1. 14 - 2/11/2000AME 150 L Subroutine & Functions (& more on HW 7)

2. 14 - 2/11/2000AME 150 L Homework 7 Additions to HW6 1) Conversion of degrees to radians 2) many Logical Statements (IF's) to reduce size of argument to range 3) Change results as a consequence of earlier logical decisions

3. 14 - 2/11/2000AME 150 L x  2  ? x = MOD ( x, 2  ) Yes x   ? No !Now x  2  x = 2  - x Negative=.NOT. Negative Yes x   /2? x   /4? No !Now x   No x =  - x Yes !Now x   /2 x =  /2 - x Cosine=.TRUE. Yes !Now x   /4 No Negative= (x<0) x= ABS(x) The ABS operator makes x positive

4. 14 - 2/11/2000AME 150 L IMPLICIT NONE REAL :: x, x1, s1 REAL, PARAMETER::pi=3.14159265, Two_pi=2.*pi REAL, PARAMETER:: deg_to_rad=pi/180. LOGICAL :: Negative, Cosine ! Get a value for x Negative = x < 0 ! Initialize Logical variables! Cosine =.FALSE. x = ABS(x) * deg_to_rad !convert degr to radians x1= MOD( x,two_pi) !0 <= x1 <= 2 pi IF (x1 > pi) THEN x1 = Two_Pi - x1 Negative =.NOT. Negative END IF ! Now x1 is less than pi IF (x1>pi/2.) x1 = pi - x1 ! Now x1 is less than pi/2 IF (x1>pi/4.) THEN x1=pi/2.-x1 Cosine=.TRUE. END IF! Now x1 is less than pi/4

5. 14 - 2/11/2000AME 150 L Truncating the Series Since the series will be calculated only for small values of x 1   /4, only need 5 terms x2 = x1*x1 sine = x*(1.-x2/6.*(1.-x2/20.*(1.-x2/42.*(1.-x2/72.)))) Note the order of evaluation of the series (it's almost backwards) Horner's Rule note also that cosine = 1.-x2/2*(1.-x2/12.*(1.-x2/30.*(1.-x2/56.)))

6. 14 - 2/11/2000AME 150 L The "MOD" function A mod P is the fractional part of A/P MOD(A,P)  A - P * INT( A / P ) where INT is the integer part of a (real) division For ordinary integers, MOD(N,10) is the ones digit of N (the remainder of  10) and MOD(N,100)/10 is the tens digit

7. 14 - 2/11/2000AME 150 L Fortran Syntax We now return to Subroutines, Functions, and other similar real and mythical beasts

8. 14 - 2/11/2000AME 150 L Programming Style It is often useful to set a very limited goal for a program module –Specify what program module is to do –Decide how program module will be invoked –Develop a testing strategy for the module –Code the program module Read B:284-348, D:81-119

9. 14 - 2/11/2000AME 150 L Invoke in·voke (n-vk) v. tr. in·voked, in·vok·ing, in·vokes. –To call on (a higher power) for assistance, support, or inspiration: “Stretching out her hands she had the air of a Greek woman who invoked a deity” (Ford Madox Ford). –To appeal to or cite in support or justification. –To call for earnestly; solicit: invoked the help of a passing motorist. –To summon with incantations; conjure. –To resort to; use or apply: “Shamelessly, he invokes coincidence to achieve ironic effect” (Newsweek). See Synonyms at enforce.enforce [Middle English envoken, from Old French invoquer, from Latin invocre: in-, in; see in- 2 + vocre, to call; see wek w - in Indo-European Roots.] The American Heritage® Dictionary of the English Language, Third EditionCopyright © 1996, 1992 by Houghton Mifflin Company.

10. 14 - 2/11/2000AME 150 L Why Modular Programming? Small modules are easy to understand, develop, and code (lots of small modules) Easy to test & verify Can be used in many separate situations Can control and isolate effect of module

11. 14 - 2/11/2000AME 150 L What is a Module? A separately compiled program unit Common usage is –Main Program (just called PROGRAM ) –External Procedures Subroutine ( argument list ) Function ( argument list )

12. 14 - 2/11/2000AME 150 L Main Programs A Main Program is invoked by the operating system, and returns control to the operating system Any Program can invoke another program –IF the interface is clearly specified Rules for transferring control Rules for transferring data (in and out)

13. 14 - 2/11/2000AME 150 L Subroutines & Functions Declarations (same as PROGRAM ) SUBROUTINE sub_name (argument_list) …Fortran statements END SUBROUTINE sub_name and FUNCTION funct_name (argument_list) …Fortran statements END FUNCTION funct_name

