Bernard Goossens
email: bernard.goossens@univ-perp.fr

David Parello
email: david.parello@univ-perp.fr

Katarzyna Porada
email: katarzyna.porada@univ-perp.fr

Djallal Rahmoune
email: djallal.rahmoune@univ-perp.fr

Toward a Core Design to Distribute an Execution on a Many-Core Processor

Keywords: Microarchitecture, Parallelism, Manycore, Automatic parallelization

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Introduction

Every parallel machine programmer dreams he can run his unchanged C programs on a parallel computer.

Figure 1 shows a C version and a pthread version of a sum reduction function. The difference does not lie in the code text (based on the same algorithm) but in its execution. The C code is run sequentially using a stack and the pthread code is run in parallel with the help of the pthread system primitives.

This paper aims to show that if we change the execution model, the C code run can have the same behaviour as the pthread run, i.e. parallel execution. But of course, the C code is much simpler. Section 2 explains how to run a C program in parallel. Section 3 evaluates the Instruction Level Parallelism (ILP) in benchmarks based on parallel algorithms and lists the main published works on ILP. Section 4 describes the parallel execution model and its core microarchitecture. Section 5 gives an analytical evaluation of the performance potential of the proposed model and core design. It also mentions the on-going developments of simulators and concludes.

u n s i g n e d l o n g sum ( u n s i g n e d l o n g t [ ] , u n s i g n e d l o n g n){ i f ( n==1) r e t u r n t [ 0 ] ; e l s e i f ( n==2) r e t u r n t [ 0 ] + t [START_REF] Shun | Brief announcement: The problem based benchmark suite[END_REF] ; e l s e r e t u r n sum ( t , n / 2 ) + sum(& t [ n / 2 ] , n-n / 2 ) ; } ( a ) C i m p l e m e n t a t i o n t y p e d e f s t r u c t {u n s i g n e d l o n g * p ; u n s i g n e d l o n g i ;} ST ; v o i d * sum ( v o i d * s t ){ ST s t r 1 , s t r 2 ; u n s i g n e d l o n g s , s1 , s 2 ; p t h r e a d t t i d 1 , t i d 2 ; i f ( ( ( ST * ) s t)->i >2){ s t r 1 . p =((ST * ) s t)->p ; s t r 1 . i =((ST * ) s t)->i / ; } e l s e i f ( ( ( ST * ) s t)->i ==1){s 1 =((ST * ) s t)->p [ 0 ] ; s 2 =0;} e l s e {s 1 =((ST * ) s t)->p [ 0 ] ; s 2 =((ST * ) s t)->p [START_REF] Shun | Brief announcement: The problem based benchmark suite[END_REF] ; } s=s 1+s 2 ; p t h r e a d e x i t ( ( v o i d * ) s ) ; } ( b ) p t h r e a d i m p l e m e n t a t i o n Fig. 1: A vector sum reduction: C and pthread implementations 2 Running a C program in parallel.

Figure 2 shows the sum function translation into x86 (gas syntax ; rightmost operand is the destination). The code is run sequentially because the hardware is unable to fork at lines 12 and 20. The control flow travels along the binary tree of calls depth first, leading to a 59 instructions run trace shown on figure 3 (figure 4 left part shows the call tree for sum(t,5)). Figure 5 shows a modified x86 code for the sum function. The hardware is assumed to be able to fork, i.e. start a second instruction flow which occurs on lines 10 and 16 (fork instructions replace call instructions of the original x86 code). Unlike a call instruction, a fork instruction does not save a return address.

Non volatile registers (i.e. rbx, rdi and rsi in this example) are copied to the forked path, replacing the stack save/restore pair. Hence push and pop are removed. The stack pointer itself (rsp) is copied to the forked path Fig. 3: The instruction trace for the run of sum(t,5).

The endfork instruction ends a flow. Unlike a return, the endfork does not give control back to a return address. t [START_REF] Wall | Limits of instruction-level parallelism[END_REF] t [START_REF] Tomasulo | An efficient algorithm for exploiting multiple arithmetic units[END_REF]+t [START_REF] Tjaden | Detection and parallel execution of independent instructions[END_REF] sum(t,5) sum(t,2) sum(&t [START_REF] Wall | Limits of instruction-level parallelism[END_REF],3) sum(&t [START_REF] Wall | Limits of instruction-level parallelism[END_REF],1) sum(&t [START_REF] Tomasulo | An efficient algorithm for exploiting multiple arithmetic units[END_REF],2)

Fig. 4: The call tree (left) for the run of sum(t,5) and its sections (right).

Figure 6 shows how the run is parallelized. The run starts on core 1 which fetches and executes instructions 1-1 to 1-5. The fork instruction starts a new flow on core 2. The new flow matches the resume path after fork, i.e instruction subq on line 11 (figure 5). Core 1 continues its own flow (callee path back to line 1, instruction cmpq). Both flows are run in parallel, leading to the fetch and execution of instructions 1-6 to 1-11 (core 1 flow) and 2-1 to 2-16 (core 2 flow).

As core 2 receives valid copies of registers rdi, rsi, rbx and rsp, instructions 2-1 and 2-3 to 2-6 can be executed. Only instruction 2-2 must wait until register rax is set by core 1 flow. The synchronisation need is easy to detect, thanks to register renaming. Instruction 2-2 consumes a source rax produced by the closest instruction writing to rax on the sequential path. As soon as instruction 1-10 writes to rax, the written value is forwarded to instruction Fig. 6: The instruction trace for the parallel run of sum(t,5).

The full run is divided into 5 flows or sections (figure 4, right part). Each section is framed by a red rectangle. The longest section is composed of 16 instructions (section 2, from 2-1 to 2-16). Sections are numbered in execution trace order as indicated by the green arrows. Instructions framed by a blue rectangle belong to the same call level (e.g. instructions 1-1 to 1-5, 2-1 to 2-6 and 5-1 to 5-3 form the same call level). A section is a full recursive descent (e.g. section 1 combines 1-1 to 1-5 for n = 5 and 1-6 to 1-11 for n = 2).

Out-of-order execution is crucial to parallelize fetch. As instruction 2-2 does not block 2-6, the second call can be run in parallel with the first one.

This example shows that if the hardware is changed, the sum function can run in parallel as in the pthread implementation. However, any link between threads in the pthread or MPI models must be explicitely added to the code through OS communication primitives (e.g. MPI Send and MPI Recv or socket based communications in pthread).

In the parallel model, the sections are totally ordered. New sections are inserted in place in the list of existing sections, possibly in parallel, building the sequential trace of the run. This structure and the renaming process (which assigns a new location to each write of each instruction in the sequential trace) ensure that each read can match the most recent preceding write. In the pthread or MPI models, this sequential structuration of threads is not available.

For example, if x is local to thread t x and y is local to thread t y , to copy y into x thread t y sends y to thread t x , which receives it (MPI rendezvous). If x is global, t x and t y can communicate through x but they must synchronize writes and reads with pthread mutex. The OS must be invoked to link the sender and the receiver or to synchronize multiple writers and readers.

In the parallel model, the equivalent of thread t y is section s y writing to y and the equivalent of thread t x is section s x reading y to copy it into x. Section s y has instruction i y writing to y (say i y is addq %rbx, %rax, with y in rax, i.e. y = y + z for some z in rbx) and section s x has instruction i x reading y (say i x is movq %rax, %rcx, with rcx being x, i.e. x = y). Instruction i y allocates rax 0 to rename rax destination. Instruction i x renames its source rax. As sections s y and s x are ordered and as no instruction updates y between i y and i x , the renaming of rax in i x matches rax 0 . Moreover, the hardware synchonizes the reader i x with the writer i y until rax 0 is full. Hence, rendezvous or mutex are not necessary and the OS need not be sollicited.

Renaming is the key to synchronization and communication between dependent flows. Renaming should be extended to all hardware locations. For example, instruction 5-1 reads the top of stack word (0(rsp)). This memory location is written by instruction 2-2. If instruction 2-2 destination a = 0(rsp) is renamed r, instruction 5-1 renames the same address a with the same name r, exhibiting the dependency with instruction 2-2. Instruction 5-1, which computes the final sum, executes after it has received rax from section 4 (second half of the sum) and a from section 2 (first half of the sum).

ILP in programs

Figure 7 displays the ILP of ten benchmarks of the PBBS suite [START_REF] Shun | Brief announcement: The problem based benchmark suite[END_REF]. The PBBS benchmarks implement various classical parallel algorithms (see table 1).

On figure 7, for each of the 10 benchmarks, the 11 leftmost bars (those with numbered keys) match eleven parallel runs of the benchmark with increasing The sequential runs consider all the dependencies excluding the register false ones (Write After Read and Write After Write), assuming an unlimited register renaming capacity, and excluding the control flow ones, assuming perfect branch prediction. The sequential runs ILP measures the ultimate performance of actual out-of-order speculative processors.

