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Diffstat (limited to 'doc/expr.n')
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1 files changed, 217 insertions, 173 deletions
@@ -17,14 +17,14 @@ expr \- Evaluate an expression .BE .SH DESCRIPTION .PP -Concatenates \fIarg\fRs, separated by a space, into an expression, and evaluates -that expression, returning its value. -The operators permitted in an expression include a subset of +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 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. -The value of an expression is often a numeric result, either an integer or a -floating-point value, but may also be a non-numeric value. +Expressions almost always yield numeric results +(integer or floating-point values). For example, the expression .PP .CS @@ -32,68 +32,79 @@ For example, the expression .CE .PP evaluates to 14.2. -Expressions differ from C expressions in the way that -operands are specified. Expressions also support -non-numeric operands, string comparisons, and some +Tcl expressions differ from C expressions in the way that +operands are specified. Also, Tcl expressions support +non-numeric operands and string comparisons, as well as some additional operators not found in C. -.PP -When an expression evaluates to an integer, the value is the decimal form of -the integer, and when an expression evaluates to a floating-point number, the -value is the form produced by the \fB%g\fR format specifier of Tcl's -\fBformat\fR command. .SS OPERANDS .PP -An expression consists of a combination of operands, operators, parentheses and -commas, possibly with whitespace between any of these elements, which is -ignored. -An integer operand may be specified in decimal (the optional first two characters are \fB0d\fR), binary -(the first two characters are \fB0b\fR), octal -(the first two characters are \fB0o\fR), or hexadecimal -(the first two characters are \fB0x\fR) form. For -compatibility with older Tcl releases, an operand that begins with \fB0\fR is -interpreted as an octal integer even if the second character is not \fBo\fR. -A floating-point number may be specified in any of several -common decimal formats, and may use the decimal point \fB.\fR, -\fBe\fR or \fBE\fR for scientific notation, and -the sign characters \fB+\fR and \fB\-\fR. The -following are all valid floating-point numbers: 2.1, 3., 6e4, 7.91e+16. -The strings \fBInf\fR -and \fBNaN\fR, in any combination of case, are also recognized as floating point -values. An operand that doesn't have a numeric interpretation must be quoted -with either braces or with double quotes. -.PP -An operand may be specified in any of the following ways: +A Tcl expression consists of a combination of operands, operators, +parentheses and commas. +White space may be used between the operands and operators and +parentheses (or commas); 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, the optional +first two characters are \fB0d\fR), 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 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. +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 +Operands may be specified in any of the following ways: .IP [1] As a numeric value, either integer or floating-point. .IP [2] As a boolean value, using any form understood by \fBstring is\fR \fBboolean\fR. .IP [3] -As a variable, using standard \fB$\fR notation. -The value of the variable is then the value of the operand. +As a Tcl variable, using standard \fB$\fR notation. +The variable's value will be used as the operand. .IP [4] As a string enclosed in double-quotes. -Backslash, variable, and command substitution are performed as described in -\fBTcl\fR. +The expression parser will perform backslash, variable, and +command substitutions on the information between the quotes, +and use the resulting value as the operand .IP [5] As a string enclosed in braces. -The operand is treated as a braced value as described in \fBTcl\fR. +The characters between the open brace and matching close brace +will be used as the operand without any substitutions. .IP [6] As a Tcl command enclosed in brackets. -Command substitution is performed as described in \fBTcl\fR. +The command will be executed and its result will be used as +the operand. .IP [7] -As a mathematical function such as \fBsin($x)\fR, whose arguments have any of the above -forms for operands. See \fBMATH FUNCTIONS\fR below for +As a mathematical function whose arguments have any of the above +forms for operands, such as \fBsin($x)\fR. See \fBMATH FUNCTIONS\fR below for a discussion of how mathematical functions are handled. .PP -Because \fBexpr\fR parses and performs substitutions on values that have -already been parsed and substituted by \fBTcl\fR, it is usually best