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Diffstat (limited to 'doc/expr.n')
| -rw-r--r-- | doc/expr.n | 366 |
1 files changed, 160 insertions, 206 deletions
@@ -1,12 +1,13 @@ '\" '\" Copyright (c) 1993 The Regents of the University of California. '\" Copyright (c) 1994-2000 Sun Microsystems, Inc. +'\" Copyright (c) 2005 by Kevin B. Kenny <kennykb@acm.org>. All rights reserved '\" '\" See the file "license.terms" for information on usage and redistribution '\" of this file, and for a DISCLAIMER OF ALL WARRANTIES. '\" .so man.macros -.TH expr n 8.4 Tcl "Tcl Built-In Commands" +.TH expr n 8.5 Tcl "Tcl Built-In Commands" .BS '\" Note: do not modify the .SH NAME line immediately below! .SH NAME @@ -14,14 +15,14 @@ expr \- Evaluate an expression .SH SYNOPSIS \fBexpr \fIarg \fR?\fIarg arg ...\fR? .BE - .SH DESCRIPTION .PP Concatenates \fIarg\fRs (adding separator spaces between them), evaluates the result as a Tcl expression, and returns the value. -The operators permitted in Tcl expressions are a subset of -the operators permitted in C expressions, and they have the -same meaning and precedence as the corresponding C operators. +The operators permitted in Tcl expressions include a subset of +the operators permitted in C expressions. For those operators +common to both Tcl and C, Tcl applies the same meaning and precedence +as the corresponding C operators. Expressions almost always yield numeric results (integer or floating-point values). For example, the expression @@ -31,36 +32,38 @@ For example, the expression evaluates to 14.2. Tcl expressions differ from C expressions in the way that operands are specified. Also, Tcl expressions support -non-numeric operands and string comparisons. -.SH OPERANDS +non-numeric operands and string comparisons, as well as some +additional operators not found in C. +.SS OPERANDS .PP A Tcl expression consists of a combination of operands, operators, and parentheses. White space may be used between the operands and operators and parentheses; it is ignored by the expression's instructions. Where possible, operands are interpreted as integer values. -Integer values may be specified in decimal (the normal case), in octal (if the -first character of the operand is \fB0\fR), or in hexadecimal (if the first -two characters of the operand are \fB0x\fR). +.VS 8.5 +Integer values may be specified in decimal (the normal case), in binary +(if the first two characters of the operand are \fB0b\fR), in octal +(if the first two characters of the operand are \fB0o\fR), or in hexadecimal +(if the first two characters of the operand are \fB0x\fR). For +compatibility with older Tcl releases, an octal integer value is also +indicated simply when the first character of the operand is \fB0\fR, +whether or not the second character is also \fBo\fR. If an operand does not have one of the integer formats given above, then it is treated as a floating-point number if that is -possible. Floating-point numbers may be specified in any of the -ways accepted by an ANSI-compliant C compiler (except that the -\fBf\fR, \fBF\fR, \fBl\fR, and \fBL\fR suffixes will not be permitted in -most installations). For example, all of the +possible. Floating-point numbers may be specified in any of several +common formats making use of the decimal digits, the decimal point \fB.\fR, +the characters \fBe\fR or \fBE\fR indicating scientific notation, and +the sign characters \fB+\fR or \fB\-\fR. For example, all of the following are valid floating-point numbers: 2.1, 3., 6e4, 7.91e+16. +Also recognized as floating point values are the strings \fBInf\fR +and \fBNaN\fR making use of any case for each character. +.VE 8.5 If no numeric interpretation is possible (note that all literal operands that are not numeric or boolean must be quoted with either braces or with double quotes), then an operand is left as a string (and only a limited set of operators may be applied to it). .PP -.VS 8.4 -On 32-bit systems, integer values MAX_INT (0x7FFFFFFF) and MIN_INT -(-0x80000000) will be represented as 32-bit values, and integer values -outside that range will be represented as 64-bit values (if that is -possible at all.) -.VE 8.4 -.PP