The parallel runs assume the trace is available when the run starts (no fetch delay) and in the same time all the destinations (including memory) are renamed. The stack pointer dependencies are not considered. The parallel runs ILP measures the ultimate performance an ideal parallel machine achieves when the run order only depends on the producer to consumer dependencies, excluding the stack pointer. Each instruction on the trace is run at the cycle next to the last source reception. The processor is assumed to run all the ready instructions in the same cycle with a single cycle latency (as in the sequential runs).

All runs are continued until completion. For each benchmark, the 11 parallel runs vary from 1M to 1G instructions (increasing factor 2) and the sequential runs are 1G instructions long.

The figure shows that sequential runs have a very low ILP (ranging from 3.2 to 5.6) and parallel runs have a very high ILP (ranging from 600 to 508K for dataset 11). The difference comes from the dominating distant ILP. Moreover, when a benchmark is data parallel its parallel run ILP increases proportionally to the dataset (e.g. benchmarks 1, 2, 5, 6, 9 and 10).

The sequential run ILP we have measured confirms ILP reported values (such as [START_REF] Wall | Limits of instruction-level parallelism[END_REF]). Since 50 years many successive research works on ILP were published.

In 1967, Tomasulo [START_REF] Tomasulo | An efficient algorithm for exploiting multiple arithmetic units[END_REF] presented an algorithm to run floating point instructions out-of-order. He introduced register renaming which is still used in today's speculative cores to parallelize on-the-fly instructions. In 1970, Tjaden and Flynn [START_REF] Tjaden | Detection and parallel execution of independent instructions[END_REF] measured the available parallelism in a 10 instructions window. They ran their test programs at 1.86 instructions per cycle.

In 1984, Nicolau and Fisher [START_REF] Nicolau | Measuring the parallelism available for very long instruction word architectures[END_REF] measured the available parallelism to feed a VLIW processor. In their experiments, they included a measure of ILP from runs on an ideal machine with infinite resources. They discovered that scientific codes present a high ILP, over 1000.

In 1991, David Wall presented the first study centered on ILP [START_REF] Wall | Limits of instruction-level parallelism[END_REF]. He measured that the available parallelism a "real" processor finds in 13 benchmarks is 5 on average, ranging from 3 to 452 . In an "ideal" processor3 , ILP ranges from 6 to 60 with an average at 25. From this study, we know that there is ILP but it seems impossible to catch more than 5 independent instructions per cycle.

In 1992, Austin and Sohi [START_REF] Austin | Dynamic dependency analysis of ordinary programs[END_REF] measured the SPEC89 suite ILP and analyzed its distribution. They showed that ILP is arbitrarily distant from the instruction pointer. They also pointed out the serializing effect of the stack manipulations. The same year, Lam and Wilson [START_REF] Lam | Limits of control flow on parallelism[END_REF] studied the impact of control on ILP. Their measures showed that a processor with a perfect branch predictor could dramatically improve its performance. As in Austin and Sohi work, distant ILP was detected. To capture this distant ILP, a processor must be able to speculate on the control flow and use multiple instruction pointers. In 1997, Moshovos and Sohi have proposed memory renaming in [START_REF] Moshovos | Dynamic speculation and synchronization of data dependences[END_REF], using a predictor to find the store renaming a load. In 1999, Postiff, Greene, Tyson and Mudge [START_REF] Postiff | The limits of instruction level parallelism in spec95 applications[END_REF] measured SPEC95 suite ILP. They pointed out that the stack introduces many parasitic dependencies. To capture distant ILP, the application should be multi-threaded.

In 2004, Cristal, Santana and Valero [START_REF] Cristal | Toward kilo-instruction processors[END_REF] described a kilo-instructions microarchitecture. The authors suggested that to capture more ILP, the processor must have access to instructions far from the fetch point. They gave solutions to allocate later and free sooner the needed resources to optimize their usage and so, take care of more "on-the-fly" instructions with the same resources. In 2012, Sharafeddine, Jothi and Akkary [START_REF] Sharafeddine | Disjoint out-of-order execution processor[END_REF] proposed an architecture to partition a run into parallel threads, forking the leading thread at call. In the sum example this leads to fork on both of the highest levels calls but not on the lower levels, capturing only a small part of the distant ILP. In 2013, Goossens and Parello [START_REF] Goossens | Limits of instruction-level parallelism capture[END_REF] analyzed distant ILP and showed that ILP could be highly increased when removing stack pointer updates and false memory dependencies.

From these works, we deduce that i) high ILP is available, ii) most of it comes from very distant instructions and iii) sequential fetch and stack are the main obstacles on the ILP capture. Two ideas are suggested to help capture distant ILP : following multiple instruction flows [START_REF] Lam | Limits of control flow on parallelism[END_REF] and renaming memory [START_REF] Moshovos | Dynamic speculation and synchronization of data dependences[END_REF]. [START_REF] Tjaden | Detection and parallel execution of independent instructions[END_REF] An execution model to run programs in parallel and its core implementation.

In section 3 we assumed the full trace is available at run start and all the destinations are pre-renamed. This is not realistic. However, code fetch and destinations renamings should occur as soon as possible to allow distant ILP capture.

Parallelizing fetch.

A section is composed of dynamically contiguous instructions. A section starts when a fork instruction creates it. It ends when an endfork instruction is reached.

A control flow instruction (jump, call or branch) does not end a section. The same section continues after the control flow instruction.

When a new section is forked, a message is sent to a hosting core 4 . The message contains the forked Instruction Pointer (IP), the stack pointer and the set of non volatile registers. It also contains the identification of the neighbour sections (e.g. the current creating section). The choosen core queues the message while it fetches another section. When the section creation message is dequeued, it fills the register file local to the fetch pipeline stage. The IP, the stack pointer and the non volatile registers are initialized and other registers are emptied.

For example, when instruction 1-5 forks, a section creation message is sent to core 2 (say), including register rdi value t, register rsi value 2 and register rbx value 5. When instruction 2-6 forks, the stack pointer rsp is transmitted to section 5, pointing on the same stack word as section 2. Hence, sections 2 and 5 share the same stack portion. Thanks to memory renaming, when instruction 5-1 reads stack word 0, it matches with instruction 2-2 write to stack word 0. Both instructions compute the same address a = rsp + 0.

The fetch pipeline stage fetches along the section pointed to by IP. The fetch stage has no branch predictor. There are two reasons for such a choice. First, moving fast along the flow is better obtained by a parallel fetch along multiple control-computed sections than by a sequential fetch along a single predicted path, even if the prediction is perfect. Second, a predictor is less cost-effective in a core if the flow is divided into sections and distributed on multiple cores. For these reasons, the fetch stage computes its control rather than predicting it. To keep the stage hardware simple, each cycle fetches and computes a single instruction. As a result, each core fetches more slowly than an actual speculative core but the cores fetch much faster altogether.

Figure 8 shows the fetch-and-decode pipeline stage. The IP addresses the Instruction Memory Hierarchy (IMH, i.e. L1 instruction cache). The fetched instruction addresses the Register File (RF) to read full registers sources. If all the needed sources are full, the instruction is computed in the ALU. Floating point instructions, memory accesses, complex integer instructions and instructions having empty sources are not computed in the fetch stage but later. Computed instructions results are written back to RF, setting the destination register to full. Uncomputed instructions set their destination register(s) to empty.

The fetch stage includes instruction decoding (not shown). When a fork instruction is decoded, it generates a section creation message. The created section starts at the next instruction. The current section continues at the fork instruction target. It ends when an endfork instruction is decoded. The IP register is set to empty and at the next cycle the fifo head message is dequeued and IP and RF are initialized, which starts the fetch of a new section.

As mentioned on figure 8, the stage critical path is longer than in a speculative out-of-order pipeline, including a L1 cache traversal, an instruction decoding, a register file read (2 read ports), an ALU (Arithmetic and Logic Unit) computation and a register file write (1 write port). This leads to a slow frequency processor, such as a GPU. Slowness is to be compensated by parallelism. Figure 9 shows the six-stages pipeline building the core microarchitecture. On the bottom part of the design we find a full size rectangle dedicated to commu-nications with other cores in the processor chip (assumed to be connected by a Network-on-Chip). The forking request unit (FRU) handles the income/outcome of section creation messages. The register renaming request unit (RRRU) handles the income/outcome of source registers renamings. The register exporting request unit (RERU) handles the import/export of renamed registers values. The address renaming request unit (ARRU) handles the income/outcome of source memory addresses renamings. The memory exporting request unit (MERU) handles the import/export of renamed memory values. The instruction exporting request unit (IERU) handles the outcome of retired instructions.

