From bf32c2d40869640b52430946f7a2fc8b5e4e0e0f Mon Sep 17 00:00:00 2001 From: Mamy Ratsimbazafy Date: Fri, 24 Feb 2023 09:47:36 +0100 Subject: [PATCH] Parallel for (#222) * introduce reserve threads to minimize latency and maximize throughput when awaiting a future * introduce a ceilDiv proc * threadpool: implement parallel-for loops * 10x perf improvement by not waking reserveBackoff on syncAll * bench overhead: new reserve system might introduce too much wakeup latency, 2x slower, for fine-grained parallelism * add parallelForStrided * Threadpool: Implement parallel reductions * refactor parallel loop codegen: introduce descriptor, parsing and codegen stages * parallel strided, test transpose bench * tight loop is faster when backoff is not inline * no POSIX stuff on windows, larger types for histogram bench * fix tests * max RSS overflow? * missed an undefined var * exit histogram on 32-bit * forgot to return early dor 32-bit --- constantine.nimble | 4 + .../hash_to_curve/h2c_hash_to_field.nim | 9 +- .../math/arithmetic/bigints_montgomery.nim | 4 +- constantine/math/arithmetic/finite_fields.nim | 1 - constantine/math/arithmetic/limbs_exgcd.nim | 14 +- constantine/math/config/curves_derived.nim | 2 - .../math/config/curves_parser_curve.nim | 4 +- .../math/config/curves_parser_field.nim | 2 - constantine/math/config/precompute.nim | 4 +- constantine/math/config/type_bigint.nim | 2 +- .../math/elliptic/ec_endomorphism_accel.nim | 8 +- .../math/elliptic/ec_multi_scalar_mul.nim | 4 +- .../ec_multi_scalar_mul_scheduler.nim | 2 +- constantine/math/elliptic/ec_scalar_mul.nim | 4 +- .../math/elliptic/ec_scalar_mul_vartime.nim | 2 +- ...ec_shortweierstrass_batch_ops_parallel.nim | 2 +- .../math/extension_fields/exponentiations.nim | 2 +- constantine/math/io/io_bigints.nim | 6 +- constantine/platforms/allocs.nim | 2 +- constantine/platforms/ast_rebuilder.nim | 77 + constantine/platforms/compilers/bitops.nim | 12 +- constantine/platforms/gpu/bindings/utils.nim | 38 +- constantine/platforms/gpu/ir.nim | 2 +- constantine/platforms/primitives.nim | 19 +- constantine/platforms/static_for.nim | 9 +- .../benchmarks/black_scholes/README.md | 9 + .../black_scholes/README_Parsec.txt | 67 + .../benchmarks/black_scholes/blackscholes.c | 509 + .../black_scholes/blackscholes.simd.c | 598 + .../benchmarks/black_scholes/c.m4.pthreads | 122 + .../benchmarks/black_scholes/inputgen.c | 85 + .../black_scholes/openmp_black_scholes.nim | 366 + .../benchmarks/black_scholes/optionData.txt | 1004 ++ .../black_scholes/test10000options.txt | 10001 ++++++++++++++++ .../threadpool_black_scholes.nim | 372 + .../benchmarks/dfs/threadpool_dfs.nim | 25 +- .../benchmarks/histogram_2D/README.md | 10 + .../histogram_2D/openmp_histogram.c | 162 + .../histogram_2D/threadpool_histogram.nim | 303 + .../threadpool/benchmarks/logsumexp/README.md | 28 + .../logsumexp/threadpool_logsumexp.nim | 402 + .../benchmarks/matrix_transposition/README.md | 14 + .../openmp_transposes.nim | 294 + .../threadpool_transposes.nim | 319 + .../benchmarks/nqueens/threadpool_nqueens.nim | 2 +- .../threadpool/crossthread/backoff.nim | 10 +- .../threadpool/crossthread/taskqueues.nim | 6 +- .../threadpool/crossthread/tasks_flowvars.nim | 159 +- .../threadpool/demos/raytracing/README.md | 142 + .../ray_trace_300samples_nim_nested.png | Bin 0 -> 1755775 bytes .../ray_trace_300samples_nim_threaded.png | Bin 0 -> 1880583 bytes .../threadpool/demos/raytracing/smallpt.cpp | 103 + .../threadpool/demos/raytracing/smallpt.nim | 339 + constantine/platforms/threadpool/design.md | 109 + .../threadpool/examples/e03_parallel_for.nim | 60 + .../examples/e04_parallel_reduce.nim | 34 + .../platforms/threadpool/instrumentation.nim | 4 + .../threadpool/parallel_offloading.nim | 767 +- .../platforms/threadpool/threadpool.nim | 583 +- helpers/prng_unsafe.nim | 2 +- tests/gpu/t_nvidia_fp.nim | 6 +- tests/math/t_bigints_mod_vs_gmp.nim | 4 +- .../math/t_bigints_mul_high_words_vs_gmp.nim | 4 +- tests/math/t_bigints_mul_vs_gmp.nim | 4 +- tests/math/t_finite_fields_vs_gmp.nim | 12 +- tests/math/t_io_unsaturated.nim | 2 +- 66 files changed, 16974 insertions(+), 303 deletions(-) create mode 100644 constantine/platforms/ast_rebuilder.nim create mode 100644 constantine/platforms/threadpool/benchmarks/black_scholes/README.md create mode 100644 constantine/platforms/threadpool/benchmarks/black_scholes/README_Parsec.txt create mode 100644 constantine/platforms/threadpool/benchmarks/black_scholes/blackscholes.c create mode 100644 constantine/platforms/threadpool/benchmarks/black_scholes/blackscholes.simd.c create mode 100644 constantine/platforms/threadpool/benchmarks/black_scholes/c.m4.pthreads create mode 100644 constantine/platforms/threadpool/benchmarks/black_scholes/inputgen.c create mode 100644 constantine/platforms/threadpool/benchmarks/black_scholes/openmp_black_scholes.nim create mode 100644 constantine/platforms/threadpool/benchmarks/black_scholes/optionData.txt create mode 100644 constantine/platforms/threadpool/benchmarks/black_scholes/test10000options.txt create mode 100644 constantine/platforms/threadpool/benchmarks/black_scholes/threadpool_black_scholes.nim create mode 100644 constantine/platforms/threadpool/benchmarks/histogram_2D/README.md create mode 100644 constantine/platforms/threadpool/benchmarks/histogram_2D/openmp_histogram.c create mode 100644 constantine/platforms/threadpool/benchmarks/histogram_2D/threadpool_histogram.nim create mode 100644 constantine/platforms/threadpool/benchmarks/logsumexp/README.md create mode 100644 constantine/platforms/threadpool/benchmarks/logsumexp/threadpool_logsumexp.nim create mode 100644 constantine/platforms/threadpool/benchmarks/matrix_transposition/README.md create mode 100644 constantine/platforms/threadpool/benchmarks/matrix_transposition/openmp_transposes.nim create mode 100644 constantine/platforms/threadpool/benchmarks/matrix_transposition/threadpool_transposes.nim create mode 100644 constantine/platforms/threadpool/demos/raytracing/README.md create mode 100644 constantine/platforms/threadpool/demos/raytracing/ray_trace_300samples_nim_nested.png create mode 100644 constantine/platforms/threadpool/demos/raytracing/ray_trace_300samples_nim_threaded.png create mode 100644 constantine/platforms/threadpool/demos/raytracing/smallpt.cpp create mode 100644 constantine/platforms/threadpool/demos/raytracing/smallpt.nim create mode 100644 constantine/platforms/threadpool/design.md create mode 100644 constantine/platforms/threadpool/examples/e03_parallel_for.nim create mode 100644 constantine/platforms/threadpool/examples/e04_parallel_reduce.nim diff --git a/constantine.nimble b/constantine.nimble index 1c6449d..c7393ef 100644 --- a/constantine.nimble +++ b/constantine.nimble @@ -250,6 +250,10 @@ const testDescThreadpool: seq[string] = @[ # "constantine/platforms/threadpool/benchmarks/matmul_cache_oblivious/threadpool_matmul_co.nim", "constantine/platforms/threadpool/benchmarks/nqueens/threadpool_nqueens.nim", # "constantine/platforms/threadpool/benchmarks/single_task_producer/threadpool_spc.nim", # Need timing not implemented on Windows + # "constantine/platforms/threadpool/benchmarks/black_scholes/threadpool_black_scholes.nim", # Need input file + "constantine/platforms/threadpool/benchmarks/matrix_transposition/threadpool_transposes.nim", + "constantine/platforms/threadpool/benchmarks/histogram_2D/threadpool_histogram.nim", + "constantine/platforms/threadpool/benchmarks/logsumexp/threadpool_logsumexp.nim", ] const testDescMultithreadedCrypto: seq[string] = @[ diff --git a/constantine/hash_to_curve/h2c_hash_to_field.nim b/constantine/hash_to_curve/h2c_hash_to_field.nim index 405f646..b62b7ea 100644 --- a/constantine/hash_to_curve/h2c_hash_to_field.nim +++ b/constantine/hash_to_curve/h2c_hash_to_field.nim @@ -26,11 +26,6 @@ import # Helpers # ---------------------------------------------------------------- -func ceilDiv(a, b: uint): uint = - ## ceil division - ## ceil(a / b) - (a + b - 1) div b - proc copyFrom[M, N: static int](output: var array[M, byte], bi: array[N, byte], cur: var uint) = static: doAssert M mod N == 0 for i in 0'u ..< N: @@ -113,7 +108,7 @@ func expandMessageXMD*[B1, B2, B3: byte|char, len_in_bytes: static int]( doAssert output.len mod 8 == 0 # By spec doAssert output.len mod 32 == 0 # Assumed by copy optimization - let ell = ceilDiv(output.len.uint, DigestSize.uint) + let ell = output.len.ceilDiv_vartime(DigestSize) var l_i_b_str0 {.noInit.