include("float-help.jl")

a = 1/3
b = 2/3
@show_float a+b
println()

The computer representation of a + b is:
  0011111111110000000000000000000000000000000000000000000000000000
  which decodes to 
  | sign |   exponent  |    mantissa    
     0     01111111111   0000000000000000000000000000000000000000000000000000
= (-1)^(0) x 2^(   +0)   x 1.00000000000000000 = 1  

a = 3/10
b = 4/10
@show_float a+b

The computer representation of a + b is:
  0011111111100110011001100110011001100110011001100110011001100110
  which decodes to 
  | sign |   exponent  |    mantissa    
     0     01111111110   0110011001100110011001100110011001100110011001100110
= (-1)^(0) x 2^(   -1)   x 1.39999999999999991 = 0.7 

@show_float Inf

The computer representation of Inf is:
  0111111111110000000000000000000000000000000000000000000000000000
  which decodes to 
  | sign |   exponent  |    mantissa    
     0     11111111111   0000000000000000000000000000000000000000000000000000
= (-1)^(0) x 2^( Inf)   x 1.00000000000000000 = Inf 

@show_float NaN

The computer representation of NaN is:
  0111111111111000000000000000000000000000000000000000000000000000
  which decodes to 
  | sign |   exponent  |    mantissa    
     0     11111111111   1000000000000000000000000000000000000000000000000000
= (-1)^(0) x 2^( Inf)   x 1.50000000000000000 = NaN 

@show_float Float64(pi)

The computer representation of Float64(pi) is:
  0100000000001001001000011111101101010100010001000010110100011000
  which decodes to 
  | sign |   exponent  |    mantissa    
     0     10000000000   1001001000011111101101010100010001000010110100011000
= (-1)^(0) x 2^(   +1)   x 1.57079632679489656 = 3.14159 

@show_float -Inf

The computer representation of -Inf is:
  1111111111110000000000000000000000000000000000000000000000000000
  which decodes to 
  | sign |   exponent  |    mantissa    
     1     11111111111   0000000000000000000000000000000000000000000000000000
= (-1)^(1) x 2^( Inf)   x 1.00000000000000000 = -Inf 

@show_float -NaN

The computer representation of -NaN is:
  1111111111111000000000000000000000000000000000000000000000000000
  which decodes to 
  | sign |   exponent  |    mantissa    
     1     11111111111   1000000000000000000000000000000000000000000000000000
= (-1)^(1) x 2^( Inf)   x 1.50000000000000000 = NaN 

@show_float 0.

The computer representation of 0.0 is:
  0000000000000000000000000000000000000000000000000000000000000000
  which decodes to 
  | sign |   exponent  |    mantissa    
     0     00000000000   0000000000000000000000000000000000000000000000000000
= (-1)^(0) x 2^(-1022)   x 0.00000000000000000 = 0  

@show_float -0.

The computer representation of -0.0 is:
  1000000000000000000000000000000000000000000000000000000000000000
  which decodes to 
  | sign |   exponent  |    mantissa    
     1     00000000000   0000000000000000000000000000000000000000000000000000
= (-1)^(1) x 2^(-1022)   x 0.00000000000000000 = -0  

@show_float(0.)

The computer representation of 0.0 is:
  0000000000000000000000000000000000000000000000000000000000000000
  which decodes to 
  | sign |   exponent  |    mantissa    
     0     00000000000   0000000000000000000000000000000000000000000000000000
= (-1)^(0) x 2^(-1022)   x 0.00000000000000000 = 0  

@show_float nextfloat(0.)

The computer representation of nextfloat(0.0) is:
  0000000000000000000000000000000000000000000000000000000000000001
  which decodes to 
  | sign |   exponent  |    mantissa    
     0     00000000000   0000000000000000000000000000000000000000000000000001
= (-1)^(0) x 2^(-1022)   x 0.00000000000000022 = 4.94066e-324 

eps(1.)

2.220446049250313e-16

eps()

2.220446049250313e-16

eps(2.)

4.440892098500626e-16

eps(0.)

5.0e-324

nextfloat(Inf)

Inf

nextfloat(-Inf)

-1.7976931348623157e308