The fetch-decode and register-rename stages follow a single section up to its end. Renamed instructions enter in-order in a Reorder Buffer (ROB in the retire stage) and in the Instruction Queue (IQ in the execute-write-back stage). Load-/store instructions enter in-order in the address renaming queue (ARQ in the address-rename stage). Register-register instructions from multiple sections are mixed in the execute-write-back stage. They read sources in a memory keeping the core renamed registers (register renaming memory or RRM). Load/store instructions compute the access address in the execute-write-back stage and save it in the ARQ. Memory addresses in ARQ are renamed in-order and renamed memory access instructions enter the Load/Store Queue (LSQ). As these instructions are renamed they can be run out-of-order. Register renaming. Each instruction in the core can be uniquely identified by its section identifier and its ordinal number in the section. If we assume the number of sections hosted by a core is bounded by max section and the number of instructions in a section is bounded by max instruction, a core can host at most max section * max instruction instructions, i.e. as many renamed destinations. Each renamed destination can be uniquely identified by a pair (#section, #instruction) (or (s,i) in short).

The fetch-decode stage delivers a partially evaluated instruction to the rename stage which renames the empty sources, i.e. either find their local (s,i) renaming or, if not hosted by the local core, look for the producing core.

If a source s may not be locally renamed by an instruction inst (no instruction previously fetched in the same section has written to s), its value is requested to the preceding section, i.e. to another hosting core through the RRRU. In the same time, a destination d is allocated in RRM for the missing register, as if s would be locally written. This destination d serves as a caching of the missing source s. Later references to s in the same section are renamed d.

The renaming request travels from section to section until a producer is found (i.e. an instruction writing to s). In the sum function example, for any size of the data, the only register to be renamed is register rax in instructions 12 and 17. In both cases, the producer is the section just preceding the renaming one.

Each core on the travel receives the renaming request in its RRRU. It renames source s. If the renaming misses, the request is propagated through the RRRU. If it hits, an export instruction is added to the IQ which waits for the requested value. When it is received, the export instruction is run, reading the value in RRM and sending it to the requesting section through the RERU.

The value reaches the requesting core through its RERU. It is written in RRM, entry d. The IQ is notified that destination d is ready, which allows the waiting instruction inst to start execution and read d in RRM as source s.

Renaming seems very sequential. To find the producer of source s, the trace of executed instructions must be travelled backward from the consumer down to the first instruction writing to s. However, i) only the portion of code ranging from the producer to the consumer is to be visited and ii) stack pointer based variables with a positive offset (e.g. 0(rsp)) benefit from a shortcut eliminating instructions belonging to a call level deeper than the consumer. Statement i) implies that if a producer is close from a consumer, the portion of code to consider is short. This is the case for function results used by the resume code (register rax in the sum function example). Statement ii) implies that if a consumer and a producer address the same stack frame, the portion of code to consider is also short, excluding in between function calls. This is the case for local variables set at function start and later used (stack location 0(rsp) in the sum example).

Only for global variables and heap pointers the travel from producer to consumer can represent a long path, as all the in between sections must be visited to make sure they do not contain any more recent producer of the consumed address. However, the caching feature ensures that the high price is rarely paid. Once renamed in an intermediary consuming section, a global or heap variable is cached and it can be consumed by neighbour sections for cheap.

Instruction 2-2 on figure 6 illustrates fast renaming applying statement i). After the renaming of register rax misses in section 2, a request is sent to the core hosting section 1. The renaming hits in section 1 (instruction 1-10) and the value of rax is sent back to the core hosting section 2.

Instruction 5-1 illustrates fast renaming applying statement ii). After the renaming of stack location 0(rsp) at address a misses in section 5, a request is sent to section 2, bypassing sections 3 and 4 which are at a lower call level than instruction 5-1. The renaming hits in section 2 (instruction 2-2) and the value of 0(rsp) is sent back to the core hosting section 5.

Instruction 1-8 illustrates high price renaming of global variable t[0]. The request travels back to the loader which installs code and global initialized data. The hardware can i) access to full cache lines instead of single words and ii) cache the accessed lines along the return path. From statement i), instruction 1-8 gets its own word t[0] but also instruction 1-10 word t [START_REF] Shun | Brief announcement: The problem based benchmark suite[END_REF]. Moreover, from statement ii), core 1 caches the memory line containing t[0] up to t [START_REF] Tjaden | Detection and parallel execution of independent instructions[END_REF] which can be consumed cheaply by sections 2 (t [START_REF] Wall | Limits of instruction-level parallelism[END_REF]) and 3 (t [START_REF] Tomasulo | An efficient algorithm for exploiting multiple arithmetic units[END_REF] and t[4]) 5 .

Memory renaming. Memory renaming is done like register renaming. Instead of a Register Alias Table (RAT), the address-rename stage uses a Memory Address Alias Table (MAAT). There is one MAAT per section, each MAAT having one entry per instruction in the section. Each MAAT is a fully associative cache. Renaming address a in section s means looking for a in section s MAAT. If the search misses, it indicates that section s does not write to a and the renaming should be looked for in the section preceding s.

A memory renaming request works like a register one. When renaming address a misses, a memory line is allocated in the MRM to host line l a containing a (it caches l a ). The renaming request travels along contiguous sections until a producer of l a is found. Each visited core receives the request in its ARRU. The renaming request is enqueued in the ARQ to avoid bypassing renamings of addresses of the same section not yet done. When the request is dequeued, if the renaming misses, it is propagated to the preceding section. When it hits, an instruction to export l a is added to the LSQ. The exported memory line travels back to the requesting core where it is received in the MERU. From there, it is written to the MRM and the LSQ is notified that a is ready.

Memory renaming transforms the code at run time into a single assignment form. Synchronisation of consumers with their producers and single assignment ensure sequential consistency without any coherency protocol requirement. Hence, the processor memory distributed in the cores is coherent.

Parallelizing retirement. Sections are created in parallel, as fork instructions are fetched and run. To keep the cores loads acceptable (no more than max section sections hosted in a core), terminated sections should retire at the same speed, i.e. retirement should be parallelized. Retirement frees the sections in the cores to allow new sections in.

Instructions retire in-order (within their section) by exporting their result to the successor section6 . To be retired, an instruction must be terminated. An instruction is not exported if it holds a result useless for successors, i.e. if i) its destination is updated later in the section or ii) it writes to a non volatile register or iii) it is a control flow instruction or iv) it writes to stack or heap in a location freed later in the section or v) it has exported its computation to a consumer. The successor discards exported instructions if their production may not be consumed anymore. An exported instruction i is discarded by the successor section s if i writes to a destination renamed or freed in s .

An exported instruction is accepted by the successor section s only if its destination is neither the source nor the destination of any instruction in s .

In the sum function example, no instruction is exported. For example, the instruction consuming the final sum to be displayed receives its source from instruction 5-1 which does not need to be exported (statement v).

An exported instruction is sent to the successor section through the IERU. It is received in the RRRU (register write) or in the ARRU (memory write). The destination is tentatively renamed and in case of a hit the exported instruction is discarded (already renamed destination). It is also discarded if it writes to stack or heap in a location later freed by the section. Otherwise, the instruction gets a new local renaming and is saved in its new section ROB.

What is new in the proposed core design ? The core shown on figure 9 is much simpler than actual speculative cores. The core is as small as possible to maximize the number of cores on the die. As the core is not speculative, there is no predictor nor renaming repair unit (checkpoints). The LSQ is simpler than the usual Load-Store Queue as loads are not speculative and store-to-load forwarding is not necessary. The data memory hierarchy is kept coherent as only the oldest section can write to and read from it. There is no memory coherency hardware (e.g. MESI protocol handler). There is no vector computing unit (e.g. XMM-like) as vectorization is better obtained through parallelism. Each core implements a single instruction path (no superscalar or VLIW path).

5 Analytical performance evaluation of the parallel execution model on the sum example and conclusion. cycle 11, renamed memory is accessed at cycle 14 (counting 3 cycles to reach the producer and return the t[0] value) and retired at cycle 15. We assume the 5 sections can be hosted in 5 different cores. We also assume each pipeline stage manipulates a single instruction. Instruction cache L1 is assumed to always hit.

From this example we see that the code is fetched in 30 cycles (last fetched instruction is 3-12), i.e. 1.5 instructions per cycle. If the data size is doubled, the fetch time is 42 cycles (104 instructions fetched, i.e. 2.5 instructions per cycle). Only fetch latency (i.e. IL1 miss rate) can impact the fetch time. It is independent of renaming and execute latencies.

The number of instructions is 45 * 2 n + 14 * (2 n -1) for the sum of a 5 * 2 n elements array (i.e. 45 for sum(t,5), 104 for sum(t,10)). The fetch time is 30 + 12 * n (i.e. 30 for sum(t,5), 42 for sum(t,10)). For 1280 elements, 15090 instructions are fetched in 126 cycles, i.e. 120 instructions per cycle. This shows that even though one instruction is fetched per cycle per core and the control is computed rather than predicted, fetching in parallel is efficient. Even for modest data sizes, it outperforms any speculative fetching hardware.

Renaming is not penalized by the distribution of the code nor by its extension to memory locations. Most of the sources are provided by register value copy at fork. Function results and stack local variables are obtained from the predecessor section. Global variables are reached quickly from the first section (which starts at the main function entrance) and then fastly propagated to other sections, thanks to full memory line caching. Eventually, instruction retirement frees the resources at the same rate they are allocated, avoiding cores saturations. The retirement time is7 43 + 15 * n. For 1280 elements, the 15090 instructions are retired in 163 cycles, i.e. 92 instructions per cycle.

