Operator’s Soundtrack
2021年2月28日Download here: http://gg.gg/oh50w
*Operator’s Soundtrack Torrent
*Song Smooth Operator Original
We offer a music package for operators delivered with our patented ”Cloud to Cable” technology..
Operators discography and songs: Music profile for Operators, formed 2013. Genres: Synthpop, Alternative Dance. Albums include Blue Wave, Radiant Dawn, and EP 1. Operator soundtrack from 2016, composed by Sage Lewis. Released by The Orchard in 2016 containing music from Operator (2016). 8-Bit Operators: The Music of Kraftwerk was released in 2007 by the group 8-Bit Operators on Kraftwerk’s US label Astralwerks and EMI Records worldwide. It features cover versions of Kraftwerk songs by several prominent chiptune artists. Inspiration for the project as quoted by Jeremy Kolosine (credited as Executive Producer of the release, and noted founder of the early 80’s electronic group.
Music for Cable includes hundreds of carefully mastered and curated music channels in all music genres.
A true multiplatform music offering, all music channels are ready for mobile apps, streaming connected devices, Smart TVs, Cable TV systems, and Satellite Systems. All in one-stop-shop.Amplify your Reach ®
All your genres, from guitar, to techno, to jazz, to latin music, including your own genres.
For a full lineup for Music for Cable TV
PDF with more information: Download PDF – Music for Cable | Streaming for Operators
Julia provides a complete collection of basic arithmetic and bitwise operators across all of its numeric primitive types, as well as providing portable, efficient implementations of a comprehensive collection of standard mathematical functions.
The following arithmetic operators are supported on all primitive numeric types:ExpressionNameDescription+xunary plusthe identity operation-xunary minusmaps values to their additive inversesx + ybinary plusperforms additionx - ybinary minusperforms subtractionx * ytimesperforms multiplicationx / ydivideperforms divisionx ÷ yinteger dividex / y, truncated to an integerx yinverse divideequivalent to y / xx ^ ypowerraises x to the yth powerx % yremainderequivalent to rem(x,y)
as well as the negation on Bool types:ExpressionNameDescription!xnegationchanges true to false and vice versa
A numeric literal placed directly before an identifier or parentheses, e.g. 2x or 2(x+y), is treated as a multiplication, except with higher precedence than other binary operations. See Numeric Literal Coefficients for details.
Julia’s promotion system makes arithmetic operations on mixtures of argument types ’just work’ naturally and automatically. See Conversion and Promotion for details of the promotion system.
Here are some simple examples using arithmetic operators:
(By convention, we tend to space operators more tightly if they get applied before other nearby operators. For instance, we would generally write -x + 2 to reflect that first x gets negated, and then 2 is added to that result.)
When used in multiplication, false acts as a strong zero:
This is useful for preventing the propagation of NaN values in quantities that are known to be zero. See Knuth (1992) for motivation.
The following bitwise operators are supported on all primitive integer types:ExpressionName~xbitwise notx & ybitwise andx | ybitwise orx ⊻ ybitwise xor (exclusive or)x >>> ylogical shift rightx >> yarithmetic shift rightx << ylogical/arithmetic shift left
Here are some examples with bitwise operators:
Every binary arithmetic and bitwise operator also has an updating version that assigns the result of the operation back into its left operand. The updating version of the binary operator is formed by placing a = immediately after the operator. For example, writing x += 3 is equivalent to writing x = x + 3:
The updating versions of all the binary arithmetic and bitwise operators are:
An updating operator rebinds the variable on the left-hand side. As a result, the type of the variable may change.
For every binary operation like ^, there is a corresponding ’dot’ operation .^ that is automatically defined to perform ^ element-by-element on arrays. For example, [1,2,3] ^ 3 is not defined, since there is no standard mathematical meaning to ’cubing’ a (non-square) array, but [1,2,3] .^ 3 is defined as computing the elementwise (or ’vectorized’) result [1^3, 2^3, 3^3]. Similarly for unary operators like ! or √, there is a corresponding .√ that applies the operator elementwise.
More specifically, a .^ b is parsed as the ’dot’ call(^).(a,b), which performs a broadcast operation: it can combine arrays and scalars, arrays of the same size (performing the operation elementwise), and even arrays of different shapes (e.g. combining row and column vectors to produce a matrix). Moreover, like all vectorized ’dot calls,’ these ’dot operators’ are fusing. For example, if you compute 2 .* A.^2 .+ sin.(A) (or equivalently @. 2A^2 + sin(A), using the @. macro) for an array A, it performs a single loop over A, computing 2a^2 + sin(a) for each element of A. In particular, nested dot calls like f.(g.(x)) are fused, and ’adjacent’ binary operators like x .+ 3 .* x.^2 are equivalent to nested dot calls (+).(x, (*).(3, (^).(x, 2))).