Operands may be specified in any of the following ways: .IP [1] As a numeric value, either integer or floating-point. @@ -84,8 +87,8 @@ The command will be executed and its result will be used as the operand. .IP [7] As a mathematical function whose arguments have any of the above -forms for operands, such as \fBsin($x)\fR. See below for a list of defined -functions. +forms for operands, such as \fBsin($x)\fR. See \fBMATH FUNCTIONS\fR below for +a discussion of how mathematical functions are handled. .LP Where the above substitutions occur (e.g. inside quoted strings), they are performed by the expression's instructions. @@ -102,27 +105,46 @@ Then the command on the left side of each of the lines below will produce the value on the right side of the line: .CS .ta 6c -\fBexpr 3.1 + $a 6.1 -expr 2 + "$a.$b" 5.6 -expr 4*[llength "6 2"] 8 -expr {{word one} < "word $a"} 0\fR +\fBexpr\fR 3.1 + $a \fI6.1\fR +\fBexpr\fR 2 + "$a.$b" \fI5.6\fR +\fBexpr\fR 4*[llength "6 2"] \fI8\fR +\fBexpr\fR {{word one} < "word $a"} \fI0\fR .CE -.SH OPERATORS +.SS OPERATORS .PP -The valid operators are listed below, grouped in decreasing order -of precedence: +The valid operators (most of which are also available as commands in +the \fBtcl::mathop\fR namespace; see the \fBmathop\fR(n) manual page +for details) are listed below, grouped in decreasing order of precedence: .TP 20 \fB\-\0\0+\0\0~\0\0!\fR Unary minus, unary plus, bit-wise NOT, logical NOT. None of these operators may be applied to string operands, and bit-wise NOT may be applied only to integers. .TP 20 +\fB**\fR +.VS 8.5 +Exponentiation. Valid for any numeric operands. +.VE 8.5 +.TP 20 \fB*\0\0/\0\0%\fR Multiply, divide, remainder. None of these operators may be applied to string operands, and remainder may be applied only to integers. The remainder will always have the same sign as the divisor and -an absolute value smaller than the divisor. +an absolute value smaller than the absolute value of the divisor. +.RS +.PP +When applied to integers, the division and remainder operators can be +considered to partition the number line into a sequence of equal-sized +adjacent non-overlapping pieces where each piece is the size of the divisor; +the division result identifies which piece the divisor lay within, and the +remainder result identifies where within that piece the divisor lay. A +consequence of this is that the result of +.QW "-57 \fB/\fR 10" +is always -6, and the result of +.QW "-57 \fB%\fR 10" +is always 3. +.RE .TP 20 \fB+\0\0\-\fR Add and subtract. Valid for any numeric operands. @@ -140,12 +162,19 @@ in which case string comparison is used. \fB==\0\0!=\fR Boolean equal and not equal. Each operator produces a zero/one result. Valid for all operand types. -.VS 8.4 .TP 20 \fBeq\0\0ne\fR Boolean string equal and string not equal. Each operator produces a zero/one result. The operand types are interpreted only as strings. -.VE 8.4 +.TP 20 +\fBin\0\0ni\fR +.VS 8.5 +List containment and negated list containment. Each operator produces +a zero/one result and treats its first argument as a string and its +second argument as a Tcl list. The \fBin\fR operator indicates +whether the first argument is a member of the second argument list; +the \fBni\fR operator inverts the sense of the result. +.VE 8.5 .TP 20 \fB&\fR Bit-wise AND. Valid for integer operands only. @@ -173,168 +202,84 @@ The \fIx\fR operand must have a boolean or numeric value. .LP See the C manual for more details on the results produced by each operator. +.VS 8.5 +The exponentiation operator promotes types like the multiply and +divide operators, and produces a result that is the same as the output +of the \fBpow\fR function (after any type conversions.) +.VE 8.5 All of the binary operators group left-to-right within the same precedence level. For example, the command .CS -\fBexpr 4*2 < 7\fR +\fBexpr\fR {4*2 < 7} .CE returns 0. .PP -The \fB&&\fR, \fB||\fR, and \fB?:\fR operators have ``lazy -evaluation'', just as in C, -which means that operands are not evaluated if they are +The \fB&&\fR, \fB||\fR, and \fB?:\fR operators have +.QW "lazy evaluation" , +just as in C, which means that operands are not evaluated