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Mixing Objects of Different Types

Mixing Objects of Different Types. Mixed Type Numeric Expressions Mixed Type Assignment Integer Division. Mixing Objects of Different Types . Mixed Type Numeric Expressions

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Mixing Objects of Different Types

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  1. Mixing Objects of Different Types • Mixed Type Numeric Expressions • Mixed Type Assignment • Integer Division

  2. Mixing Objects of Different Types • Mixed Type Numeric Expressions • In the CPU calculations must be performed between objects of the same type, so if an expression mixes type some objects must change type. • Default types have an implied ordering: • INTEGER -- lowest • REAL • DOUBLE PRECISION • COMPLEX -- highest • The result of an expression is always of the highest type, for example, • INTEGER * REAL gives a REAL, (3*2.0 is 6.0) • REAL * INTEGER gives a REAL, (3.0*2 is 6.0) • DOUBLE PRECISION * REAL gives DOUBLE PRECISION, • COMPLEX * < anytype > gives COMPLEX, • DOUBLE PRECISION * REAL * INTEGER gives DOUBLE PRECISION. • The actual operator is unimportant.

  3. Mixing Objects of Different Types • Mixed Type Assignment • Problems often occur with mixed-type arithmetic; the rules for type conversion are given below. • INTEGER = REAL (or DOUBLE PRECISION) • The RHS is evaluated, truncated (all the decimal places lopped off) then assigned to the LHS. • REAL (or DOUBLE PRECISION) = INTEGER • The RHS is promoted to be REAL and stored (approximately) in the LHS. • For example, • REAL :: a = 1.1, b = 0.1 • INTEGER :: i, j, k • i = 3.9 ! i will be 3 • j = -0.9 ! j will be 0 • k = a - b ! k will be 1 or 0 • Note: as a and b stored approximately, the value of k is uncertain.

  4. Mixing Objects of Different Types • Integer Division • Confusion often arises about integer division; in short, division of two integers produces an integer result by truncation (towards zero). Consider, • REAL :: a, b, c, d, e a = 1999/1000 ! LHS is 1 b = -1999/1000 ! LHS is -1 c = (1999+1)/1000 ! LHS is 2 d = 1999.0/1000 ! LHS is 1.999 e = 1999/1000.0 ! LHS is 1.999 • a is (about) 1.000 • b is (about) -1.000 • c is (about) 2.000 • d is (about) 1.999 • e is (about) 1.999 • Great care must be taken when using mixed type arithmetic.

  5. Intrinsic Procedures • Intrinsic Procedures • Type Conversion Functions • Mathematical Intrinsic Functions • Numeric Intrinsic Functions • Character Intrinsic Functions

  6. Intrinsic Procedures • Intrinsic Procedures • Fortran 90 has 113 in-built or intrinsic procedures to perform common tasks efficiently, they belong to a number of classes: • elemental such as: • mathematical, for example, SIN or LOG. • numeric, for example, SUM or CEILING; • character, for example, INDEX and TRIM; • bit, for example, IAND and IOR; • inquiry, for example, ALLOCATED and SIZE; • transformational, for example, REAL and TRANSPOSE; • miscellaneous (non-elemental SUBROUTINE s), for example, SYSTEM_CLOCK and DATE_AND_TIME. • Note all intrinsics which take REAL valued arguments also accept DOUBLE PRECISION arguments.

