COBOL COMP-2

Double precision floating point data type.

Overview and Purpose

COMP-2 provides double precision floating point arithmetic capabilities, following the IEEE 754 double precision standard. With approximately 15-17 decimal digits of precision and a vastly extended range compared to COMP-1, COMP-2 is ideal for scientific research, financial modeling, astronomical calculations, and any application where numerical accuracy is paramount. The increased precision comes at the cost of doubled memory usage but provides significantly improved accuracy for complex calculations.

Basic COMP-2 Declaration

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01  WS-PRECISE-CALCULATION    COMP-2.
01  WS-SCIENTIFIC-CONSTANT   COMP-2.
01  WS-FINANCIAL-MODEL       COMP-2.
01  WS-STATISTICAL-RESULT    COMP-2.

COMP-2 fields are declared without a PIC clause, similar to COMP-1, as the format follows the IEEE 754 double precision standard. Each field uses 64 bits (8 bytes) of storage and provides approximately 15-17 decimal digits of precision. These fields can store extremely large or small values with high accuracy, making them suitable for demanding computational applications.

High-Precision Mathematical Constants

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01  MATHEMATICAL-CONSTANTS.
    05  WS-PI-EXTENDED      COMP-2 VALUE 3.141592653589793.
    05  WS-E-EXTENDED       COMP-2 VALUE 2.718281828459045.
    05  WS-GOLDEN-RATIO     COMP-2 VALUE 1.618033988749895.
    05  WS-SQRT-2           COMP-2 VALUE 1.414213562373095.

This example demonstrates the definition of high-precision mathematical constants using COMP-2. The extended precision allows for more accurate representation of irrational numbers like π and e, which is crucial for scientific calculations. These constants maintain their precision through complex calculations, reducing accumulated rounding errors that might occur with lower precision data types.

Financial Modeling with Extended Precision

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01  FINANCIAL-VARIABLES.
    05  WS-PRINCIPAL        COMP-2.
    05  WS-INTEREST-RATE    COMP-2.
    05  WS-COMPOUND-PERIODS COMP-2.
    05  WS-TIME-YEARS       COMP-2.
    05  WS-FUTURE-VALUE     COMP-2.
 
CALCULATE-COMPOUND-INTEREST.
    COMPUTE WS-FUTURE-VALUE = WS-PRINCIPAL * 
        ((1 + WS-INTEREST-RATE) ** (WS-COMPOUND-PERIODS * WS-TIME-YEARS))

Financial modeling often requires extended precision to maintain accuracy over long time periods and multiple compounding calculations. This example shows compound interest calculation using COMP-2 fields, which prevents the accumulation of rounding errors that could significantly impact financial projections over extended periods. The high precision is particularly important for actuarial calculations and long-term investment modeling.

Tutorial: Building a High-Precision Scientific Calculator

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01  EXTENDED-CONSTANTS.
    05  WS-LIGHT-SPEED      COMP-2 VALUE 299792458.0.
    05  WS-PLANCK-CONSTANT  COMP-2 VALUE 6.62607015E-34.
    05  WS-AVOGADRO-NUMBER  COMP-2 VALUE 6.02214076E23.
    05  WS-BOLTZMANN        COMP-2 VALUE 1.380649E-23.

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CALCULATE-RELATIVITY-FACTOR.
    *> γ = 1 / sqrt(1 - v²/c²)
    COMPUTE WS-VELOCITY-RATIO = WS-VELOCITY / WS-LIGHT-SPEED
    COMPUTE WS-GAMMA-FACTOR = 1 / 
        ((1 - (WS-VELOCITY-RATIO ** 2)) ** 0.5)
 
CALCULATE-ENERGY-MASS-EQUIVALENCE.
    *> E = mc²
    COMPUTE WS-ENERGY = WS-MASS * (WS-LIGHT-SPEED ** 2)

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01  WS-SCIENTIFIC-DISPLAY   PIC -9(3).9(12)E-99.
 
MOVE WS-GAMMA-FACTOR TO WS-SCIENTIFIC-DISPLAY
DISPLAY "Lorentz Factor: " WS-SCIENTIFIC-DISPLAY
 
MOVE WS-ENERGY TO WS-SCIENTIFIC-DISPLAY
DISPLAY "Energy (Joules): " WS-SCIENTIFIC-DISPLAY

Practical Exercises

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01  ASTRONOMICAL-UNITS.
    05  WS-LIGHT-YEAR-KM    COMP-2 VALUE 9.4607304725808E12.
    05  WS-PARSEC-KM        COMP-2 VALUE 3.0856775814914E13.
    05  WS-AU-KM            COMP-2 VALUE 149597870.7.
    05  WS-DISTANCE-KM      COMP-2.
    05  WS-DISTANCE-LY      COMP-2.
    05  WS-DISTANCE-PC      COMP-2.
 
