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expr(1,3,n)(n) Tcl Built-In Commands expr(1,3,n)(n)NAMEexpr(1,3,n) - Evaluate an expressionSYNOPSISexpr(1,3,n)arg ?arg arg ...?DESCRIPTIONConcatenates arg's (adding separator spaces between them), evaluates the result as a Tcl expression, and returns the value. The operators permitted in(1,8) Tcl expressions are a subset of the operators permitted in(1,8) C expressions, and they have the same meaning and precedence as the corresponding C operators. Expressions almost always yield numeric results (integer or floating-point values). For example, the expres- sionexpr(1,3,n) 8.2 + 6evaluates to 14.2. Tcl expressions differ from C expressions in(1,8) the way that operands are specified. Also, Tcl expres- sions support non-numeric operands and string(3,n) comparisons.OPERANDSA Tcl expression consists of a combination of operands, operators, and parentheses. White space may be used between the operands and opera- tors and parentheses; it is ignored by the expression's instructions. Where possible, operands are interpreted as integer values. Integer values may be specified in(1,8) decimal (the normal case), in(1,8) octal (if(3,n) the first character of the operand is0), or in(1,8) hexadecimal (if(3,n) the first two characters of the operand are0x). If an operand does not have one of the integer formats given above, then it is treated as a floating- point number if(3,n) that is possible. Floating-point numbers may be speci- fied in(1,8) any of the ways accepted by an ANSI-compliant C compiler (except that thef,F,l, andLsuffixes will not be permitted in(1,8) most installations). For example, all of the following are valid floating- point numbers: 2.1, 3., 6e4, 7.91e+16. If no numeric interpretation is possible, then an operand is left as a string(3,n) (and only a limited set(7,n,1 builtins) of operators may be applied to it). 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(3,n) that is possible at all.) Operands may be specified in(1,8) any of the following ways: [1] As an numeric value, either integer or floating-point. [2] As a Tcl variable, using standard$notation. The variable's value will be used as the operand. [3] As a string(3,n) enclosed in(1,8) double-quotes. The expression parser will perform backslash, variable, and command substitutions on the information between the quotes, and use the resulting value as the operand [4] As a string(3,n) enclosed in(1,8) braces. The characters between the open(2,3,n) brace and matching close(2,7,n) brace will be used as the operand with- out any substitutions. [5] As a Tcl command enclosed in(1,8) brackets. The command will be exe- cuted and its result will be used as the operand. [6] As a mathematical function whose arguments have any of the above forms for operands, such assin($x). See below for a list of defined functions. Where substitutions occur above (e.g. inside quoted strings), they are performed by the expression's instructions. However, an additional layer of substitution may already have been performed by the command parser before the expression processor was called. As discussed below, it is usually best to enclose expressions in(1,8) braces to prevent the com- mand parser from performing substitutions on the contents. For some examples of simple expressions, suppose the variableahas the value 3 and the variablebhas 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:expr(1,3,n) 3.1 + $a 6.1 expr(1,3,n) 2 +"$a.$b" 5.6 expr(1,3,n) 4*[llength "6 2"] 8 expr(1,3,n) {{word one} < "word$a"}0OPERATORSThe valid operators are listed below, grouped in(1,8) decreasing order of precedence:- + ~ !Unary minus, unary plus, bit-wise NOT, logical NOT. None of these operands may be applied to string(3,n) op- erands, and bit-wise NOT may be applied only to integers.* / %Multiply, divide, remainder. None of these oper- ands may be applied to string(3,n) operands, and remain- der 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.+ -Add and subtract. Valid for any numeric operands.<< >>Left and right shift. Valid for integer operands only. A right shift always propagates the sign bit.< > <= >=Boolean less(1,3), greater, less(1,3) than or equal, and greater than or equal. Each operator produces 1 if(3,n) the condition is true, 0 otherwise. These opera- tors may be applied to strings as well as numeric operands, in(1,8) which case string(3,n) comparison is used.