}: array[3, byte] l_i_b_str0.dumpRawInt(output.len.uint16, cursor = 0, bigEndian) l_i_b_str0[2] = 0 @@ -200,7 +195,7 @@ func hashToField*[Field; B1, B2, B3: byte|char, count: static int]( ## it is recommended to cache the reduced DST. const - L = int ceilDiv(Field.C.getCurveBitwidth() + k, 8) + L = ceilDiv_vartime(Field.C.getCurveBitwidth() + k, 8) m = block: when Field is Fp: 1 elif Field is Fp2: 2 diff --git a/constantine/math/arithmetic/bigints_montgomery.nim b/constantine/math/arithmetic/bigints_montgomery.nim index e611e89..8ee2024 100644 --- a/constantine/math/arithmetic/bigints_montgomery.nim +++ b/constantine/math/arithmetic/bigints_montgomery.nim @@ -142,7 +142,7 @@ func powMont*[mBits, eBits: static int]( ## ## This is constant-time: the window optimization does ## not reveal the exponent bits or hamming weight - var expBE {.noInit.}: array[(ebits + 7) div 8, byte] + var expBE {.noInit.}: array[ebits.ceilDiv_vartime(8), byte] expBE.marshal(exponent, bigEndian) powMont(a, expBE, M, one, negInvModWord, windowSize, spareBits) @@ -165,7 +165,7 @@ func powMontUnsafeExponent*[mBits, eBits: static int]( ## ## This uses fixed window optimization ## A window size in the range [1, 5] must be chosen - var expBE {.noInit.}: array[(ebits + 7) div 8, byte] + var expBE {.noInit.}: array[ebits.ceilDiv_vartime(8), byte] expBE.marshal(exponent, bigEndian) powMontUnsafeExponent(a, expBE, M, one, negInvModWord, windowSize, spareBits) diff --git a/constantine/math/arithmetic/finite_fields.nim b/constantine/math/arithmetic/finite_fields.nim index f7223aa..3719f62 100644 --- a/constantine/math/arithmetic/finite_fields.nim +++ b/constantine/math/arithmetic/finite_fields.nim @@ -591,7 +591,6 @@ macro addchain*(fn: untyped): untyped = body.add s result[^1] = body - # echo result.toStrLit() # ############################################################ # diff --git a/constantine/math/arithmetic/limbs_exgcd.nim b/constantine/math/arithmetic/limbs_exgcd.nim index 31ee552..202b811 100644 --- a/constantine/math/arithmetic/limbs_exgcd.nim +++ b/constantine/math/arithmetic/limbs_exgcd.nim @@ -191,7 +191,7 @@ proc partitionDivsteps(bits, wordBitWidth: int): tuple[totalIters, numChunks, ch # For any input, for gcd(f, g) with 0 <= g <= f <= Modulus with hddivstep variant (half-delta divstep) # (inversion g == 1) (45907*bits + 26313) div 19929 - let numChunks = (totalIters + wordBitWidth-1) div wordBitWidth + let numChunks = totalIters.ceilDiv_vartime(wordBitWidth) let chunkSize = totalIters div numChunks let cutoff = totalIters mod numChunks return (totalIters, numChunks, chunkSize, cutoff) @@ -444,7 +444,7 @@ func invmod*( ## ``a`` MUST be less than M. const Excess = 2 const k = WordBitWidth - Excess - const NumUnsatWords = (bits + k - 1) div k + const NumUnsatWords = bits.ceilDiv_vartime(k) # Convert values to unsaturated repr var m2 {.noInit.}: LimbsUnsaturated[NumUnsatWords, Excess] @@ -471,7 +471,7 @@ func invmod*( const Excess = 2 const k = WordBitWidth - Excess - const NumUnsatWords = (bits + k - 1) div k + const NumUnsatWords = bits.ceilDiv_vartime(k) # Convert values to unsaturated repr const m2 = LimbsUnsaturated[NumUnsatWords, Excess].fromPackedRepr(M) @@ -647,7 +647,7 @@ func legendre*(a, M: Limbs, bits: static int): SecretWord = ## ≡ 0 (mod p), iff a is 0 const Excess = 2 const k = WordBitWidth - Excess - const NumUnsatWords = (bits + k - 1) div k + const NumUnsatWords = bits.ceilDiv_vartime(k) # Convert values to unsaturated repr var m2 {.noInit.}: LimbsUnsaturated[NumUnsatWords, Excess] @@ -667,7 +667,7 @@ func legendre*(a: Limbs, M: static Limbs, bits: static int): SecretWord = const Excess = 2 const k = WordBitWidth - Excess - const NumUnsatWords = (bits + k - 1) div k + const NumUnsatWords = bits.ceilDiv_vartime(k) # Convert values to unsaturated repr const m2 = LimbsUnsaturated[NumUnsatWords, Excess].fromPackedRepr(M) @@ -852,7 +852,7 @@ func invmod_vartime*( ## ``a`` MUST be less than M. const Excess = 2 const k = WordBitWidth - Excess - const NumUnsatWords = (bits + k - 1) div k + const NumUnsatWords = bits.ceilDiv_vartime(k) # Convert values to unsaturated repr var m2 {.noInit.}: LimbsUnsaturated[NumUnsatWords, Excess] @@ -879,7 +879,7 @@ func invmod_vartime*( const Excess = 2 const k = WordBitWidth - Excess - const NumUnsatWords = (bits + k - 1) div k + const NumUnsatWords = bits.ceilDiv_vartime(k) # Convert values to unsaturated repr const m2 = LimbsUnsaturated[NumUnsatWords, Excess].fromPackedRepr(M) diff --git a/constantine/math/config/curves_derived.nim b/constantine/math/config/curves_derived.nim index 980a38d..98cd1d6 100644 --- a/constantine/math/config/curves_derived.nim +++ b/constantine/math/config/curves_derived.nim @@ -116,5 +116,3 @@ macro genDerivedConstants*(mode: static DerivedConstantMode): untyped = M ) ) - - # echo result.toStrLit() diff --git a/constantine/math/config/curves_parser_curve.nim b/constantine/math/config/curves_parser_curve.nim index 9a0502f..a81b2af 100644 --- a/constantine/math/config/curves_parser_curve.nim +++ b/constantine/math/config/curves_parser_curve.nim @@ -95,7 +95,7 @@ proc genCurveConstants(defs: seq[CurveParams]): NimNode = exported($curve & "_sexticTwist"), newLit curveDef.sexticTwist ) - + if curveDef.eq_form == TwistedEdwards and curveDef.coef_A.kind != NoCoef and curveDef.coef_D.kind != NoCoef: curveEllipticStmts.add newConstStmt( @@ -118,8 +118,6 @@ proc genCurveConstants(defs: seq[CurveParams]): NimNode = result.add curveEllipticStmts - # echo result.toStrLit() - macro setupCurves(): untyped = result = genCurveConstants(curvesDefinitions) diff --git a/constantine/math/config/curves_parser_field.nim b/constantine/math/config/curves_parser_field.nim index 70b0c5f..0a83c4d 100644 --- a/constantine/math/config/curves_parser_field.nim +++ b/constantine/math/config/curves_parser_field.nim @@ -321,8 +321,6 @@ proc genFieldsConstants(defs: seq[CurveParams]): NimNode = exported("CurveOrderBitWidth"), MapCurveOrderBitWidth ) - # echo result.toStrLit() - macro declareCurves*(curves: untyped): untyped = ## Parse curve configuration and generates ## diff --git a/constantine/math/config/precompute.nim b/constantine/math/config/precompute.nim index cdfb6a8..dcd27e4 100644 --- a/constantine/math/config/precompute.nim +++ b/constantine/math/config/precompute.nim @@ -389,7 +389,7 @@ func primePlus1div2*(P: BigInt): BigInt = func primeMinus3div4_BE*[bits: static int]( P: BigInt[bits] - ): array[(bits+7) div 8, byte] {.noInit.} = + ): array[bits.ceilDiv_vartime(8), byte] {.noInit.} = ## For an input prime `p`, compute (p-3)/4 ## and return the result as a canonical byte array / octet string ## For use to check if a number is a square (quadratic residue) @@ -408,7 +408,7 @@ func primeMinus3div4_BE*[bits: static int]( func primeMinus5div8_BE*[bits: static int]( P: BigInt[bits] - ): array[(bits+7) div 8, byte] {.noInit.} = + ): array[bits.ceilDiv_vartime(8), byte] {.noInit.} = ## For an input prime `p`, compute (p-5)/8 ## and return the result as a canonical byte array / octet string ## For use to check if a number is a square (quadratic residue) diff --git a/constantine/math/config/type_bigint.nim b/constantine/math/config/type_bigint.nim index e5435ef..99ebcd3 100644 --- a/constantine/math/config/type_bigint.nim +++ b/constantine/math/config/type_bigint.nim @@ -11,7 +11,7 @@ import ../../platforms/abstractions func wordsRequired*(bits: int): int {.compileTime.} = ## Compute the number of limbs required # from the **announced** bit length - (bits + WordBitWidth - 1) div WordBitWidth + bits.ceilDiv_vartime(WordBitWidth) type BigInt*[bits: static int] = object diff --git a/constantine/math/elliptic/ec_endomorphism_accel.nim b/constantine/math/elliptic/ec_endomorphism_accel.nim index 97a289f..dd8333b 100644 --- a/constantine/math/elliptic/ec_endomorphism_accel.nim +++ b/constantine/math/elliptic/ec_endomorphism_accel.nim @@ -61,7 +61,7 @@ func decomposeEndo*[M, scalBits, L: static int]( static: doAssert scalBits >= L, "Cannot decompose a scalar smaller than a mini-scalar or the decomposition coefficient" # Equal when no window or no negative handling, greater otherwise - static: doAssert L >= (scalBits + M - 1) div M + 1 + static: doAssert L >= scalBits.ceilDiv_vartime(M) + 1 const w = F.C.getCurveOrderBitwidth().wordsRequired() when M == 2: @@ -129,7 +129,7 @@ func decomposeEndo*[M, scalBits, L: static int]( # (For example generating a public-key) type - Recoded[LengthInDigits: static int] = distinct array[(LengthInDigits + 7) div 8, byte] + Recoded[LengthInDigits: static int] = distinct array[LengthInDigits.ceilDiv_vartime(8), byte] GLV_SAC[M, LengthInDigits: static int] = array[M, Recoded[LengthInDigits]] ## GLV-Based Sign-Aligned-Column representation ## see Faz-Hernandez, 2013 @@ -319,7 +319,7 @@ func scalarMulEndo*[scalBits; EC]( {.error: "Unconfigured".