capital le�er and word separa�on is shown with upper camel case instead of underscores. • Names of functions and macros are in lower case, without underscores. • Func�ons that write to their arguments have julia> 1 - 2 -1 julia> 3*2/12 0.5 45 46 CHAPTER 12. MATHEMATICAL OPERATIONS AND ELEMENTARY FUNCTIONS (By conven�on, we tend to space operators more �ghtly if they get applied before other nearby operators numeric types: Here are some simple examples: 48 CHAPTER 12. MATHEMATICAL OPERATIONS AND ELEMENTARY FUNCTIONS Operator Name == equality !=, ≠ inequality < less than <=, ≤ less than or equal to > greater

capital le�er and word separa�on is shown with upper camel case instead of underscores. • Names of functions and macros are in lower case, without underscores. • Func�ons that write to their arguments have julia> 1 - 2 -1 julia> 3*2/12 0.5 47 48 CHAPTER 13. MATHEMATICAL OPERATIONS AND ELEMENTARY FUNCTIONS (By conven�on, we tend to space operators more �ghtly if they get applied before other nearby operators numeric types: Here are some simple examples: 50 CHAPTER 13. MATHEMATICAL OPERATIONS AND ELEMENTARY FUNCTIONS Operator Name == equality !=, ≠ inequality < less than <=, ≤ less than or equal to > greater

capital le�er and word separa�on is shown with upper camel case instead of underscores. • Names of functions and macros are in lower case, without underscores. • Func�ons that write to their arguments have julia> 1 - 2 -1 julia> 3*2/12 0.5 45 46 CHAPTER 12. MATHEMATICAL OPERATIONS AND ELEMENTARY FUNCTIONS (By conven�on, we tend to space operators more �ghtly if they get applied before other nearby operators numeric types: Here are some simple examples: 48 CHAPTER 12. MATHEMATICAL OPERATIONS AND ELEMENTARY FUNCTIONS Operator Name == equality !=, ≠ inequality < less than <=, ≤ less than or equal to > greater

capital le�er and word separa�on is shown with upper camel case instead of underscores. • Names of functions and macros are in lower case, without underscores. • Func�ons that write to their arguments have julia> 1 - 2 -1 julia> 3*2/12 0.5 45 46 CHAPTER 12. MATHEMATICAL OPERATIONS AND ELEMENTARY FUNCTIONS (By conven�on, we tend to space operators more �ghtly if they get applied before other nearby operators numeric types: Here are some simple examples: 48 CHAPTER 12. MATHEMATICAL OPERATIONS AND ELEMENTARY FUNCTIONS Operator Name == equality !=, ≠ inequality < less than <=, ≤ less than or equal to > greater

. . . . . . . . . . . . . . . . . 23 i ii CONTENTS 5 Mathematical Operations and Elementary Functions 25 5.1 Arithmetic Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Elementary Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 5.7 Operator Precedence . . . . . . . . . . . . . . . 32 Rounding functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Division functions . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . 23 i ii CONTENTS 5 Mathematical Operations and Elementary Functions 25 5.1 Arithmetic Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Elementary Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 5.7 Operator Precedence . . . . . . . . . . . . . . . 32 Rounding functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Division functions . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . 23 i ii CONTENTS 5 Mathematical Operations and Elementary Functions 25 5.1 Arithmetic Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Elementary Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 5.7 Operator Precedence . . . . . . . . . . . . . . . 32 Rounding functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Division functions . . . . . . . . . . . . . . . . . . . . . .

7 3 Language changes 9 4 Multi-threading changes 11 5 Build system changes 13 6 New library functions 15 7 New library features 17 8 Standard library changes 19 LinearAlgebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 12 Mathematical Operations and Elementary Functions 45 12.1 Arithmetic Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 Elementary Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 12.6 Operator

. . . . . . . . . . . . . . . . . 23 i ii CONTENTS 5 Mathematical Operations and Elementary Functions 25 5.1 Arithmetic Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Elementary Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 5.7 Operator Precedence . . . . . . . . . . . . . . . 32 Rounding functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Division functions . . . . . . . . . . . . . . . . . . . . . .

Command-line option changes 13 6 Multi-threading changes 15 7 Build system changes 17 8 New library functions 19 9 New library features 21 i ii CONTENTS 10 Standard library changes 23 LinearAlgebra . . . . . . . . . . . . . . . . . . . . . . . . . 53 17 Mathematical Operations and Elementary Functions 55 17.1 Arithmetic Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Elementary Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 17.6 Operator