Devil is in the details. Fine simulation of the model is necessary to prove that distant ILP present is captured. Two such simulators are on-going projects: a VHDL implementation of the core pipeline and a qemu and simplescalar based simulator to quantify the IPC performance of a many-core processor.

The model presented focuses on functions. In the same way, loops can be parallelized. For loops can be vectorized, each iteration forming a separate section with no control. It heritates its iteration counter that can be saved in a register and used in the iteration body. While loops can be parallelized, launching each iteration in sequence (no speculation) but parallelizing their bodies.

With the introduction of many-core chips as general purpose processors, the time has come to produce parallel programs automatically. This paper suggests that we are not so far from the goal and the hardware can greatly help.

Fig. 2 :

 2 Fig. 2: The sum function in X86

Fig. 8 :

 8 Fig. 8: Fetch-decode pipeline stage

Fig. 9 :

 9 Fig. 9: Six-stages core pipeline

Fig. 10 :

 10 Fig. 10: Execution timing of the sum(t,5) run.

  1 .

	sum: cmpq $2, %rsi	//sum(t,5)	30	ja	.L2
		ja	.L2			31	movq (%rdi), %rax
	.L2:	pushq %rbx		32	jne .L1
		pushq %rdi		33	.L1: ret
		pushq %rsi		34	popq %rbx
		shrq %rsi		35	pushq %rbx
		call sum		36	subq $8, %rsp
			sum: cmpq $2, %rsi	//sum(t,2)	37	movq %rax, 0(%rsp)
				ja .L2	38	leaq (%rdi,%rsi,8), %rdi
				movq (%rdi), %rax	39	subq %rsi, %rbx
				jne .L1	40	movq %rbx, %rsi
				addq 8(%rdi), %rax	41	call sum
			.L1: ret		42	sum: cmpq $2, %rsi	//sum(&t[3],2)
		popq %rbx		43	ja	.L2
		pushq %rbx		44	movq (%rdi), %rax
		subq $8, %rsp	45	jne .L1
		movq %rax, 0(%rsp)	46	addq 8(%rdi), %rax
		leaq (%rdi,%rsi,8), %rdi	47	.L1: ret
		subq %rsi, %rbx	48	addq 0(%rsp), %rax
		movq %rbx, %rsi	49	addq $8, %rsp
		call sum		50	popq %rsi
			sum: cmpq $2, %rsi	//sum(&t[2],3)	51	popq %rdi
				ja .L2	52	popq %rbx
			.L2:	pushq %rbx	53	ret
				pushq %rdi	54	addq 0(%rsp), %rax
				pushq %rsi	55	addq $8, %rsp
				shrq %rsi	56	popq %rsi
				call sum	57	popq %rdi
				sum: cmpq $2, %rsi	//sum(&t[2],1)	58	popq %rbx
						59	ret

Table 1 :

 1 Ten benchmarks of the PBBS suite datasets. The rightmost bar (blue colour, seq11 key) matches sequential runs with the same dataset as key 11 parallel runs.

		1e+06									1
											2
											3
											4
		100000									5
											6
											7
											8
		10000									9 10
											11
											seq11
	ILP	1000
		100
		10
		1
		1	2	3	4	5	6	7	8	9	10
				Benchmark/Dataset
	Fig. 7: ILP of ten benchmarks parallel and sequential runs
						Benchmark
	01 : breadthFirstSearch/ndBFS			02 : comparisonSort/quickSort
	03 : convexHull/quickHull				04 : dictionary/deterministicHash
	05 : integerSort/blockRadixSort			06 : maximalIndependentSet/ndMIS
	07 : maximalMatching/ndMatching		08 : minSpanningTree/parallelKruskal
	09 : nearestNeighbors/octTree2Neighbors 10 : removeDuplicates/deterministicHash

  Figure10shows 5 tables (one per core) giving the execution timing of the sum(t,5) run. The instructions numbers are given on the left of each table. The columns of a table match the 6 pipeline stages. A value in a column represents the cycle at which the instruction is treated by the corresponding pipeline stage. For example, instruction 1-8 (load) is handled by core 1, fetched at cycle 8, register renamed at cycle 9, load address is computed at cycle 10 and renamed at

			core 1 pipeline				core 2 pipeline				core 3 pipeline
		fd rr	ew	ar	ma	ret		fd rr ew ar ma ret		fd rr	ew	ar	ma ret
	1-1	1	2	3			4	2-1	7	8	9		10	3-1	19	20	21		22
	1-2	2	3	4			5	2-2	8	9	10	11 18	19	3-2	20	21	22	23	29	30
	1-3	3	4	5			6	2-3	9	10	11		20	3-3	21	22	23		31
	1-4	4	5	6			7	2-4	10	11	12		21	3-4	22	23	24		32
	1-5	5	6	7			8	2-5	11	12	13		22	3-5	23	24	25		33
	1-6	6	7	8			9	2-6	12	13	14		23	3-6	24	25	26		34
	1-7	7	8	9			10	2-7	13	14	15		24	3-7	25	26	27		35
	1-8	8	9	10	11	14	15	2-8	14	15	16		25	3-8	26	27	28		36
	1-9	9	10	11			16	2-9	15	16	17		26	3-9	27	28	29	30	33	37
	1-10	10	11	12	13 15	17	2-10	16	17	18		27	3-10	28	29	30		38
	1-11	11 12	13			18	2-11	17	18	19		28	3-11	29	30	31	32	34	39
								2-12	18	19	20		29	3-12	30 31	32		40
			core 4 pipeline		2-13 2-14	19 20	20 21	21 22	30 23 26 31			core 5 pipeline
		fd rr ew ar ma ret	2-15	21	22	23		32		fd rr	ew	ar	ma ret
								2-16	22	23	24		33
	4-1	26	27	28 29 37	38							5-1	14	15	16 17 40 41
	4-2	27	28				39							5-2	15	16			42
	4-3	28	29				40							5-3	16	17			43

the stack in each section keeps its local variables, e.g. temp on figure5.

"good" model with a 2K instructions window size, 64 instructions issued per cycle, 256 renaming registers, a branch predictor based on an infinite number of 2-bits counters and a perfect memory aliasing disambiguation

"perfect" model enhances "good" model: infinite renaming, perfect branch predictor.

stores update full lines. The loader sets a cleared line updated with t[0]. This updated line is updated again with t[START_REF] Shun | Brief announcement: The problem based benchmark suite[END_REF]. After five such updates, the full line containing t[0] up to t[START_REF] Tjaden | Detection and parallel execution of independent instructions[END_REF] is set and can be exported to consumers, i.e. sections 1, 2 and 3.

The oldest section, i.e. the only one with no predecessor, dumps its renamings to the data memory hierarchy (DMH). When it receives a renaming request which misses, it loads from DMH and exports the loaded line.

15 cycles is the fetch time of instructions (figure5) 2, 3,

8-10 (5 cycles), the creation time of the forked section (2 cycles), the fetch time of instructions 11-16 (5 cycles) and the retirement of instructions 17-19 (3 cycles).


Olivier Doaré

Sébastien

Michelin Sébastien

Energy harvesting from flutter instability of a piezoelectric plate

Energy harvesting from flutter instability of a piezoelectric plate

Olivier Doaré ⋆ and Sébastien Michelin ⋆⋆ ⋆ Unité de Mécanique,ENSTA-Paristech, 91761, Palaiseau, France ⋆⋆ LadHyX, École Polytechnique, 91128, Palaiseau, France

Drawing profit from ambient geophysical flows to create electrical power received a growing attention recently in particular for small-power or low-velocity applications where the use of traditional wind-turbine technologies is made prohibitive or inefficient by either the size, the cost or remoteness of the equipment considered. For those applications, fluid-solid instabilities generating spontaneous and self-sustained periodic oscillations of a solid body are promising energy harvesting mechanisms, provided one is able to convert into usable form the solid kinetic or elastic energy. We investigate here the energy harvesting potential of a plate in an axial flow equipped with a distributed series of small piezoelectric elements, as sketched on Figure 1a. It is now well known that a plate in axial flow displays large amplitude oscillations once a critical value of the flow velocity is reached, a phenomenon commonly referred to as "flag flutter" [START_REF] Kornecki | On the aeroelastic instability of twodimensional panels in uniform incompressible flow[END_REF]. Each of the piezoelectric pairs is connected to an energy harvesting circuit, as sketched in Figure 1b. In the this modelling, the power dissipated in the resistance represents the power effectively harvested by the system. This harvested power acts like a damping on the mechanical system and thus can affect the critical flutter velocity and the dynamics of the plate. We are then faced to a strongly coupled fluid-solid-electrical system. In a recent work [START_REF] Doaré | Piezoelectric coupling in energy-harvesting fluttering flexible plates: linear stability analysis and conversion efficiency[END_REF], considering the continuous limit where the length of the piezos is small compared to the typical wavelengths of deformation, we showed that this system is effectively able to produce electrical energy and found the conditions for maximizing the energy harvesting efficiency. We now address the consequences on the dynamics of the use of inductive electrical elements, and the effect of using non-infinitesimal length piezoelectric patches.