to enclose -expressions in braces to avoid the first round of substitutions by -\fBTcl\fR. +Where the above substitutions occur (e.g. inside quoted strings), they +are performed by the expression's instructions. +However, the command parser may already have performed one round of +substitution before the expression processor was called. +As discussed below, it is usually best to enclose expressions +in braces to prevent the command parser from performing substitutions +on the contents. .PP -Below are some examples of simple expressions where the value of \fBa\fR is 3 -and the value of \fBb\fR is 6. The command on the left side of each line -produces the value on the right side. +For some examples of simple expressions, suppose the variable +\fBa\fR has the value 3 and +the variable \fBb\fR has the value 6. +Then the command on the left side of each of the lines below +will produce the value on the right side of the line: .PP .CS .ta 6c @@ -104,41 +115,34 @@ produces the value on the right side. .CE .SS OPERATORS .PP -For operators having both a numeric mode and a string mode, the numeric mode is -chosen when all operands have a numeric interpretation. The integer -interpretation of an operand is preferred over the floating-point -interpretation. To ensure string operations on arbitrary values it is generally a -good idea to use \fBeq\fR, \fBne\fR, or the \fBstring\fR command instead of -more versatile operators such as \fB==\fR. -.PP -Unless otherwise specified, operators accept non-numeric operands. The value -of a boolean operation is 1 if true, 0 otherwise. See also \fBstring is\fR -\fBboolean\fR. The valid operators, most of which are also available as -commands in the \fBtcl::mathop\fR namespace (see \fBmathop\fR(n)), 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. These operators -may only be applied to numeric operands, and bit-wise NOT may only be -applied to integers. +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 . -Exponentiation. Valid for numeric operands. +Exponentiation. Valid for any numeric operands. .TP 20 \fB*\0\0/\0\0%\fR . -Multiply and divide, which are valid for numeric operands, and remainder, which -is valid for integers. The remainder, an absolute value smaller than the -absolute value of the divisor, has the same sign as the divisor. +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 absolute value of the divisor. .RS .PP -When applied to integers, division and remainder can be -considered to partition the number line into a sequence of -adjacent non-overlapping pieces, where each piece is the size of the divisor; -the quotient identifies which piece the dividend lies within, and the -remainder identifies where within that piece the dividend lies. A +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 @@ -148,157 +152,177 @@ is always 3. .TP 20 \fB+\0\0\-\fR . -Add and subtract. Valid for numeric operands. +Add and subtract. Valid for any numeric operands. .TP 20 \fB<<\0\0>>\fR . -Left and right shift. Valid for integers. +Left and right shift. Valid for integer operands only. A right shift always propagates the sign bit. .TP 20 \fB<\0\0>\0\0<=\0\0>=\fR . -Boolean less than, greater than, less than or equal, and greater than or equal. +Boolean less, greater, less than or equal, and greater than or equal. +Each operator produces 1 if the condition is true, 0 otherwise. +These operators may be applied to strings as well as numeric operands, +in which case string comparison is used. .TP 20 \fB==\0\0!=\fR . -Boolean equal and not equal. +Boolean equal and not equal. Each operator produces a zero/one result. +Valid for all operand types. .TP 20 \fBeq\0\0ne\fR . -Boolean string equal and string not equal. +Boolean string equal and string not equal. Each operator produces a +zero/one result. The operand types are interpreted only as strings. .TP 20 \fBin\0\0ni\fR . -List containment and negated list containment. The first argument is -interpreted as a string, the second as a list. \fBin\fR tests for membership -in the list, and \fBni\fR is the inverse. +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. .TP 20 \fB&\fR . -Bit-wise AND. Valid for integer operands. +Bit-wise AND. Valid for integer operands only. .TP 20 \fB^\fR . -Bit-wise exclusive OR. Valid for integer operands. +Bit-wise exclusive OR. Valid for integer operands only. .TP 20 \fB|\fR . -Bit-wise OR. Valid for integer operands. +Bit-wise OR. Valid for integer operands only. .TP 20 \fB&&\fR . -Logical AND. If both operands are true, the result is 1, or 0 otherwise. - +Logical AND. Produces a 1 result if both operands are non-zero, +0 otherwise. +Valid for boolean and numeric (integers or floating-point) operands only. .TP 20 \fB||\fR . -Logical OR. If both operands are false, the result is 0, or 1 otherwise. +Logical OR. Produces a 0 result if both operands are zero, 1 otherwise. +Valid for boolean and numeric (integers or floating-point) operands only. .TP 20 \fIx\fB?