CS252 Graduate Computer Architecture Lecture 10 Vector Processing October 1st, 2003 Prof. John Kubiatowicz http://www.cs.berkeley.edu/~kubitron/courses/ cs252-F03 10/1/03 CS252/Kubiatowicz Lec 10.1 Alternative Model: Vector Processing Vector processors have high-level operations that work on linear arrays of numbers: "vectors" SCALAR (1 operation) r1 r2 v1 v2 +
V1=F0+V2 scalar + vector V1=V2xV3 vector x vector V1=F0xV2 scalar x vector V1=M[R1..R1+63] load, stride=1 V1=M[R1..R1+63*R2] load, stride=R2 V1=M[R1+V2i,i=0..63] indir.("gather") VMASKi = (V1i=V2i)? comp. setmask Vec. Len. Reg. = R1 set vector length Vec. Mask = R1 set vector mask CS252/Kubiatowicz Lec 10.3 Properties of Vector Processors Each result independent of previous result => long pipeline, compiler ensures no dependencies => high clock rate Vector instructions access memory with known pattern => highly interleaved memory => amortize memory latency of over 64 elements => no (data) caches required! (Do use instruction
cache) Reduces branches and branch problems in pipelines Single vector instruction implies lots of work ( loop) => fewer instruction fetches 10/1/03 CS252/Kubiatowicz Lec 10.4 Spec92fp Program swim256 hydro2d nasa7 su2cor tomcatv wave5 mdljdp2 Operation & Instruction Count: RISC v. Vector Processor (from F. Quintana, U. Barcelona.) Operations (Millions) Instructions (M) RISC Vector R / V RISC
1.1x 27 7.2 32 52 0.6x 32 15.8 R/V 142x 71x 31x 29x 11x 4x 2x Vector reduces ops by 1.2X, instructions by 20X 10/1/03 CS252/Kubiatowicz Lec 10.5 Styles of Vector Architectures memory-memory vector processors: all vector operations are memory to memory
vector-register processors: all vector operations between vector registers (except load and store) 10/1/03 Vector equivalent of load-store architectures Includes all vector machines since late 1980s: Cray, Convex, Fujitsu, Hitachi, NEC We assume vector-register for rest of lectures CS252/Kubiatowicz Lec 10.6 Components of Vector Processor Vector Register: fixed length bank holding a single vector has at least 2 read and 1 write ports typically 8-32 vector registers, each holding 64-128 64-bit elements
Vector Functional Units (FUs): fully pipelined, start new operation every clock typically 4 to 8 FUs: FP add, FP mult, FP reciprocal (1/X), integer add, logical, shift; may have multiple of same unit Vector Load-Store Units (LSUs): fully pipelined unit to load or store a vector; may have multiple LSUs Scalar registers: single element for FP scalar or address Cross-bar to connect FUs , LSUs, registers 10/1/03 CS252/Kubiatowicz Lec 10.7 Common Vector Metrics R: MFLOPS rate on an infinite-length vector vector speed of light Real problems do not have unlimited vector lengths, and the start-up penalties encountered in real problems will be larger (Rn is the MFLOPS rate for a vector of length n)
N1/2: The vector length needed to reach one-half of R a good measure of the impact of start-up NV: The vector length needed to make vector mode faster than scalar mode measures both start-up and speed of scalars relative to vectors, quality of connection of scalar unit to vector unit 10/1/03 CS252/Kubiatowicz Lec 10.8 DAXPY (Y = a * X + Assuming vectors X, Y Y)LD F0,a ;load scalar a are length 64 Scalar vs. Vector LD F0,a ADDI R4,Rx,#512 loop: LD F2, 0(Rx) MULTD F2,F0,F2
ADDV V4,V2,V3 ;add SV ;store the result Ry,V4 ;last address to load ;load X(i) ;a*X(i) ;load Y(i) ;a*X(i) + Y(i) ;store into Y(i) ;increment index to X ;increment index to Y ;compute bound ;check if done 578 (2+9*64) vs. 321 (1+5*64) ops (1.8X) 578 (2+9*64) vs. 6 instructions (96X) 64 operation vectors + no loop overhead
also 64X fewer pipeline hazards CS252/Kubiatowicz Lec 10.9 Example Vector Machines Machine Cray 1 Cray XMP Cray YMP Cray C-90 Cray T-90 Conv. C-1 Conv. C-4 Fuj. VP200 Fuj. VP300 NEC SX/2 NEC SX/3 10/1/03 Year Clock Regs Elements FUs LSUs 1976 80 MHz 8 64 6 1 1983 120 MHz