U ∞ R R R R C χ θs (a) (b)

Figure 1 :

 1 Figure 1: (a) Schematic view of a plate in an homogeneous axial flow, equipped with small length piezoelectric patches on both sides. Each piezoelectric pair is shunted with a circuit. (b) Equivalent circuit modeling of the piezoelectric patch connected to a simple resistive circuit.


Vincent Noel
email: vincent.noel@lmd.polytechnique.fr

Helene Chepfer

Yohann Morille

Classification of ice crystal shapes in midlatitude ice clouds from three years of lidar observations over the SIRTA observatory

This paper presents a study of ice crystal shapes in midlatitude ice clouds inferred from a technique based on the comparison of ray-tracing simulations with lidar depolarization ratio measured at 532 nm. This technique is applied to three years of lidar depolarization ratio observations from the SIRTA (Site Instrumental de Recherche par Télédétection Atmosphérique) observatory in Palaiseau, France, amounting to 322 different days of ice cloud observations. Particles in clouds are classified in three major groups : plates, columns, and irregular shapes with aspect ratios close to unity. Retrieved shapes are correlated with radiosounding observations from a close-by meteorological station: temperature, relative humidity, wind speed and direction. Results show a strong dependence of the relative concentration of different crystal shapes to most atmospheric variables, such as the temperature, with a clear successive dominance by plate-like (temperature above -20°C), irregular (temperatures between -60°C and -40°C), and column-like shapes (temperatures below -60°C). Particle shapes are almost exclusively column-like below -75°C. This is in sharp contrast with previous results of the same classification applied to tropical clouds, and highlights the high geographic variability of the ice clouds distribution of microphysical properties. Results also suggest that ice clouds created by jet streams (identified by high wind speeds) are strongly dominated by column-like shapes, while front-created ice clouds (identified by lower wind speeds) show a much more variable mix of shapes, with the dominant shapes depending on other factors. Results also suggest different microphysical properties according to the average direction source of air masses and winds. Following these results, a possible parameterization of ice crystal shapes in midlatitude ice clouds as a function of temperature is provided.

Introduction

Ice clouds permanently cover as much as 40% of the Earth's surface (Liou, 1986). Moreover, recent satellite and ground-based observations suggest the coverage from subvisible ice clouds, which are hard to detect through conventional methods, may increase this to more than 50% (Wang et al. 1996, Sassen andCampbell, 2001). This large spatial coverage makes them one of the major influences in the climate evolution, and a correct estimation of their radiative impact is essential to adequately reproduce and predict the climate (Cess et al., 1990(Cess et al., , 1996)). This radiative impact depends on the poorly known balance between their albedo and greenhouse effect, which is highly influenced by each cloud local microphysical properties (Sassen et al, 1989;Stephens et al., 1990). To improve their parameterization in general circulation models, a better understanding of these microphysical properties is essential (Sun and Shine, 1995). Among these, the shape of ice particles remains one of the major sources of uncertainties, which could modify ice cloud albedo by as much as 30% (Takano and Liou, 1989). The modeled bidirectional reflectance of ice clouds, which describes how incoming sunlight is redistributed in space through scattering, is also highly sensitive to the assumed shape of ice crystals (Yang et al., 2001): using incorrect shapes for ice clouds in optical depth retrieval algorithms can modify results by a factor of 3 (Mishchenko et al., 1996). Moreover, crystal shapes in ice clouds were recently found to influence subsequent ice formation processes, leading to a feedback effects on the cloud microphysical and radiative properties (Sassen et al., 2003). In the past two decades, in situ observations from intensive field campaigns, such as the first and second International Satellite Cloud Climatology Project (ISSCP) Regional Experiment (FIRE I and II), the European Cloud and Radiation Experiment (EUCREX), the International Cloud Experiment (ICE)… have all exposed the high spatial and temporal variability of this parameter, and shown it to be one of the most difficult to study (Cox et al. 1990, Francis et al. 1994, Sauvage et al. 1999). Moreover, recent field campaigns in the tropics such as the Cirrus Regional Study of Tropical Anvils and cirrus Layers -Florida Area Cirrus Experiment (CRYSTAL-FACE, Jensen et al. 2004) concluded that ice crystals in convective ice clouds exhibit different properties from those generally assumed in most climate models (Heymsfield et al, 2002a ;Garrett et al., 2003). Several studies have tried to retrieve particle shape using observations from spaceborne instruments, such as the Moderate Resolution Imaging Spectroradiometer (MODIS, Rolland et al. 2000) and Polarization and Directionality of Earth's Reflectance (POLDER, Chepfer et al. 1999, 2001, Masuda et al. 2002). However, radiometric observations from satellite suffer from the limitations of passive remote sensing: on one hand, the lower limit of detection for optically thin clouds is not well known, which means the entire population of subvisible ice clouds (potentially more than 20%, Goldfarb et al. 2001) may be overlooked; on the other hand, the vertical distance on which the observed quantities are integrated is still unclear. A way to overcome these limitations is to use active remote sensing (Chiriaco et al 2004).

The present study uses observations of linear depolarization ratio to retrieve information on the shape of particles inside ice clouds, using an already-published shape classification technique (Noel et al, 2002). Three years of observations are considered, leading to an extensive study of ice crystal shapes that could be considered representative of midlatitude ice clouds. Retrieved information about shapes is correlated with atmospheric variables : temperature, relative humidity, wind speed and direction. Results are compared with shape information previously retrieved in midlatitude and tropical ice clouds using lidar and in-situ probes.

The instrument used in this study is first presented in Sect. 2, with a short description of the shape classification technique. The ice clouds lidar depolarization ratio dataset is then introduced in Sect. 3, along with the variability of atmospheric variables for the studied cases.

Results of the shape classification and their correlation with radiosounding variables are presented in Sect. 4. Results are discussed and conclusion is given in Sect. 5.

Ice crystal shape information from lidar depolarization ratio

The high sensitivity of the lidar instrument to optically thin clouds makes it one of the instruments best suited to the study of ice clouds (Platt, 1973), especially when equipped to monitor the state of light polarization (Sassen 1991). In this last configuration, the emitted beam of laser light is linearly polarized in a specific plane. The linear depolarization ratio

! " = I # I //
is then defined as the ratio of backscattered light intensities in the planes perpendicular ( ! I " ) and parallel ( ! I // ) to the plane of emission. This ratio ! has been shown to be extremely sensitive to the microphysical properties of probed clouds (Chen et al. 2002), and especially particle shape (Sassen, 1977). The present study uses a technique that classifies particle shapes in ice clouds by comparing observed depolarization ratios with results of a ray-tracing simulation (extensively described in Noel et al. 2001). The simulation follows modifications in light polarization as it travels through modeled hexagonal-based ice crystals, so the evolution of ! can be studied as a function of three parameters: the particle imaginary index of refraction, aspect ratio Q, and orientation in space. Effects of the index of refraction on light polarization were shown to be negligible when considering a constant lidar wavelength.

Undoubtedly more interesting, ! is highly sensitive to the aspect ratio Q in the presence of randomly oriented particles. As the slope of !(Q) is not always positive, it is not possible to link an observed ! to a specific Q, however a range of possible values for Q can be estimated and crystals can be classified into three shape groups. Low values !<0.25 are attributed to thin plate-like particles (Q<0.1), while high ! > 0.5 are found to be the signature of column-like particles (Q>1.5) and crystals of high complexity such as bullet rosettes. Experimental studies have found that particles close to sphericity (early in the particle formation, or through riming process) produce low depolarization, in the same range as plate-like particles, so these shapes will be equivalent in the lidar classification scheme. The last group describes intermediate and irregular particle shapes (with aspect ratios close to unity) that produce average depolarization ratios (0.25 < ! < 0.5). It should be stressed that this technique does not aim at retrieving the exact shape of ice crystals in ice clouds, as their infinite variety makes this an unrealistic goal.

Instead, the depolarization ratio is used to classify particles in a given cloud area into three distinct groups: plate-like, column-like and irregular shapes. It is important to note that platelike and column-like refer to particles that scatter light respectively like plates (including aggregates of plates) or columns (including aggregate of columns and bullet rosettes). As lidar observations are vertically resolved, the variability of these groups with altitude, temperature, etc. can be estimated.