} # 2. Decompose scalar into mini-scalars - const L = (scalBits + M - 1) div M + 1 # Alternatively, negative can be handled with an extra "+1" + const L = scalBits.ceilDiv_vartime(M) + 1 # Alternatively, negative can be handled with an extra "+1" var miniScalars {.noInit.}: array[M, BigInt[L]] var negatePoints {.noInit.}: array[M, SecretBool] miniScalars.decomposeEndo(negatePoints, scalar, P.F) @@ -473,7 +473,7 @@ func computeRecodedLength(bitWidth, window: int): int = # Strangely in the paper this doesn't depend # "m", the GLV decomposition dimension. # lw = ⌈log2 r/w⌉+1 (optionally a second "+1" to handle negative mini scalars) - let lw = (bitWidth + window - 1) div window + 1 + let lw = bitWidth.ceilDiv_vartime(window) + 1 result = (lw mod window) + lw func scalarMulGLV_m2w2*[scalBits; EC]( diff --git a/constantine/math/elliptic/ec_multi_scalar_mul.nim b/constantine/math/elliptic/ec_multi_scalar_mul.nim index c6cfa95..e0bb79b 100644 --- a/constantine/math/elliptic/ec_multi_scalar_mul.nim +++ b/constantine/math/elliptic/ec_multi_scalar_mul.nim @@ -44,7 +44,7 @@ func multiScalarMulImpl_reference_vartime[F, G; bits: static int]( # Prologue # -------- const numBuckets = 1 shl c - 1 # bucket 0 is unused - const numWindows = (bits + c - 1) div c + const numWindows = bits.ceilDiv_vartime(c) type EC = typeof(r) let miniMSMs = allocHeapArray(EC, numWindows) @@ -376,7 +376,7 @@ func multiScalarMul_vartime*[bits: static int, F, G]( elif F is Fp2: 4 else: {.error: "Unconfigured".} - const L = (bits + M - 1) div M + 1 + const L = bits.ceilDiv_vartime(M) + 1 let splitCoefs = allocHeapArray(array[M, BigInt[L]], N) let endoBasis = allocHeapArray(array[M, ECP_ShortW_Aff[F, G]], N) diff --git a/constantine/math/elliptic/ec_multi_scalar_mul_scheduler.nim b/constantine/math/elliptic/ec_multi_scalar_mul_scheduler.nim index 4f1e5ed..47cc90b 100644 --- a/constantine/math/elliptic/ec_multi_scalar_mul_scheduler.nim +++ b/constantine/math/elliptic/ec_multi_scalar_mul_scheduler.nim @@ -599,7 +599,7 @@ when isMainModule: let c = inputSize.bestBucketBitSize(255, useSignedBuckets = true, useManualTuning = false) let twoPow = "2^" let numNZBuckets = 1 shl (c-1) - let collisionMapSize = ((1 shl (c-1))+63) div 64 * 8 # Stored in BigInt[1 shl (c-1)] + let collisionMapSize = ceilDiv_vartime(1 shl (c-1), 64) * 8 # Stored in BigInt[1 shl (c-1)] let queueSize = 4*c*c - 16*c - 128 let numCollisions = float(inputSize*queueSize) / float(numNZBuckets) let collisionPercentage = numCollisions / float(inputSize) * 100 diff --git a/constantine/math/elliptic/ec_scalar_mul.nim b/constantine/math/elliptic/ec_scalar_mul.nim index 1fbff55..de8fdde 100644 --- a/constantine/math/elliptic/ec_scalar_mul.nim +++ b/constantine/math/elliptic/ec_scalar_mul.nim @@ -223,8 +223,8 @@ func scalarMulGeneric*[EC](P: var EC, scalar: BigInt, window: static int = 5) = ## the scalar multiplication. var scratchSpace: array[1 shl window, EC] - scalarCanonicalBE: array[(scalar.bits+7) div 8, byte] # canonical big endian representation - scalarCanonicalBE.marshal(scalar, bigEndian) # Export is constant-time + scalarCanonicalBE: array[scalar.bits.ceilDiv_vartime(8), byte] # canonical big endian representation + scalarCanonicalBE.marshal(scalar, bigEndian) # Export is constant-time P.scalarMulGeneric(scalarCanonicalBE, scratchSpace) func scalarMul*[EC]( diff --git a/constantine/math/elliptic/ec_scalar_mul_vartime.nim b/constantine/math/elliptic/ec_scalar_mul_vartime.nim index e4c34c5..585637a 100644 --- a/constantine/math/elliptic/ec_scalar_mul_vartime.nim +++ b/constantine/math/elliptic/ec_scalar_mul_vartime.nim @@ -38,7 +38,7 @@ func scalarMul_doubleAdd_vartime*[EC](P: var EC, scalar: BigInt) {.tags:[VarTime ## This MUST NOT be used with secret data. ## ## This is highly VULNERABLE to timing attacks and power analysis attacks. - var scalarCanonical: array[(scalar.bits+7) div 8, byte] + var scalarCanonical: array[scalar.bits.ceilDiv_vartime(8), byte] scalarCanonical.marshal(scalar, bigEndian) var Paff {.noinit.}: affine(EC) diff --git a/constantine/math/elliptic/ec_shortweierstrass_batch_ops_parallel.nim b/constantine/math/elliptic/ec_shortweierstrass_batch_ops_parallel.nim index 3134b11..34284bb 100644 --- a/constantine/math/elliptic/ec_shortweierstrass_batch_ops_parallel.nim +++ b/constantine/math/elliptic/ec_shortweierstrass_batch_ops_parallel.nim @@ -45,7 +45,7 @@ func computeBalancedChunks(start, stopEx, minChunkSize, maxChunkSize, targetNumC cutoff = totalIters mod numChunks elif baseChunkSize > maxChunkSize or (baseChunkSize == maxChunkSize and cutoff != 0): # After cutoff, we do baseChunkSize+1, and would run afoul of the maxChunkSize constraint (unless no remainder), hence ceildiv - numChunks = (totalIters + maxChunkSize - 1) div maxChunkSize # ceildiv + numChunks = totalIters.ceilDiv_vartime(maxChunkSize) baseChunkSize = totalIters div numChunks cutoff = totalIters mod numChunks diff --git a/constantine/math/extension_fields/exponentiations.nim b/constantine/math/extension_fields/exponentiations.nim index 61ac8cd..40bf619 100644 --- a/constantine/math/extension_fields/exponentiations.nim +++ b/constantine/math/extension_fields/exponentiations.nim @@ -183,6 +183,6 @@ func powUnsafeExponent*[F; bits: static int]( ## - memory access analysis ## - power analysis ## - timing analysis - var expBE {.noInit.}: array[(bits + 7) div 8, byte] + var expBE {.noInit.}: array[bits.ceilDiv_vartime(8), byte] expBE.marshal(exponent, bigEndian) a.powUnsafeExponent(expBE, window) diff --git a/constantine/math/io/io_bigints.nim b/constantine/math/io/io_bigints.nim index b07c5ed..2415fae 100644 --- a/constantine/math/io/io_bigints.nim +++ b/constantine/math/io/io_bigints.nim @@ -355,7 +355,7 @@ func marshal*( ## or zero-padded right for little-endian. ## I.e least significant bit is aligned to buffer boundary debug: - doAssert dst.len >= (BigInt.bits + 7) div 8, block: + doAssert dst.len >= BigInt.bits.ceilDiv_vartime(8), block: "BigInt -> Raw int conversion: destination buffer is too small\n" & " bits: " & $BigInt.bits & "\n" & " bytes allocated: " & $dst.len & '\n' @@ -389,7 +389,7 @@ func fromHex*(a: var BigInt, s: string) = ## Can work at compile-time to declare curve moduli from their hex strings # 1. Convert to canonical uint - const canonLen = (BigInt.bits + 8 - 1) div 8 + const canonLen = BigInt.bits.ceilDiv_vartime(8) var bytes: array[canonLen, byte] bytes.paddedFromHex(s, bigEndian) @@ -428,7 +428,7 @@ func appendHex*(dst: var string, big: BigInt, order: static Endianness = bigEndi ## This function may allocate. # 1. Convert Big Int to canonical uint - const canonLen = (big.bits + 8 - 1) div 8 + const canonLen = big.bits.ceilDiv_vartime(8) var bytes: array[canonLen, byte] marshal(bytes, big, order) diff --git a/constantine/platforms/allocs.nim b/constantine/platforms/allocs.nim index 36ebb3b..f45ed54 100644 --- a/constantine/platforms/allocs.nim +++ b/constantine/platforms/allocs.nim @@ -67,7 +67,7 @@ func roundNextMultipleOf(x: int, n: static int): int {.inline.