3 2 1996 100 MHz 8-256 32-1024 3 2 1984 160 MHz 8+8K 256+var 16 8 1995 400 MHz 8+8K 256+var 16 8 CS252/Kubiatowicz Lec 10.10 Vector Example with dependency /* Multiply a[m][k] * b[k][n] to get c[m][n] */ for (i=1; i
10/1/03 CS252/Kubiatowicz Lec 10.11 Straightforward Solution: Use scalar processor This type of operation is called a reduction Grab one element at a time from a vector register and send to the scalar unit? Usually bad, since path between scalar processor and vector processor not usually optimized all that well Alternative: Special operation in vector processor shift all elements left vector length elements or collapse into a compact vector all elements not masked Supported directly by some vector processors Usually not as efficient as normal vector operations (Number of cycles probably logarithmic in number of bits!) 10/1/03 CS252/Kubiatowicz Lec 10.12 Novel Matrix Multiply Solution
You don't need to do reductions for matrix multiply You can calculate multiple independent sums within one vector register You can vectorize the j loop to perform 32 dot-products at the same time (Assume Maximul Vector Length is 32) Show it in C source code, but can imagine the assembly vector instructions from it 10/1/03 CS252/Kubiatowicz Lec 10.13 Optimized Vector Example /* Multiply a[m][k] * b[k][n] to get c[m][n] */ for (i=1; i
c[i][j:j+31] = sum[0:31]; } } 10/1/03 CS252/Kubiatowicz Lec 10.14 Novel, Step #2 It's actually better to interchange the i and j loops, so that you only change vector length once during the whole matrix multiply To get the absolute fastest code you have to do a little register blocking of the innermost loop. 10/1/03 CS252/Kubiatowicz Lec 10.15 CS 252 Administrivia Exam: Monday 10/13 Location: 306 Soda Hall
TIME: 5:30 - 8:30 This info is on the Lecture page (has been) Meet at LaVals afterwards for Pizza and Beverages Assignment up Soon (I lied): Done in pairs. Put both names on papers. Make sure you have partners! Feel free to use mailing list for this. 10/1/03 CS252/Kubiatowicz Lec 10.16 Vector Implementation Vector register file Each register is an array of elements Size of each register determines maximum vector length Vector length register determines vector length for a particular operation Multiple parallel execution units = lanes (sometimes called pipelines or pipes) 10/1/03
CS252/Kubiatowicz 33 Lec 10.17 Vector Terminology: 4 lanes, 2 vector functional units (Vector Functional Unit) 10/1/03 CS252/Kubiatowicz 34 Lec 10.18 Vector Execution Time Time = f(vector length, data dependicies, struct. hazards) Initiation rate: rate that FU consumes vector elements (= number of lanes; usually 1 or 2 on Cray T-90) Convoy: set of vector instructions that can begin execution in same clock (no struct. or data hazards) Chime: approx. time for a vector operation
m convoys take m chimes; if each vector length is n, then they take approx. m x n clock cycles (ignores overhead; good approximization for long vectors) 1: LV V1,Rx ;load vector X 2: MULV V2,F0,V1 ;vector-scalar mult. LV V3,Ry ;load vector Y 3: ADDV V4,V2,V3 ;add 4: SV 10/1/03 Ry,V4 ;store the result 4 convoys, 1 lane, VL=64 => 4 x 64 = 256 clocks (or 4 clocks per result)
CS252/Kubiatowicz Lec 10.19 Hardware Vector Length What to do when software vector length doesnt exactly match hardware vector length? vector-length register (VLR) controls the length of any vector operation, including a vector load or store. (cannot be > the length of vector registers) do 10 i = 1, n 10 Y(i) = a * X(i) + Y(i) Don't know n until runtime! n > Max. Vector Length (MVL)? 10/1/03 CS252/Kubiatowicz Lec 10.20 Strip Mining Suppose Vector Length > Max. Vector Length (MVL)? Strip mining: generation of code such that each vector operation is done for a size to the MVL
