Memory Optimization

MEMORY OPTIMIZATION Christer Ericson Sony Computer Entertainment, Santa Monica (christer_ericson@playstation.sony.com)

Talk contents 1/2 Problem statement Why “memory optimization?” Brief architecture overview The memory hierarchy Optimizing for (code and) data cache General suggestions Data structures Prefetching and preloading Structure layout Tree structures Linearization caching …

Talk contents 2/2 … Aliasing Abstraction penalty problem Alias analysis (type-based) ‘ restrict’ pointers Tips for reducing aliasing

Problem statement For the last 20-something years… CPU speeds have increased ~60%/year Memory speeds only decreased ~10%/year Gap covered by use of cache memory Cache is under-exploited Diminishing returns for larger caches Inefficient cache use = lower performance How increase cache utilization? Cache-awareness!

Need more justification? 1/3 SIMD instructions consume data at 2-8 times the rate of normal instructions! Instruction parallelism:

Need more justification? 2/3 Improvements to compiler technology double program performance every ~18 years ! Proebsting’s law: Corollary: Don’t expect the compiler to do it for you!

Need more justification? 3/3 Consoles don’t follow it (as such) Fixed hardware 2nd/3rd generation titles must get improvements from somewhere On Moore’s law:

Brief cache review Caches Code cache for instructions, data cache for data Forms a memory hierarchy Cache lines Cache divided into cache lines of ~32/64 bytes each Correct unit in which to count memory accesses Direct-mapped For n KB cache, bytes at k, k+n, k+2n, … map to same cache line N-way set-associative Logical cache line corresponds to N physical lines Helps minimize cache line thrashing

The memory hierarchy Main memory L2 cache L1 cache CPU ~1-5 cycles ~5-20 cycles ~40-100 cycles 1 cycle Roughly:

Some cache specs † 16K data scratchpad important part of design ‡ configurable as 16K 4-way + 16K scratchpad L1 cache (I/D) L2 cache PS2 16K/8K † 2-way N/A GameCube 32K/32K ‡ 8-way 256K 2-way unified XBOX 16K/16K 4-way 128K 8-way unified PC ~32-64K ~128-512K

Foes: 3 C’s of cache misses Compulsory misses Unavoidable misses when data read for first time Capacity misses Not enough cache space to hold all active data Too much data accessed inbetween successive use Conflict misses Cache thrashing due to data mapping to same cache lines

Friends: Introducing the 3 R’s Rearrange (code, data) Change layout to increase spatial locality Reduce (size, # cache lines read) Smaller/smarter formats, compression Reuse (cache lines) Increase temporal (and spatial) locality Compulsory Capacity Conflict Rearrange X (x) X Reduce X X (x) Reuse (x) X

Measuring cache utilization Profile CPU performance/event counters Give memory access statistics But not access patterns (e.g. stride) Commercial products SN Systems’ Tuner, Metrowerks’ CATS, Intel’s VTune Roll your own In gcc ‘-p’ option + define _mcount() Instrument code with calls to logging class Do back-of-the-envelope comparison Study the generated code

Code cache optimization 1/2 Locality Reorder functions Manually within file Reorder object files during linking (order in makefile) __attribute__ ((section ("xxx"))) in gcc Adapt coding style Monolithic functions Encapsulation/OOP is less code cache friendly Moving target Beware various implicit functions (e.g. fptodp)

Code cache optimization 2/2 Size Beware: inlining, unrolling, large macros KISS Avoid featuritis Provide multiple copies (also helps locality) Loop splitting and loop fusion Compile for size (‘-Os’ in gcc) Rewrite in asm (where it counts) Again, study generated code Build intuition about code generated

Data cache optimization Lots and lots of stuff… “ Compressing” data Blocking and strip mining Padding data to align to cache lines Plus other things I won’t go into What I will talk about… Prefetching and preloading data into cache Cache-conscious structure layout Tree data structures Linearization caching Memory allocation Aliasing and “anti-aliasing”

Prefetching and preloading Software prefetching Not too early – data may be evicted before use Not too late – data not fetched in time for use Greedy Preloading (pseudo-prefetching) Hit-under-miss processing

Software prefetching const int kLookAhead = 4; // Some elements ahead for (int i = 0; i < 4 * n; i += 4) { Prefetch(elem[i + kLookAhead]); Process(elem[i + 0]); Process(elem[i + 1]); Process(elem[i + 2]); Process(elem[i + 3]); } // Loop through and process all 4n elements for (int i = 0; i < 4 * n; i++) Process(elem[i]);