\fIy\fB:\fIz\fR . -If-then-else, as in C. If \fIx\fR is false , the result is the value of -\fIy\fR. Otherwise the result is the value of \fIz\fR. -.PP -The exponentiation operator promotes types in the same way that the multiply -and divide operators do, and the result is is the same as the result of -\fBpow\fR. -Exponentiation groups right-to-left within a precedence level. Other binary -operators group left-to-right. For example, the value of +If-then-else, as in C. If \fIx\fR +evaluates to non-zero, then the result is the value of \fIy\fR. +Otherwise the result is the value of \fIz\fR. +The \fIx\fR operand must have a boolean or numeric value. +.PP +See the C manual for more details on the results +produced by each operator. +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.) +All of the binary operators but exponentiation group left-to-right +within the same precedence level; exponentiation groups right-to-left. For example, the command .PP .CS \fBexpr\fR {4*2 < 7} .CE .PP -is 0, while the value of +returns 0, while .PP .CS \fBexpr\fR {2**3**2} .CE .PP -is 512. +returns 512. .PP -As in C, \fB&&\fR, \fB||\fR, and \fB?:\fR feature +The \fB&&\fR, \fB||\fR, and \fB?:\fR operators have .QW "lazy evaluation" , -which means that operands are not evaluated if they are -not needed to determine the outcome. For example, in +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 .PP .CS \fBexpr\fR {$v ? [a] : [b]} .CE .PP -only one of \fB[a]\fR or \fB[b]\fR is evaluated, -depending on the value of \fB$v\fR. This is not true of the normal Tcl parser, -so it is normally recommended to enclose the arguments to \fBexpr\fR in braces. -Without braces, as in -\fBexpr\fR $v ? [a] : [b] -both \fB[a]\fR and \fB[b]\fR are evaluated before \fBexpr\fR is even called. -.PP -For more details on the results -produced by each operator, see the documentation for C. +only one of +.QW \fB[a]\fR +or +.QW \fB[b]\fR +will actually be evaluated, +depending on the value of \fB$v\fR. Note, however, that this is +only true if the entire expression is enclosed in braces; otherwise +the Tcl parser will evaluate both +.QW \fB[a]\fR +and +.QW \fB[b]\fR +before invoking the \fBexpr\fR command. .SS "MATH FUNCTIONS" .PP -A mathematical function such as \fBsin($x)\fR is replaced with a call to an ordinary -Tcl command in the \fBtcl::mathfunc\fR namespace. The evaluation -of an expression such as +When the expression parser encounters a mathematical function +such as \fBsin($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: .PP .CS \fBexpr\fR {sin($x+$y)} .CE .PP -is the same in every way as the evaluation of +is the same in every way as the processing of: .PP .CS \fBexpr\fR {[tcl::mathfunc::sin [\fBexpr\fR {$x+$y}]]} .CE .PP -which in turn is the same as the evaluation of +which in turn is the same as the processing of: .PP .CS tcl::mathfunc::sin [\fBexpr\fR {$x+$y}] .CE .PP -\fBtcl::mathfunc::sin\fR is resolved as described in -\fBNAMESPACE RESOLUTION\fR in the \fBnamespace\fR(n) documentation. Given the -default value of \fBnamespace path\fR, \fB[namespace -current]::tcl::mathfunc::sin\fR or \fB::tcl::mathfunc::sin\fR are the typical -resolutions. +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 -As in C, a mathematical function may accept multiple arguments separated by commas. Thus, +Some mathematical functions have several arguments, separated by commas like in C. Thus: .PP .CS \fBexpr\fR {hypot($x,$y)} .CE .PP -becomes +ends up as .PP .CS tcl::mathfunc::hypot $x $y .CE .PP -See the \fBmathfunc\fR(n) documentation for the math functions that are +See the \fBmathfunc\fR(n) manual page for the math functions that are available by default. .SS "TYPES, OVERFLOW, AND PRECISION" .PP -When needed to guarantee exact performance, internal computations involving -integers use the LibTomMath multiple precision integer library. In Tcl releases -prior to 8.5, integer calculations were performed using one of the C types +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 should instead call -\fBint()\fR or \fBwide()\fR, which do truncate. +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. .PP -Internal floating-point computations are -performed using the \fIdouble\fR C type. -When converting a string to floating-point value, exponent overflow is +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 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 -fairly reliable. +pretty reliable. .PP -Conversion among internal representations for integer, floating-point, and -string operands is done automatically as needed. For arithmetic computations, -integers are used until some floating-point number is introduced, after which -floating-point values are used. For example, +Conversion among internal representations for integer, floating-point, +and string operands is done automatically as needed. +For arithmetic computations, integers are used until some +floating-point number is introduced, after which floating-point is used. +For example, .PP .CS \fBexpr\fR {5 / 4} @@ -312,62 +336,82 @@ returns 1, while .CE .PP both return 1.25. -A floating-point result can be distinguished from an integer result by the -presence of either +Floating-point values are always returned with a .QW \fB.