1st loop do short piece (n mod MVL), rest VL = MVL low = 1 VL = (n mod MVL) /*find the odd size piece*/ do 1 j = 0,(n / MVL) /*outer loop*/ do 10 i = low,low+VL-1 /*runs for length VL*/ Y(i) = a*X(i) + Y(i) /*main operation*/ 10 continue low = low+VL /*start of next vector*/ VL = MVL /*reset the length to max*/ CS252/Kubiatowicz 10/1/03 Lec 10.21 DLXV Start-up Time Start-up time: pipeline latency time (depth of FU pipeline); another sources of overhead Operation Start-up penalty (from CRAY1) Vector load/store 12 Vector multiply 7 Vector add 6 Convoy
Start 1st overlap; result last result Assume convoys don't vector length = n: 1. LV 0 12 11+n (=12+n-1) 12+n 12+n+7 18+2n Multiply startup 12+n+1 12+n+13
CS252/Kubiatowicz Lec 10.22 Vector Opt #1: Chaining Suppose: MULV V1,V2,V3 ADDV V4,V1,V5 ; separate convoy? chaining: vector register (V1) is not as a single entity but as a group of individual registers, then pipeline forwarding can work on individual elements of a vector Flexible chaining: allow vector to chain to any other active vector operation => more read/write ports As long as enough HW, increases convoy size Unchained 7 7 Chained 10/1/03 64 MULTV 64 MULTV
Lec 10.24 Vector Stride Suppose adjacent elements not sequential in memory do 10 i = 1,100 do 10 j = 1,100 A(i,j) = 0.0 do 10 k = 1,100 10 A(i,j) = A(i,j)+B(i,k)*C(k,j) Either B or C accesses not adjacent (800 bytes between) stride: distance separating elements that are to be merged into a single vector (caches do unit stride) => LVWS (load vector with stride) instruction Think of addresses per vector element 10/1/03 CS252/Kubiatowicz Lec 10.25 Memory operations Load/store operations move groups of data between registers and memory Three types of addressing Unit stride
Contiguous block of information in memory Fastest: always possible to optimize this Non-unit (constant) stride Harder to optimize memory system for all possible strides Prime number of data banks makes it easier to support different strides at full bandwidth Indexed (gather-scatter) Vector equivalent of register indirect Good for sparse arrays of data Increases number of programs that vectorize 10/1/03 CS252/Kubiatowicz 32 Lec 10.26 Interleaved Memory Layout Vector Processor Unpipelined DRAM Unpipelined DRAM Unpipelined
DRAM Unpipelined DRAM Unpipelined DRAM Unpipelined DRAM Unpipelined DRAM Unpipelined DRAM Addr Addr Addr Addr Addr Mod 8 Mod 8 Mod 8 Mod 8 Mod 8 =0 =2 =3 =4 =1 Addr Addr Addr Mod 8 Mod 8 Mod 8
=7 =6 =5 Great for unit stride: Contiguous elements in different DRAMs Startup time for vector operation is latency of single read What about non-unit stride? Above good for strides that are relatively prime to 8 Bad for: 2, 4 Better: prime number of banks! 10/1/03 CS252/Kubiatowicz Lec 10.27 How to get full bandwidth for Unit Stride? Memory system must sustain (# lanes x word) /clock No. memory banks > memory latency to avoid stalls m banks m words per memory lantecy l clocks if m < l, then gap in memory pipeline: clock: 0 ll+1 l+2 l+m- 1 l+m 2 l word: -- 01 2 m-1 --m
may have 1024 banks in SRAM If desired throughput greater than one word per cycle Either more banks (start multiple requests simultaneously) Or wider DRAMS. Only good for unit stride or large data types More banks/weird numbers of banks good to support more strides at full bandwidth Will read paper on how to do prime number of banks efficiently 10/1/03 CS252/Kubiatowicz Lec 10.28 Vector Opt #2: Sparse Matrices Suppose: do 100 i = 1,n 100 A(K(i)) = A(K(i)) + C(M(i)) gather (LVI) operation takes an index vector and fetches data from each address in the index vector This produces a dense vector in the vector registers After these elements are operated on in dense
form, the sparse vector can be stored in expanded form by a scatter store (SVI), using the same index vector Can't be figured out by compiler since can't know elements distinct, no dependencies Use CVI to create index 0, 1xm, 2xm, ..., 63xm CS252/Kubiatowicz 10/1/03 Lec 10.29 Sparse Matrix Example Cache (1993) vs. Vector (1988) IBM RS6000 Cray YMP Clock 72 MHz 167 MHz Cache 256 KB 0.25 KB Linpack 140 MFLOPS 160 (1.1) Sparse Matrix 17 MFLOPS 125 (7.3) (Cholesky Blocked ) Cache: 1 address per cache block (32B to 64B)
