《数字信号处理》教学参考资料（Numerical Recipes in C，The Art of Scientific Computing Second Edition）Chapter 01.1 Preliminaries 1.1 Program Organization and Control Structures

1.1 Program Organization and Control Structures 5 Kernighan,B..and Ritchie,D.1978.The C Programming Language (Englewood Cliffs,NJ: Prentice-Hall).[2][Reference for K&R"traditional"C.Later editions of this book conform to the ANSI C standard.] Meeus,J.1982.Astronomical Formulae for Calculators,2nd ed.,revised and enlarged (Rich- mond,VA:Willmann-Bell).[3] 1.1 Program Organization and Control Structures 83g We sometimes like to point out the close analogies between computer programs, on the one hand,and written poetry or written musical scores,on the other.All three present themselves as visual media,symbols on a two-dimensional page or computer screen.Yet,in all three cases,the visual,two-dimensional,frozen-in-time representation communicates (or is supposed to communicate)something rather different,namely a process that unfolds in time.A poem is meant to be read;music, 令 played;a program,executed as a sequential series of computer instructions In all three cases.the target of the communication.in its visual form.is a human being.The goal is to transfer to him/her,as efficiently as can be accomplished, the greatest degree of understanding,in advance,of how the process will unfold in time.In poetry,this human target is the reader.In music,it is the performer.In 8% 9 programming,it is the program user Now,you may object that the target of communication of a program is not a human but a computer,that the program user is only an irrelevant intermediary, a lackey who feeds the machine.This is perhaps the case in the situation where 6 the business executive pops a diskette into a desktop computer and feeds that computer a black-box program in binary executable form.The computer,in this case,doesn't much care whether that program was written with"good programming practice”or not. We envision,however,that you,the readers of this book,are in quite a different 10621 situation.You need,or want,to know not just what a program does,but also how Numerica it does it,so that you can tinker with it and modify it to your particular application. You need others to be able to see what you have done,so that they can criticize or admire.In such cases.where the desired goal is maintainable or reusable code.the g多 targets of a program's communication are surely human,not machine. One key to achieving good programming practice is to recognize that pro- gramming,music,and poetry-all three being symbolic constructs of the human brain-are naturally structured into hierarchies that have many different nested levels.Sounds(phonemes)form small meaningful units(morphemes)which in turn form words;words group into phrases,which group into sentences;sentences make paragraphs,and these are organized into higher levels of meaning.Notes form musical phrases,which form themes,counterpoints,harmonies,etc.;which form movements,which form concertos,symphonies,and so on. The structure in programs is equally hierarchical.Appropriately,good program- ming practice brings different techniques to bear on the different levels [1-31.At a low level is the ascii character set.Then,constants,identifiers,operands,operators

1.1 Program Organization and Control Structures 5 Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyin Copyright (C) 1988-1992 by Cambridge University Press. Programs Copyright (C) 1988-1992 by Numerical Recipes Software. Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) g of machine￾readable files (including this one) to any server computer, is strictly prohibited. To order Numerical Recipes books or CDROMs, visit website http://www.nr.com or call 1-800-872-7423 (North America only), or send email to directcustserv@cambridge.org (outside North America). Kernighan, B., and Ritchie, D. 1978, The C Programming Language (Englewood Cliffs, NJ: Prentice-Hall). [2] [Reference for K&R “traditional” C. Later editions of this book conform to the ANSI C standard.] Meeus, J. 1982, Astronomical Formulae for Calculators, 2nd ed., revised and enlarged (Rich￾mond, VA: Willmann-Bell). [3] 1.1 Program Organization and Control Structures We sometimes like to point out the close analogies between computer programs, on the one hand, and written poetry or written musical scores, on the other. All three present themselves as visual media, symbols on a two-dimensional page or computer screen. Yet, in all three cases, the visual, two-dimensional, frozen-in-time representation communicates (or is supposed to communicate) something rather different, namely a process that unfolds in time. A poem is meant to be read; music, played; a program, executed as a sequential series of computer instructions. In all three cases, the target of the communication, in its visual form, is a human being. The goal is to transfer to him/her, as efficiently as can be accomplished, the greatest degree of understanding, in advance, of how the process will unfold in time. In poetry, this human target is the reader. In music, it is the performer. In programming, it is the program user. Now, you may object that the target of communication of a program is not a human but a computer, that the program user is only an irrelevant intermediary, a lackey who feeds the machine. This is perhaps the case in the situation where the business executive pops a diskette into a desktop computer and feeds that computer a black-box program in binary executable form. The computer, in this case, doesn’t much care whether that program was written with “good programming practice” or not. We envision, however, that you, the readers of this book, are in quite a different situation. You need, or want, to know not just what a program does, but also how it does it, so that you can tinker with it and modify it to your particular application. You need others to be able to see what you have done, so that they can criticize or admire. In such cases, where the desired goal is maintainable or reusable code, the targets of a program’s communication are surely human, not machine. One key to achieving good programming practice is to recognize that pro￾gramming, music, and poetry — all three being symbolic constructs of the human brain — are naturally structured into hierarchies that have many different nested levels. Sounds (phonemes) form small meaningful units (morphemes) which in turn form words; words group into phrases, which group into sentences; sentences make paragraphs, and these are organized into higher levels of meaning. Notes form musical phrases, which form themes, counterpoints, harmonies, etc.; which form movements, which form concertos, symphonies, and so on. The structure in programs is equally hierarchical. Appropriately, good program￾ming practice brings different techniques to bear on the different levels [1-3]. At a low level is the ascii character set. Then, constants, identifiers, operands, operators

