, and it required

complicated manual operations for setting

up a program on plugboards. Long before

ENIAC was completed, it became clear to

the designers that they could utilize the

equipment more efficiently if they would

adopt serial methods instead of so much

parallelism; so in January 1944 they sketched

out a "magnetic calculating machine" in

which successive digits of numbers were

transmitted serially from a memory device

to central electronic computing circuits and

back again. Early in 1944, Eckert and

Mauchly invented an acoustic delay-line

memory device which made it possible to

obtain a fairly large storage capacity with

comparatively little hardware; so it became

evident that great improvements over

ENIAC could be made, at considerably less

cost. "Therefore, by July, 1944, it was

agreed that when work on the ENIAC

permitted, the development and construc-

tion of such a machine should be undertaken.

This machine has come to be known as the

EDVAC (Electronic Discrete VAriable

Computer)" [5].

In the latter part of 1944, John yon Neu-

mann (a consultant to BRL) became a

consultant to the EDVAC project. He con-

tributed to many discussions on logical

circuitry, and he designed the order code

which was to be used. In the spring of 1945,

he wrote a preliminary report [17] which

gives a detailed discussion of arithmetic

circuitry and the motivation for various

design decisions which were made as EDVAC

evolved. This takes us to the beginning of

our story.

THE EARLY EDVAC

VOD Neumann's first draft report [17, 18] on

the EDVAC proposed building a serial

computer with three 32-bit registers and

8192 32-bit words of auxiliary memory. The

three registers were called i and j (for inputs

to the arithmetic circuitry) and o (for out-

put) ; for convenience in what follows we will

denote these registers by the upper-case

letters I, J, and A. The EDVAC memory

was to be divided into 256 "tanks" of 32

words each, operating in a cyclic fashion.

Word 0 of each tank would pass a reading

station one bit at a time, then (32 bit-times

later) word 1 would be available,..., finally

word 31, then word 0 again, etc. Thus the

accessing of information from tanks is essen-

tially the same as we now have from drums

or head-per-track disks. A bit-time was to be

1 #sec, so the cycle time for each tank came

Computing Surveys, Vol 2, No. 4, December 1970

250 • D. E. Knuth

to 32 × 32 = 1024 ~sec. The tanks were to

be constructed from Eckert and Mauchly's

mercury delay lines; this concept was later

used in the memory of the UNIVAC I

computer (1951). Although yon Neumann

realized that faster operation could be

achieved with a random-access memory, the

only known way of building such memories

economically was the "iconoscope" (like a

TV tube, with light or dark spots created and

sensed by an electron beam), and he tem-

porarily rejected it since its reliability was

still unproved.

Each 32-bit word was either a number or

an instruction code; the first bit was 0 for

numbers and 1 for instructions. Von Neu-

mann suggested writing binary numbers in

reverse order, with the least significant

digits at the left, since binary notation was

unfamiliar anyway and since the serial

circuitry found it most convenient to process

least significant digits first. The last bit of a

number, following the most significant bit,

was its sign; numbers were represented in

two's complement notation. Thus the word

boblb2b3 ... b3ob31 , bo = O,

denoted the number

2-~°bl +

2-2962 -}- 2-2Sb3 +4- "''

+ 2-1b30 -- b31,

and 30-bit fractions in the range --1 _~

x < 1 were representable. For addition,

subtraction, and conversion operations, the

number could also be regarded as the integer

bl + 2b2 + 4b3 + ... + 229b30 - 23°b31,

so that integers in the range -230 ~ x < 23°

were representable. Binary coded decimal

integers (abcdefg)lo were also allowed, in the

form

0 0 0 0 ala2a3a4blb2b3b4 • • • glgsgag4,

where

ala2aaa4

was the code for digit a, and

blb2b3b4 was the code for digit b, etc., in

reverse binary order. (Thus 0000 = 0,

1000 = 1, 0100 = 2,---, 0001 = 8,

1001

= 9.)

Instruction words were to have the form

I aoa~aaa3a4bob~b2OOOOOOOOOOyoyly2y, y.xcx~xaxax, xtX6XT,

where a = aoala2a3a4 denoted an operation

code, b = boblb2 denoted a variant, y --

y0 + 2yl + 4y2.+ 8y3 Jr 16y4 denoted a

word position within a tank, and x =

x0 + 2Xl -4- .'. + 128x7 denoted a tank

number. The following arithmetic operation

codes were proposed, affecting the registers

I, J, and A :

• AD (a = 00000). SetA (--IA-J.

• SB (a = 00001). SetA ~--I- J

*ML (a = 00010). Set A (-- A -4- I X J

(rounded).

• DV (a = 00011). Set A ~-- I/J (rounded).

• SQ (a = 00100). Set A ~-- ~/I (rounded).

• II (a = 00101). SetA~--l.

• JJ (a = 00110). SetA ~--J.

• SL (a = 00111). if A > 0, set A ~-- I; if

A < 0, setA~--J

• DB (a = 01000). Set A ~-- binary equivalent

of decimal number I.

• BD (a = 01001) Set A ~- decimal equiva-

lent of binary number I.

(As stated in the Introduction, we are

changing von Neumann's notation; the

mnemonic symbols for these codes are ad hoc

symbols contriv0d solely for the purposes of

the present paper. Note that multiplication,

division, and square root were to produce

rounded results. Not all details of these

operations were fully specified by yon

Neumann; division and square root would

change the contents of I, but it is not clear

that a valid remainder would be left there.

The decimal-to-binary and binary-to-deci-

mal operations were not worked out. Ap-

parently overflow conditions caused no

special action.)

