MATH-MATIC

MATH-MATIC

MATH-MATIC

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MATH-MATIC is the marketing name for the AT-3 (Algebraic Translator 3) compiler, an early programming language for the UNIVAC I and UNIVAC II.

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MATH-MATIC was written beginning around 1955 by a team led by Charles Katz under the direction of Grace Hopper. A preliminary manual[1] was produced in 1957 and a final manual[2] the following year.

Syntactically, MATH-MATIC was similar to Univac's contemporaneous business-oriented language, FLOW-MATIC, differing in providing algebraic-style expressions and floating-point arithmetic, and arrays rather than record structures.

Notable features

Expressions in MATH-MATIC could contain numeric exponents, including decimals and fractions, by way of a custom typewriter.[3]

MATH-MATIC programs could include inline assembler sections of ARITH-MATIC code and UNIVAC machine code.[4]

The UNIVAC I had only 1000 words of memory, and the successor UNIVAC II as little as 2000. MATH-MATIC allowed for larger programs, automatically generating code to read overlay segments from UNISERVO tape as required. The compiler attempted to avoid splitting loops across segments.[5]

Influence

In proposing the collaboration with the ACM that led to ALGOL 58, the Gesellschaft für Angewandte Mathematik und Mechanik wrote that it considered MATH-MATIC the closest available language to its own proposal.[6]

In contrast to Backus' FORTRAN, MATH-MATIC did not emphasise execution speed of compiled programs. The UNIVAC machines did not have floating-point hardware, and MATH-MATIC was translated via A-3 (ARITH-MATIC) pseudo-assembler code rather than directly to UNIVAC machine code, limiting its usefulness. [7]

MATH-MATIC Sample program

A sample MATH-MATIC program:[8]

(2)  TYPE-IN ALPHA . 
(2A) READ A B C SERVO 4 STORAGE A IF SENTINEL JUMP TO SENTENCE 8 . 
(3)  READ D F SERVO 5 . 
(4)  VARY Y 1 (0.1) 3 SENTENCE 5 THRU 6 . 
(5)  X1 = (7*10<sup>3</sup>*Y*A*SIN ALPHA)<sup>3</sup> / (B POW D+C POW E) . 
(6)  WRITE AND EDIT A Y D E X1 SERVO 6 . 
(7)  JUMP TO SENTENCE 2A . 
(8)  CLOSE-INPUT AND REWIND SENTENCE 3 . 
(9)  CLOSE-OUTPUT SENTENCE 6 . 
(10) READ F G H N SERVO 4 STORAGE A IF SENTINEL JUMP TO SENTENCE 20 . 
(11) EXECUTE SENTENCE 3 . 
(12) X2 = (3 ROOT (E-G)+LOG (D+N)) / (F<sup>2.6</sup>*EXP H) . 
(13) WRITE EDIT F D F X2 SERVO 6 . 
(16) JUMP TO SENTENCE 10 . 
(20) STOP .

Notes

  1. [1]
    Ash (1957)
  2. [2]
    Univac (1958)
  3. [3]
    Sammet (1969) p. 135
  4. [4]
    Sammet (1969) p. 137
  5. [5]
    Sammet (1969) p. 137
  6. [6]
    Bemer (1969) p. 161
  7. [7]
    Knuth (1976) p. 90
  8. [8]
    Univac (1958) p. 8

References

  • Ash, R.; Broadwin, E.; Della Valle, V.; Greene, M.; Jenny, A.; Katz, C.; Yu, L. (1957-04-19). Preliminary Manual for MATH-MATIC and ARITH-MATIC Systems for Algebraic Translation and Compilation for UNIVAC I and II (PDF) (Technical report). Philadelphia: Remington Rand Univac. Archived from the original (PDF) on 2014-12-26. Retrieved 2016-03-19.
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