Greedy prefetching void PreorderTraversal(Node *pNode) { // Greedily prefetch left traversal path Prefetch(pNode->left); // Process the current node Process(pNode); // Greedily prefetch right traversal path Prefetch(pNode->right); // Recursively visit left then right subtree PreorderTraversal(pNode->left); PreorderTraversal(pNode->right); }

Preloading (pseudo-prefetch) (NB: This code reads one element beyond the end of the elem array.) Elem a = elem[0]; for (int i = 0; i < 4 * n; i += 4) { Elem e = elem[i + 4]; // Cache miss, non-blocking Elem b = elem[i + 1]; // Cache hit Elem c = elem[i + 2]; // Cache hit Elem d = elem[i + 3]; // Cache hit Process(a); Process(b); Process(c); Process(d); a = e; }

Structures Cache-conscious layout Field reordering (usually grouped conceptually) Hot/cold splitting Let use decide format Array of structures Structures of arrays Little compiler support Easier for non-pointer languages (Java) C/C++: do it yourself

Field reordering Likely accessed together so store them together! void Foo(S *p, void *key, int k) { while (p) { if (p->key == key) { p->count[k]++; break; } p = p->pNext; } } struct S { void *key; int count[20]; S *pNext; }; struct S { void *key; S *pNext; int count[20]; };

Hot/cold splitting Allocate all ‘struct S’ from a memory pool Increases coherence Prefer array-style allocation No need for actual pointer to cold fields Hot fields: Cold fields: struct S { void *key; S *pNext; S2 *pCold; }; struct S2 { int count[10]; };

Beware compiler padding Assuming 4-byte floats, for most compilers sizeof(X) == 40, sizeof(Y) == 40, and sizeof(Z) == 24. Decreasing size! struct X { int8 a; int64 b; int8 c; int16 d; int64 e; float f; }; struct Z { int64 b; int64 e; float f; int16 d; int8 a; int8 c; }; struct Y { int8 a, pad_a[7]; int64 b; int8 c, pad_c[1]; int16 d, pad_d[2]; int64 e; float f, pad_f[1]; };

Cache performance analysis Usage patterns Activity – indicates hot or cold field Correlation – basis for field reordering Logging tool Access all class members through accessor functions Manually instrument functions to call Log() function Log() function… takes object type + member field as arguments hash-maps current args to count field accesses hash-maps current + previous args to track pairwise accesses

Tree data structures Rearrange nodes Increase spatial locality Cache-aware vs. cache-oblivious layouts Reduce size Pointer elimination (using implicit pointers) “ Compression” Quantize values Store data relative to parent node

Breadth-first order Pointer-less: Left(n)=2n, Right(n)=2n+1 Requires storage for complete tree of height H

Depth-first order Left(n) = n + 1, Right(n) = stored index Only stores existing nodes

van Emde Boas layout “ Cache-oblivious” Recursive construction

A compact static k-d tree union KDNode { // leaf, type 11 int32 leafIndex_type; // non-leaf, type 00 = x, // 01 = y, 10 = z-split float splitVal_type; };

Linearization caching Nothing better than linear data Best possible spatial locality Easily prefetchable So linearize data at runtime! Fetch data, store linearized in a custom cache Use it to linearize… hierarchy traversals indexed data other random-access stuff

Memory allocation policy Don’t allocate from heap, use pools No block overhead Keeps data together Faster too, and no fragmentation Free ASAP, reuse immediately Block is likely in cache so reuse its cachelines First fit, using free list

The curse of aliasing What is aliasing? Aliasing is also missed opportunities for optimization What value is returned here? Who knows! Aliasing is multiple references to the same storage location int Foo(int *a, int *b) { *a = 1; *b = 2; return *a; } int n; int *p1 = &n; int *p2 = &n;

The curse of aliasing What is causing aliasing? Pointers Global variables/class members make it worse What is the problem with aliasing? Hinders reordering/elimination of loads/stores Poisoning data cache Negatively affects instruction scheduling Hinders common subexpression elimination (CSE), loop-invariant code motion, constant/copy propagation, etc.