Each of the above arithmetic operations

was to be used with one of several variants

specified by b = boblb2 :

• H (b = 111). Do the operation as described

above, holding the result in A.

• A (b = 100) Do the operation as described

above, then set J *-- I, I ~-- A, A <-- 0.

• S (b = 000). Do the operation as described

above, then store the result A in memory location

yx and set A ~-- 0.

• F (b = 101). Do the operation as described

above, then store the result into the word immedi-

ately following this instruction, set A ~ 0, and

perform the altered instruction.

• N (b = 110) Do the operation as described

above, then store the result into the word immedi-

Computing Surveys, Vol. 2, No. 4, December 1970

Von Neumann's First Computer Program •

251

ately following this instruction, set A ~-- 0, and

skip

the altered instruction.

Thus, for example, ADS

would have the

effect of setting location

to I -{- J, and

clearing A to zero; JJA would interchange

the contents of I and J, and clear A; SLH

would set A to either I or J, according as the

previous sign of A was 0 or 1. (The memory

specification

was ignored on all variants

except S.)

Besides arithmetic operations, the ma-

chine could do the following:

• JMP (a --- "11000, b -- 000). Take the next

instruction from location

(then 1 W

yx,

ete ).

• LOD (a--- 10000, b = 000). SetJ~I, then

set I to the contents of memory location

yx.

Further codes a = 01010, 01011, 01100,

01101, 01110, 01111 were reserved for input

and output operations (which were not yet

specified) and stopping the machine.

There was an important exception to the

operations as we have described them: Only

numbers (not instructions) ever appeared ill

the registers I, J, and A. When the LOD

operations specified a memory address con-

taining an instruction, only the

part of

that instruction was to be loaded into I;

the other bits were cleared. Conversely, when

storing into memory by means of variants

S, F, and N, only the least significant 13

bits of the number in A were to be stored

in the

part, if the memory location con-

tained an instruction word.

Instructions were to be executed from

consecutive locations, unless the sequence of

control was modified by a JMP order. If

the control sequence would come across a

number (not an instruction word), the effect

would be as if an LOD instruction were per-

formed referring to this number.

Most instructions would be performed in

one word-time, so that the machine could

keep up with the speed of the long tanks

where instructions were stored. But multi-

plication, division, square root, and radix

conversion took 33 word-times (1056 ~sec).

References to memory, by means of LOD

operations and the S variant, would require

an additional 1024 ~sec unless the memory

address was perfectly synchronized to match

the following word of instructions. (For

multiplication, division, and square root

extraction, there was a little more leeway,

since those operations actually were com-

pleted in about 950 ~sec.)

The reader will note that much of the

space in instruction words is wasted. Von

Neumann realized this, but did not think it

important at the time, since [17, p. 96] the

programming problems he had considered

required only a small fraction of the memory

for instruction storage. But we will see that

he changed his mind later.

The machine we have considered here

differs slightly from yon Neumann's de-

scription iD [17], since the modifications

stated in his letter [18] have been included.

He wrote, from Los Alamos to Philadelphia,

"The contents of this letter belong, of course,

into the manuscript [17], and I will continue

the manuscript and incorporate these things

also, after I get it back from you--if possible

with comments.., from you, Pres Eckert,

John Mauchly, and the others." But the

manuscript was never completed, nor were

the modifications inserted when it was typed

a month later, presumably because there

were so many other things to be done. It is

interesting to note that yon Neumann's

letter [18] also proposed the design of a

special typewriter for preparing programs

from partially mnemonic input. Pushing a

key marked -[- would cause the bits 100000

to be assembled (the first six bits of an addi-

tion instruction); then a key marked H

would insert the subsequent bits 111000...00,

forming a complete instruction word on a

magnetic tape.

The differences between [17] and the

machine described here are chiefly concerned

with improvements in the logistics of instruc-

tion modification. (a) There was no variant

N; instead, variant F would not treat the

altered word as an instruction if it turned

out to be a number. (b) The convention on

loading only 13 bits of instructions was not

present (although the convention about

storing only 13 bits into instruction words

was). (c) Three other variants, like S, A, F

but not clearing register A, were originally

included.

Computing Surveys, Vol. 2, No. 4, December 1970

252

• D. E. Knuth

THE NEXT EDVAC

Von Neumann's letter says, "I have also

worked on sorting questions .... I will

write you about the details very soon." He

said that he had written an internal sorting

program requiring about 130 words of in-

structions; it could sort 500 p-word items

on a one-word key in about 1 + .425 (p -- 1)

minutes.

suspect that these arrangements,

which represent only a first attempt, could

be improved ....

"At

any rate the moral seems to be that

the EDVAC, with the logical controls as

planned for 'mathematical' problems, and

without any modifications for 'sorting'

problems, is definitely faster than the

[contemporary IBM sorters, about 400

cards/minute] .... Since the IBM's are

really very good in sorting, and since accord-

ing to the above, sorting can be meshed with

the other operations of the EDVAC without

human intervention or need for additional

equipment, etc., the situation looks reason-

ably satisfactory to me .... It is legitimate

to conclude already on the basis of the now

available evidence, that the EDVAC is

very nearly an 'all-purpose' machine, and

that the present principles for the logical

controls are sound."

But von Neumann's code for this sorting

program does not seem to have survived; we

can only say that his timing estimates look

reasonable, since for large p they come to

slightly over 5 msec per pass per word

transferred. The program which now is in

Dr. Goldstine's files is roughly 80 times

faster, due to important improvements in

machine organization which yon Neumann

considered shortly afterward. This second

EDVAC design was apparently never de-

fined in as much detail as the previous one,

but a brief summary of its instruction codes

appears in [5, p. 76] and we can deduce other

properties by studying yon Neumann's

program. Therefore we can reconstruct the

main features of the machine.