Vector: 1 address per element (4B) 10/1/03 CS252/Kubiatowicz Lec 10.30 Vector Opt #3: Conditional Execution Suppose: do 100 i = 1, 64 if (A(i) .ne. 0) then A(i) = A(i) B(i) endif 100 continue vector-mask control takes a Boolean vector: when vector-mask register is loaded from vector test, vector instructions operate only on vector elements whose corresponding entries in the vector-mask register are 1. Still requires clock even if result not stored; if still performs operation, what about divide by 0? 10/1/03 CS252/Kubiatowicz Lec 10.31 Parallelism and Power
If code is vectorizable, then simple hardware, more energy efficient than Out-of-order machines. Can decrease power by lowering frequency so that voltage can be lowered, then duplicating hardware to make up for slower clock: Power CV 2 f 1 f f 0 n Performanc e Constant Note that V can be made
as small as permissible within process Lanes n Lanes0 n 2 constraints by simply increasing : 1 PowerChange V V ; 1 0 o 10/1/03 CS252/Kubiatowicz Lec 10.32 Vector Options Use vectors for inner loop parallelism (no surprise)
One dimension of array: A[0, 0], A[0, 1], A[0, 2], ... think of machine as, say, 16 vector regs each with 32 elements 1 instruction updates 32 elements of 1 vector register and for outer loop parallelism! 1 element from each column: A[0,0], A[1,0], A[2,0], ... think of machine as 32 virtual processors (VPs) each with 16 scalar registers! ( multithreaded processor) 1 instruction updates 1 scalar register in 64 VPs Hardware identical, just 2 compiler perspectives 10/1/03 CS252/Kubiatowicz Lec 10.33 Virtual Processor Vector Model: Treat like SIMD multiprocessor Vector operations are SIMD (single instruction multiple data) operations Each virtual processor has as many scalar registers as there are vector registers There are as many virtual processors as current vector length.
Each element is computed by a virtual processor (VP) 10/1/03 CS252/Kubiatowicz Lec 10.34 Vector Architectural State Virtual Processors ($vlr) VP0 General Purpose Registers VP1 VP$vlr-1 vr0 vr1 Control Registers vr31 $vdw bits
Flag Registers (32) vcr0 vcr1 vf0 vf1 vcr31 32 bits vf31 1 bit 10/1/03 CS252/Kubiatowicz Lec 10.35 Designing a Vector Processor
10/1/03 Changes to scalar How Pick Vector Length? How Pick Number of Vector Registers? Context switch overhead Exception handling Masking and Flag Instructions CS252/Kubiatowicz Lec 10.36 Changes to scalar processor to run vector instructions Decode vector instructions Send scalar registers to vector unit (vector-scalar ops) Synchronization for results back from vector register, including exceptions Things that dont run in vector dont have high ILP, so can make scalar CPU simple 10/1/03 CS252/Kubiatowicz
Lec 10.37 How Pick Vector Length? Longer good because: 1) Hide vector startup 2) lower instruction bandwidth 3) tiled access to memory reduce scalar processor memory bandwidth needs 4) if know max length of app. is < max vector length, no strip mining overhead 5) Better spatial locality for memory access Longer not much help because: 1) diminishing returns on overhead savings as keep doubling number of element 2) need natural app. vector length to match physical register length, or no help (lots of short vectors in modern codes!) 10/1/03 CS252/Kubiatowicz Lec 10.38 How Pick Number of Vector Registers? More Vector Registers: 1) Reduces vector register spills (save/restore)
20% reduction to 16 registers for su2cor and tomcatv 40% reduction to 32 registers for tomcatv others 10%-15% 2) Aggressive scheduling of vector instructinons: better compiling to take advantage of ILP Fewer: 1) Fewer bits in instruction format (usually 3 fields) 2) Easier implementation 10/1/03 CS252/Kubiatowicz Lec 10.39 Context switch overhead: Huge amounts of state! Extra dirty bit per processor If vector registers not written, dont need to save on context switch Extra valid bit per vector register, cleared on process start Dont need to restore on context switch until needed 10/1/03