if they are not needed to determine the outcome. For example, in the command .CS \fBexpr {$v ? [a] : [b]}\fR .CE -only one of \fB[a]\fR or \fB[b]\fR will actually be evaluated, +only one of +.QW \fB[a]\fR +or +.QW \fB[b]\fR +will actually be evaluated, depending on the value of \fB$v\fR. Note, however, that this is only true if the entire expression is enclosed in braces; otherwise -the Tcl parser will evaluate both \fB[a]\fR and \fB[b]\fR before -invoking the \fBexpr\fR command. -.SH "MATH FUNCTIONS" +the Tcl parser will evaluate both +.QW \fB[a]\fR +and +.QW \fB[b]\fR +before invoking the \fBexpr\fR command. +.SS "MATH FUNCTIONS" +.PP +.VS 8.5 +When the expression parser encounters a mathematical function +such as \fBsin($x)\fR, it replaces it with a call to an ordinary +Tcl function in the \fBtcl::mathfunc\fR namespace. The processing +of an expression such as: +.CS +\fBexpr {sin($x+$y)}\fR +.CE +is the same in every way as the processing of: +.CS +\fBexpr {[tcl::mathfunc::sin [expr {$x+$y}]]}\fR +.CE +which in turn is the same as the processing of: +.CS +\fBtcl::mathfunc::sin [expr {$x+$y}]\fR +.CE .PP -Tcl supports the following mathematical functions in expressions, all -of which work solely with floating-point numbers unless otherwise noted: -.DS -.ta 3c 6c 9c -\fBabs\fR \fBcosh\fR \fBlog\fR \fBsqrt\fR -\fBacos\fR \fBdouble\fR \fBlog10\fR \fBsrand\fR -\fBasin\fR \fBexp\fR \fBpow\fR \fBtan\fR -\fBatan\fR \fBfloor\fR \fBrand\fR \fBtanh\fR -\fBatan2\fR \fBfmod\fR \fBround\fR \fBwide\fR -\fBceil\fR \fBhypot\fR \fBsin\fR -\fBcos\fR \fBint\fR \fBsinh\fR -.DE +The executor will search for \fBtcl::mathfunc::sin\fR using the usual +rules for resolving functions in namespaces. Either +\fB::tcl::mathfunc::sin\fR or \fB[namespace +current]::tcl::mathfunc::sin\fR will satisfy the request, and others +may as well (depending on the current \fBnamespace path\fR setting). .PP -.TP -\fBabs(\fIarg\fB)\fR -Returns the absolute value of \fIarg\fR. \fIArg\fR may be either -integer or floating-point, and the result is returned in the same form. -.TP -\fBacos(\fIarg\fB)\fR -Returns the arc cosine of \fIarg\fR, in the range [\fI0\fR,\fIpi\fR] -radians. \fIArg\fR should be in the range [\fI-1\fR,\fI1\fR]. -.TP -\fBasin(\fIarg\fB)\fR -Returns the arc sine of \fIarg\fR, in the range [\fI-pi/2\fR,\fIpi/2\fR] -radians. \fIArg\fR should be in the range [\fI-1\fR,\fI1\fR]. -.TP -\fBatan(\fIarg\fB)\fR -Returns the arc tangent of \fIarg\fR, in the range [\fI-pi/2\fR,\fIpi/2\fR] -radians. -.TP -\fBatan2(\fIy, x\fB)\fR -Returns the arc tangent of \fIy\fR/\fIx\fR, in the range [\fI-pi\fR,\fIpi\fR] -radians. \fIx\fR and \fIy\fR cannot both be 0. If \fIx\fR is greater -than \fI0\fR, this is equivalent to \fBatan(\fIy/x\fB)\fR. -.TP -\fBceil(\fIarg\fB)\fR -Returns the smallest integral floating-point value (i.e. with a zero -fractional part) not less than \fIarg\fR. -.TP -\fBcos(\fIarg\fB)\fR -Returns the cosine of \fIarg\fR, measured in radians. -.TP -\fBcosh(\fIarg\fB)\fR -Returns the hyperbolic cosine of \fIarg\fR. If the result would cause -an overflow, an error is returned. -.TP -\fBdouble(\fIarg\fB)\fR -If \fIarg\fR is a floating-point value, returns \fIarg\fR, otherwise converts -\fIarg\fR to floating-point and returns the converted value. -.TP -\fBexp(\fIarg\fB)\fR -Returns the exponential of \fIarg\fR, defined as \fIe\fR**\fIarg\fR. -If the result would cause an overflow, an error is returned. -.TP -\fBfloor(\fIarg\fB)\fR -Returns the largest integral floating-point value (i.e. with a zero -fractional part) not greater than \fIarg\fR. -.TP -\fBfmod(\fIx, y\fB)\fR -Returns the floating-point remainder of the division of \fIx\fR by -\fIy\fR. If \fIy\fR is 0, an error is returned. -.TP -\fBhypot(\fIx, y\fB)\fR -Computes the length of the hypotenuse of a right-angled triangle -\fBsqrt(\fIx\fR*\fIx\fR+\fIy\fR*\fIy\fB)\fR. -.TP -\fBint(\fIarg\fB)\fR -.VS 8.4 -If \fIarg\fR is an integer value of the same width as the machine -word, returns \fIarg\fR, otherwise -converts \fIarg\fR to an integer (of the same size as a machine word, -i.e. 32-bits on 32-bit systems, and 64-bits on 64-bit systems) by -truncation and returns the converted