} = # n is a power of 2. (If compiler cannot prove that x>0 it does not make the optim) result = (x + n - 1) and not(n - 1) else: - result = ((x + n - 1) div n) * n + result = x.ceilDiv_vartime(n) * n # Stack allocation # ---------------------------------------------------------------------------------- diff --git a/constantine/platforms/ast_rebuilder.nim b/constantine/platforms/ast_rebuilder.nim new file mode 100644 index 0000000..a9db59d --- /dev/null +++ b/constantine/platforms/ast_rebuilder.nim @@ -0,0 +1,77 @@ +# Constantine +# Copyright (c) 2018-2019 Status Research & Development GmbH +# Copyright (c) 2020-Present Mamy André-Ratsimbazafy +# Licensed and distributed under either of +# * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT). +# * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0). +# at your option. This file may not be copied, modified, or distributed except according to those terms. + +import std/macros + +proc rebuildUntypedAst*(ast: NimNode, dropRootStmtList = false): NimNode = + ## In some cases (generics or static proc) Nim gives us + ## typed NimNode which are hard to process. + ## This rebuilds an untyped AST. + ## + ## Additionally this allows dropping the root StmtList that + ## may wrap the typed AST from early symbol resolution + proc rebuild(node: NimNode): NimNode = + proc defaultMultipleChildren(node: NimNode): NimNode = + var rTree = node.kind.newTree() + for child in node: + rTree.add rebuild(child) + return rTree + + case node.kind: + of {nnkIdent, nnkSym}: + return ident($node) + of nnkEmpty: + return node + of nnkLiterals: + return node + of nnkHiddenStdConv: + if node[1].kind == nnkIntLit: + return node[1] + else: + expectKind(node[1], nnkSym) + return ident($node[1]) + of nnkConv: # type conversion needs to be replaced by a function call in untyped AST + var rTree = nnkCall.newTree() + for child in node: + rTree.add rebuild(child) + return rTree + of {nnkCall, nnkInfix, nnkPrefix}: + if node[0].kind == nnkOpenSymChoice: + if node[0][0].eqIdent"contains": + var rTree = nnkInfix.newTree() + rTree.add ident"in" + rTree.add rebuild(node[2]) + rTree.add rebuild(node[1]) + return rTree + else: + var rTree = node.kind.newTree() + rTree.add rebuild(node[0][0]) + for i in 1 ..< node.len: + rTree.add rebuild(node[i]) + return rTree + elif node[0].kind == nnkClosedSymChoice: + if node[0][0].eqIdent"addr": + node.expectLen(1) + return nnkAddr.newTree(rebuild(node[1])) + else: + var rTree = node.kind.newTree() + rTree.add rebuild(node[0][0]) + for i in 1 ..< node.len: + rTree.add rebuild(node[i]) + return rTree + else: + return defaultMultipleChildren(node) + of nnkClosedSymChoice: + return rebuild(node[0]) + else: + return defaultMultipleChildren(node) + + if dropRootStmtList and ast.kind == nnkStmtList: + return rebuild(ast[0]) + else: + result = rebuild(ast) \ No newline at end of file diff --git a/constantine/platforms/compilers/bitops.nim b/constantine/platforms/compilers/bitops.nim index 5913e9a..218a8fa 100644 --- a/constantine/platforms/compilers/bitops.nim +++ b/constantine/platforms/compilers/bitops.nim @@ -31,12 +31,12 @@ when GCC_Compatible: 0 else: when sizeof(n) == 8: - cint(64) - builtin_clzll(n) + cint(63) - builtin_clzll(n) else: cint(31) - builtin_clz(n.uint32) func ctz_c_compiler_vartime*(n: SomeUnsignedInt): cint {.inline.} = - ## Compute the number of trailing zeros + ## Compute the number of trailing zeros ## in the bit representation of n using compiler builtin ## ⚠ Depending on the compiler: ## - It is undefined if n == 0 @@ -72,7 +72,7 @@ elif defined(icc): if fnc(index.addr, v) == 0: return default return index.int - + func log2_c_compiler_vartime*(n: SomeUnsignedInt): cint {.inline.} = ## Compute the log2 of n using compiler builtin ## ⚠ Depending on the compiler: @@ -82,7 +82,7 @@ elif defined(icc): bitscan(bitScanReverse64, n, default = 0) else: bitscan(bitScanReverse, c.uint32, default = 0) - + func ctz_c_compiler_vartime*(n: SomeUnsignedInt): cint {.inline.} = ## Compute the number of trailing zero bits of n using compiler builtin ## ⚠ Depending on the compiler: @@ -116,7 +116,7 @@ elif defined(vcc): if fnc(index.addr, v) == 0: return 0 return index.int - + func log2_c_compiler_vartime*(n: SomeUnsignedInt): cint {.inline.} = ## Compute the log2 of n using compiler builtin ## ⚠ Depending on the compiler: @@ -126,7 +126,7 @@ elif defined(vcc): bitscan(bitScanReverse64, n, default = 0) else: bitscan(bitScanReverse, c.uint32, default = 0) - + func ctz_c_compiler_vartime*(n: SomeUnsignedInt): cint {.inline.} = ## Compute the number of trailing zero bits of n using compiler builtin ## ⚠ Depending on the compiler: diff --git a/constantine/platforms/gpu/bindings/utils.nim b/constantine/platforms/gpu/bindings/utils.nim index 610628f..0ca9a71 100644 --- a/constantine/platforms/gpu/bindings/utils.nim +++ b/constantine/platforms/gpu/bindings/utils.nim @@ -7,6 +7,7 @@ # at your option. This file may not be copied, modified, or distributed except according to those terms. import std/macros +import ../../ast_rebuilder # ############################################################ # @@ -33,33 +34,6 @@ func flag*[E: enum](e: varargs[E]): Flag[E] {.inline.} = # Macros # ------------------------------------------------------------ -proc replaceSymsByIdents*(ast: NimNode): NimNode = - proc inspect(node: NimNode): NimNode = - case node.kind: - of {nnkIdent, nnkSym}: - return ident($node) - of nnkEmpty: - return node - of nnkLiterals: - return node - of nnkHiddenStdConv: - if node[1].kind == nnkIntLit: - return node[1] - else: - expectKind(node[1], nnkSym) - return ident($node[1]) - of nnkConv: # type conversion needs to be replaced by a function call in untyped AST - var rTree = nnkCall.newTree() - for child in node: - rTree.add inspect(child) - return rTree - else: - var rTree = node.kind.newTree() - for child in node: - rTree.add inspect(child) - return rTree - result = inspect(ast) - macro replacePragmasByInline(procAst: typed): untyped = ## Replace pragmas by the inline pragma ## We need a separate "typed" macro @@ -76,7 +50,7 @@ macro replacePragmasByInline(procAst: typed): untyped = result.add newProc( name = procAst.name, params = params, - body = procAst.body.replaceSymsByIdents(), + body = procAst.body.rebuildUntypedAst(), procType = nnkProcDef, pragmas = nnkPragma.newTree(ident"inline", ident"nimcall") ) @@ -84,19 +58,19 @@ macro replacePragmasByInline(procAst: typed): untyped = result.add nnkPragma.newTree(ident"pop") macro wrapOpenArrayLenType*(ty: typedesc, procAst: untyped): untyped = - ## Wraps pointer+len library calls in properly typed and converted openArray calls + ## Wraps pointer+len library calls in properly typed and converted openArray calls ## ## ``` ## {.push cdecl.} ## proc foo*(r: int, a: openArray[CustomType], b: int) {.wrapOpenArrayLenType: uint32, importc: "foo", dynlib: "libfoo.so".} ## {.pop.} ## ``` - ## + ## ## is transformed into - ## + ## ## ``` ## proc foo(r: int, a: ptr CustomType, aLen: uint32, b: int) {.cdecl, importc: "foo", dynlib: "libfoo.so".} - ## + ## ## proc foo*(r: int, a: openArray[CustomType], b: int) {.inline.} = ## foo(r, a[0].unsafeAddr, a.len.uint32, b) ## ``` diff --git a/constantine/platforms/gpu/ir.nim b/constantine/platforms/gpu/ir.nim index 70bee53..a8709ed 100644 --- a/constantine/platforms/gpu/ir.nim +++ b/constantine/platforms/gpu/ir.nim @@ -9,7 +9,7 @@ import ../../math/config/[curves, precompute], ../../math/io/io_bigints, - ../primitives, ../bithacks, ../endians, + ../primitives, ../bithacks, ../endians, ../codecs, ./llvm # ############################################################ diff --git a/constantine/platforms/primitives.nim b/constantine/platforms/primitives.nim index fc98b59..2990714 100644 --- a/constantine/platforms/primitives.nim +++ b/constantine/platforms/primitives.nim @@ -52,8 +52,25 @@ template debug*(body: untyped): untyped = when defined(debugConstantine): body -func unreachable*() {.noReturn.} = +proc builtin_unreachable(){.nodecl, importc: "__builtin_unreachable".} + +func unreachable*() {.noReturn, inline.} = doAssert false, "Unreachable" + when GCC_Compatible: + builtin_unreachable() + +# ############################################################ +# +# Arithmetic +# +# ############################################################ + +func ceilDiv_vartime*(a, b: auto): auto {.inline.} = + ## ceil division, to be used only on length or at compile-time + ## ceil(a / b) + # "LengthInDigits: static int" doesn't match "int" + # if "SomeInteger" is used instead of "autoi" + (a + b - 1) div b # ############################################################ # diff --git a/constantine/platforms/static_for.nim b/constantine/platforms/static_for.nim index 4dca6e6..3c896f9 100644 --- a/constantine/platforms/static_for.nim +++ b/constantine/platforms/static_for.nim @@ -32,16 +32,14 @@ macro staticFor*(idx: untyped{nkIdent}, start, stopEx: static int, body: untyped for i in start ..