. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1600 101.22 Julia SSA-form IR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1602 101.23 EscapeAnalysis -9223372036854775808 julia> x + 1 == typemin(Int64) true Thus, arithmetic with Julia integers is actually a form of modular arithmetic. This reflects the characteristics of the underlying arithmetic of integers interpreted as the numeric literal 1 multiplied by the variable e10, and similarly with the equivalent E form. • The 32-bit floating-point literal expression 1.5f22 could be interpreted as the numeric literal

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1600 101.22 Julia SSA-form IR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1602 101.23 EscapeAnalysis -9223372036854775808 julia> x + 1 == typemin(Int64) true Thus, arithmetic with Julia integers is actually a form of modular arithmetic. This reflects the characteristics of the underlying arithmetic of integers interpreted as the numeric literal 1 multiplied by the variable e10, and similarly with the equivalent E form. • The 32-bit floating-point literal expression 1.5f22 could be interpreted as the numeric literal

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1889 105.23 Julia SSA-form IR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1891 105.24 EscapeAnalysis interpreted as the numeric literal 1 multiplied by the variable e10, and similarly with the equivalent E form. • The 32-bit floating-point literal expression 1.5f22 could be interpreted as the numeric literal julia> 5//-15 -1//3 julia> -4//-12 1//3CHAPTER 7. COMPLEX AND RATIONAL NUMBERS 46 This normalized form for a ratio of integers is unique, so equality of rational values can be tested by checking for equality

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1889 105.23 Julia SSA-form IR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1891 105.24 EscapeAnalysis interpreted as the numeric literal 1 multiplied by the variable e10, and similarly with the equivalent E form. • The 32-bit floating-point literal expression 1.5f22 could be interpreted as the numeric literal julia> 5//-15 -1//3 julia> -4//-12 1//3CHAPTER 7. COMPLEX AND RATIONAL NUMBERS 46 This normalized form for a ratio of integers is unique, so equality of rational values can be tested by checking for equality

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1889 105.23 Julia SSA-form IR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1891 105.24 EscapeAnalysis interpreted as the numeric literal 1 multiplied by the variable e10, and similarly with the equivalent E form. • The 32-bit floating-point literal expression 1.5f22 could be interpreted as the numeric literal julia> 5//-15 -1//3 julia> -4//-12 1//3CHAPTER 7. COMPLEX AND RATIONAL NUMBERS 46 This normalized form for a ratio of integers is unique, so equality of rational values can be tested by checking for equality

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1940 106.23 Julia SSA-form IR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1942 106.24 EscapeAnalysis interpreted as the numeric literal 1 multiplied by the variable e10, and similarly with the equivalent E form. • The 32-bit floating-point literal expression 1.5f22 could be interpreted as the numeric literal julia> 5//-15 -1//3 julia> -4//-12 1//3CHAPTER 7. COMPLEX AND RATIONAL NUMBERS 46 This normalized form for a ratio of integers is unique, so equality of rational values can be tested by checking for equality

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1943 106.23 Julia SSA-form IR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1945 106.24 EscapeAnalysis interpreted as the numeric literal 1 multiplied by the variable e10, and similarly with the equivalent E form. • The 32-bit floating-point literal expression 1.5f22 could be interpreted as the numeric literal julia> 5//-15 -1//3 julia> -4//-12 1//3CHAPTER 7. COMPLEX AND RATIONAL NUMBERS 46 This normalized form for a ratio of integers is unique, so equality of rational values can be tested by checking for equality

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1940 106.23 Julia SSA-form IR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1942 106.24 EscapeAnalysis interpreted as the numeric literal 1 multiplied by the variable e10, and similarly with the equivalent E form. • The 32-bit floating-point literal expression 1.5f22 could be interpreted as the numeric literal julia> 5//-15 -1//3 julia> -4//-12 1//3CHAPTER 7. COMPLEX AND RATIONAL NUMBERS 46 This normalized form for a ratio of integers is unique, so equality of rational values can be tested by checking for equality

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1940 106.23 Julia SSA-form IR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1942 106.24 EscapeAnalysis interpreted as the numeric literal 1 multiplied by the variable e10, and similarly with the equivalent E form. • The 32-bit floating-point literal expression 1.5f22 could be interpreted as the numeric literal julia> 5//-15 -1//3 julia> -4//-12 1//3CHAPTER 7. COMPLEX AND RATIONAL NUMBERS 46 This normalized form for a ratio of integers is unique, so equality of rational values can be tested by checking for equality

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1931 105.23 Julia SSA-form IR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1933 105.24 EscapeAnalysis interpreted as the numeric literal 1 multiplied by the variable e10, and similarly with the equivalent E form. • The 32-bit floating-point literal expression 1.5f22 could be interpreted as the numeric literal julia> 5//-15 -1//3 julia> -4//-12 1//3CHAPTER 7. COMPLEX AND RATIONAL NUMBERS 46 This normalized form for a ratio of integers is unique, so equality of rational values can be tested by checking for equality