The chief improvement incorporated into

this version of EDVAC was the introduction

of "short tanks" whose capacity was one

word each; this provided a small fast-access

memory which essentially increased the

number of registers, and the old I and J

disappeared. Block transfer operations be-

tween the short and the long tanks made

many processes faster. The tentative plans

in [5] call for 32 short tanks, and 2048 addi-

tional words in 64 long tanks. "Combining

this with the almost unlimited memory

capacity of the magnetic tape (even though

the numbers are not available here so

quickly) it seems that very few problems

will exceed this capacity" [5, p. 81].

Here are the basic operations allowed by

the new EDVAC code, exclusive of multi-

plication and division [let

C(s)

denote the

contents of short tank number s]:

*PIK

s,t,x

Transfer s consecutive words,

starting at long tank location x, to s consecutive

short tanks, starting at short tank number t. If x

is unspecified, the next s words following this

instruction are used, and the (s + 1)-th is the next

instruction

*PUT

s,t,x

Transfer s consecutive words,

starting at short tank number t, to s consecutive

long tank positions starting at location x. If x is

unspecified, the next s words following this instruc o

tion are used, and the (s + 1)-th is the next in-

struction.

*ADD

s,t. SetA (--C(s) + C(t).

-SUB

s,t.

SetA

~-C(s) - C(t).

*SEL s,/ IrA ~

O, setA~--C(s);ifA ~ O,

set

A ~-- C(t)

• TRA x. Go to long tank location x (then x +

1. etc.) for subsequent instructions

• JMP s. Go to short tank number s (then

s + 1, etc ) for subsequent instructions.

• STOs. Set

C(s) ~--A.

• SET s,t

SetC(s)(--C(t)

As before, operations which did not refer to

long tank addresses took just one word-

time (32 t~sec), with the exception of "long"

arithmetic operations like multiplication and

division. When a long tank location was

specified, the machine waited until the

desired word was accessible; at least two

word-times were needed for the instruction

TRAx, due to "long tank switching," if

the instruction was executed from a short

tank.

A distinction was made, as before, be-

tween numbers and instruction words: When

STO or SET attempted to store a new value

into an instruction word, only that part of

the instruction which specified a long tank

Computing Surveys, Vol. 2, No. 4, December 1970

Von Neumann's First Computer Program • 253

location x was to be affected, and the value

in A was regarded as an integer•

Tentative plans for representing the

instructions in memory are discussed briefly

in [5, pp. 83-86].

THE SORTING PROGRAM

Now we are ready to discuss von Neumann's

program• His manuscript, written in ink, is

23 pages long; the first page still shows

traces of the penciled phrase "TOP

SECRET," which was subsequently erased•

(In 1945, work on computers was classified,

due to its connections with military prob-

lems.) A facsimile of page 5, the first page of

the program itself, appears as Figure 1.

Von Neumann begins his memo by de-

fining the idea of sorting records into order,

and of merging two strings of records that

have been sorted separately into a single

sorted sequence. Then he states the purpose

of the program: "We wish to formulate

code instructions for sorting and for mesh-

ing [i.e. merging], and to see how much

control-capacity they tie up and how much

time they require."

He never actually gets around to coding

the entire sorting routine in this document;

only the merging process is described. For

the merging problem, we assume that n

records Xo, xx, • • •, x,_x are given, consist-

ing of p words each; the first word of each

record is called its "key," and we have

key(xo) _< key(x1) _< .-. < key(x,_l). An

additional m p-word records y0, yl, "",

ym-1 are also given, with key(y0) _< key(yl) g

• .- < key(y~_l); the problem is to put the

x's and y's together into the merged se-

quence go, zl, ... , z,+,~-i, in such a way

that key(zo) _< key(z1) g ..- < key(z,+~_l).

He formulated the merging method as

follows (based on a procedure then used

with the IBM collator): Assume that we

have found the first l records Zo, ...,

z~_l, where 0 _< l _< n + m; and assume

further that these l records consist of Xo,

• • •

, x,,_l and Yo, • • • , y~,,-1 in some order,

where0_< n' _< n, 0 < m' < m, andn'-l-

m ~ = l. There are four cases:

(a) n' < n, m' < m. There are two sub-

cases:

(al) key(x,,) _< key(y~,). Let zz = xn,,

and replace (l, n', m') by (l + 1, n' + 1, m').

(a2) key(x,,) > key(y~,). Let zz = y~,,

and replace (/, n', m') by (l + 1, n', m' + 1).

(l~) n' < n, m' = m. Same action as

(al).

(~) n' = n, m' < m. Same action as

(a2).

(6) n' -- n, m' = m. The process has

been completed.

His program is divided up according to

cases in this same way (sort of a "decision

table" arrangement). In order to make his

coding reasonably easy to follow, it is trans-

literated here into a symbolic assembly

language such as people might use with the

machine if it existed today. We use the

pseudo-operation a RST k (RST means

"reserve short tank") to mean that symbol

is to refer to the first of k consecutive short

tank locations. The first RST in a program

reserves short tank number 0, and short

tanks are reserved consecutively thereafter•

The other notations of our assembly lan-

guage are more familiar: "EQU" denotes

"equivalence", "CON" denotes an integer

constant, an asterisk denotes the current

location, and "**" denotes an address

which will be filled in dynamically as the

program runs.