Furthermore, ’dotted’ updating operators like a .+= b (or @. a += b) are parsed as a .= a .+ b, where .= is a fused in-place assignment operation (see the dot syntax documentation).
Note the dot syntax is also applicable to user-defined operators. For example, if you define ⊗(A,B) = kron(A,B) to give a convenient infix syntax A ⊗ B for Kronecker products (kron), then [A,B] .⊗ [C,D] will compute [A⊗C, B⊗D] with no additional coding.
Combining dot operators with numeric literals can be ambiguous. For example, it is not clear whether 1.+x means 1. + x or 1 .+ x. Therefore this syntax is disallowed, and spaces must be used around the operator in such cases.
Standard comparison operations are defined for all the primitive numeric types:OperatorNameequality!=, ≠inequality<less than<=, ≤less than or equal to’>>greater than=’>>=, =’>≥greater than or equal to
Here are some simple examples:
Integers are compared in the standard manner – by comparison of bits. Floating-point numbers are compared according to the IEEE 754 standard:
*Finite numbers are ordered in the usual manner.
*Positive zero is equal but not greater than negative zero.
*Inf is equal to itself and greater than everything else except NaN.
*-Inf is equal to itself and less than everything else except NaN.
*NaN is not equal to, not less than, and not greater than anything, including itself.
The last point is potentially surprising and thus worth noting:
and can cause headaches when working with arrays:
Julia provides additional functions to test numbers for special values, which can be useful in situations like hash key comparisons:FunctionTests ifisequal(x, y)x and y are identicalisfinite(x)x is a finite numberisinf(x)x is infiniteisnan(x)x is not a number
isequal considers NaNs equal to each other:
isequal can also be used to distinguish signed zeros:
Mixed-type comparisons between signed integers, unsigned integers, and floats can be tricky. A great deal of care has been taken to ensure that Julia does them correctly.
For other types, isequal defaults to calling , so if you want to define equality for your own types then you only need to add a method. If you define your own equality function, you should probably define a corresponding hash method to ensure that isequal(x,y) implies hash(x) hash(y).Operator’s Soundtrack Torrent
Unlike most languages, with the notable exception of Python, comparisons can be arbitrarily chained:
Chaining comparisons is often quite convenient in numerical code. Chained comparisons use the && operator for scalar comparisons, and the & operator for elementwise comparisons, which allows them to work on arrays. For example, 0 .< A .< 1 gives a boolean array whose entries are true where the corresponding elements of A are between 0 and 1.
Note the evaluation behavior of chained comparisons:
The middle expression is only evaluated once, rather than twice as it would be if the expression were written as v(1) < v(2) && v(2) <= v(3). However, the order of evaluations in a chained comparison is undefined. It is strongly recommended not to use expressions with side effects (such as printing) in chained comparisons. If side effects are required, the short-circuit && operator should be used explicitly (see Short-Circuit Evaluation).
Julia provides a comprehensive collection of mathematical functions and operators. These mathematical operations are defined over as broad a class of numerical values as permit sensible definitions, including integers, floating-point numbers, rationals, and complex numbers, wherever such definitions make sense.
Moreover, these functions (like any Julia function) can be applied in ’vectorized’ fashion to arrays and other collections with the dot syntaxf.(A), e.g. sin.(A) will compute the sine of each element of an array A.
Julia applies the following order and associativity of operations, from highest precedence to lowest:CategoryOperatorsAssociativitySyntax. followed by ::LeftExponentiation^RightUnary+ - √Right[1]Bitshifts<< >> >>>LeftFractions//LeftMultiplication* / % & ÷Left[2]Addition+ - | ⊻Left[2]Syntax: ..LeftSyntax|>LeftSyntax<|RightComparisons> < >= <= != ! <:Non-associativeControl flow&& followed by || followed by ?RightPair=>RightAssignments= += -= *= /= //= = ^= ÷= %= |= &= ⊻= <<= >>= >>>=Right
For a complete list of every Julia operator’s precedence, see the top of this file: src/julia-parser.scm
Numeric literal coefficients, e.g. 2x, are treated as multiplications with higher precedence than any other binary operation, and also have higher precedence than ^.