CS252/Kubiatowicz Lec 10.40 Exception handling: External Interrupts? If external exception, can just put pseudo-op into pipeline and wait for all vector ops to complete Alternatively, can wait for scalar unit to complete and begin working on exception code assuming that vector unit will not cause exception and interrupt code does not use vector unit 10/1/03 CS252/Kubiatowicz Lec 10.41 Exception handling: Arithmetic Exceptions Arithmetic traps harder Precise interrupts => large performance loss! Alternative model: arithmetic exceptions set vector flag registers, 1 flag bit per element
Software inserts trap barrier instructions from SW to check the flag bits as needed IEEE Floating Point requires 5 flag bits 10/1/03 CS252/Kubiatowicz Lec 10.42 Exception handling: Page Faults Page Faults must be precise Instruction Page Faults not a problem Could just wait for active instructions to drain Also, scalar core runs page-fault code anyway Data Page Faults harder Option 1: Save/restore internal vector unit state Freeze pipeline, dump vector state perform needed ops Restore state and continue vector pipeline 10/1/03 CS252/Kubiatowicz Lec 10.43
Exception handling: Page Faults Option 2: expand memory pipeline to check addresses before send to memory + memory buffer between address check and registers multiple queues to transfer from memory buffer to registers; check last address in queues before load 1st element from buffer. Per Address Instruction Queue (PAIQ) which sends to TLB and memory while in parallel go to Address Check Instruction Queue (ACIQ) When passes checks, instruction goes to Committed Instruction Queue (CIQ) to be there when data returns. On page fault, only save intructions in PAIQ and ACIQ 10/1/03 CS252/Kubiatowicz Lec 10.44 Masking and Flag Instructions Flag have multiple uses (conditional, arithmetic exceptions) Alternative is conditional move/merge Clear that fully masked is much more effiecient
that with conditional moves Not perform extra instructions, avoid exceptions Downside is: 1) extra bits in instruction to specify the flag regsiter 2) extra interlock early in the pipeline for RAW hazards on Flag registers 10/1/03 CS252/Kubiatowicz Lec 10.45 Flag Instruction Ops Do in scalar processor vs. in vector unit with vector ops? Disadvantages to using scalar processor to do flag calculations (as in Cray): 1) if MVL > word size => multiple instructions; also limits MVL in future 2) scalar exposes memory latency 3) vector produces flag bits 1/clock, but scalar consumes at 64 per clock, so cannot chain together Proposal: separate Vector Flag Functional Units and instructions in VU
10/1/03 CS252/Kubiatowicz Lec 10.46 MIPS R10000 vs. T0 *See http://www.icsi.berkeley.edu/real/spert/t0-intro.html CS252/Kubiatowicz 10/1/03 Lec 10.47 Vectors Are Inexpensive Scalar N ops per cycle 2) circuitry HP PA-8000 4-way issue reorder buffer: 850K transistors
10/1/03 incl. 6,720 5-bit register number comparators Vector N ops per cycle 2) circuitry T0 vector micro 24 ops per cycle 730K transistors total only 23 5-bit register number comparators No floating point
CS252/Kubiatowicz Lec 10.48 Vectors Lower Power Single-issue Scalar One instruction fetch, decode, dispatch per operation Arbitrary register accesses, adds area and power Loop unrolling and software pipelining for high performance increases instruction cache footprint All data passes through cache; waste power if no temporal locality One TLB lookup per load or store
Off-chip access in whole cache 10/1/03 lines Vector One inst fetch, decode, dispatch per vector Structured register accesses Smaller code for high performance, less power in instruction cache misses Bypass cache One TLB lookup per group of loads or stores Move only necessary data across chip boundary CS252/Kubiatowicz Lec 10.49 Superscalar Energy Efficiency Even Worse Superscalar
