. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Sta�s�cs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575 51 Mathema�cs 577 51.1 Mathema�cal Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1114 97 Sparse Arrays 1115 98 Sta�s�cs 1125 99 Unit Tes�ng 1133 99.1 Tes�ng Base Julia . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Sta�s�cs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577 52 Mathema�cs 579 52.1 Mathema�cal Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1116 98 Sparse Arrays 1117 99 Sta�s�cs 1127 100Unit Tes�ng 1135 100.1Tes�ng Base Julia . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Sta�s�cs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581 53 Mathema�cs 583 53.1 Mathema�cal Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1138 100Sparse Arrays 1139 101Sta�s�cs 1149 102Unit Tes�ng 1157 102.1Tes�ng Base Julia . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Sta�s�cs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579 52 Mathema�cs 581 52.1 Mathema�cal Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1136 99 Sparse Arrays 1137 100Sta�s�cs 1147 101Unit Tes�ng 1155 101.1Tes�ng Base Julia . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Sta�s�cs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560 51 Mathema�cs 561 51.1 Mathema�cal Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1080 95 Sparse Arrays 1081 96 Sta�s�cs 1091 97 Unit Tes�ng 1099 97.1 Tes�ng Base Julia . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Sta�s�cs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558 51 Mathema�cs 559 51.1 Mathema�cal Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1078 xvi CONTENTS 95 Sparse Arrays 1079 96 Sta�s�cs 1089 97 Unit Tes�ng 1097 97.1 Tes�ng Base Julia . . . . . . . . . . . . . . . . . . . . . . . .

%rax # imm = 0x9502F9 addq $-2441406, %rax # imm = 0xFFDABF42 Source line: 5 popq %rbp retq nopw %cs:(%rax,%rax) Because the compiler knows that integer addition and multiplication are associative and Broadcast.combine_axes(1, 1, 1) () source Base.Broadcast.combine_styles – Function. combine_styles(cs...) -> BroadcastStyle Decides which BroadcastStyle to use for any number of value arguments. Uses RandomDevice: for OS-provided entropy. This may be used for cryptographically secure random numbers (CS(P)RNG). • MersenneTwister: an alternate high-quality PRNG which was the default in older versions

%rax # imm = 0x9502F9 addq $-2441406, %rax # imm = 0xFFDABF42 Source line: 5 popq %rbp retq nopw %cs:(%rax,%rax) Because the compiler knows that integer addition and multiplication are associative and Broadcast.combine_axes(1, 1, 1) () source Base.Broadcast.combine_styles – Function. combine_styles(cs...) -> BroadcastStyle Decides which BroadcastStyle to use for any number of value arguments. Uses RandomDevice: for OS-provided entropy. This may be used for cryptographically secure random numbers (CS(P)RNG). • MersenneTwister: an alternate high-quality PRNG which was the default in older versions

%rax # imm = 0x9502F9 addq $-2441406, %rax # imm = 0xFFDABF42 Source line: 5 popq %rbp retq nopw %cs:(%rax,%rax) Because the compiler knows that integer addition and multiplication are associative and Broadcast.combine_axes(1, 1, 1) () source Base.Broadcast.combine_styles – Function. combine_styles(cs...) -> BroadcastStyle Decides which BroadcastStyle to use for any number of value arguments. Uses RandomDevice: for OS-provided entropy. This may be used for cryptographically secure random numbers (CS(P)RNG). • MersenneTwister: an alternate high-quality PRNG which was the default in older versions

%rax # imm = 0x9502F9 addq $-2441406, %rax # imm = 0xFFDABF42 Source line: 5 popq %rbp retq nopw %cs:(%rax,%rax) Because the compiler knows that integer addition and multiplication are associative and Broadcast.combine_axes(1, 1, 1) () source Base.Broadcast.combine_styles – Function. combine_styles(cs...) -> BroadcastStyle Decides which BroadcastStyle to use for any number of value arguments. Uses RandomDevice: for OS-provided entropy. This may be used for cryptographically secure random numbers (CS(P)RNG). • MersenneTwister: an alternate high-quality PRNG which was the default in older versions