Von Neumann's first step in coding the

program was to consider the four-way divi-

sion into cases; see (A). (Note: All numbers

manipulated in the program are treated as

integers.) This code assumes that the short

tank locations have been set up appropri-

ately; in particular, location SWITCH

contains a TRA instruction. The code in (A)

(line 22) sets the address of that TRA to

either ALPHA, BETA, GAMMA, or

DELTA.

Next comes the code for routines (a), (f~),

(~), and (6); see (B). Here we have a rather

awkward piece of coding; von Neumann

thought of a tricky way to reduce cases (f~)

and (~,) to case (a) by giving artificial

values 0 and -1 to key(y~,) - key(x,,).

But he didn't realize the far simpler approach

of making (8) and (~) identical, respec-

tively, to (al) and (a2). Thus, he could have

Computing

Surveys, Vol. 2, No.

December 1970

254

• D.E. Knuth

X:,~5 ) ~ ~, , z, , ...

¢ ) T Y, o) w'.~'-.~.,.~

~,) ~., 7,, ,,'> ,.: ,~ ,.,., -:/t.....,-

~,) a- -. 7i, ~2) /¢"/r .,o, "d,"," ",'.~ ",-

.- ~.)

... ~ "~

~,.~.

/o,) ~-. ~"

Ab/A~I~¢

7~,..,..,, .,~ ,,~ .,.,.,.~.,,-f" ,'¢.~ ~ ~.,:, ~ a, /,,, /,, /,.,

c,~,) ~ co,,.v, --,',.~-~,/-,.~/',-- ~ "~,-~ "I" < ~2.

FIG. 1. The original manuscript.

simply changed line 27 to "SEL BETA,

GAMMA", omitting lines 24, 25, 30, 31, 32,

33, 34, 35 entirely, and then he could have

used BETA and GAMMA instead of

ALPHA1 and ALPHA2 in the remainder of

the program. This would have saved four of

the precious short tank locations, and it

would have made the calculation slightly

faster. Similarly line 36 is unnecessary, since

location EXIT could be stored in LDELTA.

Computing Surveys, Voi. 2, No. 4, December 19T0

Von Neumann's First Computer Program

(A)

• 255

Line no. Location

I NPRIME RST

2 MPRIME RST

$ XKEY RST

4 YKEY RST

5 N

RST

6 M

RST

7 LALPHA RST

8 LBETA RST

9 LGAMMA RST

LDELTA RST

SWITCH RST

12 TEMP1 RST

IS TEMP2 RST

14 COMPARE SUB

SEL

STO

SUB

SEL

STO

20 SUB

21 SEL

22 STO

~S JMP

Address(es) Remarks

1 n'

1 m ~

1 key(x.,)

1 key(y~,,)

1 n

1 m

1 Location ALPHA

1 Location BETA

1 Location GAMMA

1 Location DELTA

1 Instruction TRA **

1 Temporary storage

NPRIME,N

A ,--n' - n.

LGAMMA, LALPHA A ~- if n' ~ n then GAMMA

else

ALPHA.

TEMP1 TEMP1 *-- A.

NPRIME,N A ~-- n' - n.

LDELTA, LBETA A ~-- if n ~ ~ n then DELTA

else

BETA.

TEMP2 TEMP2 ~-- A.

MPRIME,M A (-- m' -- m.

TEMP2,TEMP1 A ~- if m' ~ m then[TEMP2]eise[TEMP1].

SWITCH SWITCH ~-- TRA [A].

SWITCH

(B)

Lint no.

Locat*on Op

24 LALPHAI RST

25 LALPHA2 RST

$6 ALPHA SUB

27 SEL

28 STO

29 JMP

20 ZERO RST

Sl MONE RST

82 BETA SUB

$8 TRA

$4 GAMMA SUB

S5 TRA

$6 DELTA TRA

Address(es)

Rcmarhs

1 Location ALPHA1

1 Location ALPHA2

YKEY,XKEY A ~-- key(y~,) -- key(x~,).

LALPHA1,LALPHA2 ira _~ 0 then ALPHA1

else

ALPHA2.

SWITCH

1 0

1 --1

ZERO, ZERO A *- 0.

ALPHA+I Go to AI PHA+I.

MONE,ZERO A ~-- -I.

ALPHA+I Go co ALPHA+I.

EXIT Merging is complete.

Apparently the idea of making equivalent

program states identical is not a natural con-

cept, since even yon Neumann missed it

here.

(It is perhaps in bad taste to make such

detailed criticism of the programming, since

yon Neumann was not intending to write

an optimum program for sorting; he was

merely experimenting with a tentative order

code. Every great mathematician has a

wastebasket full of things he doesn't want

people to study carefully ! On the other hand,

this particular manuscript was not merely a

rough sketch, it was evidently put together

with some care, so it seems fair to look closely

at it in an attempt to discern which aspects

of programming were most difficult in their

conception. The idea is not to chortle over

the fact that yon Neumann's program isn't

perfect; it is rather to realize that the im-

perfections give some historical insights,

because of when the program was written.)

