C++ in Scientific Application:A Case Study of Genericity

Walter E. BrownFermi National Accelerator Laboratory

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ACAT 2000 2

The Basis of All Scientific Computation

“We must measure what is measurable, and make measurable what is not so.”

– Galileo

ACAT 2000 3

Mensuration has a Long History

“Ye shall do no unrighteousness in judgment, in measures of length, of weight, or of quantity.”

– Leviticus 19:35

ACAT 2000 4

We’ve Made Progress, e.g.

“And he made a molten sea, ten cubits from brim to brim…, and a line of thirty cubits did compass it round about.”

– I Kings 7:23

ACAT 2000 5

Standardized Units Came Later

“Throughout the kingdom there shall be standard measures of wine, ale, and corn.… Weights [also] are to be standardized similarly.”

– Magna Carta

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Accepted First Principles

• “In carrying out any calculation, always … attach the proper units to the final result, for the result is meaningless without this…”

• “You should check the dimensions of all the equations you use.”

• “One way to spot an erroneous equation is to check the dimensions of all its terms….”

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Parallel Principles for Software, too!

• “One way to spot an erroneous equation is to check the dimensions of all its terms.”

– Halliday & Resnick, 1970

• “One way to spot an erroneous program is to check the data types of all its objects !”

– W. E. Brown, 1998

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Type-Checking is Not New

“There is no transfer into another kind, like the transfer from length to area and from area to solid.”

– Aristotle

ACAT 2000 9

Such Checking is Still Needed

“[A] famous bug in this shop is

2*pi+r*w

as the area of a strip of a cylinder, which escaped notice for years….”

– Name withheld by request

ACAT 2000 10

Unit Errors are Costly…

“NASA's Mars Climate Orbiter was lost… because engineers failed to [convert] from English units to metric, an embarrassing lapse that sent the $125 million craft fatally close to the Martian surface….”

– The Washington Post, 1 Oct. ‘99

ACAT 2000 11

… and Very Hard to Find!

“[T]he error had affected the orbiter mission from its launching almost 10 months and 416 million miles before its… failure. And yet the problem was never caught and corrected ….”

– The Washington Post, 1 Oct. ‘99

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Static Type-Checking Provides …

… succinct, intelligible, consistent (!) program documentation.

… information that a compiler could exploit to produce more efficient code.

… important programmer feedback via early (compile-time) error detection.

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Numeric Programming TodayExtensive inspection of code samples shows:

heavy use of native numeric types (e.g., double)

occasional use of synonymous types (e.g., CLHEP’s HepDouble).

But these are inadequate! Avogadro’s number + speed of light ???? Distance + Energy ? Mass + Momentum ? Alas, arbitrary combinations will compile!

ACAT 2000 14

Past Limitations

• Inadequate expressiveness in early lang’s:– Data types were limited to those in hardware.– General utility seemed to suffice.– We just didn’t know what we were missing!

• Programmer-defined data types came later:– Validated data abstraction methodology– Lacked enough power for generic programming

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We Can Now Do Better!

• Modern C++ gives us expressive power via:– classes and namespaces– templates (“parametric polymorphism”)

• Data abstraction has evolved:– Object-oriented design and programming– Generic programming technology

• Static type-checking is the norm

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SIunits Project Goals

Application of contemporary technology to computation involving physical concepts

Convenient (near-trivial) expression General utility based on existing standards Nomenclature from our problem domain No run-time performance penalties!

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SIunits Highlights 1

• Based on le Système internationale d’unités:– Specifies base and derived quantities – Specifies corresponding units of measure

• Features compile-time static type-checking:– Permits only meaningful combinations– Forbids all incommensurate expressions!– Generates implied dimensions automatically

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SIunits Highlights 2

• Attaches no run-time overhead:– No extra memory space per object– No extra execution time for user functions– Small initialization costs for I/O, etc.

• Includes a spectrum of five models:– Ranges from standard to natural (c=k=ħ=G=1).– Models are upwardly compatible.

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SIunits Programming

• Dimensions are types:– Base 7: Length, Mass, Time, Current, …– Derived: Energy, Force, Entropy, …

• Units behave as right-hand constants:– Base 7: meter, second, ampere, mole, …– Composite 21: joule, watt, hertz, …– Also (sub)multiples: mega_, nano_, ...

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Examples 1: Instantiation

using namespace si;

typedef Length<float> Len;

Len d1; // implicitly 0.0F

Len d2( 2.5*meter );

Len d3( 1.2*centimeter );

Len d4( 5*d3 );

Len d5( 1.23*pico_*meter);

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Examples 2: Bad Instantiations

Len d6( d2*d3 ); // no!

Len d7( 3.5 ); // no!

Len d8 = 3.5; // no!

Len d9; // ok, but …

d9 = 3.5; // no!

// but:

Len d10( d2+d3 ); // ok

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Type-Checking is Still Needed

“[T]hese are really insidious bugs, very hard to find by proofreading ... because your brain knows what the expression is supposed to be [so] you tend to see the intent and not the error.”

– Name withheld by request

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A User Viewpoint

“ [SIunits] is the first really good reason I’ve seen to switch from Fortran to C++.”

(Thank you!)

ACAT 2000 24

Personal Viewpoints

• SIunits could not have been carried out absent C++ metaprogramming

• C++ vendor support is rapidly improving

• Alas, the concepts underlying C++ seem well understood and well applied by only a small percentage of the scientific community

C++ in Scientific Application:A Case Study of Genericity

Walter E. BrownFermi National Accelerator Laboratory

f