  7. Intrinsic Procedures • Type Conversion Functions • It is easy to transform the type of an entity, • REAL(i) converts i to a real approximation, • INT(x) truncates x to the integer equivalent, • DBLE(a) converts a to DOUBLE PRECISION, • IACHAR(c) returns the position of CHARACTER c in the ASCII collating sequence, • ACHAR(i) returns the character in the ASCII collating sequence. • All above are intrinsic functions. For example, • PRINT*, REAL(1), INT(1.7), INT(-0.9999) • PRINT*, IACHAR('C'), ACHAR(67) • are equal to • 1.000000 • 1 0 67 C

  8. Intrinsic Procedures • Mathematical Intrinsic Functions • Summary,

  9. Intrinsic Procedures Numeric Intrinsic FunctionsSummary,

  10. Intrinsic Procedures • Character Intrinsic Functions • Summary,

  11. More Intrinsic Functions • Random Number Intrinsic • Vector and Matrix Multiply Intrinsics • Maximum and Minimum Intrinsics • Array Location Intrinsics • Array Reduction Intrinsics • Array Reduction Intrinsics (Cont'd)

  12. More Intrinsic Functions • Random Number Intrinsic • RANDOM_NUMBER(HARVEST) will return a scalar (or array of) pseudorandom number(s) in the range . • For example, • REAL :: HARVEST • REAL, DIMENSION(10,10) :: HARVEYS CALL RANDOM_NUMBER(HARVEST) • CALL RANDOM_NUMBER(HARVEYS) • RANDOM_SEED([SIZE=< int >]) finds the size of the seed. • RANDOM_SEED([PUT=< array >]) seeds the random number generator. • CALL RANDOM_SEED(SIZE=isze) CALL RANDOM_SEED(PUT=IArr(1:isze))

  13. More Intrinsic Functions • Vector and Matrix Multiply Intrinsics • There are two types of intrinsic matrix multiplication: • DOT_PRODUCT(VEC1, VEC2) -- inner (dot) product of two rank 1 arrays. For example, • DP = DOT_PRODUCT(A,B) is equivalent to: • DP = A(1)*B(1) + A(2)*B(2) + ... For LOGICAL arrays, the corresponding operation is a logical .AND.. • DP = LA(1) .AND. LB(1) .OR. & LA(2) .AND. LB(2) .OR. ... • MATMUL(MAT1, MAT2) -- `traditional' matrix-matrix multiplication: • if MAT1 has shape (n, m) and MAT2 shape (m, k) then the result has shape (n, k); • if MAT1 has shape (m) and MAT2 shape (m, k) then the result has shape (k); • if MAT1 has shape (n, m) and MAT2 shape (m) then the result has shape (n); • For LOGICAL arrays, the corresponding operation is a logical .AND..

  14. More Intrinsic Functions • Maximum and Minimum Intrinsics • There are two intrinsics in this class: • MAX(SOURCE1,SOURCE2[,SOURCE3[,...]]) -- maximum values over all source objects • MIN(SOURCE1,SOURCE2[,SOURCE3[,...]]) -- minimum values over all source objects • Scan from left to right, choose first occurrence if there are duplicates • MAX(1,2,3) is 3 • MIN((/1,2/),(/-3,4/)) is (/-3,2/) • MAX((/1,2/),(/-3,4/)) is (/1,4/)

  15. More Intrinsic Functions • Array Location Intrinsics • There are two intrinsics in this class: • MINLOC(SOURCE[,MASK]) -- Location of a minimum value in an array under an optional mask. • MAXLOC(SOURCE [,MASK]) -- Location of a maximum value in an array under an optional mask. • A 1D example, • A 2D example. If • then • MINLOC(Array) is (/3,4/) • MAXLOC(Array,Array.LE.7) is (/1,4/) • MAXLOC(MAXLOC(Array,Array.LE.7)) is (/2/) (array valued).

  16. More Intrinsic Functions • Array Reduction Intrinsics • PRODUCT(SOURCE[,DIM][,MASK]) -- product of array elements (in an optionally specified dimension under an optional mask); • SUM(SOURCE[,DIM][,MASK]) -- sum of array elements (in an optionally specified dimension under an optional mask). • The following 1D example demonstrates how the 11 values are reduced to just one by the SUM reduction: • Consider this 2D example, if • PRODUCT(A) is 720 • PRODUCT(A,DIM=1) is (/2, 12, 30/) • PRODUCT(A,DIM=2) is (/15, 48/)

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