Computing Surveys, Vol. 2, No. 4, December 1970

256

• D. E. Knuth

(C)

Line no. Location Op Address(es)

$7 XPTR RST 1

38 YPTR RST 1

39 ZPTR RST 1

40 SIZE RST 1

41 MOVEIN RST 1

112 MOVEOUT RST 1

]v5 RETURN RST 1

44 ONE RST 1

]~ BUFFER RST p+l

$6 ALPHA1 SET MOVEIN, XPTR

47 SET MOVEOUT, ZPTR

68 PIK 1, RETURN

$9 [ TRA BACK1

JMP MOVEIN

BACK1 ADD NPRIME, ONE

52 STO NPRIME

5S SET XKEY, BUFFER+p

54 ADD XPTR,SIZE

55 STO XPTR

ADD ZPTR, SIZE

STO ZPTR

TRA COMPARE

Remarks

Location of x,,

Location of y~,

Location of z,,+m,

Instruction PIK p+I,BUFFER,**

Instruction PUT p,BUFFER,**

Instruction TRA BACK1 or BACK2

Place for record being transferred

MOVEIN ~- PIK pT1,BUFFER,[XPTR]

MOVEOUT *-- PUT p,BUFFER, [ZPTR].

RETURN *- TRA BACK1

(This line "picked.")

Execute three commands in short tank.

A*---n'+l.

n'*--A.

Update key(x.,).

A *- [XPTR]+p.

Update location of x~,.

A ~-- [ZPTR]+p.

Update location of z,,+m,.

Return to COMPARE.

The sorting program continues with the

routine for case (al): In (C) a block of

p + 1 words (including the key for the next

record) is transferred into short tanks, and

p words are moved into the z area. This is a

good way to avoid the latency problems of

delay-line memories, and it accounts for the

considerable increase in speed in this pro-

gram compared to what was possible with the

first EDVAC code.

A slight improvement could be made here

if ZPTR were omitted, letting MOVEOUT

keep track of tile current z location; a short

tank would be saved, as well as the instruc-

tion in line 47 (and a similar instruction for

case (,2)). However this trick would have

made the setup somewhat less symmetrical.

Line 58 could have been omitted if the code

for COMPARE were placed right after line

57. If line 51 were changed to "SUB

NPRIME,MONE", another short tank

could have been saved. Since yon Neumann

didn't mention these simplifications, while

his work on logic design strongly suggests

that he would have thought of them, it is

plausible to say that he wasn't especially

concerned with saving space in short tanks,

although he does mention that the scarcity of

short tanks places limits on the record size p.

(He says that p _< 8 would be required if

there were only 32 short tanks, while p < 40

if there were 64; perhaps he was purposely

wasting short tanks, in order to convince

other people that at least 64 short tanks are

desirable !)

We need not discuss the code for (a2),

since it is essentially the same as that for

(al). All that is left, therefore, is to write an

initialization routine that gets everything

started properly. For this purpose, yon

Neumann juggled the short tank locations so

that the six which are set up from outside

this routine (namely N, M, XPTR, YPTR,

ZPTR, SIZE) come first; then come two

which are somewhat special (namely XKEY

and YKEY, which must contain key(x0)

and key(y0)); then come 14 which are to be

set to certain constant values; and then

come the remaining "scratch" locations.

Figure 2 shows the resulting complete pro-

gram, including the initialization of the

short tanks. (At this point in his discussion,

yon Neumann apparently forgot about

TEMP1 and TEMP2; Figure 2 assigns them

to the buffer area.)