6 Chapter 1.Preliminaries Then program statements,like a[j+1]=b+c/3.0;.Here,the best programming advice is simply be clear,or (correspondingly)don't be too tricky.You might momentarily be proud of yourself at writing the single line k=(2-j)*(1+3*j)/2; if you want to permute cyclically one of the values j=(0,1,2)into respectively k =(1,2,0).You will regret it later,however,when you try to understand that line.Better,and likely also faster,is k=j+1; 1f(k=3)k=0; Many programming stylists would even argue for the ploddingly literal 。% 100 switch (i){ case 0:k=1;break; case 1:k=2;break; RECIPES I case 2:k=0;break; default: fprintf(stderr,"unexpected value for j"); ex1t(1); (North America server computer, 2 9访 on the grounds that it is both clear and additionally safeguarded from wrong assump- tions about the possible values of j.Our preference among the implementations is for the middle one. 绿 OF SCIENTIFIC In this simple example,we have in fact traversed several levels of hierarchy: Statements frequently come in“groups'”or“blocks'”which make sense only taken as a whole.The middle fragment above is one example.Another is swap=a[j]; COMPUTING (ISBN 1888129200 a[j]=b[j]; b[i]=swap; which makes immediate sense to any programmer as the exchange of two variables, while uction, Numerical Recipes 10621 43106 ans=sum=0.0; (outside n=1; North Software. is very likely to be an initialization of variables prior to some iterative process.This level of hierarchy in a program is usually evident to the eye.It is good programming practice to put in comments at this level,e.g.,“initialize”or“exchange variables.” The next level is that of control structures.These are things like the switch construction in the example above,for loops,and so on.This level is sufficiently important,and relevant to the hierarchical level of the routines in this book,that we will come back to it just below. At still higher levels in the hierarchy,we have functions and modules,and the whole "global organization of the computational task to be done.In the musical analogy,we are now at the level of movements and complete works.At these levels

6 Chapter 1. Preliminaries Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyin Copyright (C) 1988-1992 by Cambridge University Press. Programs Copyright (C) 1988-1992 by Numerical Recipes Software. Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) g of machine￾readable files (including this one) to any server computer, is strictly prohibited. To order Numerical Recipes books or CDROMs, visit website http://www.nr.com or call 1-800-872-7423 (North America only), or send email to directcustserv@cambridge.org (outside North America). Then program statements, like a[j+1]=b+c/3.0;. Here, the best programming advice is simply be clear, or (correspondingly) don’t be too tricky. You might momentarily be proud of yourself at writing the single line k=(2-j)*(1+3*j)/2; if you want to permute cyclically one of the values j = (0, 1, 2) into respectively k = (1, 2, 0). You will regret it later, however, when you try to understand that line. Better, and likely also faster, is k=j+1; if (k == 3) k=0; Many programming stylists would even argue for the ploddingly literal switch (j) { case 0: k=1; break; case 1: k=2; break; case 2: k=0; break; default: { fprintf(stderr,"unexpected value for j"); exit(1); } } on the grounds that it is both clear and additionally safeguarded from wrong assump￾tions about the possible values of j. Our preference among the implementations is for the middle one. In this simple example, we have in fact traversed several levels of hierarchy: Statements frequently come in “groups” or “blocks” which make sense only taken as a whole. The middle fragment above is one example. Another is swap=a[j]; a[j]=b[j]; b[j]=swap; which makes immediate sense to any programmer as the exchange of two variables, while ans=sum=0.0; n=1; is very likely to be an initialization of variables prior to some iterative process. This level of hierarchy in a program is usually evident to the eye. It is good programming practice to put in comments at this level, e.g., “initialize” or “exchange variables.” The next level is that of control structures. These are things like the switch construction in the example above, for loops, and so on. This level is sufficiently important, and relevant to the hierarchical level of the routines in this book, that we will come back to it just below. At still higher levels in the hierarchy, we have functions and modules, and the whole “global” organization of the computational task to be done. In the musical analogy, we are now at the level of movements and complete works. At these levels

