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Exhaustive testing is the execution of every possible test case. Rarely can we do exhaustive testing. Even simple systems have too many possible test cases. For example, a program with two integer inputs on a machine with a 32-bit word would have 264 possible test cases (see Review Question 10.1). Thus, testing is always executing a very small percentage of the possible test cases. Two basic concerns in software testing are (1) what test cases to use (test case selection) and (2) how many test cases are necessary (stopping criterion). Test case selection can be based on either the speci cations (functional), the structure of the code (structural), the ow of data (data ow), or random selection of test cases. Test case selection can be viewed as an attempt to space the test cases throughout the input space. Some areas in the domain may be especially error-prone and may need extra attention. The stopping criterion can be based on a coverage criterion, such as executing n test cases in each subdomain, or the stopping criterion can be based on a behavior criteria, such as testing until an error rate is less than a threshold x. A program can be thought of as a mapping from a domain space to an answer space or range. Given an input, which is a point in the domain space, the program produces an output, which is a point in the range. Similarly, the speci cation of the program is a map from a domain space to an answer space.

2.28 2.28

(area under normal curve between z 2(area between z 2(0.4887) 0.9774 2.28 and z 0 and z 2.28) 2.28)

Fig. 14-54

1 1 2 2

15.1 SPICE AND PSPICE Spice (Simulation Program with Integrated Circuit Emphasis) is a computer program developed in the 1970s at the University of California at Berkeley for simulating electronic circuits. It is used as a tool for analysis, design, and testing of integrated circuits as well as a wide range of other electronic and electrical circuits. Spice is a public domain program. Commercial versions, such as PSpice by MicroSim Corporation, use the same algorithm and syntax as Spice but provide the technical support and addons that industrial customers need. This chapter introduces the basic elements of Spice/PSpice and their application to some simple circuits. Examples are run on the evaluation version of PSpice which is available free of charge.

0.0456 2.19

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The circuit description is entered in the computer in the form of a series of statements in a text le prepared by any ASCII text editor and called the source le. It may also be entered graphically by constructing the circuit on the computer monitor with the Schematic Capture program from MicroSim. In this chapter, we use the source le with the generic name SOURCE.CIR. To solve the circuit, we run the circuit solver on the source le. The computer puts the solution in a le named SOURCE.OUT.

0.40 0.50 0.0456 0.60 0.50 0.0456

2.19 and z 2.19, i.e., Therefore, the required probability is the area under the normal curve between z 2(0.4857) 0.9714. Although this result is accurate to two significant figures, it does not agree exactly since we have not used 1 1 the fact that the proportion is actually a discrete variable. To account for this, we subtract from 2n 2(120) 1 1 0.40 and add to 0.60. Therefore, the required proportions in standard units are, since 2n 2(120) 1>240 0.00417, 0.40 0.00417 0.0456 0.50 2.28 and 0.60 0.00417 0.0456 0.50 2.28

A speci cation is essential to software testing. Correctness in software is de ned as the program mapping being the same as the speci cation mapping. A good saying to remember is a program without a speci cation is always correct. A program without a speci cation cannot be tested against a speci cation, and the program does what it does and does not violate its speci cation. A test case should always include the expected output. It is too easy to look at an output from the computer and think that it is correct. If the expected output is di erent from the actual output, then the tester and/or user can decide which is correct.

EXAMPLE 15.1 Use PSpice to nd the dc steady-state voltage across the 5-mF capacitor in Fig. 15-1(a).

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