During the classification, two phenomenons need to be accounted for. First, multiple scattering can greatly modify observations of depolarization ratio (Hu et al, 2001), thus a specific Monte-Carlo multiple scattering code has been implemented to simulate this phenomenon in ice clouds of variable composition and optical depths, showing it varies greatly with particle shape (Noel et al, 2002), and therefore the depolarization ranges given for each shape class need to be adjusted for each lidar profile, with respect to the optical depth of the studied cloud. Moreover, Noel et al 2001 showed that horizontally oriented crystals, which are known to occur in midlatitude and high-latitude ice clouds (Platt, 1977;Sassen, 1980;Noel and Sassen 2005), especially at cloud top (Sassen et al. 2003), usually produce high backscattering and almost-zero depolarization ratios (! < 0.1) in good agreement with experimental studies (Platt et al., 1978). In that case, the depolarization ratio is not sensitive to other parameters anymore, and the shape classification technique used in the present study cannot be applied. Fluid dynamics studies (Jayaweera and Cottis 1969) show that the fall attitude of crystals strongly depends on their Reynolds number Re: while particles with low Re (below unity) will adopt a random orientation, crystals with Re above unity will adopt a preferential orientation close to the horizontal plane. Moreover, crystals with Re > 200 will tend to oscillate and flutter (Jayaweera and Mason, 1965), with amplitudes dependent on the crystal aspect ratio: planar particles will follow horizontal orientation more closely than complex and irregular shapes (Heymsfield and Kajikawa 1987) with the lidar, etc. Thus, numbers shown in Fig. 1 are rather meant to ensure that the following analysis will not be biased towards a specific time of the year.

Radiosounding observations used in the present study come from the Meteo-France Trappes station, located 15 km away from the SIRTA site. Two radiosoundings are available daily, at 00:00 and 12:00 UT. For each data point observed by the lidar (and thus each retrieved shape class) thermodynamic variables like temperature, relative humidity, wind speed and direction were interpolated between radiosoundings, at the time and altitude of lidar observation. As the temperature profile in the upper troposphere does not change significantly without stratosphere/troposphere exchange, this interpolation should not introduce significant bias in temperature ; however, probe measurements of relative humidity can change dramatically on short timescales, depending of the balloon's flight path in the upper troposphere, as it may fly tens of kilometers away across various regions not representative of the area observed by the lidar. Observations of relative humidity should therefore be treated with caution.

The distribution of data points observed in ice clouds as a function of temperature (in bins of 2°C) is shown in Fig. 2a. An important number of points (~23%) show temperatures above -30°C, however most are observed between -60°C and -40°C (~43%), with only a few between -60°C and -70°C (~12%). Colder temperatures (<-70°C) represent ~44000 points of observations, which is small by comparison (less than 0.5%). The distribution of Relative Humidity with respect to ice RH ICE for each data point observed by the lidar in a ice cloud is shown in Fig. 2b. The distribution is roughly Gaussian, with a definite trend towards higher humidities and a marked maximum for 85%<RH ICE <115% (more than 65% of all points).

RH ICE <50% represents less than 10% of all points. A distribution centered on high values is consistent with Heymsfield and Miloshevich (1995).

The distribution of data points in ice clouds as a function of wind properties at the altitude of lidar observation is given in Fig. 3 group shows speeds below 45 m.s -1 (Fig. 3b). Considering these low speeds, the related ice clouds should be associated with the presence of atmospheric fronts. Winds in that speed range mostly show directions between 180° and 360° (Fig. 3c), meaning they mostly originate from the Atlantic Ocean, which is consistent with the general circulation model. In this domain, four major modes appear (Fig. 3a), centered on 200° (i.e. SSW), 245° (i.e. WSW), 295° (ie WNW) and 340° (NNW). A distinct separate group appears for speeds in the 60-70 m.s -1 range (Fig. 3c), typical of jet streams, which can also initiate the formation of ice clouds (Mace et al, 1995). The importance of this group is relatively small, as it does not appear on the linear scales of Fig. 3a and3b. Nonetheless, there are more than 79400 data points in that speed range -a small number compared to the entire dataset (less than 1%), but still significant. Due to the specific ice creation process associated to the presence of jet streams, specific microphysical properties are to be expected. For this group the wind directions are almost essentially between 0° and 200°, meaning these winds mostly come from the European continent. This disagreement with general circulation means that this relatively small dataset could be dominated by small-scale, local phenomenons, so its representativeness is hard to estimate.

Results of the shape classification

The shape classification technique was applied to the entire dataset of 322 days of ice cloud observations.

Example case : June 2 nd 2004

The June 2 nd 2004 case was selected to illustrate the shape classification technique. That day, an ice cloud located between 9 and 11.5 km was observed by the lidar for 2 hours. Lidar depolarization ratios (Fig. 4a) show high variability, from 0.15 to 0.55. The associated profiles of temperature, pressure and RH ICE from a radiosounding probe launched at 23:06 UTC are shown in Fig. 4b. Temperatures between -40°C (cloud base, 9km) and -60°C (cloud top, 11.5km), added to high depolarization ratios, confirm the cloud is composed of ice crystals. Values of RH ICE (Fig. 4b) are stable (50%-55%) in the cloud altitude range.

Fig. 4c shows the results of the ice particle shape classification. Blue areas are dominated by plate-like particles; yellow denotes irregular crystal shapes (~unity aspect ratios); and red areas are dominated by column-like crystal shapes. The cloud originates at high altitude (10.5

to 11.5km at 20:30 UTC), showing a wide range of depolarization ratios (Fig. 4a) that suggests a mixture of particle shapes (Fig. 4c) -plates, columns and irregulars. Between 21:00 and 21:15 UTC, the layer extends down to 9.5 km, with high depolarization ratios (! > 0.45) suggesting column-like particles dominate the cloud (red, Fig. 4c). From then on, the cloud layer stays stable between 9 and 11km, while the depolarization ratio decreases (0.2<!<0.4). This suggests crystals undergo shape modifications due to size increase, by vapor deposition or secondary crystal formation mechanisms (aggregation/fragmentation from sedimentation or movement inside the cloud), leading eventually to dominance by irregular shapes (yellow, Fig. 4c). Areas immediately outside the cloud layer (9 and 11.5km) show low depolarization ratios (Fig. 4a) -these are classified as plate-like particles, but could also be explained by evaporation at cloud boundaries, leading to a general rounding of particles.

Results on the entire dataset

The annual distribution of shape class relative concentrations does not reveal any remarkable trend. Between January and April, clouds are marked by a lot of irregular shapes (up to 55%

in March) and only a few plate-like particles. From May to December, plate-like and irregular shapes appear in similar concentrations. Concentration of column-like shapes is usually low, reaching a minimum of 16% in May. However, as measurements are not evenly distributed over time (Sect. 3), it is unclear whether these numbers are representative of mid-latitude ice clouds.

More significantly, the shape of ice particles appears highly sensitive to temperature (Fig. 5) :

for temperatures above -20°C, plate-like particles are predominant (50%-70%), followed by irregular particles (25%-40%), and a minority of column-like particles (less than 10%). As altitude increases and temperatures drop, the importance of plate-like particles decreases, with a simultaneous increase in the two other classes. A threshold is reached at -50°C, where the relative concentration of irregular shapes (~unity aspect ratio) reaches its maximum (~50% of all particles), while at the same time column-like particles become more frequent than platelike particles. For colder temperatures (below -50°C), the concentration of irregular shapes and plate-like particles decreases to fall below 20% at -75°C, while the proportion of columnlike particles goes on increasing to reach its maximum (over 70%) at -75°C. A pronounced change seems to be occurring for even colder temperatures (below -75°C) with a sharp fall in column-like concentrations and a sharp increase in plate-like particles.

The shape class relative concentrations are shown in Fig. 6 while the irregular particles rise above 60%. However there are less than 500 data points in this range (i.e. less than 0.1%) so the representativity of this behavior is unclear.

The shape class relative concentrations are shown in Fig. 7 as a function of wind speed.

Winds below 20 m.s -1 show more than 40% of plate-like, 30-40% of irregular and 20-30% of column-like particles. Distributions are stable from 20 to 50 m.s -1 , with similar concentrations of column-like and irregular particles (30-45%) and less plate-like particles (15-20%). At 60 m.s -1 , the relative concentration of column-like particles jumps sharply above 55%, while irregular and plate-like shape concentrations fall respectively to less than 30% and 15%.

The shape relative concentrations are shown in Fig. 8 45°C, where they both reach ~25%. Winds between 275° and 315° show more column-like (35-50%) than plate-like particles (below 25%). Winds between 315° and 360° show very little column-like particles (less than 5%) at temperatures above -30°C, but a lot of plate-like particles (more than 50%). Between -35°C and -30°C irregular shapes represent 70%, but their number decreases below -40°C while column-like particles become dominant (5% at -30°C, 55% at -45°C). It should also be noted that below -75°C winds from the West (Fig 8b andc) show a sharp increase in plate-like and a decrease in column-like particles that is not seen in winds from the South (Fig. 8a) or North (Fig. 8d).

The shape class relative concentrations are shown in Fig. 9 as a function of wind direction.

