Chapter 2: variables
- names can contain utf-8

Chapter 3: numbers
see last post

Chapter 4: basic operations

- c-like operators with additions:
x ÷ y integer divide x / y, truncated to an integer
x \ y inverse divide equivalent to y / x
x ^ y power raises x to the yth power
x ⊻ y bitwise xor (exclusive or)
x ⊼ y bitwise nand (not and)
x ⊽ y bitwise nor (not or)
x >>> y logical shift right
x >> y arithmetic shift right
√
- binary operators are all available as in-place op= forms too. using this may retype the lvalue.

÷ can be typed with \div<tab> in the repl, see also manual section https://docs.julialang.org/en/v1/manual/unicode-input/#Unicode-Input or called as div()
note: false * anything = 0, even NaN . This can be used to prevent propagation of nans.

- boolean operators (&& ||) are short-circuiting

- xor() nand() nor() can be called by name as binary functions

Each operator has a .op form that performs elementwise operation on arrays.

julia> [1,2,3] .^ 3
3-element Vector{Int64}:
  1
  8
 27

This is simply a use of the further . operator, which broadcasts functions over array parameters:

julia> nand.([1,2,3],[4,3,2])
3-element Vector{Int64}:
 -1
 -3
 -3

Multiple dot operators in a single expression, even in-place assignment, are all fused into a single underlying loop over the combined datasize.

Comparisons can be chained:

julia> 1 < 2 <= 2 < 3 == 3 > 2 >= 1 == 1 < 3 != 5
true

Chaining works with elementwise comparison.

Operators can be referenced as values by preceding them with a : .

Details of operator precedence are canonically defined in the julia source code https://github.com/JuliaLang/julia/blob/master/src/julia-parser.scm . Precedence and associativity can be queried at runtime by passing an operator to Base.operator_precedence or Base.operator_associativity .

To convert floats to integers without throwing, use round(), ceil(), floor(), or trunc() . These can be passed a value: round(1.2), or a type and then a value: round(UInt8, 1.2).

fld(x,y) floored division; quotient rounded towards -Inf
cld(x,y) ceiling division; quotient rounded towards +Inf
rem(x,y) remainder; satisfies x == div(x,y)*y + rem(x,y); sign matches x
mod(x,y) modulus; satisfies x == fld(x,y)*y + mod(x,y); sign matches y
mod1(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) < 2pi
divrem(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,...
Sign and absolute value functions
Function Description
abs(x) a positive value with the magnitude of x
abs2(x) the squared magnitude of x
sign(x) indicates the sign of x, returning -1, 0, or +1
signbit(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 y
flipsign(x,y) a value with the magnitude of x and the sign of x*y
Powers, logs and roots
Function Description
sqrt(x), √x square root of x
cbrt(x), ∛x cube root of x
hypot(x,y) hypotenuse of right-angled triangle with other sides of length x and y
exp(x) natural exponential function at x
expm1(x) accurate exp(x)-1 for x near zero
ldexp(x,n) x*2^n computed efficiently for integer values of n
log(x) natural logarithm of x
log(b,x) base b logarithm of x
log2(x) base 2 logarithm of x
log10(x) base 10 logarithm of x
log1p(x) accurate log(1+x) for x near zero
exponent(x) binary exponent of x
significand(x) binary significand (a.k.a. mantissa) of a floating-point number x

sin    cos    tan    cot    sec    csc
sinh   cosh   tanh   coth   sech   csch
asin   acos   atan   acot   asec   acsc
asinh  acosh  atanh  acoth  asech  acsch
sinc   cosc
, with atan also accepting two arguments corresponding to a traditional atan2 function.

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. 

sind   cosd   tand   cotd   secd   cscd
asind  acosd  atand  acotd  asecd  acscd

More functions:

Homework: Write a julia script that produces a 2x2 matrix containing pixels for a raytraced sphere.