You can also find the numerical precedence for any given operator via the built-in function Base.operator_precedence, where higher numbers take precedence:
A symbol representing the operator associativity can also be found by calling the built-in function Base.operator_associativity:
Note that symbols such as :sin return precedence 0. This value represents invalid operators and not operators of lowest precedence. Similarly, such operators are assigned associativity :none.
Julia supports three forms of numerical conversion, which differ in their handling of inexact conversions.
*
The notation T(x) or convert(T,x) converts x to a value of type T.
*If T is a floating-point type, the result is the nearest representable value, which could be positive or negative infinity.
*If T is an integer type, an InexactError is raised if x is not representable by T.
*
x % T converts an integer x to a value of integer type T congruent to x modulo 2^n, where n is the number of bits in T. In other words, the binary representation is truncated to fit.
*
The Rounding functions take a type T as an optional argument. For example, round(Int,x) is a shorthand for Int(round(x)).
The following examples show the different forms.
See Conversion and Promotion for how to define your own conversions and promotions.FunctionDescriptionReturn typeround(x)round x to the nearest integertypeof(x)round(T, x)round x to the nearest integerTfloor(x)round x towards -Inftypeof(x)floor(T, x)round x towards -InfTceil(x)round x towards +Inftypeof(x)ceil(T, x)round x towards +InfTtrunc(x)round x towards zerotypeof(x)trunc(T, x)round x towards zeroTFunctionDescriptiondiv(x,y), x÷ytruncated division; quotient rounded towards zerofld(x,y)floored division; quotient rounded towards -Infcld(x,y)ceiling division; quotient rounded towards +Infrem(x,y)remainder; satisfies x div(x,y)*y + rem(x,y); sign matches xmod(x,y)modulus; satisfies x fld(x,y)*y + mod(x,y); sign matches ymod1(x,y)mod with offset 1; returns r∈(0,y] for y>0 or r∈[y,0) for y<0, where mod(r, y) mod(x, y)mod2pi(x)modulus with respect to 2pi; 0 <= mod2pi(x) < 2pidivrem(x,y)returns (div(x,y),rem(x,y))fldmod(x,y)returns (fld(x,y),mod(x,y))gcd(x,y...)greatest positive common divisor of x, y,...lcm(x,y...)least positive common multiple of x, y,...FunctionDescriptionabs(x)a positive value with the magnitude of xabs2(x)the squared magnitude of xsign(x)indicates the sign of x, returning -1, 0, or +1signbit(x)indicates whether the sign bit is on (true) or off (false)copysign(x,y)a value with the magnitude of x and the sign of yflipsign(x,y)a value with the magnitude of x and the sign of x*yFunctionDescriptionsqrt(x), √xsquare root of xcbrt(x), ∛xcube root of xhypot(x,y)hypotenuse of right-angled triangle with other sides of length x and yexp(x)natural exponential function at xexpm1(x)accurate exp(x)-1 for x near zeroldexp(x,n)x*2^n computed efficiently for integer values of nlog(x)natural logarithm of xlog(b,x)base b logarithm of xlog2(x)base 2 logarithm of xlog10(x)base 10 logarithm of xlog1p(x)accurate log(1+x) for x near zeroexponent(x)binary exponent of xsignificand(x)binary significand (a.k.a. mantissa) of a floating-point number x
For an overview of why functions like hypot, expm1, and log1p are necessary and useful, see John D. Cook’s excellent pair of blog posts on the subject: expm1, log1p, erfc, and hypot.
All the standard trigonometric and hyperbolic functions are also defined:
These are all single-argument functions, with atan also accepting two arguments corresponding to a traditional atan2 function.
Additionally, sinpi(x) and cospi(x) are provided for more accurate computations of sin(pi*x) and cos(pi*x) respectively.
In order to compute trigonometric functions with degrees instead of radians, suffix the function with d. For example, sind(x) computes the sine of x where x is specified in degrees. The complete list of trigonometric functions with degree variants is:Song Smooth Operator Original
Many other special mathematical functions are provided by the package SpecialFunctions.jl.
*1The unary operators + and - require explicit parentheses around their argument to disambiguate them from the operator ++, etc. Other compositions of unary operators are parsed with right-associativity, e. g., √√-a as √(√(-a)).
*2The operators +, ++ and * are non-associative. a + b + c is parsed as +(a, b, c) not +(+(a, b), c). However, the fallback methods for +(a, b, c, d...) and *(a, b, c, d...) both default to left-associative evaluation.