< stopEx: result.add nnkBlockStmt.newTree( ident("unrolledIter_" & $idx & $i), - body.replaceNodes(idx, newLit i) - ) + body.replaceNodes(idx, newLit i)) macro staticForCountdown*(idx: untyped{nkIdent}, start, stopIncl: static int, body: untyped): untyped = result = newStmtList() for i in countdown(start, stopIncl): result.add nnkBlockStmt.newTree( ident("unrolledIter_" & $idx & $i), - body.replaceNodes(idx, newLit i) - ) + body.replaceNodes(idx, newLit i)) {.experimental: "dynamicBindSym".} @@ -62,5 +60,4 @@ macro staticFor*(ident: untyped{nkIdent}, choices: typed, body: untyped): untype for choice in choices: result.add nnkBlockStmt.newTree( ident($ident & "_" & $choice.intVal), - body.replaceNodes(ident, choice) - ) + body.replaceNodes(ident, choice)) diff --git a/constantine/platforms/threadpool/benchmarks/black_scholes/README.md b/constantine/platforms/threadpool/benchmarks/black_scholes/README.md new file mode 100644 index 0000000..f7381f3 --- /dev/null +++ b/constantine/platforms/threadpool/benchmarks/black_scholes/README.md @@ -0,0 +1,9 @@ +# Black & Scholes European Option Pricing + +https://www.investopedia.com/terms/b/blackscholes.asp + +Benchmarks from the PARSEC benchmark suite + +https://parsec.cs.princeton.edu + +Reference C implementation by Intel diff --git a/constantine/platforms/threadpool/benchmarks/black_scholes/README_Parsec.txt b/constantine/platforms/threadpool/benchmarks/black_scholes/README_Parsec.txt new file mode 100644 index 0000000..e799274 --- /dev/null +++ b/constantine/platforms/threadpool/benchmarks/black_scholes/README_Parsec.txt @@ -0,0 +1,67 @@ +Name: Black Scholes + +Description: The Black-Scholes equation is a differential equation that +describes how, under a certain set of assumptions, the value of an option +changes as the price of the underlying asset changes. + +The formula for a put option is similar. The cumulative normal distribution +function, CND(x), gives the probability that normally distributed random +variable will have a value less than x. There is no closed form expression for +this function, and as such it must be evaluated numerically. Alternatively, +the values of this function may be pre-computed and hard-coded in the table; in +this case, they can be obtained at runtime using table lookup. We compare both +of these approaches in our work. The other parameters are as follows: +S underlying asset.s current price, X the strike price, T time to the +expiration date, r risk-less rate of return, and v stock.s volatility. + +Based on this formula, one can compute the option price analytically based on +the five input parameters. Using this analytical approach to price option, +the limiting factor lies with the amount of floating-point calculation a +processor can perform. + +Parallelization: Our parallelization algorithms is very simple: we simply price +multiple options in parallel using Black-Scholes formula. Each thread prices an +individual option. In practice financial houses price 10.s to 100.s of thousandsof options using Black-Scholes. + +======================================= +Programming Languages & Libraries: + +C/C++ and Pthread is used to implement this benchmark. + +======================================= +System requirements: + + 1) Intel(R) C++ Compiler: version 9.0 or higher + 2) GNU gcc/g++: version 3.3 or higher + 3) sed: version 4.0.9 or higher recommended. +The minimum required memory size is 140 MBytes. +======================================= +Input/Output: +The input data file of this benchmark includes an array of data of +options. + +The output benchmark will output the price of the options based on the five +input parameters in the dataset file. + + +======================================= +Characteristics: + +(1) Hotspot +Hotspot of the benchmark includes computing the price of options using +black scholes formula and the cumulative normal distribution function. +They are implemented in BlkSchlsEqEuroNoDiv and CNDF in "bs.c" respectly. + +======================================= +Revision History + +Date: Person-making-revision brief-description-of-revision + +======================================= +Author: Victor Lee, Mikhail Smelyanskiy + +Acknowledgements: + +References: +[Black73] Black, Fischer, and M. Scholes. The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81:637--659, May--June 1973. + diff --git a/constantine/platforms/threadpool/benchmarks/black_scholes/blackscholes.c b/constantine/platforms/threadpool/benchmarks/black_scholes/blackscholes.c new file mode 100644 index 0000000..0cabac0 --- /dev/null +++ b/constantine/platforms/threadpool/benchmarks/black_scholes/blackscholes.c @@ -0,0 +1,509 @@ +// Copyright (c) 2007 Intel Corp. + +// Black-Scholes +// Analytical method for calculating European Options +// +// +// Reference Source: Options, Futures, and Other Derivatives, 3rd Edition, Prentice +// Hall, John C. Hull, + +#include +#include +#include +#include + +#ifdef ENABLE_PARSEC_HOOKS +#include +#endif + +// Multi-threaded pthreads header +#ifdef ENABLE_THREADS +// Add the following line so that icc 9.0 is compatible with pthread lib. +#define __thread __threadp +MAIN_ENV +#undef __thread +#endif + +// Multi-threaded OpenMP header +#ifdef ENABLE_OPENMP +#include +#endif + +#ifdef ENABLE_TBB +#include "tbb/blocked_range.h" +#include "tbb/parallel_for.h" +#include "tbb/task_scheduler_init.h" +#include "tbb/tick_count.h" + +using namespace std; +using namespace tbb; +#endif //ENABLE_TBB + +// Multi-threaded header for Windows +#ifdef WIN32 +#pragma warning(disable : 4305) +#pragma warning(disable : 4244) +#include +#endif + +//Precision to use for calculations +#define fptype float + +#define NUM_RUNS 100 + +typedef struct OptionData_ { + fptype s; // spot price + fptype strike; // strike price + fptype r; // risk-free interest rate + fptype divq; // dividend rate + fptype v; // volatility + fptype t; // time to maturity or option expiration in years + // (1yr = 1.0, 6mos = 0.5, 3mos = 0.25, ..., etc) + char OptionType; // Option type. "P"=PUT, "C"=CALL + fptype divs; // dividend vals (not used in this test) + fptype DGrefval; // DerivaGem Reference Value +} OptionData; + +OptionData *data; +fptype *prices; +int numOptions; + +int * otype; +fptype * sptprice; +fptype * strike; +fptype * rate; +fptype * volatility; +fptype * otime; +int numErrors = 0; +int nThreads; + +//////////////////////////////////////////////////////////////////////////////// +//////////////////////////////////////////////////////////////////////////////// +/////////////////////////////////////////////////////////////////////////////// +//////////////////////////////////////////////////////////////////////////////// +// Cumulative Normal Distribution Function +// See Hull, Section 11.8, P.243-244 +#define inv_sqrt_2xPI 0.39894228040143270286 + +fptype CNDF ( fptype InputX ) +{ + int sign; + + fptype OutputX; + fptype xInput; + fptype xNPrimeofX; + fptype expValues; + fptype xK2; + fptype xK2_2, xK2_3; + fptype xK2_4, xK2_5; + fptype xLocal, xLocal_1; + fptype xLocal_2, xLocal_3; + + // Check for negative value of InputX + if (InputX < 0.0) { + InputX = -InputX; + sign = 1; + } else + sign = 0; + + xInput = InputX; + + // Compute NPrimeX term common to both four & six decimal accuracy calcs + expValues = exp(-0.5f * InputX * InputX); + xNPrimeofX = expValues; + xNPrimeofX = xNPrimeofX * inv_sqrt_2xPI; + + xK2 = 0.2316419 * xInput; + xK2 = 1.0 + xK2; + xK2 = 1.0 / xK2; + xK2_2 = xK2 * xK2; + xK2_3 = xK2_2 * xK2; + xK2_4 = xK2_3 * xK2; + xK2_5 = xK2_4 * xK2; + + xLocal_1 = xK2 * 0.319381530; + xLocal_2 = xK2_2 * (-0.356563782); + xLocal_3 = xK2_3 * 1.781477937; + xLocal_2 = xLocal_2 + xLocal_3; + xLocal_3 = xK2_4 * (-1.821255978); + xLocal_2 = xLocal_2 + xLocal_3; + xLocal_3 = xK2_5 * 1.330274429; + xLocal_2 = xLocal_2 + xLocal_3; + + xLocal_1 = xLocal_2 + xLocal_1; + xLocal = xLocal_1 * xNPrimeofX; + xLocal = 1.0 - xLocal; + + OutputX = xLocal; + + if (sign) { + OutputX = 1.0 - OutputX; + } + + return OutputX; +} + +////////////////////////////////////////////////////////////////////////////////////// +////////////////////////////////////////////////////////////////////////////////////// +////////////////////////////////////////////////////////////////////////////////////// +////////////////////////////////////////////////////////////////////////////////////// +fptype BlkSchlsEqEuroNoDiv( fptype sptprice, + fptype strike, fptype rate, fptype volatility, + fptype time, int otype, float timet ) +{ + fptype OptionPrice; + + // local private working variables