Transcript Document

PRACTICAL COMMON LISP
1
Peter Seibel
http://www.gigamonkeys.com/book/
CHAPTER 10
NUMBERS,
CHARACTERS,
AND STRINGS
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INTRODUCTION


Common Lisp provides built-in support for most of the data types typically
found in modern languages:
 numbers (integer, floating point, and complex),
 characters,
 strings,
 arrays (including multidimensional arrays),
 lists,
 hash tables,
 input and output streams, and
 an abstraction for portably representing filenames.
This chapter will cover the built-in “scalar” data types: numbers, characters,
and strings.
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NUMBERS

Lisp was originally designed by a mathematician (數學家) as a tool for
studying mathematical functions.
 Its numbers behave more like true mathematical numbers than the
approximations of numbers.
 For instance
 Integers in Common Lisp can be almost arbitrarily large rather
than being limited by the size of a machine word.
 And dividing two integers results in an exact ratio, not a
truncated value.
 Common Lisp also offers several types of floating-point numbers.
 Common Lisp supports complex numbers—the numbers that result
from doing things such as taking square roots and logarithms of
negative numbers.
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NUMERIC LITERALS


For a given number of a given type, there can be many different textual
representations, all of which will be translated to the same object
representation by the Lisp reader.
For instance, you can write the integer 10 as 10, 20/2, #xA, or any of a
number of other ways, but the reader will translate all these to the same
object.
CL-USER>
10
CL-USER>
10
CL-USER>
10
CL-USER>
10
CL-USER>
10
10
20/2
#xa
;十六進位表示法 #xa - #xf
#b1010
;二進位表示法
#o12
;八進位表示法
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NUMERIC LITERALS

It’s also possible to write rationals (有理數) in bases other than 10.

If preceded by #B or #b, a rational literal is read as a binary number
with 0 and 1 as the only legal digits.

An #O or #o indicates an octal number (legal digits 0–7), and
#X or #x indicates hexadecimal (legal digits 0–F or 0–f).

You can write rationals in other bases from 2 to 36 with #nR where n is
the base (always written in decimal).

Additional “digits” beyond 9 are taken from the letters A–Z or a–z.
#b10101 → 21
#b1010/1011 → 10/11
#o777 → 511
#xDADA → 56026
#36rABCDEFGHIJKLMNOPQRSTUVWXYZ →
8337503854730415241050377135811259267835
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NUMERIC LITERALS

You can also write floating-point numbers in a variety of ways.
 Common Lisp defines four subtypes of floating-point number: short,
single, double, and long.
 The exponent markers s, f, d, l (and their uppercase equivalents)
indicate short, single, double, and long floats, respectively.
(https://www.cs.cmu.edu/Groups/AI/html/cltl/clm/node19.html)
 The letter does double duty: it marks the beginning of the
exponent and indicates what floating point representation should
be used for the number.
 The letter e indicates that the default representation (initially
single-float) should be used.
1.0
→ 1.0
1e0
→ 1.0
1d0
→ 1.0d0
123.0
→ 123.0
123e0
→ 123.0
0.123
→ 0.123
.123
→ 0.123
123e-3
→ 0.123
123E-3 → 0.123
0.123e20 → 1.23e19
123d23 → 1.23d25
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NUMERIC LITERALS

Complex numbers are written in their own syntax,

#C or #c followed by a list of two real numbers representing the
real(實數) and imaginary(虛數) part of the complex number.

No complex numbers have a rational real component and a zero
imaginary part, they’re represented by the appropriate rational value.
#c(2 1) → #c(2
#c(2/3 3/4)
#c(2 1.0)
#c(2.0 1.0d0)
#c(1/2 1.0)
#c(3 0) → 3
#c(3.0 0.0)
#c(1/2 0)
#c(-6/3 0)
1)
→
→
→
→
#c(2/3 3/4)
#c(2.0 1.0)
#c(2.0d0 1.0d0)
#c(0.5 1.0)
→ #c(3.0 0.0)
→ 1/2
→ -2
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BASIC MATH

The basic arithmetic operations—addition, subtraction, multiplication,
and division—are supported for all the different kinds of Lisp numbers
with the functions +, -, *, and /.
(+ 1 2)
→3
(+ 10.0 3.0) → 13.0
(- 5 4)
→1
(- 10 3 5)
→2
(* 2 3 4)
→ 24
(/ 10 5 2) → 1