Download here: http://gg.gg/oh50w
https://diarynote-jp.indered.space
*Operator’s Soundtrack Torrent
*Song Smooth Operator Original
We offer a music package for operators delivered with our patented ”Cloud to Cable” technology..
Operators discography and songs: Music profile for Operators, formed 2013. Genres: Synthpop, Alternative Dance. Albums include Blue Wave, Radiant Dawn, and EP 1. Operator soundtrack from 2016, composed by Sage Lewis. Released by The Orchard in 2016 containing music from Operator (2016). 8-Bit Operators: The Music of Kraftwerk was released in 2007 by the group 8-Bit Operators on Kraftwerk’s US label Astralwerks and EMI Records worldwide. It features cover versions of Kraftwerk songs by several prominent chiptune artists. Inspiration for the project as quoted by Jeremy Kolosine (credited as Executive Producer of the release, and noted founder of the early 80’s electronic group.
Music for Cable includes hundreds of carefully mastered and curated music channels in all music genres.
A true multiplatform music offering, all music channels are ready for mobile apps, streaming connected devices, Smart TVs, Cable TV systems, and Satellite Systems. All in one-stop-shop.Amplify your Reach ®
All your genres, from guitar, to techno, to jazz, to latin music, including your own genres.
For a full lineup for Music for Cable TV
PDF with more information: Download PDF – Music for Cable | Streaming for Operators
Julia provides a complete collection of basic arithmetic and bitwise operators across all of its numeric primitive types, as well as providing portable, efficient implementations of a comprehensive collection of standard mathematical functions.
The following arithmetic operators are supported on all primitive numeric types:ExpressionNameDescription+xunary plusthe identity operation-xunary minusmaps values to their additive inversesx + ybinary plusperforms additionx - ybinary minusperforms subtractionx * ytimesperforms multiplicationx / ydivideperforms divisionx ÷ yinteger dividex / y, truncated to an integerx yinverse divideequivalent to y / xx ^ ypowerraises x to the yth powerx % yremainderequivalent to rem(x,y)
as well as the negation on Bool types:ExpressionNameDescription!xnegationchanges true to false and vice versa
A numeric literal placed directly before an identifier or parentheses, e.g. 2x or 2(x+y), is treated as a multiplication, except with higher precedence than other binary operations. See Numeric Literal Coefficients for details.
Julia’s promotion system makes arithmetic operations on mixtures of argument types ’just work’ naturally and automatically. See Conversion and Promotion for details of the promotion system.
Here are some simple examples using arithmetic operators:
(By convention, we tend to space operators more tightly if they get applied before other nearby operators. For instance, we would generally write -x + 2 to reflect that first x gets negated, and then 2 is added to that result.)
When used in multiplication, false acts as a strong zero:
This is useful for preventing the propagation of NaN values in quantities that are known to be zero. See Knuth (1992) for motivation.
The following bitwise operators are supported on all primitive integer types:ExpressionName~xbitwise notx & ybitwise andx | ybitwise orx ⊻ ybitwise xor (exclusive or)x >>> ylogical shift rightx >> yarithmetic shift rightx << ylogical/arithmetic shift left
Here are some examples with bitwise operators:
Every binary arithmetic and bitwise operator also has an updating version that assigns the result of the operation back into its left operand. The updating version of the binary operator is formed by placing a = immediately after the operator. For example, writing x += 3 is equivalent to writing x = x + 3:
The updating versions of all the binary arithmetic and bitwise operators are:
An updating operator rebinds the variable on the left-hand side. As a result, the type of the variable may change.
For every binary operation like ^, there is a corresponding ’dot’ operation .^ that is automatically defined to perform ^ element-by-element on arrays. For example, [1,2,3] ^ 3 is not defined, since there is no standard mathematical meaning to ’cubing’ a (non-square) array, but [1,2,3] .^ 3 is defined as computing the elementwise (or ’vectorized’) result [1^3, 2^3, 3^3]. Similarly for unary operators like ! or √, there is a corresponding .√ that applies the operator elementwise.
More specifically, a .^ b is parsed as the ’dot’ call(^).(a,b), which performs a broadcast operation: it can combine arrays and scalars, arrays of the same size (performing the operation elementwise), and even arrays of different shapes (e.g. combining row and column vectors to produce a matrix). Moreover, like all vectorized ’dot calls,’ these ’dot operators’ are fusing. For example, if you compute 2 .* A.^2 .+ sin.(A) (or equivalently @. 2A^2 + sin(A), using the @. macro) for an array A, it performs a single loop over A, computing 2a^2 + sin(a) for each element of A. In particular, nested dot calls like f.(g.(x)) are fused, and ’adjacent’ binary operators like x .+ 3 .* x.^2 are equivalent to nested dot calls (+).(x, (*).(3, (^).(x, 2))).