How do we do ‘anti-aliasing’? What can be done about aliasing? Better languages Less aliasing, lower abstraction penalty † Better compilers Alias analysis such as type-based alias analysis † Better programmers (aiding the compiler) That’s you, after the next 20 slides! Leap of faith -fno-aliasing † To be defined

Matrix multiplication 1/3 Consider optimizing a 2x2 matrix multiplication: How do we typically optimize it? Right, unrolling! Mat22mul(float a[2][2], float b[2][2], float c[2][2]){ for (int i = 0; i < 2; i++) { for (int j = 0; j < 2; j++) { a[i][j] = 0.0f; for (int k = 0; k < 2; k++) a[i][j] += b[i][k] * c[k][j]; } } }

Matrix multiplication 2/3 But wait! There’s a hidden assumption! a is not b or c! Compiler doesn’t (cannot) know this! (1) Must refetch b[0][0] and b[0][1] (2) Must refetch c[0][0] and c[1][0] (3) Must refetch b[0][0], b[0][1], c[0][0] and c[1][0] Staightforward unrolling results in this: // 16 memory reads, 4 writes Mat22mul(float a[2][2], float b[2][2], float c[2][2]){ a[0][0] = b[0][0]*c[0][0] + b[0][1]*c[1][0]; a[0][1] = b[0][0]*c[0][1] + b[0][1]*c[1][1]; //(1) a[1][0] = b[1][0]*c[0][0] + b[1][1]*c[1][0]; //(2) a[1][1] = b[1][0]*c[0][1] + b[1][1]*c[1][1]; //(3) }

Matrix multiplication 3/3 A correct approach is instead writing it as: … before producing outputs Consume inputs… // 8 memory reads, 4 writes Mat22mul(float a[2][2], float b[2][2], float c[2][2]){ float b00 = b[0][0], b01 = b[0][1]; float b10 = b[1][0], b11 = b[1][1]; float c00 = c[0][0], c01 = c[0][1]; float c10 = c[1][0], c11 = c[1][1]; a[0][0] = b00*c00 + b01*c10; a[0][1] = b00*c01 + b01*c11; a[1][0] = b10*c00 + b11*c10; a[1][1] = b10*c01 + b11*c11; }

Abstraction penalty problem Higher levels of abstraction have a negative effect on optimization Code broken into smaller generic subunits Data and operation hiding Cannot make local copy of e.g. internal pointers Cannot hoist constant expressions out of loops Especially because of aliasing issues

C++ abstraction penalty Lots of (temporary) objects around Iterators Matrix/vector classes Objects live in heap/stack Thus subject to aliasing Makes tracking of current member value very difficult But tracking required to keep values in registers! Implicit aliasing through the this pointer Class members are virtually as bad as global variables

C++ abstraction penalty Pointer members in classes may alias other members: Code likely to refetch numVals each iteration! numVals not a local variable! May be aliased by pBuf ! class Buf { public: void Clear() { for (int i = 0; i < numVals; i++) pBuf[i] = 0; } private: int numVals, *pBuf; }

C++ abstraction penalty We know that aliasing won’t happen, and can manually solve the aliasing issue by writing code as: class Buf { public: void Clear() { for (int i = 0, n = numVals; i < n; i++) pBuf[i] = 0; } private: int numVals, *pBuf; }

C++ abstraction penalty Since pBuf[i] can only alias numVals in the first iteration, a quality compiler can fix this problem by peeling the loop once, turning it into: Q: Does your compiler do this optimization?! void Clear() { if (numVals >= 1) { pBuf[0] = 0; for (int i = 1, n = numVals; i < n; i++) pBuf[i] = 0; } }

Type-based alias analysis Some aliasing the compiler can catch A powerful tool is type-based alias analysis Use language types to disambiguate memory references!

Type-based alias analysis ANSI C/C++ states that… Each area of memory can only be associated with one type during its lifetime Aliasing may only occur between references of the same compatible type Enables compiler to rule out aliasing between references of non-compatible type Turned on with –fstrict-aliasing in gcc

Compatibility of C/C++ types In short… Types compatible if differing by signed , unsigned , const or volatile char and unsigned char compatible with any type Otherwise not compatible (See standard for full details.)

What TBAA can do for you into this: It can turn this: Possible aliasing between v[i] and *n No aliasing possible so fetch *n once! void Foo(float *v, int *n) { for (int i = 0; i < *n; i++) v[i] += 1.0f; } void Foo(float *v, int *n) { int t = *n; for (int i = 0; i < t; i++) v[i] += 1.0f; }

What TBAA can also do Cause obscure bugs in non-conforming code! Beware especially so-called “type punning” Required by standard Allowed By gcc Illegal C/C++ code! uint32 i; float f; i = *((uint32 *)&f); uint32 i; union { float f; uchar8 c[4]; } u; u.f = f; i = (u.c[3]<<24L)+ (u.c[2]<<16L)+ ...; uint32 i; union { float f; uint32 i; } u; u.f = f; i = u.i;

Restrict-qualified pointers restrict keyword New to 1999 ANSI/ISO C standard Not in C++ standard yet, but supported by many C++ compilers A hint only, so may do nothing and still be conforming A restrict-qualified pointer (or reference)… … is basically a promise to the compiler that for the scope of the pointer, the target of the pointer will only be accessed through that pointer (and pointers copied from it). (See standard for full details.)