For speeds below 40 m.s -1 (Fig. 9a), winds between 180° and 360° (from the Atlantic Ocean)

show similar concentrations for the three classes (30-35%) ; winds between 0° and 180° (from the European continent) show more than 60% of plate-like particles and very little columnlike particles (10% between 100° and 150°). Winds between 45° and 55° show an increase in column-like (more than 25%) and a decrease in plate-like particles. High-speed winds (Fig. 9b) show between 0° and 180° more than 60% of column-like, followed by irregular (30-45%) and finally plate-like shapes (less than 10%). As these winds from Europe are mostly associated with jet streams (Fig. 3c), this is coherent with the wind speed influence evidenced by Fig. 8. Winds from the Atlantic show little column-like particles (below 20%) in the 180°"200° range and the 330°"360° range, while concentrations increase for the two other shapes. At 275°, column concentrations reach 90% while the other shapes disappearhowever, there is little observation for high-speed winds between 180° and 360° (Fig. 3c), so it is unclear if these observations are representative of actual ice clouds.

In summary, the dependence of crystal shape relative concentrations with temperature (Fig. 5) and relative humidity (Fig. 6) are the most clearly marked, and should be the easiest to model.

However, as was previously noted, it is impossible to assess with confidence that relative humidity observations from radiosoundings are representative of ice clouds probed by the lidar. Conversely, temperature measurements can be relied upon, and the evolution of each shape class relative concentration with temperature seems smooth enough to propose a parametrization based on it. Parameters for second-order polynomial regressions, of the form C i =a i T 2 +b i T+c i , are given in Table 1, with the associated curves plotted in dashed lines in Fig. 5. The concentrations variation with temperature is well reproduced.

Discussion and conclusion

A technique for classifying ice cloud areas into three major shape groups (plate-like, irregular or column-like shapes) based on observations of lidar depolarization ratio (Sect. 2) has been applied to three years of ice clouds observations over the SIRTA ground-based site (Sect. 3).

Results of the shape classification (Sect. 4) have been compared with atmospheric variables like temperature, relative humidity, wind speed and direction. A strong correlation of particle shape with most atmospheric variables is found.

The correlation of retrieved particle shapes with relative humidity (Fig. 6) shows that columnlike particles are rare for low (<20%) or high (>120%) values of RH ICE . High values (110% < RH ICE < 150%) are strongly dominated by plate-like particles, while the most frequent values (80% < RH ICE <120%) show a balanced mix of plate-like, irregular and column-like shapes (30-45% for each shape). However, as relative humidity measurements from probes are difficult at the high altitude of ice clouds due to the high spatial variability of this parameter, more detailed observations (e.g. from coincident in situ probes, Heymsfield and Miloshevitch 1995) are therefore needed to confirm these results.

Correlation of particle shapes with wind direction (Fig. 8 and9) shows that different composition of air masses coming from different sources have a strong impact on the microphysical properties of the created ice cloud: winds from the East (0-180°) show a specific composition (low concentration of column-like particles, dominance of plate-like particles for low wind speeds and irregular for high wind speeds), different from the one of winds from the West (column-like particles dominate, whatever the wind speed). The correlation of retrieved particle shapes with wind speed (Fig. 8) shows that higher wind speeds lead to more column-like particles, with a specific shape distribution for wind speeds ~60 m.s -1 . This suggests that ice clouds created in the presence of jet streams are dominated by column-like particles (more than 50%) or particles of high complexity such as bullet rosettes (Heymsfield et al, 2002b), followed by lower concentrations of irregular shapes (~30%) and a marked minority of plate-like shapes (~10%). As jet streams are generally present at coldest temperatures, close to the tropopause, this is consistent with the temperature distribution of shape classes (Fig. 5), which shows a majority of columns in such temperature ranges. column-like shapes are however not restricted to jet-created ice clouds. The distribution of wind speeds (Fig. 3) shows that high wind speeds are poorly represented in ice clouds observed over the SIRTA (less than 1% of the entire population of ice clouds). This might suggests that ice cloud creation by jet streams is of limited importance at this location, but it might also be explained by correlation of jet streams with lower, optically thick cloud systems that would hide the ice cloud to the lidar. Such a correlation could be coincidental, or due to some unexplained relationship between low-level cloud systems and jet streams. Jetcreated ice clouds would then be under-represented in the current dataset.

The correlation between particle shapes and temperature is maybe the most pronounced one (Fig. 5), with a clear and successive dominance by plate-like, irregular and column-like shapes as temperature decreases. This evolution is due to the different physical processes dominating crystal formation at different temperatures (Sassen et al 1989), which are however still unclear at this point. Concentration of plate-like particles is higher in warm ice clouds (above -20°C) and decreases with colder temperatures while concentration of irregular shapes slowly increases. This mixture of plate-like and irregular shapes is coherent with the temperature range, which is identified with the plate and dendrite growth regime (Pruppacher and Klett 1997). The concentration of column-like particle slowly increases with decreasing temperatures, to completely dominate the particle population at coldest temperatures (below -70°C), where the more pristine and geometric particles are to be expected. This trend, coherent with results from [START_REF] Hallett | Faceted snow crystals[END_REF], can be explained either by in-situ formation of pristine and geometric particles at extremely cold temperatures, or by general changes in the shape of crystals as they move from warmer to colder temperatures (Sassen and Benson, 2001). Relative concentration of irregular shapes is low at extreme temperatures (both coldest and warmest), but dominates the ice particles population at midlevel temperatures (-50°C to -40°C). For the coldest temperatures (below -75°C), a sharp increase in the concentration of plate-like particles is observed, coupled to a decrease in column-like particle concentrations.

This last change might just be a local effect due to the small number of data points in this temperature range (Fig. 2a). However, the possibility that these observations are significant of extremely cold ice cloud that would exhibit specific microphysical properties (Heymsfield, 1986) should not be excluded. The evolution of shape class relative concentrations with temperature is reproduced quite well by 2 nd order polynomial regressions. As the crystal shape influences its fall speed in the cloud (Heymsfield and Iaquinta, 2000), these relative concentrations could also help refine the parameterization of ice particle sedimentation speeds as a function of temperature or latitude, once a more comprehensive lidar dataset is available.

Even if the considered dataset extends over a large time period, the observations remain local, and it is unclear whether they are actually representative of the entire population of midlatitude ice clouds. It can be noted however that these results are consistent with previous studies using lidar observations, such as the 6-years midlatitude ice cloud climatology presented by Sassen and Benson (2001), which shows a regular increase in depolarization ratio with falling temperatures (from !=0.25 at -17.5°C to !=0.45 at -77.5°C), and concludes to high concentrations of plate-like particles for temperatures above -20°C. For temperatures below -55°C, ice crystal observations from in-situ airborne PMS probes stress the high frequency of column-like particles [START_REF] Heymsfield | A parametrization of the particle size[END_REF] In that respect, it is interesting to compare the present retrievals with results of the same analysis applied to 3 days of tropical convective ice clouds (Noel et al. 2004), observed with the airborne and downward-looking Cloud Physics Lidar (CPL, McGill et al 2002) during the CRYSTAL-FACE campaign (Jensen et al., 2004), that showed a constant minority of column-like particles (less than 10%) coupled with a quasi-linear decrease of the concentration of plate-like particles (from 65% at -20°C to 10% at -70°C) and a simultaneous increase in irregular shapes (from 30% at -20°C to more than 80% at -70°C). Tropical convective ice clouds thus showed dominance of plate-like particles at warmest temperatures (above -35°C, similar to midlatitude ice clouds), while irregular shapes dominated all temperatures below -35°C, with no trace of the regular increase in columns observed in midlatitude ice clouds (Fig. 6).

These strong differences between tropical and midlatitude ice clouds remind us that different formation processes lead to different microphysical properties, which in turn lead to strong differences in the clouds radiative impact (Takano and Liou, 1989). These differences need to be taken into account in numerical models of climate prediction. The large observation dataset of the present study (three years of observations) ensures that the suggested parameterizations may be considered representative of midlatitude ice clouds with some confidence. Of course, this assumes that ice clouds observed over the SIRTA ground-based sites are representative of midlatitude ice clouds -in order to validate that hypothesis, and make sure that no local synoptic process due to the proximity to the Atlantic Ocean is at work, more midlatitude ice clouds from different locations should be studied. Similar studies in tropical convective ice clouds suggest that similar parameterizations could be done at other latitudes, however there too more observations are be required to get representative results.

Unfortunately, lidar studies of tropical convective systems are extremely difficult due to their high optical thickness that blocks lidar penetration from the ground. In this context, the spacebased Cloud Aerosol Lidar and Infrared Pathfinder Satellite Observations mission (CALIPSO, Winker et al. 2003) will send a 532-nm lidar into orbit in July 2005 to observe ice cloud properties from above, even on top of optically thick cloud systems, all around the globe. The shape classification technique featured in the present study has been selected by NASA to be applied on an operational basis on the linear depolarization ratios observed from the CALIPSO lidar, and the retrieved shape class relative concentrations will be integrated into the level 2 products available as soon as January 2006. At this point, it is important to stress out the limitations of the classification scheme: only three shape categories can be considered, which reflects only partially the infinite variety of particles found in ice clouds.