(+ 1 2 3)
(+ #c(1 2)
(- 2)
(* 2 3)
(/ 10 5)
(/ 4)
→6
#c(3 4)) → #c(4 6)
→ -2
→6
→2
→ 1/4
If any of the arguments are complex, any real arguments are converted
to the complex equivalents.
(+ 1 2.0)
→ 3.0
(+ #c(1 2) 3)
→ #c(4 2)
(+ #c(1 1) #c(2 -1)) → 3
(/ 2 3.0)
→ 0.6666667
(+ #c(1 2) 3/2) → #c(5/2 2)
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BASIC MATH

Because / doesn’t truncate, Common Lisp provides four flavors of
truncating and rounding for converting a real number to an integer:

FLOOR truncates toward negative infinity, returning the largest
integer less than or equal to the argument.

CEILING truncates toward positive infinity, returning the smallest
integer greater than or equal to the argument.

TRUNCATE truncates toward zero, making it equivalent to FLOOR
for positive arguments and to CEILING for negative arguments.

And ROUND rounds to the nearest integer.

If the argument is exactly halfway between two integers, it rounds
to the nearest even integer.
> (floor 30 4)
7;
2
> (ceiling 30 4)
8;
-2
> (truncate 30 4)
7;
2
> (truncate 29 4)
7;
1
> (round 30 4)
8;
-2
> (round 29 4)
7;
1
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BASIC MATH


Two related functions are MOD and REM, which return the modulus and
remainder of a truncating division on real numbers.
These two functions are related to the FLOOR and TRUNCATE functions
as follows:
(+ (* (floor (/ x y)) y) (mod x y)) ≡ x
(+ (* (truncate (/ x y)) y) (rem x y)) ≡ x
> (floor 29 4)
7;
1
> (mod 29 4)
1
> (truncate 29 4)
7;
1
> (rem 29 4)
1
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BASIC MATH


The functions 1+ and 1- provide a shorthand way to express adding and
subtracting one from a number.

Note that these are different from the macros INCF and DECF.

1+ and 1- are just functions that return a new value, but INCF and
DECF modify a place.
The following equivalences show the relation between INCF/DECF,
1+/1-, and +/-:
(incf x)
≡ (setf x (1+ x))
(decf x) ≡ (setf x (1- x))
≡ (setf x (+ x 1))
≡ (setf x (- x 1))
(incf x 10)
≡ (setf x (+ x 10))
(decf x 10)
≡ (setf x (- x 10))
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NUMERIC COMPARISONS

The function = is the numeric equality predicate.
 It compares numbers by mathematical value, ignoring differences in
type.
(= 1 1) → T
(= 10 20/2) → T
(= 1 1.0 #c(1.0 0.0) #c(1 0)) → T

The /= function returns true only if all its arguments are different
values.
(/= 1 1)
→ NIL
(/= 1 2)
→T
(/= 1 2 3)
→T
(/= 1 2 3 1)
→ NIL
(/= 1 2 3 1.0)
→ NIL
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NUMERIC COMPARISONS


The functions <, >, <=, and >= order rationals and floating-point
numbers.
(< 2 3)
→T
(> 2 3)
→ NIL
(> 3 2)
→T
(< 2 3 4)
→T
(<= 2 3 3)
→T
(< 2 3 3)
→ NIL
(<= 2 3 3 4)
→T
(<= 2 3 4 3)
→ NIL
To pick out the smallest or largest of several numbers, we can use the
function MIN or MAX, which takes any number of real number
arguments and returns the minimum or maximum value.
(max 10 11)
→ 11
(min -12 -10)
→ -12
(max -1 2 -3 4 5 6)
→6
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NUMERIC COMPARISONS



Some other functions are ZEROP, MINUSP, and PLUSP, which test
whether a single real number is equal to, less than, or greater than zero.
Two other predicates, EVENP and ODDP, test whether a single integer
argument is even or odd.
 The P suffix on the names of these functions is a standard naming
convention for predicate functions, functions that test some condition
and return a boolean.
Lisp also supports
 logarithms: LOG;
 exponentiation: EXP and EXPT;
 the basic trigonometric functions: SIN, COS, and TAN;
 their inverses: ASIN, ACOS, and ATAN;
 hyperbolic functions: SINH, COSH, and TANH; and
 their inverses: ASINH, ACOSH, and ATANH.
 It also provides functions to get at the individual bits of an integer
and to extract the parts of a ratio or a complex number.
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EXERCISE