== !=Boolean equal and not equal. Each operator pro- duces a zero/one result. Valid for all operand types.eq neBoolean string(3,n) equal and string(3,n) not equal. Each operator produces a zero/one result. The operand types are interpreted only as strings.&Bit-wise AND. Valid for integer operands only.^Bit-wise exclusive OR. Valid for integer operands only.|Bit-wise OR. Valid for integer operands only.&&Logical AND. Produces a 1 result if(3,n) both operands are non-zero, 0 otherwise. Valid for boolean and numeric (integers or floating-point) operands only.||Logical OR. Produces a 0 result if(3,n) both operands are zero, 1 otherwise. Valid for boolean and numeric (integers or floating-point) operands only. x?y:z If-then-else, as in(1,8) C. If x evaluates to non-zero, then the result is the value of y. Otherwise the result is the value of z. The x operand must have a numeric value. See the C manual for more details on the results produced by each oper- ator. All of the binary operators group left-to-right within the same precedence level. For example, the commandexpr(1,3,n) 4*2 < 7returns 0. The&&,||, and?:operators have ``lazy evaluation'', just as in(1,8) C, which means that operands are not evaluated if(3,n) they are not needed to determine the outcome. For example, in(1,8) the commandexpr(1,3,n) {$v ? [a] :[b]}only one of[a]or[b]will actually be evaluated, depending on the value of$v. Note, however, that this is only true if(3,n) the entire expression is enclosed in(1,8) braces; otherwise the Tcl parser will evalu- ate both[a]and[b]before invoking theexpr(1,3,n)command.MATH FUNCTIONSTcl supports the following mathematical functions in(1,8) expressions, all of which work solely with floating-point numbers unless otherwise noted:abs cosh log sqrt acos dou-ble log10 srand asin exp pow tanatan floor rand(1,3) tanhatan2 fmod round wide ceil hypot sincos int sinhabs(arg)Returns the absolute value of arg. Arg may be either integer or floating-point, and the result is returned in(1,8) the same form.acos(arg)Returns the arc cosine of arg, in(1,8) the range [0,pi] radians. Arg should be in(1,8) the range [-1,1].asin(arg)Returns the arc sine of arg, in(1,8) the range [-pi/2,pi/2] radians. Arg should be in(1,8) the range [-1,1].atan(arg)Returns the arc tangent of arg, in(1,8) the range [-pi/2,pi/2] radi- ans.atan2(y, x)Returns the arc tangent of y/x, in(1,8) the range [-pi,pi] radians. x and y cannot both be 0. If x is greater than 0, this is equivalent toatan(y/x).ceil(arg)Returns the smallest integral floating-point value (i.e. with a zero fractional part) not less(1,3) than arg.cos(arg)Returns the cosine of arg, measured in(1,8) radians.cosh(arg)Returns the hyperbolic cosine of arg. If the result would cause an overflow, an error(8,n) is returned.double(arg)If arg is a floating-point value, returns arg, otherwise con- verts arg to floating-point and returns the converted value.exp(arg)Returns the exponential of arg, defined as e**arg. If the result would cause an overflow, an error(8,n) is returned.floor(arg)Returns the largest integral floating-point value (i.e. with a zero fractional part) not greater than arg.fmod(x, y)Returns the floating-point remainder of the division of x by y. If y is 0, an error(8,n) is returned.hypot(x, y)Computes the length of the hypotenuse of a right-angled trianglesqrt(x*x+y*y).int(arg)If arg is an integer value of the same width as the machine word, returns arg, otherwise converts arg 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 con- verted value.log(arg)Returns the natural logarithm of arg. Arg must be a positive value.log10(arg)Returns the base 10 logarithm of arg. Arg must be a positive value.pow(x, y)Computes the value of x raised to the power y. If x is nega- tive, y must be an integer value.rand(1,3)()Returns a pseudo-random floating-point value in(1,8) the range (0,1). The generator algorithm is a simple linear congruential genera- tor that is not cryptographically secure. Each result fromrand(1,3)completely determines all future results from subsequent calls torand(1,3), sorand(1,3)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(3,n) of the machine