10/1/03 Control logic grows quad-ratically with issue width Control logic consumes energy regardless of available parallelism Speculation to increase visible parallelism wastes energy Vector Control logic grows linearly with issue width Vector unit switches off when not in use Vector instructions expose parallelism without speculation Software control of speculation when desired:
Whether to use vector mask or compress/expand for conditionals CS252/Kubiatowicz Lec 10.50 Vector Applications Limited to scientific computing? Multimedia Processing (compress., graphics, audio synth, image proc.) Standard benchmark kernels (Matrix Multiply, FFT, Convolution, Sort) Lossy Compression (JPEG, MPEG video and audio) Lossless Compression (Zero removal, RLE, Differencing, LZW) Cryptography (RSA, DES/IDEA, SHA/MD5) Speech and handwriting recognition Operating systems/Networking (memcpy, memset, parity, checksum)
Databases (hash/join, data mining, image/video serving) Language run-time support (stdlib, garbage collection) even SPECint95 10/1/03 CS252/Kubiatowicz Lec 10.51 Reality: Sony Playstation 2000 (as reported in Microprocessor Report, Vol 13, No. 5) Emotion Engine: 6.2 GFLOPS, 75 million polygons per second Graphics Synthesizer: 2.4 Billion pixels per second Claim: Toy Story realism brought to games! 10/1/03 CS252/Kubiatowicz Lec 10.52 Playstation 2000 Continued Emotion Engine: Superscalar MIPS core Vector Coprocessor
Pipelines RAMBUS DRAM interface 10/1/03 Sample Vector Unit 2-wide VLIW Includes Microcode Memory High-level instructions like matrix-multiply CS252/Kubiatowicz Lec 10.53 Vector for Multimedia? Intel MMX: 57 additional 80x86 instructions (1st since 386) similar to Intel 860, Mot. 88110, HP PA-71000LC, UltraSPARC 3 data types: 8 8-bit, 4 16-bit, 2 32-bit in 64bits reuse 8 FP registers (FP and MMX cannot mix) short vector: load, add, store 8 8-bit operands + Claim: overall speedup 1.5 to 2X for 2D/3D graphics, audio, video, speech, comm., ... use in drivers or added to library routines; no compiler 10/1/03
CS252/Kubiatowicz Lec 10.54 MMX Instructions Move 32b, 64b Add, Subtract in parallel: 8 8b, 4 16b, 2 32b opt. signed/unsigned saturate (set to max) if overflow Shifts (sll,srl, sra), And, And Not, Or, Xor in parallel: 8 8b, 4 16b, 2 32b Multiply, Multiply-Add in parallel: 4 16b Compare = , > in parallel: 8 8b, 4 16b, 2 32b sets field to 0s (false) or 1s (true); removes branches Pack/Unpack Convert 32b<> 16b, 16b <> 8b Pack saturates (set to max) if number is too large 10/1/03 CS252/Kubiatowicz Lec 10.55 New Architecture Directions media processing will become the dominant force in computer arch. & microprocessor
design. ... new media-rich applications... involve significant real-time processing of continuous media streams, and make heavy use of vectors of packed 8-, 16-, and 32-bit integer and Fl. Pt. Needs include high memory BW, high network BW, continuous media data types, real-time response, fine grain parallelism How Multimedia Workloads Will Change Processor Design, Diefendorff & Dubey, IEEE Computer (9/97) 10/1/03 CS252/Kubiatowicz Lec 10.56 Return of vectors: Tentative VIRAM-1 Floorplan 0.18 m DRAM 32 MB in 16 banks x 256b, 128 subbanks 0.25 m, 5 Metal Logic 200 MHz MIPS,
16K I$, 16K D$ I/O 4 200 MHz FP/int. vector units die: 16x16 mm xtors: 270M power: 2 Watts Memory (128 Mbits / 16 MBytes) Ringbased Switch C P 4 Vector Pipes/Lanes U +$ Memory (128 Mbits / 16 MBytes) 10/1/03
CS252/Kubiatowicz Lec 10.57 Summary Vector is alternative model for exploiting ILP If code is vectorizable, then simpler hardware, more energy efficient, and better real-time model than Out-of-order machines Design issues include number of lanes, number of functional units, number of vector registers, length of vector registers, exception handling, conditional operations Will multimedia popularity revive vector architectures? 10/1/03 CS252/Kubiatowicz Lec 10.58
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