14. 14 - 2/11/2000AME 150 L Invocation CALL sub_name (argument_list) –executable Fortran Statement –Transfers control and passes data The function is slightly more complex in that it may appear in an expression and returns a value var = funct_name (argument_list) A function can be used anywhere a variable or constant can appear (on the right hand side), or as an argument of an expression

15. 14 - 2/11/2000AME 150 L Argument List Arguments are separated by commas, and can be –Any Expression Constants Expressions Other Functions –Pointers to arrays of data –Keyword controlled (Fortran 90 & later)

16. 14 - 2/11/2000AME 150 L ar·gu·ment (ärgy-mnt) noun (1) A discussion in which disagreement is expressed; a debate. A quarrel; a dispute. Archaic. A reason or matter for dispute or contention: “sheath'd their swords for lack of argument” (Shakespeare). A course of reasoning aimed at demonstrating truth or falsehood: presented a careful argument for extraterrestrial life. A fact or statement put forth as proof or evidence; a reason: The current low mortgage rates are an argument for buying a house now. A summary or short statement of the plot or subject of a literary work. A topic; a subject: “You and love are still my argument” (Shakespeare).

17. 14 - 2/11/2000AME 150 L ar·gu·ment (ärgy-mnt) noun (2) Logic. The minor premise in a syllogism. Mathematics. The independent variable of a function. The amplitude of a complex number. Computer Science. A value used to evaluate a procedure or subroutine. [bad definition]

18. 14 - 2/11/2000AME 150 L ar·gu·ment (ärgy-mnt) noun (3) [Middle English from Old French from Latin argmentum, from arguere, to make clear; see argue.] Synonyms: argument, dispute, controversy. These nouns denote discussion involving conflicting points of view. Argument stresses the advancement by each side of facts and reasons buttressing its contention and intended to persuade the other side: Emotions are seldom swayed by argument. Dispute stresses division of opinion by its implication of contradictory points of view and often implies animosity: A dispute arose among union members about the terms of the new contract. Controversy is especially applicable to major differences of opinion involving large groups of people rather than individuals: The use of nuclear power is the subject of widespread controversy.

19. 14 - 2/11/2000AME 150 L Examples: Subroutine/Function Calls CALL SUB1(X,Y,Z,a,b,c) CALL SUB2(input_data, result) CALL SUB3(SUB1, SUB2(a,b) ) result=FUN1(a,b,result_2) result=FUN2(x)*FUN3(y) IF(FUN3(x)<=FUN4(Y))THEN … WRITE(*,*)a,b,FUN7(a,b,SUB4(x))

20. 14 - 2/11/2000AME 150 L Declaration of Arguments Argument can carry data, defined in calling program, in to the subprogram INTENT(IN) Argument can point to a location defined in the calling program, that the subprogram will use to store results INTENT(OUT)

21. 14 - 2/11/2000AME 150 L Declaration of Arguments (2) Argument can point to a location defined in the calling program, that the subprogram will use as input, and then modify INTENT(INOUT) or (IN OUT) Argument can point to the name of another external subroutine or function EXTERNAL

22. 14 - 2/11/2000AME 150 L Declaration of Arguments (3) SUBROUTINE sub1 (a, b, i, My_Func) IMPLICIT NONE REAL, INTENT(IN):: a REAL, INTENT(OUT)::b INTEGER, INTENT(INOUT)::i REAL, EXTERNAL:: My_Func … RETURN … END SUBROUTINE sub1

23. 14 - 2/11/2000AME 150 L Declaration of Arguments (4) REAL FUNCTION Funct (a, i, My_Func) IMPLICIT NONE REAL, INTENT(IN):: a INTEGER, INTENT(INOUT)::i REAL, EXTERNAL:: My_func … Funct = {some expression} RETURN … END FUNCTION Funct

24. 14 - 2/11/2000AME 150 L Scope of Variables Arguments are variables that exist in the calling program, that the subprogram can use in calculations if INTENT(IN) Other variables are local –Local variables exist only in the subprogram –Local variables have SAVE attribute by default, unless SAVE is explicitly used in TYPE statements (unless some are named, then others are not)

25. 14 - 2/11/2000AME 150 L Checking arguments by Compiler Mismatch of arguments is a very common source of Fortran error If the Compiler could check, it can become an early error (not a run-time error) The CONTAINS statement/construct is used to pass information about subprograms to the compiler and the calling program