CONVERT-DISTANCES.
    COMPUTE WS-DISTANCE-LY = WS-DISTANCE-KM / WS-LIGHT-YEAR-KM
    COMPUTE WS-DISTANCE-PC = WS-DISTANCE-KM / WS-PARSEC-KM

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01  STATISTICAL-DATA.
    05  WS-DATA-ARRAY       COMP-2 OCCURS 1000 TIMES.
    05  WS-SAMPLE-SIZE      COMP-2.
    05  WS-MEAN             COMP-2.
    05  WS-VARIANCE         COMP-2.
    05  WS-STD-DEVIATION    COMP-2.
    05  WS-SUM-SQUARES      COMP-2.
 
CALCULATE-VARIANCE.
    PERFORM VARYING WS-I FROM 1 BY 1 UNTIL WS-I > WS-SAMPLE-SIZE
        COMPUTE WS-DEVIATION = WS-DATA-ARRAY(WS-I) - WS-MEAN
        COMPUTE WS-SUM-SQUARES = WS-SUM-SQUARES + (WS-DEVIATION ** 2)
    END-PERFORM
    COMPUTE WS-VARIANCE = WS-SUM-SQUARES / (WS-SAMPLE-SIZE - 1)
    COMPUTE WS-STD-DEVIATION = WS-VARIANCE ** 0.5

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01  QUANTUM-CALCULATIONS.
    05  WS-FREQUENCY        COMP-2.
    05  WS-WAVELENGTH       COMP-2.
    05  WS-ENERGY           COMP-2.
    05  WS-PHOTON-ENERGY    COMP-2.
 
CALCULATE-PHOTON-ENERGY.
    *> E = hf (Planck's equation)
    COMPUTE WS-PHOTON-ENERGY = WS-PLANCK-CONSTANT * WS-FREQUENCY
 
CALCULATE-WAVELENGTH.
    *> λ = c/f
    COMPUTE WS-WAVELENGTH = WS-LIGHT-SPEED / WS-FREQUENCY
 
CALCULATE-ENERGY-WAVELENGTH.
    *> E = hc/λ
    COMPUTE WS-ENERGY = (WS-PLANCK-CONSTANT * WS-LIGHT-SPEED) / 
                        WS-WAVELENGTH

Advanced COMP-2 Techniques

Precision Comparison and Validation

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01  PRECISION-TEST.
    05  WS-COMP1-RESULT     COMP-1.
    05  WS-COMP2-RESULT     COMP-2.
    05  WS-PRECISION-DIFF   COMP-2.
 
COMPARE-PRECISION.
    COMPUTE WS-COMP1-RESULT = 1.0 / 3.0
    COMPUTE WS-COMP2-RESULT = 1.0 / 3.0
    COMPUTE WS-PRECISION-DIFF = WS-COMP2-RESULT - WS-COMP1-RESULT

This example demonstrates the precision difference between COMP-1 and COMP-2. The COMP-2 result will maintain more decimal places of accuracy, which becomes crucial in iterative calculations where small errors can accumulate. Use such comparisons to validate when extended precision is necessary for your specific application requirements.

Error Accumulation Prevention

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ITERATIVE-CALCULATION.
    MOVE 0.0 TO WS-ACCUMULATED-RESULT
    PERFORM VARYING WS-ITERATION FROM 1 BY 1 
        UNTIL WS-ITERATION > 1000000
        COMPUTE WS-SMALL-VALUE = 1.0 / WS-ITERATION
        ADD WS-SMALL-VALUE TO WS-ACCUMULATED-RESULT
    END-PERFORM

In iterative calculations involving many small values, COMP-2's extended precision helps prevent the accumulation of rounding errors that could significantly affect final results. This is particularly important in numerical integration, series summation, and Monte Carlo simulations where millions of small calculations are performed.

Memory and Performance Considerations

While COMP-2 provides superior precision, it uses twice the memory of COMP-1 and may have slightly slower performance. Consider using COMP-2 selectively for critical calculations while using COMP-1 for intermediate values where extreme precision isn't required. Profile your application to ensure the precision benefits justify any performance costs.