More research and simulations are therefore needed to refine this classification Moreover, the impact of orientation and shape on depolarization ratios is still not fully understood, thus the interpretation of these results could change based on new advances in light scattering models or laboratory experiment. In the present day, however, this kind of study is one of the few that can provide large-scale retrieval of information about particle shape, leading to global maps of particle shape class concentrations and giving an invaluable insight into the microphysical properties of ice clouds, whatever the latitude. Moreover, results of this classification will be used operationally in algorithms of particle size retrieval using observations from the threechannel Infrared Imager (IIR) radiometer, also present on the CALIPSO platform [START_REF] Haeffelin | SIRTA, a ground-based atmospheric observatory for cloud and aerosol research[END_REF]. These observations will provide a unique point of view on the microphysical properties of ice clouds that will allow studying the link between thermodynamic variables and the particle shape associated to various ice cloud formations types in different regions of the globe.

! Breon F. M., B. Dubrulle 2004 : Horizontally oriented plates in clouds, J. Atmos. Sci.

61, 2888-2898.

! Cess, R.D., G.L. Potter, J.P. Blanchet, G.J. Boer, A.D. Del Genio, M. Deque, V.

Dymnikov, V. Galin, W.L. Gates, S.J. Ghan, J.T.

Figures Captions

Fig.

  : Fig. 3a (top panel) shows the distribution as a function of wind direction (in bins of 10°), Fig. 3b (right panel) as a function of wind speed (in bins of 2 m.s -1 ) and Fig. 3c (center panel) as a function of both, on a 2d histogram using a logarithmic color scale. Half of the data points show a wind speed below 20 m.s -1 , and the main wind

  as a function of temperature, for the four wind directions identified inSect. 3 (Fig 3c). Above -20°C, shape class concentrations in all directions follow the trend identified in Fig.5: a majority of plate-like shapes, followed by irregular and finally column-like shapes. Irregular shapes also follows the same trend: concentrations are low for warm (>-20°C) and cold (<-60°C) temperatures, and high between -45°C and -55°C. Winds between 175° and 225° show high concentrations of irregular shapes (above 60%) for temperatures below -60°C, at the expense of the two other shape classes (below 30%). When compared with Fig.5, plate-like and column-like particles compensate for each other : lower-than-average concentrations of column-like particles are balanced by how low concentrations of column-like particles and higher-than-average concentrations of plate-like and irregular shapes until -70°C, where the situation is reversed. For winds between 220° and 275°, plate-like and column-like concentrations are symmetric and opposite around -

Fig 2 :

 2 Fig. 1 : Distribution of ice cloud observations over an annual cycle during the 2002-2004

Fig. 3 :

 3 Fig. 3 : (a) Distribution of lidar data points observed in ice clouds as a function of wind

Fig 4 Fig. 5 :

 45 Fig 4 (a) : Observations of lidar depolarization ratio as a function of time and altitude for the June 2 nd 2004 case (top panel). (b) Profiles of temperature (°C), pressure (hPa) and relative

Fig. 6 :Fig. 7 :

 67 Fig. 6 : Distribution of shape class relative concentrations as a function of atmospheric

Fig. 8 :

 8 Fig. 8 : Distribution of shape class relative concentrations as a function of temperature, for

Fig. 9 :Fig 2 :

 92 Fig. 9 : Distribution of shape class relative concentrations as a function of wind direction, for wind speeds (a) below 45 m.s -1 and (b) above 45 m.s -1 .

Fig. 3 :

 3 Fig. 3 : (a, top panel) Distribution of lidar data points observed in ice clouds as a function of

Fig 4c :

 4c Fig 4c : Results of the shape classification technique as a function of time and altitude for the June 2 nd 2004 case.

Fig. 5 :Fig. 6 :Fig. 8 :Fig. 9 :

 5689 Fig. 5 : Distribution of shape class relative concentrations as a function of atmospheric temperature, with 2 nd -order polynomial regression (dashed lines).

3 The SIRTA Ice Cloud Dataset

  As it stands, this distribution stems from the natural temporal distribution of ice clouds, but is also influenced by the presence of precipitation (or optically thick low-level clouds) hiding higher ice clouds from the lidar, by non-meteorological causes like technical problems

		classification technique can be trusted with a reasonable level of confidence. 79 sightings in winter and 83 in autumn. However, as these numbers come from only 3 years
		of observation, the statistical variability of ice cloud occurrences from one year to the next is
		only partially represented. The uncertainty for a month with N ice cloud sightings can be
		The 532-nm Lidar Nuages Aerosols (LNA) is operated 5 days a week from 8 AM to 8 PM, estimated by supposing these follow a Poisson distribution, leading to a standard deviation of
		except during precipitation, at the SIRTA observatory located at 48.713N, 2.208E (Haeffelin N .
		. For pristine particles such as et al., 2005). Its laser beam, pointing at the zenith, leads to a nominal temporal resolution of
	!	the planar crystals used in the present classification scheme, Re is typically lower than 200 10 seconds (200 integrated pulses) and a vertical resolution of 15 meters. The dataset used in
		(Mitchell 1996), and thus such particles would tend to follow a horizontal orientation. Recent this study extends from 2002 to 2004 ; on this period backscattered profiles were analyzed to
		studies using polarized observations from the spaceborne radiometer POLDER (Breon and produce a "cloud mask" with a multi-test algorithm called STRAT (STRucture of the
		Dubrulle 2004; Noel and Chepfer 2004) have confirmed these findings, showing that oriented ATmosphere) that identifies the boundary layer, molecular (i.e. particle-free) layers, and
		crystals can be found in half of ice clouds, in small concentrations however (0.1 to 1%). As particle layers in the troposphere (Morille et al., 2005). Cloud and aerosol layers were
		the present study assumes random orientation of particles, to remain coherent with radiative detected using a combination of wavelet transform analysis (to detect signal discontinuities at
		transfer studies, occurrences of oriented crystals had to be excluded from the observation layer boundaries) and backscattered signal thresholding (to remove variations due to noise).
		dataset. This was achieved by removing cases with very low values of !, as only a small Moreover, the LNA produces observations of linear depolarization ratio (Sect. 2), which is
		concentration of oriented crystals is enough to strongly affect the depolarization (Sassen and calibrated by detecting for each observation period a low-level, cloud-free region and
		Benson 2001). normalizing this region to the standard molecular depolarization ratio of 2.79% (Young
		This technique was first applied in Noel et al. (2002) on twelve cases of ground-based lidar 1980). STRAT separates liquid water clouds from ice clouds using a depolarization threshold
		observation of ! in midlatitude ice clouds, with results in good agreement with previous in of 0.25. Ice clouds were successfully detected by the lidar on 322 days during the studied
		situ studies (Korolev and Isaac, 1999; Sassen and Benson, 2001). More recently, this period, totaling more than 2400 hours of observation and more than 10 7 points of data. The
		technique was applied to observations of ice clouds on top of convective systems in the distribution of ice cloud sightings (i.e. days when the lidar was operated and ice clouds were
		tropics during the CRYSTAL-FACE campaign (Noel et al. 2004b), highlighting their specific detected) over an annual cycle is shown in Fig. 1. The maximum number of observations
		microphysical properties. In this last study, classification results were compared with direct (over 35) occurs in September, following a marked minimum (~20) in July and August. There
		ice particle images observed from collocated in-situ probes, showing a good agreement. The is a high number of observations (29 to 34) between January and April, while the smallest
		technique was also compared to other remote sensing shape retrieval technique (Chepfer et al. number of observations (17 to 20) occurs between November and December. The total days
		2005) leading to consistent results. These last validation and comparisons mean the when ice clouds were detected for each season goes from 66 in summer to 94 in spring, with

  45%-50%), followed by less than 25% of column-like particles. At higher humidity, the proportion of plate-like shapes decreases while column-like particles increase. This behavior stops at RH ICE =100% (the most frequent value, Fig.2b), with plate-like particles below 30%, and column-like reaching almost 30%. For R H ICE >100% plate-like concentrations increase (reaching 55% around RH ICE =140%) and column-like concentrations fall (below 10% at RH ICE =150%). Such high values of RH ICE may suggest the presence of mixed-phase clouds. The concentration of irregular shapes stays between 35 and 50% overall.A sharp change can be observed for RH ICE > 160%: plate-like concentrations fall below 25%

as a function of relative humidity with respect to ice R H ICE . Low humidity is dominated equally by plate-like and irregular shapes (

Table 1 :

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!

Acknowledgments : This research was supported in part by the NASA Langley Research Center under contract NAS1-02058. The authors would like to thank the SIRTA technical and computer staff (Christophe Boitel, Florian Lapouge, Dr. Christophe Pietras, Bernard Romand) for taking the observations and making the dataset easily accessible. The authors would like to thank Dave M. Winker for his support.

Table Captions

Table 1 : Parameters for 2 nd order polynomial regression of each shape group i relative concentration as a function of temperature : C i =a i T 2 +b i T+c i