Write a function NUMCOM which can read two positive number, and
calculate all the prime numbers between their sum and product values.
For example:
>(numcom)
Please input two positive numbers: 2 7
The prime numbers between 9 and 14 are 11 and 13.
Do you want to try again? Y
Please input two positive numbers: 2 -7
-7 is not a positive number.
Do you want to try again? Y
Please input two positive numbers: a 7
a is not a number.
Do you want to try again? N
NIL
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CHARACTERS

Common Lisp characters are a distinct type of object from numbers.
 The read syntax for characters objects is simple: #\ followed by the
desired character.
 Thus, #\x is the character x.
 Any character can be used after the #\, including otherwise special
characters such as ", (, and whitespace.
 We can write #\Space instead of #\ , though the latter is
technically legal.
 Other semistandard names are Tab, Page, Rubout, Linefeed(換行),
Return, and Backspace.
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CHARACTER COMPARISONS


The main thing you can do with characters, other than putting them into
strings, is to compare them with other characters.
For example:
> (char= #\e #\E)
NIL
> (char-equal #\e #\E)
T
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STRINGS

Literal strings are written enclosed in double quotes.
 We can include any character supported by the character set in a
literal string except double quote (") and backslash (\).

For examples:
> "foo\"bar"
"foo\"bar"
> (format t "foo\"bar")
foo"bar
NIL
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STRING COMPARISONS


We can compare strings using a set of functions that follow the same
naming convention as the character comparison functions except with
STRING as the prefix rather than CHAR.
For example:
> (string= "THIS" "this")
NIL
> (string-equal "THIS" "this")
T
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STRING COMPARISONS

The string comparators can compare two substrings.
 The arguments—:start1, :end1, :start2, and :end2—specify the
starting (inclusive) and ending (exclusive) indices of substrings in the
first and second string arguments.
 For example,
(string= "foobarbaz" "quuxbarfoo" :start1 3 :end1 6 :start2 4 :end2 7)
compares the substring “bar” in the two arguments and returns true.
The :end1 and :end2 arguments can be NIL (or the keyword
argument omitted altogether) to indicate that the corresponding
substring extends to the end of the string.
 For examples:

Break 10 [11]> (string= "foobarbaz" "quuxbarfoo" :start1 3 :start2 4 )
NIL
Break 10 [11]> (string= "foobar" "quuxbar" :start1 3 :start2 4 )
T
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STRING COMPARISONS

The comparators that return true when their arguments differ.

All of them except STRING= and STRING-EQUAL return the index
in the first string where the mismatch was detected.
(string/= "lisp" "lissome") → 3
(string/= "lisp" "lisp")

→ NIL
If the first string is a prefix of the second, the return value will be the
length of the first string.
(string< "lisp" "lisper") → 4
(string< "lisper" "lisp") → NIL

When comparing substrings, the resulting value is still an index into
the string as a whole.

For instance, the following compares the substrings “bar” and “baz” but
returns 5 because that’s the index of the r in the first string:
(string< "foobar" "abaz" :start1 3 :start2 1) → 5
;not 2
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EXERCISE

Please write a function STRCOM, which can read two input strings STR1 and STR2
and check if STR1 is a substring of STR2 or STR2 is a substring of STR1.
> (STRCOM)
Please input the first string STR1: abcdefghijk
Please input the second string STR2: cdefg
STR2 is a substring of STR1 from position 2 to position 6.
Do you want to check other strings? Y
Please input the first string STR1: aaaa
Please input the second string STR2: cccaaaaaaccc
STR1 is a substring of STR2 from position 3 to position 6.
Do you want to check other strings? Y
Please input the first string STR1: abcd
Please input the second string STR2: ccaacc
STR1 is not a substring of STR2 and STR2 is not a substring of STR1.
Do you want to check other strings? N
NIL
PS. Access substrings: http://cl-cookbook.sourceforge.net/strings.html#substrings
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