Data
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Arrays
- One-dimensional
- Multi-dimensional
- Multi-level
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Structures
- Allocation
- Access
- Alignment
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Floating Point
Array Allocation
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Basic Principle
- T A[L]
- Array of data type T and length L
- Contiguously allocated region of L * sizeof (T) bytes in memory
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Reference
- &A[L]
- *A
Multidimensional (Nested) Arrays
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Declaration
- T A[R][C]
- 2D array of data type T
- R rows, C columns
- Type T element requires K bytes
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Array Size
- R * C * K bytes
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Arrangement
- Row-Major Ordering
Nested Array Row Access
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Row Vectors
- A[i] is array of C elements
- Each element of type T requires K bytes
- Starting address A + i*(C*K)
Nested Array Element Access
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Array Elements
- A[i][j] is element of type T, which requires L bytes
- Address A + i * (C* K) + j * K = A + (i * C + j) * K
Element Access in Multi-Level Array
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Computation
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Element access Mem[Mem[univ+8index]+4digit]
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Must do two memory reads
- First get pointer to row array
- Then access element within array
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N x N Matrix
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Fixed dimensions
- Know value of N at compile time
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Variable dimensions, explicit indexing
- Traditional way to implement dynamic arrays
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Variable dimensions, implicit indexing
- Now supported by gcc
Structure Representation
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Structure represented as block of memory
- Big enough to hold all of the fields
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Fields ordered according to declaration
- Even if another ordering could yield a more compact representation
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Compiler determines overall size + positions of fields
- Machine-level program has no understanding of the structures in the source code
Alignment Principles
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Aligned Data
- Primitive data type requires K bytes
- Address must be multiple of K
- Required on some machines; advised on x86-64
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Motivation for Aligning Data
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Memory accessed by (aligned) chunks of 4 or 8 bytes (system dependent)
- Inefficient to load or store datum that spans quad word boundaries
- Virtual memory trickier when datum spans 2 pages
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Compiler
- Inserts gaps in structure to ensure correct alignment of fields
Specific Cases of Alignment (x86-64)
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1 byte: char, …
- no restrictions on address
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2 bytes: short, …
- lowest 1 bit of address must be 0 2 _2 2
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4 bytes: int, float, …
- lowest 2 bits of address must be 00 2 _2 2
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8 bytes: double, long, char *, …
- lowest 3 bits of address must be 000 2 _2 2
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16 bytes: long double
- lowest 4 bits of address must be 0000 2 _2 2
Satisfying Alignment with Structures
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Within structure:
- Must satisfy each element’s alignment requirement
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Overall structure placement
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Each structure has alignment requirement K
- K = Largest alignment of any element
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Initial address & structure length must be multiples of K
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Floating Point Basics
- Arguments passed in %xmm0, %xmm1, …
- Result returned in %xmm0
- All XMM registers caller-saved
FP Memory Referencing
- Integer (and pointer) arguments passed in regular registers
- FP values passed in XMM registers
- Different mov instructions to move between XMM registers, and between memory and XMM registers
Other Aspects of FP code
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Lots of instructions
- Different operations, different formats, …
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Floating-point comparisons
- Instructions ucomiss and ucomisd
- Set condition codes CF, ZF, and PF
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Using constant values
- Set XMM0 register to 0 with instruction xorpd %xmm0, %xmm0
- Others loaded from memory