Like nearly all programs, this one has a

Computing Surveys,

Vol. 2, No. 4, December 1970

Von Neumann's First Computer Program • 257

N RST I

M RST 1

XPTR RST 1

YPTR RST 1

ZPTR RST 1

SIZE RST 1

XKEY RST 1

YKEY RST 1

NPRIME RST 1

MPRIME RST 1

LALPHA RST 1

LBETA RST 1

LGAMMA RST 1

LDELTA RST 1

SWITCH RST 1

LALPHA1 RST 1

LALPHA2 RST 1

ZERO RST 1

MONE RST 1

ONE RST 1

MOVEIN RST 1

MOVEOUT RST 1

RETURN RST 1

BUFFER RST p-}-I

TEMPI EQU BUFFER+I

TEMP2 EQU BUFFER+2

COMPARE SUB NPRIME,N e+27

SEL LGAMMA,LALPHA e-F28

STO TEMPI e-{-29

SUB

NPRIME,N e+30

SEL LDELTA,LBETA a+31

STO TEMP2 e+32

SUB MPRIME,M e+33

SEL TEMP2,TEMP1 e-]-34

STO SWITCH e+35

JMP

SWITCH

e+36

ALPHA SUB YKEY,XKEY e+43

SEL LALPHAI,LALPHA2 e+44

STO SWITCH e+45

JMP SWITCH "e+46

BETA SUB ZERO,ZERO e+39

TRA ALPHA+I e+40

GAMMA SUB MONE,ZERO e+41

TRA ALPHA+I e+42

DELTA TRA EXIT e+81

ALPHA1

SET

MOVEIN,XPTR e+47

SET MOVEOUT,ZPTR e+48

BACKI

ALPIdLA2

BACK2

BRING

MERGE

BACK3

PIK I,RETURN 6+49

[ TRA BACKI ¢+50

JMP MOVEIN e-i-51

ADD NPRIME,ONE e-t-56

STO NPRIME e+57

SET XKEY,BUFFER+p e+58

ADD XPTR,SIZE e-i-59

STO XPTR a+60

ADD ZPTR,SIZE e+61

STO ZPTR ¢~+62

TRA COMPARE ~+63

SET MOVEIN,YPTR e+6t

SET MOVEOUT,ZPTR e+65

PIK 1,RETURN ~+66

[ TRA BACK2

e+67

JMP MOVEIN e-F68

ADD MPRIME,ONE ¢+73

STO MPRIME e+74

SET YKEY,BUFFER+p e-t-75

ADD YPTR,SIZE e+76

STO YPTR e+77

ADD ZPTR,SIZE e+78

STO ZPTR

e+79

TRA COMPARE e+80

EQU NPRIME

PIK 3,BRING e÷O

PIK I,XKEY,** e-{-I

PIK I,YKEY,** e+2

TRA BACK3 ~-F3

SET BRING,XPTR e+4

SET BRING+I,YPTR e+5

JMP BRING e+6

PIK 14,NPRIME e+ll

CON

e+12

CON 0 e+13

CON ALPHA e+14

CON BETA e+15

CON GAMMA e+16

CON DELTA e-}-17

TRA ** e+18

CON ALPHA1 e+19

CON ALPHA2 e+20

CON 0 e-}-21

CON --1 e+22

PIK p+I,BUFFER,** e+23

PUT p,BUFFER,** c+24

_CON 1 e+25

TRA COMPARE e+26

FIG. 2

bug: The second-last instruction "CON

actually belongs two lines earlier. If von

Neumann had had an EDVAC on which to

run this program, he would have discovered

debugging i

STORAGE ALLOCATION AND TIMING

Although von Neumann didn't use a sym-

bolic language to express his instructions, as

done here, his notation wasn't completely

Computing Surveys, Vol. 2, No 4, December 1970

258

• D. E. Knuth

numeric either. He used il, 21, "" for short

tanks NPRIME, MPRIME, etc. in the first

piece of code, and later is, ~2, "'" for the

short tanks in the second, etc. Long tank

locations were represented by unbarred

numbers with subscripts; for example, lines

and 33 in his notation were written as

follows:

"18) ~ -

~ ~)

~ o

2~) 2~-+ ¢

and from here on like (a) with 0,0 for

xn0, y0 .,, This was essentially a "regional"

addressing technique, which was used by

many programmers in the ensuing decade.

After having written the program, he

assigned actual addresses to the subscripted

ones. In order to make the code reloeatable,

for use as a general open subroutine, he

assigned the addresses relative to an un-

specified starting location e. His address

assignments are shown in Figure 2 at the

right of the instructions.

He made an interesting and rather subtle

error of judgment here, regarding latency

time. Since the instruction in location

ALPHA1-}-4 (line 50 of the program in the

preceding section) jumps into the short

tanks to execute three commands and

transfer to BACK1, he didn't want BACK1

to occupy location ALPHAI+5 since the

long tank wouldn't be ready for that instruc-

tion until at least 33 word times after

ALPHAI+4. So he intercalated 4 empty

words between ALPHAI+4 and BACK1,

"in

order to avoid a delay of about one long

tank." But since the instructions in

MOVEIN and MOVEOUT make essen-

tially random references to long tanks, an

elementary argument can be given to prove

that the

average

computation time which

elapses between the execution of instruction

ALPHAI+4 and the execution of instruc-

tion BACK1 is 2p + 49.5 word times, com-

pletely

independent

of the location of

BACKli Therefore BACK1 should really

have been placed so that its

subsequent

instructions are optimally located, i.e. so

that the TRA COMPARE takes the least

amount of time. Von Neumann inserted

extra blank words into the initialization

routine for the same fallacious reason. On

the other hand his allocation of ALPHA,

BETA, and GAMMA vis-a-vis each other

and the COMPARE routine was correctly

handled; the instruction in SWITCH is not

a random memory reference, so his intuition

didn't mislead him here. (ALPHA1 and

ALPHA2 .were placed badly; this was ap-

parently an oversight.)

Von Neumann discussed the relocatability

of this routine by enumerating the nine

instructions which are variable (those whose

codes depend on p, EXIT, or the relocation

factor e). He didn't say exactly how these

instructions were to be changed after they

have been read in from tape; he apparently

did not yet realize that the limited EDVAC

code he had proposed (with no shift instruc-

tions, for example) made it difficult to insert

p into the "PIK" and "PUT" instructions,

since the machine could only store into the

address field of instruction words.

It is perhaps significant that he thought of

this program as an open subroutine, not

closed, since he did not regard EXIT as a

parameter on a par with n, m, location(x0),

etc.

He concludes his memorandum with an

analysis of the running time, leading to a

total time of 2.60

+ (n + m)(p/16 +

2.61)

msec. (His actual figure was 1.61 instead of

2.61, due to a slip in arithmetic.) Some

errors in the calculation of latency times,

related to his misunderstanding cited above,

make this analysis slightly invalid; the

reader may verify that the actual running

time (averaged over all possible placements

of x0, y0, and z0 in the long tanks) is 3056 +

(n + m)(64p +

4016) ~sec. If we incorporate

all of the improvements to the coding that

have been mentioned above, the average

time decreases to 2576

+ (n + m)(64p +

2560) ~sec.

THE SEQUEL

After World War II came to an end, the

original EDVAC group disbanded; Eckert

and Mauehly remained in Philadelphia, to

form their own company, while Goldstine

and yon Neumann went to the Institute for

Advanced Study in Princeton. The veil of

Computing Surveys, Vol. 2, No. 4, December 1970

Von Neumann's First Computer Program •

259

secrecy surrounding electronic computers

was lifted when ENIAC was dedicated, and

the great potential for high speed computing

was gradually realized by more and more

people. The principles of EDVAC's design

were very strong influences on all of the

computers constructed during the next

decade (see [14]).