value. -.VE 8.4 -.TP -\fBlog(\fIarg\fB)\fR -Returns the natural logarithm of \fIarg\fR. \fIArg\fR must be a -positive value. -.TP -\fBlog10(\fIarg\fB)\fR -Returns the base 10 logarithm of \fIarg\fR. \fIArg\fR must be a -positive value. -.TP -\fBpow(\fIx, y\fB)\fR -Computes the value of \fIx\fR raised to the power \fIy\fR. If \fIx\fR -is negative, \fIy\fR must be an integer value. -.TP -\fBrand()\fR -Returns a pseudo-random floating-point value in the range (\fI0\fR,\fI1\fR). -The generator algorithm is a simple linear congruential generator that -is not cryptographically secure. Each result from \fBrand\fR completely -determines all future results from subsequent calls to \fBrand\fR, so -\fBrand\fR should not be used to generate a sequence of secrets, such as -one-time passwords. The seed of the generator is initialized from the -internal clock of the machine or may be set with the \fBsrand\fR function. -.TP -\fBround(\fIarg\fB)\fR -If \fIarg\fR is an integer value, returns \fIarg\fR, otherwise converts -\fIarg\fR to integer by rounding and returns the converted value. -.TP -\fBsin(\fIarg\fB)\fR -Returns the sine of \fIarg\fR, measured in radians. -.TP -\fBsinh(\fIarg\fB)\fR -Returns the hyperbolic sine of \fIarg\fR. If the result would cause -an overflow, an error is returned. -.TP -\fBsqrt(\fIarg\fB)\fR -Returns the square root of \fIarg\fR. \fIArg\fR must be non-negative. -.TP -\fBsrand(\fIarg\fB)\fR -The \fIarg\fR, which must be an integer, is used to reset the seed for -the random number generator of \fBrand\fR. Returns the first random -number (see \fBrand()\fR) from that seed. Each interpreter has its own seed. -.TP -\fBtan(\fIarg\fB)\fR -Returns the tangent of \fIarg\fR, measured in radians. -.TP -\fBtanh(\fIarg\fB)\fR -Returns the hyperbolic tangent of \fIarg\fR. -.TP -\fBwide(\fIarg\fB)\fR -.VS 8.4 -Converts \fIarg\fR to an integer value at least 64-bits wide (by sign-extension -if \fIarg\fR is a 32-bit number) if it is not one already. -.VE 8.4 +See the \fBmathfunc\fR(n) manual page for the math functions that are +available by default. +.VE 8.5 +.SS "TYPES, OVERFLOW, AND PRECISION" .PP -In addition to these predefined functions, applications may -define additional functions using \fBTcl_CreateMathFunc\fR(). -.SH "TYPES, OVERFLOW, AND PRECISION" +.VS 8.5 +All internal computations involving integers are done calling on the +LibTomMath multiple precision integer library as required so that all +integer calculations are performed exactly. Note that in Tcl releases +prior to 8.5, integer calculations were performed with one of the C types +\fIlong int\fR or \fITcl_WideInt\fR, causing implicit range truncation +in those calculations where values overflowed the range of those types. +Any code that relied on these implicit truncations will need to explicitly +add \fBint()\fR or \fBwide()\fR function calls to expressions at the points +where such truncation is required to take place. +.VE 8.5 .PP -All internal computations involving integers are done with the C type -\fIlong\fR, and all internal computations involving floating-point are +All internal computations involving floating-point are done with the C type \fIdouble\fR. When converting a string to floating-point, exponent overflow is -detected and results in a Tcl error. -For conversion to integer from string, detection of overflow depends -on the behavior of some routines in the local C library, so it should -be regarded as unreliable. -In any case, integer overflow and underflow are generally not detected -reliably for intermediate results. Floating-point overflow and underflow +detected and results in the \fIdouble\fR value of \fBInf\fR or +\fB\-Inf\fR as appropriate. Floating-point overflow and underflow are detected to the degree supported by the hardware, which is generally pretty reliable. .PP @@ -344,35 +289,37 @@ For arithmetic computations, integers are used until some floating-point number is introduced, after which floating-point is used. For example, .CS -\fBexpr 5 / 4\fR +\fBexpr\fR {5 / 4} .CE returns 1, while .CS -\fBexpr 5 / 4.0\fR -\fBexpr 5 / ( [string length "abcd"] + 0.0 )\fR +\fBexpr\fR {5 / 4.0} +\fBexpr\fR {5 / ( [string length "abcd"] + 0.0 )} .CE both return 1.25. -Floating-point values are always returned with a ``\fB.