Furthermore, ’dotted’ updating operators like a .+= b (or @. a += b) are parsed as a .= a .+ b, where .= is a fused in-place assignment operation (see the dot syntax documentation).
Note the dot syntax is also applicable to user-defined operators. For example, if you define ⊗(A,B) = kron(A,B) to give a convenient infix syntax A ⊗ B for Kronecker products (kron), then [A,B] .⊗ [C,D] will compute [A⊗C, B⊗D] with no additional coding.
Combining dot operators with numeric literals can be ambiguous. For example, it is not clear whether 1.+x means 1. + x or 1 .+ x. Therefore this syntax is disallowed, and spaces must be used around the operator in such cases.
Standard comparison operations are defined for all the primitive numeric types:OperatorNameequality!=, ≠inequality<less than<=, ≤less than or equal to’>>greater than=’>>=, =’>≥greater than or equal to
Here are some simple examples:
Integers are compared in the standard manner – by comparison of bits. Floating-point numbers are compared according to the IEEE 754 standard:
*Finite numbers are ordered in the usual manner.
*Positive zero is equal but not greater than negative zero.
*Inf is equal to itself and greater than everything else except NaN.
*-Inf is equal to itself and less than everything else except NaN.
*NaN is not equal to, not less than, and not greater than anything, including itself.
The last point is potentially surprising and thus worth noting:
and can cause headaches when working with arrays:
Julia provides additional functions to test numbers for special values, which can be useful in situations like hash key comparisons:FunctionTests ifisequal(x, y)x and y are identicalisfinite(x)x is a finite numberisinf(x)x is infiniteisnan(x)x is not a number
isequal considers NaNs equal to each other:
isequal can also be used to distinguish signed zeros:
Mixed-type comparisons between signed integers, unsigned integers, and floats can be tricky. A great deal of care has been taken to ensure that Julia does them correctly.
For other types, isequal defaults to calling , so if you want to define equality for your own types then you only need to add a method. If you define your own equality function, you should probably define a corresponding hash method to ensure that isequal(x,y) implies hash(x) hash(y).Operator’s Soundtrack Torrent
Unlike most languages, with the notable exception of Python, comparisons can be arbitrarily chained:
Chaining comparisons is often quite convenient in numerical code. Chained comparisons use the && operator for scalar comparisons, and the & operator for elementwise comparisons, which allows them to work on arrays. For example, 0 .< A .< 1 gives a boolean array whose entries are true where the corresponding elements of A are between 0 and 1.
Note the evaluation behavior of chained comparisons:
The middle expression is only evaluated once, rather than twice as it would be if the expression were written as v(1) < v(2) && v(2) <= v(3). However, the order of evaluations in a chained comparison is undefined. It is strongly recommended not to use expressions with side effects (such as printing) in chained comparisons. If side effects are required, the short-circuit && operator should be used explicitly (see Short-Circuit Evaluation).
Julia provides a comprehensive collection of mathematical functions and operators. These mathematical operations are defined over as broad a class of numerical values as permit sensible definitions, including integers, floating-point numbers, rationals, and complex numbers, wherever such definitions make sense.
Moreover, these functions (like any Julia function) can be applied in ’vectorized’ fashion to arrays and other collections with the dot syntaxf.(A), e.g. sin.(A) will compute the sine of each element of an array A.
Julia applies the following order and associativity of operations, from highest precedence to lowest:CategoryOperatorsAssociativitySyntax. followed by ::LeftExponentiation^RightUnary+ - √Right[1]Bitshifts<< >> >>>LeftFractions//LeftMultiplication* / % & ÷Left[2]Addition+ - | ⊻Left[2]Syntax: ..LeftSyntax|>LeftSyntax<|RightComparisons> < >= <= != ! <:Non-associativeControl flow&& followed by || followed by ?RightPair=>RightAssignments= += -= *= /= //= = ^= ÷= %= |= &= ⊻= <<= >>= >>>=Right
For a complete list of every Julia operator’s precedence, see the top of this file: src/julia-parser.scm
Numeric literal coefficients, e.g. 2x, are treated as multiplications with higher precedence than any other binary operation, and also have higher precedence than ^.