for the calculation + fptype xStockPrice; + fptype xStrikePrice; + fptype xRiskFreeRate; + fptype xVolatility; + fptype xTime; + fptype xSqrtTime; + + fptype logValues; + fptype xLogTerm; + fptype xD1; + fptype xD2; + fptype xPowerTerm; + fptype xDen; + fptype d1; + fptype d2; + fptype FutureValueX; + fptype NofXd1; + fptype NofXd2; + fptype NegNofXd1; + fptype NegNofXd2; + + xStockPrice = sptprice; + xStrikePrice = strike; + xRiskFreeRate = rate; + xVolatility = volatility; + + xTime = time; + xSqrtTime = sqrt(xTime); + + logValues = log( sptprice / strike ); + + xLogTerm = logValues; + + + xPowerTerm = xVolatility * xVolatility; + xPowerTerm = xPowerTerm * 0.5; + + xD1 = xRiskFreeRate + xPowerTerm; + xD1 = xD1 * xTime; + xD1 = xD1 + xLogTerm; + + xDen = xVolatility * xSqrtTime; + xD1 = xD1 / xDen; + xD2 = xD1 - xDen; + + d1 = xD1; + d2 = xD2; + + NofXd1 = CNDF( d1 ); + NofXd2 = CNDF( d2 ); + + FutureValueX = strike * ( exp( -(rate)*(time) ) ); + if (otype == 0) { + OptionPrice = (sptprice * NofXd1) - (FutureValueX * NofXd2); + } else { + NegNofXd1 = (1.0 - NofXd1); + NegNofXd2 = (1.0 - NofXd2); + OptionPrice = (FutureValueX * NegNofXd2) - (sptprice * NegNofXd1); + } + + return OptionPrice; +} + +#ifdef ENABLE_TBB +struct mainWork { + mainWork() {} + mainWork(mainWork &w, tbb::split) {} + + void operator()(const tbb::blocked_range &range) const { + fptype price; + int begin = range.begin(); + int end = range.end(); + + for (int i=begin; i!=end; i++) { + /* Calling main function to calculate option value based on + * Black & Scholes's equation. + */ + + price = BlkSchlsEqEuroNoDiv( sptprice[i], strike[i], + rate[i], volatility[i], otime[i], + otype[i], 0); + prices[i] = price; + +#ifdef ERR_CHK + fptype priceDelta = data[i].DGrefval - price; + if( fabs(priceDelta) >= 1e-5 ){ + fprintf(stderr,"Error on %d. Computed=%.5f, Ref=%.5f, Delta=%.5f\n", + i, price, data[i].DGrefval, priceDelta); + numError ++; + } +#endif + } + } +}; + +#endif // ENABLE_TBB + +////////////////////////////////////////////////////////////////////////////////////// +////////////////////////////////////////////////////////////////////////////////////// +////////////////////////////////////////////////////////////////////////////////////// +////////////////////////////////////////////////////////////////////////////////////// + +#ifdef ENABLE_TBB +int bs_thread(void *tid_ptr) { + int j; + tbb::affinity_partitioner a; + + mainWork doall; + for (j=0; j(0, numOptions), doall, a); + } + + return 0; +} +#else // !ENABLE_TBB + +#ifdef WIN32 +DWORD WINAPI bs_thread(LPVOID tid_ptr){ +#else +int bs_thread(void *tid_ptr) { +#endif + int i, j; + fptype price; + fptype priceDelta; + int tid = *(int *)tid_ptr; + int start = tid * (numOptions / nThreads); + int end = start + (numOptions / nThreads); + + for (j=0; j= 1e-4 ){ + printf("Error on %d. Computed=%.5f, Ref=%.5f, Delta=%.5f\n", + i, price, data[i].DGrefval, priceDelta); + numError ++; + } +#endif + } + } + + return 0; +} +#endif //ENABLE_TBB + +int main (int argc, char **argv) +{ + FILE *file; + int i; + int loopnum; + fptype * buffer; + int * buffer2; + int rv; + +#ifdef PARSEC_VERSION +#define __PARSEC_STRING(x) #x +#define __PARSEC_XSTRING(x) __PARSEC_STRING(x) + printf("PARSEC Benchmark Suite Version "__PARSEC_XSTRING(PARSEC_VERSION)"\n"); + fflush(NULL); +#else + printf("PARSEC Benchmark Suite\n"); + fflush(NULL); +#endif //PARSEC_VERSION +#ifdef ENABLE_PARSEC_HOOKS + __parsec_bench_begin(__parsec_blackscholes); +#endif + + if (argc != 4) + { + printf("Usage:\n\t%s \n", argv[0]); + exit(1); + } + nThreads = atoi(argv[1]); + char *inputFile = argv[2]; + char *outputFile = argv[3]; + + //Read input data from file + file = fopen(inputFile, "r"); + if(file == NULL) { + printf("ERROR: Unable to open file `%s'.\n", inputFile); + exit(1); + } + rv = fscanf(file, "%i", &numOptions); + if(rv != 1) { + printf("ERROR: Unable to read from file `%s'.\n", inputFile); + fclose(file); + exit(1); + } + if(nThreads > numOptions) { + printf("WARNING: Not enough work, reducing number of threads to match number of options.\n"); + nThreads = numOptions; + } + +#if !defined(ENABLE_THREADS) && !defined(ENABLE_OPENMP) && !defined(ENABLE_TBB) + if(nThreads != 1) { + printf("Error: must be 1 (serial version)\n"); + exit(1); + } +#endif + + // alloc spaces for the option data + data = (OptionData*)malloc(numOptions*sizeof(OptionData)); + prices = (fptype*)malloc(numOptions*sizeof(fptype)); + for ( loopnum = 0; loopnum < numOptions; ++ loopnum ) + { + rv = fscanf(file, "%f %f %f %f %f %f %c %f %f", &data[loopnum].s, &data[loopnum].strike, &data[loopnum].r, &data[loopnum].divq, &data[loopnum].v, &data[loopnum].t, &data[loopnum].OptionType, &data[loopnum].divs, &data[loopnum].DGrefval); + if(rv != 9) { + printf("ERROR: Unable to read from file `%s'.\n", inputFile); + fclose(file); + exit(1); + } + } + rv = fclose(file); + if(rv != 0) { + printf("ERROR: Unable to close file `%s'.\n", inputFile); + exit(1); + } + +#ifdef ENABLE_THREADS + MAIN_INITENV(,8000000,nThreads); +#endif + printf("Num of Options: %d\n", numOptions); + printf("Num of Runs: %d\n", NUM_RUNS); + +#define PAD 256 +#define LINESIZE 64 + + buffer = (fptype *) malloc(5 * numOptions * sizeof(fptype) + PAD); + sptprice = (fptype *) (((unsigned long long)buffer + PAD) & ~(LINESIZE - 1)); + strike = sptprice + numOptions; + rate = strike + numOptions; + volatility = rate + numOptions; + otime = volatility + numOptions; + + buffer2 = (int *) malloc(numOptions * sizeof(fptype) + PAD); + otype = (int *) (((unsigned long long)buffer2 + PAD) & ~(LINESIZE - 1)); + + for (i=0; i +#include +#include +#include + +#ifndef WIN32 +#include +#else +#include +#endif + +#ifdef ENABLE_PARSEC_HOOKS +#include +#endif + +// Multi-threaded pthreads header +#ifdef ENABLE_THREADS +// Add the following line so that icc 9.0 is compatible with pthread lib. +#define __thread __threadp +MAIN_ENV +#undef __thread +#endif + +// Multi-threaded OpenMP header +#ifdef ENABLE_OPENMP +#include +#endif + +#ifdef ENABLE_TBB +#include "tbb/blocked_range.h" +#include "tbb/parallel_for.h" +#include "tbb/task_scheduler_init.h" +#include "tbb/tick_count.h" + +using namespace std; +using namespace tbb; +#endif //ENABLE_TBB + +// Multi-threaded header for Windows +#ifdef WIN32 +#pragma warning(disable : 4305) +#pragma warning(disable : 4244) +#include +#endif + +#ifdef __GNUC__ +#define _MM_ALIGN16 __attribute__((aligned (16))) +#define MUSTINLINE __attribute__((always_inline)) +#else +#define MUSTINLINE __forceinline +#endif + +// NCO = Number of Concurrent Options = SIMD Width +// NCO is currently set in the Makefile. +#ifndef NCO +#error NCO must be defined. +#endif + +#if (NCO==2) +#define fptype double +#define SIMD_WIDTH 2 +#define _MMR __m128d +#define _MM_LOAD _mm_load_pd +#define _MM_STORE _mm_store_pd +#define _MM_MUL _mm_mul_pd +#define _MM_ADD _mm_add_pd +#define _MM_SUB _mm_sub_pd +#define _MM_DIV _mm_div_pd +#define _MM_SQRT _mm_sqrt_pd +#define _MM_SET(A) _mm_set_pd(A,A) +#define _MM_SETR _mm_set_pd +#endif + +#if (NCO==4) +#define fptype float +#define SIMD_WIDTH 4 +#define _MMR __m128 +#define _MM_LOAD _mm_load_ps +#define _MM_STORE _mm_store_ps +#define _MM_MUL _mm_mul_ps +#define _MM_ADD _mm_add_ps +#define _MM_SUB _mm_sub_ps +#define _MM_DIV _mm_div_ps +#define _MM_SQRT _mm_sqrt_ps +#define _MM_SET(A) _mm_set_ps(A,A,A,A) +#define _MM_SETR _mm_set_ps +#endif + +#define NUM_RUNS 100 + +typedef struct OptionData_ { + fptype s; // spot price + fptype strike; // strike price + fptype r; // risk-free interest rate + fptype divq; // dividend rate + fptype v; // volatility + fptype t; // time to maturity or option expiration in years + // (1yr = 1.0, 6mos = 0.5, 3mos = 0.25, ..., etc) + char OptionType; // Option type. "P"=PUT, "C"=CALL + fptype divs; // dividend vals (not used in this test) + fptype DGrefval; // DerivaGem Reference Value +} OptionData; + +_MM_ALIGN16 OptionData* data; +_MM_ALIGN16 fptype* prices; +int numOptions; + +int * otype; +fptype * sptprice; +fptype * strike; +fptype * rate; +fptype * volatility; +fptype * otime; +int numError = 0; +int nThreads; + +//////////////////////////////////////////////////////////////////////////////// +//////////////////////////////////////////////////////////////////////////////// +/////////////////////////////////////////////////////////////////////////////// +//////////////////////////////////////////////////////////////////////////////// +// Cumulative Normal Distribution Function +// See Hull, Section 11.8, P.243-244 +#define inv_sqrt_2xPI 0.39894228040143270286 + +MUSTINLINE void CNDF ( fptype * OutputX, fptype * InputX ) +{ + int sign[SIMD_WIDTH]; + int i; + _MMR xInput; + _MMR xNPrimeofX; + _MM_ALIGN16 fptype expValues[SIMD_WIDTH]; + _MMR xK2; + _MMR xK2_2, xK2_3, xK2_4, xK2_5; + _MMR xLocal, xLocal_1, xLocal_2, xLocal_3; + + for (i=0; i &range) const { + fptype price[NCO]; + fptype priceDelta; + int begin = range.begin(); + int end = range.end(); + + for (int i=begin; i!