\fR'' -or an \fBe\fR so that they will not look like integer values. For -example, +Floating-point values are always returned with a +.QW \fB.\fR +or an +.QW \fBe\fR +so that they will not look like integer values. For example, .CS -\fBexpr 20.0/5.0\fR +\fBexpr\fR {20.0/5.0} .CE returns \fB4.0\fR, not \fB4\fR. -.SH "STRING OPERATIONS" +.SS "STRING OPERATIONS" .PP String values may be used as operands of the comparison operators, although the expression evaluator tries to do comparisons as integer or floating-point when it can, i.e., when all arguments to the operator allow numeric interpretations, -.VS 8.4 except in the case of the \fBeq\fR and \fBne\fR operators. -.VE 8.4 If one of the operands of a comparison is a string and the other -has a numeric value, the numeric operand is converted back to -a string using the C \fIsprintf\fR format specifier -\fB%d\fR for integers and \fB%g\fR for floating-point values. -For example, the commands +has a numeric value, a canonical string representation of the numeric +operand value is generated to compare with the string operand. +Canonical string representation for integer values is a decimal string +format. Canonical string representation for floating-point values +is that produced by the \fB%g\fR format specifier of Tcl's +\fBformat\fR command. For example, the commands .CS \fBexpr {"0x03" > "2"}\fR \fBexpr {"0y" > "0x12"}\fR @@ -380,14 +327,10 @@ For example, the commands both return 1. The first comparison is done using integer comparison, and the second is done using string comparison. Because of Tcl's tendency to treat values as numbers whenever -possible, it isn't generally a good idea to use operators like \fB==\fR +possible, it is not generally a good idea to use operators like \fB==\fR when you really want string comparison and the values of the -operands could be arbitrary; it's better in these cases to use -.VS 8.4 -the \fBeq\fR or \fBne\fR operators, or -.VE 8.4 -the \fBstring\fR command instead. - +operands could be arbitrary; it is better in these cases to use +the \fBeq\fR or \fBne\fR operators, or the \fBstring\fR command instead. .SH "PERFORMANCE CONSIDERATIONS" .PP Enclose expressions in braces for the best speed and the smallest @@ -410,7 +353,7 @@ then the \fBexpr\fR command will evaluate the expression \fB$a + 2*4\fR. Most expressions do not require a second round of substitutions. Either they are enclosed in braces or, if not, their variable and command substitutions yield numbers or strings -that don't themselves require substitutions. +that do not themselves require substitutions. However, because a few unbraced expressions need two rounds of substitutions, the bytecode compiler must emit @@ -419,12 +362,18 @@ The most expensive code is required for unbraced expressions that contain command substitutions. These expressions must be implemented by generating new code each time the expression is executed. +.VS 8.5 +When the expression is unbraced to allow the substitution of a function or +operator, consider using the commands documented in the \fBmathfunc\fR(n) or +\fBmathop\fR(n) manual pages directly instead. +.VE 8.5 .SH EXAMPLES -Define a procedure that computes an "interesting" mathematical -function: +Define a procedure that computes an +.QW interesting +mathematical function: .CS -proc calc {x y} { - \fBexpr\fR { ($x*$x - $y*$y) / exp($x*$x + $y*$y) } +proc tcl::mathfunc::calc {x y} { + \fBexpr\fR { ($x**2 - $y**2) / exp($x**2 + $y**2) } } .CE .PP @@ -461,9 +410,14 @@ Generate a random integer in the range 0..99 inclusive: .CS set randNum [\fBexpr\fR { int(100 * rand()) }] .CE - .SH "SEE ALSO" -array(n), for(n), if(n), string(n), Tcl(n), while(n) - +array(n), for(n), if(n), mathfunc(n), mathop(n), namespace(n), proc(n), +string(n), Tcl(n), while(n) .SH KEYWORDS arithmetic, boolean, compare, expression, fuzzy comparison +.SH COPYRIGHT +.nf +Copyright (c) 1993 The Regents of the University of California. +Copyright (c) 1994-2000 Sun Microsystems Incorporated. +Copyright (c) 2005 by Kevin B. Kenny <kennykb@acm.org>. All rights reserved. +.fi |