You can also find the numerical precedence for any given operator via the built-in function Base.operator_precedence, where higher numbers take precedence:
A symbol representing the operator associativity can also be found by calling the built-in function Base.operator_associativity:
Note that symbols such as :sin return precedence 0. This value represents invalid operators and not operators of lowest precedence. Similarly, such operators are assigned associativity :none.
Julia supports three forms of numerical conversion, which differ in their handling of inexact conversions.
*
The notation T(x) or convert(T,x) converts x to a value of type T.
*If T is a floating-point type, the result is the nearest representable value, which could be positive or negative infinity.
*If T is an integer type, an InexactError is raised if x is not representable by T.
*
x % T converts an integer x to a value of integer type T congruent to x modulo 2^n, where n is the number of bits in T. In other words, the binary representation is truncated to fit.
*
The Rounding functions take a type T as an optional argument. For example, round(Int,x) is a shorthand for Int(round(x)).
The following examples show the different forms.
See Conversion and Promotion for how to define your own conversions and promotions.FunctionDescriptionReturn typeround(x)round x to the nearest integertypeof(x)round(T, x)round x to the nearest integerTfloor(x)round x towards -Inftypeof(x)floor(T, x)round x towards -InfTceil(x)round x towards +Inftypeof(x)ceil(T, x)round x towards +InfTtrunc(x)round x towards zerotypeof(x)trunc(T, x)round x towards zeroTFunctionDescriptiondiv(x,y), x÷ytruncated division; quotient rounded towards zerofld(x,y)floored division; quotient rounded towards -Infcld(x,y)ceiling division; quotient rounded towards +Infrem(x,y)remainder; satisfies x div(x,y)*y + rem(x,y); sign matches xmod(x,y)modulus; satisfies x fld(x,y)*y + mod(x,y); sign matches ymod1(x,y)mod with offset 1; returns r∈(0,y] for y>0 or r∈[y,0) for y<0, where mod(r, y) mod(x, y)mod2pi(x)modulus with respect to 2pi; 0 <= mod2pi(x) < 2pidivrem(x,y)returns (div(x,y),rem(x,y))fldmod(x,y)returns (fld(x,y),mod(x,y))gcd(x,y...)greatest positive common divisor of x, y,...lcm(x,y...)least positive common multiple of x, y,...FunctionDescriptionabs(x)a positive value with the magnitude of xabs2(x)the squared magnitude of xsign(x)indicates the sign of x, returning -1, 0, or +1signbit(x)indicates whether the sign bit is on (true) or off (false)copysign(x,y)a value with the magnitude of x and the sign of yflipsign(x,y)a value with the magnitude of x and the sign of x*yFunctionDescriptionsqrt(x), √xsquare root of xcbrt(x), ∛xcube root of xhypot(x,y)hypotenuse of right-angled triangle with other sides of length x and yexp(x)natural exponential function at xexpm1(x)accurate exp(x)-1 for x near zeroldexp(x,n)x*2^n computed efficiently for integer values of nlog(x)natural logarithm of xlog(b,x)base b logarithm of xlog2(x)base 2 logarithm of xlog10(x)base 10 logarithm of xlog1p(x)accurate log(1+x) for x near zeroexponent(x)binary exponent of xsignificand(x)binary significand (a.k.a. mantissa) of a floating-point number x
For an overview of why functions like hypot, expm1, and log1p are necessary and useful, see John D. Cook’s excellent pair of blog posts on the subject: expm1, log1p, erfc, and hypot.
All the standard trigonometric and hyperbolic functions are also defined:
These are all single-argument functions, with atan also accepting two arguments corresponding to a traditional atan2 function.
Additionally, sinpi(x) and cospi(x) are provided for more accurate computations of sin(pi*x) and cos(pi*x) respectively.
In order to compute trigonometric functions with degrees instead of radians, suffix the function with d. For example, sind(x) computes the sine of x where x is specified in degrees. The complete list of trigonometric functions with degree variants is:Song Smooth Operator Original
Many other special mathematical functions are provided by the package SpecialFunctions.jl.
*1The unary operators + and - require explicit parentheses around their argument to disambiguate them from the operator ++, etc. Other compositions of unary operators are parsed with right-associativity, e. g., √√-a as √(√(-a)).
*2The operators +, ++ and * are non-associative. a + b + c is parsed as +(a, b, c) not +(+(a, b), c). However, the fallback methods for +(a, b, c, d...) and *(a, b, c, d...) both default to left-associative evaluation.
Download here: http://gg.gg/oh50w
https://diarynote-jp.indered.space
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