1.1 Program Organization and Control Structures 7 modularization and encapsulation become important programming concepts,the general idea being that program units should interact with one another only through clearly defined and narrowly circumscribed interfaces.Good modularization practice is an essential prerequisite to the success of large,complicated software projects. especially those employing the efforts of more than one programmer.It is also good practice (if not quite as essential)in the less massive programming tasks that an individual scientist.or reader of this book.encounters Some computer languages,such as Modula-2 and C++,promote good modular- ization with higher-level language constructs absent in C.In Modula-2,for example. 三 functions,type definitions,and data structures can be encapsulated into"modules" that communicate through declared public interfaces and whose internal workings g are hidden from the rest of the program [41.In the C++language,the key concept is"class,"a user-definable generalization of data type that provides for data hiding, automatic initialization of data,memory management,dynamic typing,and operator overloading (i.e.,the user-definable extension of operators like and so as to be appropriate to operands in any particular class)[5].Properly used in defining the data 之 structures that are passed between program units,classes can clarify and circumscribe these units'public interfaces,reducing the chances of programming error and also allowing a considerable degree of compile-time and run-time error checking. 9 Beyond modularization,though depending on it,lie the concepts of object- oriented programming.Here a programming language,such as C++or Turbo Pascal 5.5 [6],allows a module's public interface to accept redefinitions of types or actions. and these redefinitions become shared all the way down through the module's hierarchy (so-called polymorphism).For example,a routine written to invert a matrix 三兰∽9 ofreal numbers could-dynamically,at run time-be made able to handle complex 心客a OF SCIENTIFIC numbers by overloading complex data types and corresponding definitions of the arithmetic operations.Additional concepts of inheritance (the ability to define a data type that"inherits"all the structure of another type,plus additional structure of its own),and object extensibility (the ability to add functionality to a module without access to its source code,e.g.,at run time),also come into play. We have not attempted to modularize,or make objects out of,the routines in this book,for at least two reasons.First,the chosen language,C,does not really make this possible.Second,we envision that you,the reader,might want to incorporate 10621 the algorithms in this book,a few at a time,into modules or objects with a structure Numerical Recipes 43106 of your own choosing.There does not exist,at present,a standard or accepted set of"classes"for scientific object-oriented computing.While we might have tried to invent such a set,doing so would have inevitably tied the algorithmic content of the 腿 book(which is its raison d'etre)to some rather specific,and perhaps haphazard,set of choices regarding class definitions. North On the other hand,we are not unfriendly to the goals of modular and object- oriented programming.Within the limits of C,we have therefore tried to structure our programs to be "object friendly."That is one reason we have adopted ANSI C with its function prototyping as our default C dialect (see $1.2).Also,within our implementation sections,we have paid particular attention to the practices of structured programming,as we now discuss