\fR -or +or an .QW \fBe\fR -.PP -. For example, +so that they will not look like integer values. For example, .PP .CS \fBexpr\fR {20.0/5.0} .CE .PP returns \fB4.0\fR, not \fB4\fR. +.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, +except in the case of the \fBeq\fR and \fBne\fR operators. +If one of the operands of a comparison is a string and the other +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 +.PP +.CS +\fBexpr\fR {"0x03" > "2"} +\fBexpr\fR {"0y" > "0x12"} +.CE +.PP +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 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 is better in these cases to use +the \fBeq\fR or \fBne\fR operators, or the \fBstring\fR command instead. .SH "PERFORMANCE CONSIDERATIONS" .PP -Where an expression contains syntax that Tcl would otherwise perform -substitutions on, enclosing an expression in braces or otherwise quoting it -so that it's a static value allows the Tcl compiler to generate bytecode for -the expression, resulting in better speed and smaller storage requirements. -This also avoids issues that can arise if Tcl is allowed to perform -substitution on the value before \fBexpr\fR is called. +Enclose expressions in braces for the best speed and the smallest +storage requirements. +This allows the Tcl bytecode compiler to generate the best code. +.PP +As mentioned above, expressions are substituted twice: +once by the Tcl parser and once by the \fBexpr\fR command. +For example, the commands .PP -In the following example, the value of the expression is 11 because the Tcl parser first -substitutes \fB$b\fR and \fBexpr\fR then substitutes \fB$a\fR. Enclosing the -expression in braces would result in a syntax error. .CS set a 3 set b {$a + 2} \fBexpr\fR $b*4 .CE .PP - -When an expression is generated at runtime, like the one above is, the bytcode -compiler must ensure that new code is generated each time the expression -is evaluated. This is the most costly kind of expression from a performance -perspective. In such cases, consider directly using the commands described in -the \fBmathfunc\fR(n) or \fBmathop\fR(n) documentation instead of \fBexpr\fR. - -Most expressions are not formed at runtime, but are literal strings or contain -substitutions that don't introduce other substitutions. To allow the bytecode -compiler to work with an expression as a string literal at compilation time, -ensure that it contains no substitutions or that it is enclosed in braces or -otherwise quoted to prevent Tcl from performing substitutions, allowing -\fBexpr\fR to perform them instead. +return 11, not a multiple of 4. +This is because the Tcl parser will first substitute \fB$a + 2\fR for +the variable \fBb\fR, +then the \fBexpr\fR command will evaluate the expression \fB$a + 2*4\fR. +.PP +Most expressions do not require a second round of substitutions. +Either they are enclosed in braces or, if not, +their variable and command substitutions yield numbers or strings +that do not themselves require substitutions. +However, because a few unbraced expressions +need two rounds of substitutions, +the bytecode compiler must emit +additional instructions to handle this situation. +The most expensive code is required for +unbraced expressions that contain command substitutions. +These expressions must be implemented by generating new code +each time the expression is executed. +When the expression is unbraced to allow the substitution of a function or +operator, consider using the commands documented in the \fBmathfunc\fR(n) or +\fBmathop\fR(n) manual pages directly instead. .SH EXAMPLES .PP -A numeric comparison whose result is 1: -.CS -\fBexpr\fR {"0x03" > "2"} -.CE -.PP -A string comparison whose result is 1: -.CS -\fBexpr\fR {"0y" > "0x12"} -.CE -.PP Define a procedure that computes an .QW interesting mathematical function: @@ -401,8 +445,8 @@ each other: puts "a and b are [\fBexpr\fR {$a eq $b ? {equal} : {different}}]" .CE .PP -Set a variable indicating whether an environment variable is defined and has -value of true: +Set a variable to whether an environment variable is both defined at +all and also set to a true boolean value: .PP .CS set isTrue [\fBexpr\fR { |