or may be set(7,n,1 builtins) with thesrandfunction.round(arg)If arg is an integer value, returns arg, otherwise converts arg to integer by rounding and returns the converted value.sin(arg)Returns the sine of arg, measured in(1,8) radians.sinh(arg)Returns the hyperbolic sine of arg. If the result would cause an overflow, an error(8,n) is returned.sqrt(arg)Returns the square root of arg. Arg must be non-negative.srand(arg)The arg, which must be an integer, is used to reset(1,7,1 tput) the seed for the random(3,4,6) number generator ofrand(1,3). Returns the first random(3,4,6) number (seerand(1,3)()) from that seed. Each interpreter has its own seed.tan(arg)Returns the tangent of arg, measured in(1,8) radians.tanh(arg)Returns the hyperbolic tangent of arg.wide(arg)Converts arg to an integer value at least 64-bits wide (by sign- extension if(3,n) arg is a 32-bit number) if(3,n) it is not one already. In addition to these predefined functions, applications may define additional functions usingTcl_CreateMathFunc().TYPES, OVERFLOW, AND PRECISIONAll internal computations involving integers are done with the C type long, and all internal computations involving floating-point are done with the C type double. When converting a string(3,n) to floating-point, exponent overflow is detected and results in(1,8) a Tcl error. For conver- sion to integer from string(3,n), detection of overflow depends on the behavior of some routines in(1,8) 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. Float- ing-point overflow and underflow are detected to the degree supported by the hardware, which is generally pretty reliable. Conversion among internal representations for integer, floating-point, and string(3,n) 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,expr(1,3,n) 5 /4returns 1, whileexpr(1,3,n) 5 / 4.0 expr(1,3,n) 5 / ( [string(3,n) length "abcd"] + 0.0)both return 1.25. Floating-point values are always returned with a ``.'' or aneso that they will not look(1,8,3 Search::Dict) like integer values. For example,expr(1,3,n) 20.0/5.0returns4.0, not4.STRING OPERATIONSString 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, except in(1,8) the case of theeqandneopera- tors. If one of the operands of a comparison is a string(3,n) and the other has a numeric value, the numeric operand is converted back to a string(3,n) using the C sprintf format specifier%dfor integers and%gfor float- ing-point values. For example, the commandsexpr(1,3,n) {"0x03" > "2"} expr(1,3,n){"0y" < "0x12"}both return 1. The first comparison is done using integer comparison, and the second is done using string(3,n) comparison after the second operand is converted to the string(3,n)18. Because of Tcl's tendency to treat values as numbers whenever possible, it isn't generally a good idea to use operators like==when you really want string(3,n) comparison and the values of the operands could be arbitrary; it's better in(1,8) these cases to use theeqorneoperators, or thestring(3,n)command instead.PERFORMANCE CONSIDERATIONSEnclose expressions in(1,8) braces for the best speed and the smallest stor- age requirements. This allows the Tcl bytecode compiler to generate the best code. As mentioned above, expressions are substituted twice: once by the Tcl parser and once by theexpr(1,3,n)command. For example, the commandsset(7,n,1 builtins) a 3set(7,n,1 builtins) b {$a + 2} expr(1,3,n) $b*4return 11, not a multiple of 4. This is because the Tcl parser will first substitute$a + 2for the variableb, then theexpr(1,3,n)command will evaluate the expression$a + 2*4. Most expressions do not require a second round of substitutions. Either they are enclosed in(1,8) braces or, if(3,n) not, their variable and com- mand substitutions yield numbers or strings that don't themselves require substitutions. However, because a few unbraced expressions need two rounds of substitutions, the bytecode compiler must emit addi- tional instructions to handle this situation. The most expensive code is required for unbraced expressions that contain command substitu- tions. These expressions must be implemented by generating new code each time(1,2,n) the expression is executed.SEE ALSOarray(n), string(3,n)(n), Tcl(n)KEYWORDSarithmetic, boolean, compare, expression, fuzzy comparison Tcl 8.4 expr(1,3,n)(n)