1.1 Program Organization and Control Structures 7 Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyin Copyright (C) 1988-1992 by Cambridge University Press. Programs Copyright (C) 1988-1992 by Numerical Recipes Software. Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) g of machine￾readable files (including this one) to any server computer, is strictly prohibited. To order Numerical Recipes books or CDROMs, visit website http://www.nr.com or call 1-800-872-7423 (North America only), or send email to directcustserv@cambridge.org (outside North America). modularization and encapsulation become important programming concepts, the general idea being that program units should interact with one another only through clearly defined and narrowly circumscribed interfaces. Good modularization practice is an essential prerequisite to the success of large, complicated software projects, especially those employing the efforts of more than one programmer. It is also good practice (if not quite as essential) in the less massive programming tasks that an individual scientist, or reader of this book, encounters. Some computer languages, such as Modula-2 and C++, promote good modular￾ization with higher-level language constructs absent in C. In Modula-2, for example, functions, type definitions, and data structures can be encapsulated into “modules” that communicate through declared public interfaces and whose internal workings are hidden from the rest of the program [4]. In the C++ language, the key concept is “class,” a user-definable generalization of data type that provides for data hiding, automatic initialization of data, memory management, dynamic typing, and operator overloading (i.e., the user-definable extension of operators like + and * so as to be appropriate to operands in any particular class) [5]. Properly used in defining the data structures that are passed between program units, classes can clarify and circumscribe these units’ public interfaces, reducing the chances of programming error and also allowing a considerable degree of compile-time and run-time error checking. Beyond modularization, though depending on it, lie the concepts of object￾oriented programming. Here a programming language, such as C++ or Turbo Pascal 5.5 [6], allows a module’s public interface to accept redefinitions of types or actions, and these redefinitions become shared all the way down through the module’s hierarchy (so-called polymorphism). For example, a routine written to invert a matrix of real numbers could — dynamically, at run time — be made able to handle complex numbers by overloading complex data types and corresponding definitions of the arithmetic operations. Additional concepts of inheritance (the ability to define a data type that “inherits” all the structure of another type, plus additional structure of its own), and object extensibility (the ability to add functionality to a module without access to its source code, e.g., at run time), also come into play. We have not attempted to modularize, or make objects out of, the routines in this book, for at least two reasons. First, the chosen language, C, does not really make this possible. Second, we envision that you, the reader, might want to incorporate the algorithms in this book, a few at a time, into modules or objects with a structure of your own choosing. There does not exist, at present, a standard or accepted set of “classes” for scientific object-oriented computing. While we might have tried to invent such a set, doing so would have inevitably tied the algorithmic content of the book (which is its raison d’etre ˆ ) to some rather specific, and perhaps haphazard, set of choices regarding class definitions. On the other hand, we are not unfriendly to the goals of modular and object￾oriented programming. Within the limits of C, we have therefore tried to structure our programs to be “object friendly.” That is one reason we have adopted ANSI C with its function prototyping as our default C dialect (see §1.2). Also, within our implementation sections, we have paid particular attention to the practices of structured programming, as we now discuss

8 Chapter 1. Preliminaries Control Structures An executing program unfolds in time,but not strictly in the linear order in which the statements are written.Program statements that affect the order in which statements are executed,or that affect whether statements are executed.are called control statements.Control statements never make useful sense by themselves.They make sense only in the context of the groups or blocks of statements that they in turn control.If you think of those blocks as paragraphs containing sentences,then the control statements are perhaps best thought of as the indentation of the paragraph and the punctuation between the sentences,not the words within the sentences. 81 We can now say what the goal of structured programming is.It is to make program control manifestly apparent in the visual presentation of the program.You see that this goal has nothing at all to do with how the computer sees the program As already remarked,computers don't care whether you use structured programming or not.Human readers,however,do care.You yourself will also care,once you discover how much easier it is to perfect and debug a well-structured program than 以 one whose control structure is obscure. You accomplish the goals of structured programming in two complementary 乏 ways.First,you acquaint yourself with the small number of essential control structures that occur over and over again in programming,and that are therefore given convenient representations in most programming languages.You should learn to think about your programming tasks,insofar as possible,exclusively in terms of these standard control structures.In writing programs,you should get into the habit of representing these standard control structures in consistent,conventional ways. 9是 "Doesn't this inhibit creativity?"our students sometimes ask.Yes,just OF SCIENTIFIC as Mozart's creativity was inhibited by the sonata form,or Shakespeare's by the metrical requirements of the sonnet.The point is that creativity,when it is meant to communicate,does well under the inhibitions of appropriate restrictions on format. Second,you avoid,insofar as possible,control statements whose controlled blocks or objects are difficult to discern at a glance.This means,in practice,that you must try to avoid named labels on statements and goto's.It is not the goto's that are dangerous(although they do interrupt one's reading of a program);the named statement labels are the hazard.In fact,whenever you encounter a named statement Numerical Recipes 10621 label while reading a program,you will soon become conditioned to get a sinking 43108 feeling in the pit of your stomach.Why?Because the following questions will,by habit,immediately spring to mind:Where did control come from in a branch to this label?It could be anywhere in the routine!What circumstances resulted in a branch (outside to this label?They could be anything!Certainty becomes uncertainty,understanding Software. dissolves into a morass of possibilities North Some examples are now in order to make these considerations more concrete (see Figure 1.1.1). Catalog of Standard Structures Iteration. In C,simple iteration is performed with a for loop,for example for(j=2;j<=1000;j+){ b[j]=a[j-1]; a[j-1]=j;