After yon Neumann's first two versions of

instruction codes had been digested by a

number of people, other variations began

to be proposed. In November 1945, Calvin

N. Mooers devised a three-address code as

an alternative to yon Neumann's idea; and

in August 1946, he lectured at the Moore

School about a further development, the

use of flagged data for terminating loops [13,

Vol. 4, lect. 39]. Another interesting three-

address code, due to John Mauchly, was de-

scribed by Eckert in the same series of lec-

tures [13, Vol. 1, lect. 10]. Meanwhile yon

Neumann had developed his ideas somewhat

further; he and Goldstine, in collaboration

with Arthur W. Burks, prepared a mono-

graph which was to be the first widely cir-

culated document about high speed com-

puters, "Preliminary discussion of the logical

design of an electronic computing instru-

ment" [2]. By this time, their proposed ma-

chine had already changed somewhat dras-

tically: It was to have a random-access

(iconoscope) memory of 4096 40-bit words.

Instructions were 20 bits long, packed two

to a word. The operation codes had a differ-

ent flavor, too, resembling today's IBM

7094: "Clear and add x", etc. Left and right

shift operations were included for the first

time.

The EDVAC project itself continued at

the Moore School until August 1949, when

EDVAC was delivered to the BRL. In its

final form, the EDVAC had a four-address

instruction code (the fourth address specify-

ing the location of the next instruction), de-

vised by Samuel Lubkin. Its memory con-

sisted of 128 long tanks, each containing

eight 44-bit words, plus six one-word non-

addressable short tanks, and an auxiliary

drum. One of the only things that remained

unchanged throughout most of its design

was the basic clock rate of one ~sec per bit;

the completed machine processed one word

every 48 ~sec, leaving four "blank" bits be-

tween words. Further development work on

input/output devices was necessary before

EDVAC became operational late in 1951;

then it continued steady and inexpensive

operation for many years, averaging, for

example, 145 hours of useful work per week

in 1961 [11]. It was finally retired from service

in December 1962.

For the story of yon Neumann's other

pioneering contributions to computing, see

Goldstine's recent account [6]. Goldstine and

yon Neumann published three important

supplements to [2] during the next years;

these famous documents [7-9] formed the

foundation for computer programming tech-

niques, covering a wide range of topics from

flowcharts to numerical analysis to reloeat-

able loading routines. Reference [8, Sec. 11]

deals with sorting and merging in consider-

able detail; von Neumann here put the fin-

ishing touches onto the work he had sketched

in 1945.

ACKNOWLEDGMENTS

I wish to thank Drs. Goldstine and Mauehly

for considerable assistance in checking the

historical details presented in this paper,

and for several delightfully informative dis-

cussions.

REFERENCES

1. AUGUSTA, ADA, COUNTESS OF LOVELACE.

Annotated transl, of Menabrea, L. F., Sketch

of the Analytical Engine invented by Charles

Babbage. In Charles Babbage and h~s Cal(ulat-

~ng Engines (Phihp Morrison and Emily Mor-

rison, Eds.), Dover, New York, 1961, pp. 225-

297; see also p. 68.

2. BURKS, ARTHUR W., HERMAN H. GOLDSTINE,

ANn JOHN VON NEUMANN Preliminary discus-

sion of the logical design of an electronic com-

puting instrument. Inst. for Advanced Study,

Princeton, N. J., June 28, 1946; 2nd ed., Sept.

2, 1947 (42 pp). (Reprinted in yon Neumann's

Collected Works, Vol. 5, A. H. Taub, Ed. (Per-

gamon, London, 1963), pp 34-79.

3. DESMONDE, WILLIAM H., AND KLAUS J. BERK o

LING. The Zuse Z-3. Datamation 1~ (Sept.

1966), 30-31

4. ECKERT, J. PRESPER, JR., AND JOHN W.

MAUCHLY. Application of analyzer to a set of

equations for external ballistics. In Proposal

for an electronic difference analyzer (J. G.

Brainerd, Ed ), Moore School of Elec. Eng.,

Computing Surveys, Vol. 2, No. 4,

December 1970

260

* D. E. Knuth

U of Pennsylvania, Philadelphia, Pa., April

1943, App. C (4 pp). (Originally classified

"Confidential.")

5. ECKERT, J. PRESPER, JR.,

AND JOHN

MAUCHLY. Automatic high-speed computing-

A progress report on the EDVAC. Moore

School of Elec Eng., U. of Pennsylvania,

Philadelphia, Pa., Sept. 30, 1945 (111 pages)

(Originally classified "Confidential.")

6. GOLDSTINE, HERMAN H. Chapter 3 in Com-

puters and Their Role ~n the Physical Sciences

(S Fernbach and A. H. Taub, Eds ), Gordon

and Breach, New York, 1970.

7. GOLDSTINE, HERMAN H , AND JOHN YON

NEUMANN. Planmng and coding of problems

for an electronic computing instrument, Vol.

1. Inst. for Advanced Study, Princeton, N. J,

Apml 1, 1947 (69 pp.). (Reprinted in von Neu-

mann's Collected Works, Vol 5, A H Taub,

Ed., Pergamon, London, 1963, pp. 80-151.)

8 GOLDSTINE, HERMAN H., AND JOHN YON NEU-

MANN. Planning and coding of problems for

an electromc computing instrument, Vol. 2

Inst. for Advanced Study, Princeton, N. J,

April 15, 1948 (68 pp.). (Reprinted m yon Neu-

mann's Collected Works, Vol. 5, A. H. Taub,

Ed., Pergamon, London, 1963, pp 152-214 )

9. GOLDSTINE, HERMAN H., AND JOHN YON NEU-

MANN. Planning and coding of problems for

an electronic computing instrument, Vol. 3

Inst. for Advanced Study, Princeton, N J.,

Aug. 16, 1948 (23 pp.). (Reprinted in yon

Neumann's Collected Works, Vol. 5, A H

Taub, Ed., Pergamon, London, 1963, pp

215-235 )

10. HARVARD UNIVERSITY, STAFF OF THE COMPU-

TATION LABORATORY. Annals of the Computa-

tion Laboratory, Vol I, A Manual of Operation

for the Automatic Sequence-Controlled Calcu-

lator (H Alken et al , Eds.), Harvard U. Press,

Cambridge, Mass, 1946

11 KEMPF, KARL. Electronic computers within

the Ordnance Corps Aberdeen Proving

Ground, Aberdeen, Md., Nov. 1961 (140 pp.)