=end; i+=NCO) { + /* Calling main function to calculate option value based on + * Black & Scholes's equation. + */ + + BlkSchlsEqEuroNoDiv( price, NCO, &(sptprice[i]), &(strike[i]), + &(rate[i]), &(volatility[i]), &(otime[i]), + &(otype[i]), 0); + for (int k=0; k= 1e-5 ){ + fprintf(stderr,"Error on %d. Computed=%.5f, Ref=%.5f, Delta=%.5f\n", + i+k, price, data[i+k].DGrefval, priceDelta); + numError ++; + } +#endif + } + } + } +}; + +#endif // ENABLE_TBB + +////////////////////////////////////////////////////////////////////////////////////// +////////////////////////////////////////////////////////////////////////////////////// +////////////////////////////////////////////////////////////////////////////////////// +////////////////////////////////////////////////////////////////////////////////////// + +#ifdef ENABLE_TBB +int bs_thread(void *tid_ptr) { + int j; + tbb::affinity_partitioner a; + + mainWork doall; + for (j=0; j(0, numOptions), doall, a); + } + + return 0; +} +#else // !ENABLE_TBB + +#ifdef WIN32 +DWORD WINAPI bs_thread(LPVOID tid_ptr){ +#else +int bs_thread(void *tid_ptr) { +#endif + int i, j, k; + fptype price[NCO]; + fptype priceDelta; + int tid = *(int *)tid_ptr; + int start = tid * (numOptions / nThreads); + int end = start + (numOptions / nThreads); + + for (j=0; j= 1e-4) { + printf("Error on %d. Computed=%.5f, Ref=%.5f, Delta=%.5f\n", + i + k, price[k], data[i+k].DGrefval, priceDelta); + numError ++; + } + } +#endif + } + } + + return 0; +} +#endif //ENABLE_TBB + +int main (int argc, char **argv) +{ + FILE *file; + int i; + int loopnum; + fptype * buffer; + int * buffer2; + int rv; + +#ifdef PARSEC_VERSION +#define __PARSEC_STRING(x) #x +#define __PARSEC_XSTRING(x) __PARSEC_STRING(x) + printf("PARSEC Benchmark Suite Version "__PARSEC_XSTRING(PARSEC_VERSION)"\n"); + fflush(NULL); +#else + printf("PARSEC Benchmark Suite\n"); + fflush(NULL); +#endif //PARSEC_VERSION +#ifdef ENABLE_PARSEC_HOOKS + __parsec_bench_begin(__parsec_blackscholes); +#endif + + if (argc != 4) + { + printf("Usage:\n\t%s \n", argv[0]); + exit(1); + } + nThreads = atoi(argv[1]); + char *inputFile = argv[2]; + char *outputFile = argv[3]; + + //Read input data from file + file = fopen(inputFile, "r"); + if(file == NULL) { + printf("ERROR: Unable to open file `%s'.\n", inputFile); + exit(1); + } + rv = fscanf(file, "%i", &numOptions); + if(rv != 1) { + printf("ERROR: Unable to read from file `%s'.\n", inputFile); + fclose(file); + exit(1); + } + if(NCO > numOptions) { + printf("ERROR: Not enough work for SIMD operation.\n"); + fclose(file); + exit(1); + } + if(nThreads > numOptions/NCO) { + printf("WARNING: Not enough work, reducing number of threads to match number of SIMD options packets.\n"); + nThreads = numOptions/NCO; + } + +#if !defined(ENABLE_THREADS) && !defined(ENABLE_OPENMP) && !defined(ENABLE_TBB) + if(nThreads != 1) { + printf("Error: must be 1 (serial version)\n"); + exit(1); + } +#endif + + data = (OptionData*)malloc(numOptions*sizeof(OptionData)); + prices = (fptype*)malloc(numOptions*sizeof(fptype)); + for ( loopnum = 0; loopnum < numOptions; ++ loopnum ) + { + rv = fscanf(file, "%f %f %f %f %f %f %c %f %f", &data[loopnum].s, &data[loopnum].strike, &data[loopnum].r, &data[loopnum].divq, &data[loopnum].v, &data[loopnum].t, &data[loopnum].OptionType, &data[loopnum].divs, &data[loopnum].DGrefval); + if(rv != 9) { + printf("ERROR: Unable to read from file `%s'.\n", inputFile); + fclose(file); + exit(1); + } + } + rv = fclose(file); + if(rv != 0) { + printf("ERROR: Unable to close file `%s'.\n", inputFile); + exit(1); + } + +#ifdef ENABLE_THREADS + MAIN_INITENV(,8000000,nThreads); +#endif + printf("Num of Options: %d\n", numOptions); + printf("Num of Runs: %d\n", NUM_RUNS); + +#define PAD 256 +#define LINESIZE 64 + + buffer = (fptype *) malloc(5 * numOptions * sizeof(fptype) + PAD); + sptprice = (fptype *) (((unsigned long long)buffer + PAD) & ~(LINESIZE - 1)); + strike = sptprice + numOptions; + rate = strike + numOptions; + volatility = rate + numOptions; + otime = volatility + numOptions; + + buffer2 = (int *) malloc(numOptions * sizeof(fptype) + PAD); + otype = (int *) (((unsigned long long)buffer2 + PAD) & ~(LINESIZE - 1)); + + for (i=0; i + +extern pthread_t _M4_threads[MAX_THREADS]; +extern pthread_mutexattr_t _M4_normalMutexAttr; +extern int _M4_numThreads; +') + +define(MAIN_ENV, +` +#ifdef _XOPEN_SOURCE +#undef _XOPEN_SOURCE +#define _XOPEN_SOURCE 700 +#endif +#ifndef _GNU_SOURCE +#define _GNU_SOURCE +#endif +#ifndef __USE_XOPEN2K +#define __USE_XOPEN2K +#endif +#ifndef __USE_UNIX98 +#define __USE_UNIX98 +#endif +#include +#include + +#define MAX_THREADS 128 + +pthread_t _M4_threadsTable[MAX_THREADS]; +int _M4_threadsTableAllocated[MAX_THREADS]; +pthread_mutexattr_t _M4_normalMutexAttr; +int _M4_numThreads = MAX_THREADS; +') + +define(MAIN_INITENV, ` + pthread_mutexattr_init( &_M4_normalMutexAttr); +// pthread_mutexattr_settype( &_M4_normalMutexAttr, PTHREAD_MUTEX_NORMAL); + _M4_numThreads = $3; + { + int _M4_i; + for ( _M4_i = 0; _M4_i < MAX_THREADS; _M4_i++) { + _M4_threadsTableAllocated[_M4_i] = 0; + } + } +') +define(MAIN_END, `') + + +define(CREATE_WITH_ARG, ` + { + int _M4_i; + for ( _M4_i = 0; _M4_i < MAX_THREADS; _M4_i++) { + if ( _M4_threadsTableAllocated[_M4_i] == 0) break; + } + pthread_create(&_M4_threadsTable[_M4_i],NULL,(void *(*)(void *))$1,(void *)$2); + _M4_threadsTableAllocated[_M4_i] = 1; + } +') + +define(CREATE, `CREATE_WITH_ARG($1,NULL);') + +define(SELF, `( long)pthread_self()') + +define(BARDEC, `pthread_barrier_t $1;') +define(BARINIT, `pthread_barrier_init(&($1),NULL,_M4_numThreads);') +define(BARRIER, `pthread_barrier_wait(&($1))') + +define(LOCKDEC, `pthread_mutex_t $1;') +define(LOCKINIT, `pthread_mutex_init(&($1), &_M4_normalMutexAttr);') +define(LOCK, `pthread_mutex_lock(&($1));') +define(UNLOCK, `pthread_mutex_unlock(&($1));') + +define(LOCKRDEC, `pthread_mutex_t $1;') +define(LOCKRINIT, `pthread_mutex_init(&($1), NULL);') +define(LOCKR, `pthread_mutex_lock(&($1));') +define(UNLOCKR, `pthread_mutex_unlock(&($1));') + +define(CVDEC, `pthread_cond_t $1;') +define(CVINIT, `pthread_cond_init(&$1,NULL);') +define(CVWAIT, `pthread_cond_wait(&$1,&$2);') +define(CVWAITREL, `pthread_cond_wait(&$1,&$2); pthread_mutex_unlock(&$2);') +define(CVSIGNALALL, `pthread_cond_broadcast(&$1);') +define(CVSIGNALONE, `pthread_cond_signal(&$1);') + +define(ACQUIRE, `pthread_mutex_lock(&($1));') +define(RELEASE, `pthread_mutex_unlock(&($1));') + +define(ALOCKDEC, `pthread_mutex_t ($1[$2]);') +define(ALOCKINIT, `{ + int _M4_loop_j; + for(_M4_loop_j=0; _M4_loop_j < $2; _M4_loop_j++){ + pthread_mutex_init((pthread_mutex_t*)&($1[_M4_loop_j]), NULL); + } + }') +define(ALOCK, `pthread_mutex_lock((pthread_mutex_t*)&($1[$2]));') +define(AULOCK, `pthread_mutex_unlock((pthread_mutex_t*)&($1[$2]));') + +define(AACQUIRE, `pthread_mutex_lock(&($1[$2]));') +define(ARELEASE, `pthread_mutex_unlock(&($1[$2]));') + +define(WAIT_FOR_END, ` + { + int _M4_i; + void *_M4_ret; + for ( _M4_i = 0; _M4_i < MAX_THREADS;_M4_i++) { + if ( _M4_threadsTableAllocated[_M4_i] == 0) break; + pthread_join( _M4_threadsTable[_M4_i], &_M4_ret); + } + } +') +define(JOIN, `{pthread_join( _M4_threadsTable[($1)], NULL );}') + +define(CLOCK, `{long time(); ($1) = time(0);}') + +define(GET_PID, `$1 = pthread_self();') +define(AUG_ON, `') +define(AUG_OFF, `') + +define(G_MALLOC, `malloc($1);') +define(MALLOC, `malloc($1);') + diff --git a/constantine/platforms/threadpool/benchmarks/black_scholes/inputgen.c b/constantine/platforms/threadpool/benchmarks/black_scholes/inputgen.c new file mode 100644 index 0000000..c7b886c --- /dev/null +++ b/constantine/platforms/threadpool/benchmarks/black_scholes/inputgen.c @@ -0,0 +1,85 @@ +//Copyright (c) 2009 Princeton University +//Written by Christian Bienia +//Generate input files for blackscholes benchmark + +#include +#include + + + +//Precision to use +#define fptype double + +typedef struct OptionData_ { + fptype s; // spot price + fptype strike; // strike price + fptype r; // risk-free interest rate + fptype divq; // dividend rate + fptype v; // volatility + fptype t; // time to maturity or option expiration in years + // (1yr = 1.0, 6mos = 0.5, 3mos = 0.25, ..., etc) + const char *OptionType; // Option type. "P"=PUT, "C"=CALL + fptype divs; // dividend vals (not used in this test) + fptype DGrefval; // DerivaGem Reference Value +} OptionData; + +//Total number of options in optionData.txt +#define MAX_OPTIONS 1000 + +OptionData data_init[] = { + #include "optionData.txt" +}; + + + +int main (int argc, char **argv) { + int numOptions; + char *fileName; + int rv; + int i; + + if (argc != 3) { + printf("Usage:\n\t%s \n", argv[0]); + exit(1); + } + numOptions = atoi(argv[1]); + fileName = argv[2]; + if(numOptions < 1) { + printf("ERROR: Number of options must at least be 1.