8 Chapter 1. Preliminaries Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyin Copyright (C) 1988-1992 by Cambridge University Press. Programs Copyright (C) 1988-1992 by Numerical Recipes Software. Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) g of machine￾readable files (including this one) to any server computer, is strictly prohibited. To order Numerical Recipes books or CDROMs, visit website http://www.nr.com or call 1-800-872-7423 (North America only), or send email to directcustserv@cambridge.org (outside North America). Control Structures An executing program unfolds in time, but not strictly in the linear order in which the statements are written. Program statements that affect the order in which statements are executed, or that affect whether statements are executed, are called control statements. Control statements never make useful sense by themselves. They make sense only in the context of the groups or blocks of statements that they in turn control. If you think of those blocks as paragraphs containing sentences, then the control statements are perhaps best thought of as the indentation of the paragraph and the punctuation between the sentences, not the words within the sentences. We can now say what the goal of structured programming is. It is to make program control manifestly apparent in the visual presentation of the program. You see that this goal has nothing at all to do with how the computer sees the program. As already remarked, computers don’t care whether you use structured programming or not. Human readers, however, do care. You yourself will also care, once you discover how much easier it is to perfect and debug a well-structured program than one whose control structure is obscure. You accomplish the goals of structured programming in two complementary ways. First, you acquaint yourself with the small number of essential control structures that occur over and over again in programming, and that are therefore given convenient representations in most programming languages. You should learn to think about your programming tasks, insofar as possible, exclusively in terms of these standard control structures. In writing programs, you should get into the habit of representing these standard control structures in consistent, conventional ways. “Doesn’t this inhibit creativity?” our students sometimes ask. Yes, just as Mozart’s creativity was inhibited by the sonata form, or Shakespeare’s by the metrical requirements of the sonnet. The point is that creativity, when it is meant to communicate, does well under the inhibitions of appropriate restrictions on format. Second, you avoid, insofar as possible, control statements whose controlled blocks or objects are difficult to discern at a glance. This means, in practice, that you must try to avoid named labels on statements and goto’s. It is not the goto’s that are dangerous (although they do interrupt one’s reading of a program); the named statement labels are the hazard. In fact, whenever you encounter a named statement label while reading a program, you will soon become conditioned to get a sinking feeling in the pit of your stomach. Why? Because the following questions will, by habit, immediately spring to mind: Where did control come from in a branch to this label? It could be anywhere in the routine! What circumstances resulted in a branch to this label? They could be anything! Certainty becomes uncertainty, understanding dissolves into a morass of possibilities. Some examples are now in order to make these considerations more concrete (see Figure 1.1.1). Catalog of Standard Structures Iteration. In C, simple iteration is performed with a for loop, for example for (j=2;j<=1000;j++) { b[j]=a[j-1]; a[j-1]=j; }

1.1 Program Organization and Control Structures 9 iteration yes while false complete? condition no true Permission is block block increment index FOR iteration http://www.nr.com or call 1-800-872-7423 (North America WHILE iteration (a) (b) readable files (including this one)to any server computer,is strictly prohibited. granted for internet users to make one paper copy for their block block break true only),orsend email to directcustserv@cambridge.org(outside North America). own personal use.Further reproduction,or Copyright (C)1988-1992 by Cambridge University Press.Programs Copyright(C)1988-1992 by Numerical Recipes Sample page from NUMERICAL RECIPES IN C:THE ART OF SCIENTIFIC COMPUTING(ISBN 0-521-43108-5) condition true while false condition block false Software. DO WHILE iteration BREAK iteration (c) (d) Figure 1.1.1.Standard control structures used in structured programming:(a)for iteration;(b)while iteration;(c)do while iteration;(d)break iteration;(e)if structure;(f)switch structure

1.1 Program Organization and Control Structures 9 Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyin Copyright (C) 1988-1992 by Cambridge University Press. Programs Copyright (C) 1988-1992 by Numerical Recipes Software. Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) g of machine￾readable files (including this one) to any server computer, is strictly prohibited. To order Numerical Recipes books or CDROMs, visit website http://www.nr.com or call 1-800-872-7423 (North America only), or send email to directcustserv@cambridge.org (outside North America). yes no FOR iteration (a) false true WHILE iteration (b) true false BREAK iteration (d) true false DO WHILE iteration (c) iteration complete? block increment index while condition while condition block break condition block block block Figure 1.1.1. Standard control structures used in structured programming: (a) for iteration; (b) while iteration; (c) do while iteration; (d) break iteration; (e) if structure; (f) switch structure