12 PANTAGES, ANGELINE Computing's early

years. Datamation 13 (Oct. 1967), 60-65.

13 PATTERSON, GEORGE W. (ED). Theory and

Techniques for the Design of Electronic Digital

Computers, Vol. ~ Moore School of Elec.

Eng., U of Pennsylvania, Philadelphia, Pa.,

1946 (4 vols.)

14 ROSEN, SAUL. Electronic computers: A his-

torical survey Comput Surveys 1, 1 (March

1969), 7-36

15. STIBITZ, GEORGE R., as told to Mrs Evelyn

Loveday The relay computers at Bell Labs.

Datamation 13 (April 1967), 35-44; 13 (May

1967), 45-49.

16 TURING, A. M. On computable numbers,

with an application to the Entscheidungs-

problem. Proc. London Math. Soc. {2} ~i2 (1936),

230-265; {2} 43 (1937), 544-546.

17. YON NEUMANN, JOHN First draft of a report

on the EDVAC. Moore School of Elec Eag,

U. of Pennsylvania, Philadelphia, Pa, June 30,

1945 (101 pp). (This draft was written in

March-April 1945.)

18. VON NEUMANN, JOHN. Letter to Herman H.

Goldstme dated May 8, 1945.

Computing Surveys, Vol. 2, No. 4, December

1970

Discussion

The ENIAC was about 300 times faster than the Mark 1 at addition. As Knuth states, at times it could be quite complicated to reprogram, sometimes taking up to 2 days to set up a program, after having completely worked it out on paper. ![ENIAC](http://www.columbia.edu/cu/computinghistory/eniac1.jpg) The sorting algorithm described by von Neumann would eventually be known as **Merge Sort**. ![Merge sort](https://upload.wikimedia.org/wikipedia/commons/c/cc/Merge-sort-example-300px.gif) ### Delay lines Delay lines are a form of computer memory. Delay lines operate by transforming the electrical signal to be delayed into a mechanical signal in some fluid and then transforming it back again to an electrical one. The delay comes from the fact that transmission of mechanical signals through a fluid is rather slow when compared to that of electricity through a wire. As long as the power stays on you can “hold" signals in the delay line circuit indefinitely. Unlike modern RAM (random access memory) delay line memory is sequential-access (you read the pulses in the same order they were entered). Early delay-line memory systems had capacities of a few thousand bits and provided way of storing data at 1/100 of the cost of doing the same with vacuum tubs. Alan Turing visited von Neumann for a few weeks when mercury lines were being proposed for the EDVAC and he argued that they would never work. Turing’s arguments were based on various signal-to-noise ratio considerations. Experiments eventually proved him wrong. [Here is a video of the EDSAC Project about Mercury delay lines](https://youtu.be/xGEAPVCuwvY) ![delay lines](https://i.imgur.com/XZs8ZAs.jpg) #### Complex Number Calculator The Complex Number Calculator designed by George Stibitz was a machine capable of adding, subtracting, multiplying, and dividing complex numbers. ![complex number calculator](http://history-computer.com/ModernComputer/Relays/images/StibitzTerminal.jpg) #### Harvard Mark I Howard Aiken was an American physicist. During his time as a physics Phd student at Harvard he encountered differential equations that he could only solve numerically. He imagined an electro-mechanical device that could do much of the tedious and repetitive work for him. The device Aiken developed was originally called ASCC (Automatic Sequence Controller Calculator) and it was later renamed Harvard Mark I ![Harvard Mark 1](https://cdn.britannica.com/700x450/93/23593-004-4D70E9A0.jpg) Here is a nicely formatted version of the [“First Draft of a Report on the EDVAC”](https://www.wiley.com/legacy/wileychi/wang_archi/supp/appendix_a.pdf) ![draft](http://images.computerhistory.org/revonline/images/102689072-03-01.jpg?w=600) If you are interested in learning more about Ada Lovelace’s story in computing you should read Stephen Wolfram’s [blogpost](http://blog.stephenwolfram.com/2015/12/untangling-the-tale-of-ada-lovelace/). John Von Neumann was an Hungarian-born American mathematician that made numerous contributions in computing and mathematics. He is generally regarded as one of the most important mathematicians of his time. A child prodigy, Von Neumann grew up in an affluent Jewish family in Budapest. From a very young age he showed a strong aptitude for mathematics. However, upon completing his secondary education his father discouraged him from pursuing a career in mathematics, fearing that there was not enough money in the field. As a compromise, von Neumann simultaneously studied chemistry and mathematics. He earned a degree in chemical engineering (1925) from the Swiss Federal Institute in Zürich and a doctorate in mathematics (1926) from the University of Budapest. In 1933, at the age of 30, von Neumann was offered a lifetime professorship on the faculty of Princeton's Institute for Advanced Study. ![von neumann](https://news.brown.edu/files/styles/horizontal/public/article_images/VonNeumann.jpg?itok=7Yr9wfGI)

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