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CMSC430 Spring 2007 (^1)
Array accessing
- An array is an ordered sequence of identical objects.
- The ordering is determined by a scalar data object (usually integer or enumeration data). This value is called the subscript or index, and written as A[I] for array A and subscript I.
- Multidimensional arrays have more than one subscript. A 2- dimensional array can be modeled as the boxes on a rectangular grid.
- The L-value for array element A[I,J]is given by the accessing formula on the next slide
CMSC430 Spring 2007 (^2)
Array storage
CMSC430 Spring 2007 (^3)
Array accessing (continued)
Rewriting access equation: L-value(A[I,J]) = α - d1L1 - d2L2 +Id1 + Jd Set I = 0; J= 0; L-value(A[0,0]) = α - d1L1 - d2L2 +0d1 + 0d L-value(A[0,0]) = α - d1L1 - d2L2, which is a constant.
- Call this constant the virtual origin (VO); It represents the address of the 0th element of the array. L-value(A[I,J]) = VO +Id1 + Jd
- To access an array element, typically use a dope vector:
CMSC430 Spring 2007 (^4)
Array accessing summary
To create arrays:
- Allocate total storage beginning at α: (U2-L2+1)(U1-L1+1)eltsize
- d2 = eltsize
- d1 = (U2-L2+1)*d
- VO = α - L1d1 - L2d
- To access A[I,J]: Lvalue(A[I,J]) = VO + Id1 + Jd This works for 1, 2 or more dimensions.
- May not require runtime dope vector if all values are known at compile time. (e.g., in Pascal, d1, d2, and VO can be computed by compiler.)
- Next slide: Storage representation for 2-dimensional array.
CMSC430 Spring 2007 (^7)
Slices
CMSC430 Spring 2007 (^8)
Array slices
Given array : A[L1:U1, L2:U2]: Give d1, d2, and VO for vector:
Dope vector A[I,] = B[L2:U2] VO = L-value(A[I,L2]) - d2L M1 = eltsize = d
Dope vector A[,J] = B[L1:U1] VO = L-value(A[L1,J]) - d1L M1 = rowsize = d
Create new dope vector that accesses original data
CMSC430 Spring 2007 (^9)
More on slices
VO = L-value(A[L1,L2])
- d1L1 - d2L M1 = d1 + d
- Other possibilities:
CMSC430 Spring 2007 (^10)
Associative arrays
Access information by name without having a predefined ordering or enumeration:
- Example: Names and grades for students in a class: NAME[I] = name of Ith student GRADE[I] = Grade for Ith student
Associative array: Use Name as index: CLASS[name] will be grade.
Problem: Do not know enumeration before obtaining data so dope vector method of accessing will not work.
Implemented in Perl and in SNOBOL4 (as a table)
CMSC430 Spring 2007 (^13)
Variant records
type PayType=(Salaried, Hourly); var Employee:record ID: integer; Dept: array[1..3] of char; Age: integer; case PayClass: PayType of Salaried:(MonthlyRate:real; StartDate:integer); Hourly:(HourRate:real; Reg:integer; Overtime:integer) end
CMSC430 Spring 2007 (^14)
Variant records (continued)
Tagged union type - Pascal variant records type whichtype = (inttype, realtype, chartype); type uniontype = record case V: whichtype of inttype: (X: integer); realtype: (Y: real); chartype: (Z: char4); Assumes string of length 4 end But can still subvert tagging: var P: uniontype P.V = inttype; P.X = 142; P.V = chartype; What is P.V value now?