Using the restrict keyword Given this code: You really want the compiler to treat it as if written: But because of possible aliasing it cannot! void Foo(float v[], float *c, int n) { for (int i = 0; i < n; i++) v[i] = *c + 1.0f; } void Foo(float v[], float *c, int n) { float tmp = *c + 1.0f; for (int i = 0; i < n; i++) v[i] = tmp; }

Using the restrict keyword giving for the first version: and for the second version: For example, the code might be called as: The compiler must be conservative, and cannot perform the optimization! v[] = 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 v[] = 1, 1, 1, 1, 1, 2, 2, 2, 2, 2 float a[10]; a[4] = 0.0f; Foo(a, &a[4], 10);

Solving the aliasing problem The fix? Declaring the output as restrict : Alas, in practice may need to declare both pointers restrict! A restrict-qualified pointer can grant access to non-restrict pointer Full data-flow analysis required to detect this However, two restrict-qualified pointers are trivially non-aliasing! Also may work declaring second argument as “float * const c” void Foo(float * restrict v, float *c, int n) { for (int i = 0; i < n; i++) v[i] = *c + 1.0f; }

‘ const’ doesn’t help Some might think this would work: Wrong! const promises almost nothing! Says *c is const through c , not that *c is const in general Can be cast away For detecting programming errors, not fixing aliasing Since *c is const, v[i] cannot write to it, right? void Foo(float v[], const float *c, int n) { for (int i = 0; i < n; i++) v[i] = *c + 1.0f; }

SIMD + restrict = TRUE restrict enables SIMD optimizations Independent loads and stores. Operations can be performed in parallel! Stores may alias loads. Must perform operations sequentially. void VecAdd(int *a, int *b, int *c) { for (int i = 0; i < 4; i++) a[i] = b[i] + c[i]; } void VecAdd(int * restrict a, int *b, int *c) { for (int i = 0; i < 4; i++) a[i] = b[i] + c[i]; }

Restrict-qualified pointers Important, especially with C++ Helps combat abstraction penalty problem But beware… Tricky semantics, easy to get wrong Compiler won’t tell you about incorrect use Incorrect use = slow painful death!

Tips for avoiding aliasing Minimize use of globals, pointers, references Pass small variables by-value Inline small functions taking pointer or reference arguments Use local variables as much as possible Make local copies of global and class member variables Don’t take the address of variables (with &) restrict pointers and references Declare variables close to point of use Declare side-effect free functions as const Do manual CSE, especially of pointer expressions

That’s it! – Resources 1/2 Ericson, Christer. Real-time collision detection. Morgan-Kaufmann, 2005. (Chapter on memory optimization) Mitchell, Mark. Type-based alias analysis. Dr. Dobb’s journal, October 2000. Robison, Arch. Restricted pointers are coming. C/C++ Users Journal, July 1999. http://www.cuj.com/articles/1999/9907/9907d/9907d.htm Chilimbi, Trishul. Cache-conscious data structures - design and implementation. PhD Thesis. University of Wisconsin, Madison, 1999. Prokop, Harald. Cache-oblivious algorithms. Master’s Thesis. MIT, June, 1999. …

Resources 2/2 … Gavin, Andrew. Stephen White. Teaching an old dog new bits: How console developers are able to improve performance when the hardware hasn’t changed. Gamasutra. November 12, 1999 http://www.gamasutra.com/features/19991112/GavinWhite_01.htm Handy, Jim. The cache memory book. Academic Press, 1998. Macris, Alexandre. Pascal Urro. Leveraging the power of cache memory. Gamasutra. April 9, 1999 http://www.gamasutra.com/features/19990409/cache_01.htm Gross, Ornit. Pentium III prefetch optimizations using the VTune performance analyzer. Gamasutra. July 30, 1999 http://www.gamasutra.com/features/19990730/sse_prefetch_01.htm Truong, Dan. François Bodin. Andr é Seznec. Improving cache behavior of dynamically allocated data structures.

Memory Optimization

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