\n"); + exit(1); + } + + FILE *file; + file = fopen(fileName, "w"); + if(file == NULL) { + printf("ERROR: Unable to open file `%s'.\n", fileName); + exit(1); + } + + //write number of options + rv = fprintf(file, "%i\n", numOptions); + if(rv < 0) { + printf("ERROR: Unable to write to file `%s'.\n", fileName); + fclose(file); + exit(1); + } + + //write values for options + for(i=0; i= 1e-4: + c_printf("Error on %d. Computed=%.5f, Ref=%.5f, Delta=%.5f\n", + i.int, price, ctx.data[i].dgrefval, priceDelta + ) + ctx.numErrors += 1 + +func blackScholesSequential(ctx: var Context) = + + for j in 0 ..< ctx.numRuns: + for i in 0 ..< ctx.numOptions: + let price = blackScholesEqEuroNoDiv( + ctx.spot[i], ctx.strike[i], + ctx.riskFreeRate[i], ctx.volatility[i], + ctx.expiry[i], ctx.otype[i], 0 + ) + ctx.prices[i] = price + + when defined(check): + checkErrors(ctx, i, price) + +proc blackScholesOpenMP(ctx: ptr Context) = + + # Stacktraces will create issues between thread-local GC and OpenMP + {.push stackTrace: off.} + for j in 0 ..< ctx.numRuns: + for i in 0||(ctx.numOptions-1): + let price = blackScholesEqEuroNoDiv( + ctx.spot[i], ctx.strike[i], + ctx.riskFreeRate[i], ctx.volatility[i], + ctx.expiry[i], ctx.otype[i], 0 + ) + ctx.prices[i] = price + + when defined(check): + checkErrors(ctx[], i, price) + {.pop.} + +proc dump[T](ctx: Context[T], file: string) = + + let stream = openFileStream(file, fmWrite) + defer: stream.close() + + stream.write($ctx.numOptions) + stream.write("\n") + + for i in 0 ..< ctx.numOptions: + stream.write($ctx.prices[i]) + stream.write("\n") + +proc parseOptions[T](ctx: var Context[T], optFile: string) = + + let stream = openFileStream(optFile, fmRead) + defer: stream.close() + + var line: string + discard stream.readLine(line) + + # Allocate the buffers + # Note sure why the original bench uses a struct of arrays + let numOptions = line.parseInt() + ctx.initialize(numOptions) + echo "Reading ", numOptions, " options" + + # For parsing Nim uses float64 by default + var + spot, strike, riskfree, divrate, vol, expiry: float64 + optKind: string + divvals, dgrefval: float64 + + for i in 0 ..< ctx.numOptions: + discard stream.readLine(line) + let isLineParsed = scanf(line, "$f $f $f $f $f $f $w $f $f", + spot, strike, riskFree, + divrate, vol, expiry, + optKind, divvals, dgrefval + ) + doAssert isLineParsed + + ctx.data[i].spot = spot.T + ctx.data[i].strike = strike.T + ctx.data[i].riskfree = riskfree.T + ctx.data[i].divrate = divrate.T + ctx.data[i].vol = vol.T + ctx.data[i].expiry = expiry.T + ctx.data[i].divvals = divvals.T + ctx.data[i].dgrefval = dgrefval.T + + if optKind == "C": + ctx.data[i].kind = Call + elif optKind == "P": + ctx.data[i].kind = Put + else: + raise newException(ValueError, "Invalid option kind: \"" & optKind & '"') + + ctx.otype[i] = ctx.data[i].kind + ctx.spot[i] = ctx.data[i].spot + ctx.strike[i] = ctx.data[i].strike + ctx.riskFreeRate[i] = ctx.data[i].riskfree + ctx.volatility[i] = ctx.data[i].vol + ctx.expiry[i] = ctx.data[i].expiry + +proc main() = + + var + input = "" + output = "" + numRounds = 2000 + + if paramCount() == 0: + let exeName = getAppFilename().extractFilename() + echo &"Usage: {exeName} " + quit 0 + elif paramCount() == 1: + input = paramStr(1) + elif paramCount() == 2: + input = paramStr(1) + output = paramStr(2) + elif paramCount() == 3: + input = paramStr(1) + output = paramStr(2) + numRounds = paramStr(3).parseInt() + else: + let exeName = getAppFilename().extractFilename() + echo &"Usage: {exeName} " + quit 1 + + var ctx: Context[float32] + ctx.numRuns = numRounds + ctx.parseOptions(input) + + var nthreads: int + if existsEnv"OMP_NUM_THREADS": + nthreads = getEnv"OMP_NUM_THREADS".parseInt() + else: + nthreads = countProcessors() + + var ru: Rusage + getrusage(RusageSelf, ru) + var + rss = ru.ru_maxrss + flt = ru.ru_minflt + + let start = wtime_msec() + blackScholesOpenMP(ctx.addr) + let stop = wtime_msec() + + getrusage(RusageSelf, ru) + rss = ru.ru_maxrss - rss + flt = ru.ru_minflt - flt + + echo "--------------------------------------------------------------------------" + echo "Scheduler: OpenMP (Nim)" + echo "Benchmark: Black & Scholes Option Pricing" + echo "Threads: ", nthreads + echo "Time(ms) ", round(stop - start, 3) + echo "Max RSS (KB): ", ru.ru_maxrss + echo "Runtime RSS (KB): ", rss + echo "# of page faults: ", flt + echo "--------------------------------------------------------------------------" + echo "# of rounds: ", numRounds + echo "# of options: ", ctx.numOptions + + if output != "": + echo "\nDumping prices to \"", output, '"' + dump(ctx, output) + + delete(ctx) + + quit 0 + +main() \ No newline at end of file diff --git a/constantine/platforms/threadpool/benchmarks/black_scholes/optionData.txt b/constantine/platforms/threadpool/benchmarks/black_scholes/optionData.txt new file mode 100644 index 0000000..b713ce3 --- /dev/null +++ b/constantine/platforms/threadpool/benchmarks/black_scholes/optionData.txt @@ -0,0 +1,1004 @@ +// #include file of test data inpout params and DerivaGem control reference value +// +// S, K, r, q, vol, T, P/C, Divs, DG RefValue + +{42.00, 40.00, 0.1000, 0.00, 0.20, 0.50, "C", 0.00, 4.759423036851750000}, +{42.00, 40.00, 0.1000, 0.00, 0.20, 0.50, "P", 0.00, 0.808600016880314000}, +{100.00, 100.00, 0.0500, 0.00, 0.15, 1.00, "P", 0.00, 3.714602051381290000}, +{100.00, 100.00, 0.0500, 0.00, 0.15, 1.00, "C", 0.00, 8.591659601309890000}, +{60.00, 65.00, 0.0800, 0.00, 0.30, 0.25, "C", 0.00, 2.133371966735750000}, +{100.00, 90.00, 0.1000, 0.00, 0.10, 0.10, "C", 0.00, 10.895610714794000000}, +{100.00, 90.00, 0.1000, 0.00, 0.10, 0.50, "C", 0.00, 14.421570828843300000}, +{100.00, 90.00, 0.1000, 0.00, 0.10, 1.00, "C", 0.00, 18.630859120667500000}, +{100.00, 100.00, 0.1000, 0.00, 0.10, 0.10, "C", 0.00, 1.814984118378420000}, +{100.00, 100.00, 0.1000, 0.00, 0.10, 0.50, "C", 0.00, 5.850273604284980000}, +{100.00, 100.00, 0.1000, 0.00, 0.10, 1.00, "C", 0.00, 10.308147243666800000}, +{100.00, 110.00, 0.1000, 0.00, 0.10, 0.10, "C", 0.00, 0.003523074865584340}, +{100.00, 110.00, 0.1000, 0.00, 0.10, 0.50, "C", 0.00, 1.140722843827410000}, +{100.00, 110.00, 0.1000, 0.00, 0.10, 1.00, "C", 0.00, 4.216747020308850000}, +{100.00, 90.00, 0.1000, 0.00, 0.25, 0.10, "C", 0.00, 11.135244618346700000}, +{100.00, 90.00, 0.1000, 0.00, 0.25, 0.50, "C", 0.00, 16.092638844092300000}, +{100.00, 90.00, 0.1000, 0.00, 0.25, 1.00, "C", 0.00, 21.163454658480100000}, +{100.00, 100.00, 0.1000, 0.00, 0.25, 0.10, "C", 0.00, 3.659962660310000000}, +{100.00, 100.00, 0.1000, 0.00, 0.25, 0.50, "C", 0.00, 9.582231441086730000}, +{100.00, 100.00, 0.1000, 0.00, 0.25, 1.00, "C", 0.00, 14.975798441718900000}, +{100.00, 110.00, 0.1000, 0.00, 0.25, 0.10, "C", 0.00, 0.589613262035413000}, +{100.00, 110.00, 0.1000, 0.00, 0.25, 0.50, "C", 0.00, 5.123575416865320000}, +{100.00, 110.00, 0.1000, 0.00, 0.25, 1.00, "C", 0.00, 10.160055944516600000}, +{100.00, 90.00, 0.1000, 0.00, 0.50, 0.10, "C", 0.00, 12.919509619564700000}, +{100.00, 90.00, 0.1000, 0.00, 0.50, 0.50, "C", 0.00, 21.438280655724400000}, +{100.00, 90.00, 0.1000, 0.00, 0.50, 1.00, "C", 0.00, 28.643647264488200000}, +{100.00, 100.00, 0.1000, 0.00, 0.50, 0.10, "C", 0.00, 6.779936664291260000}, +{100.00, 100.00, 0.1000, 0.00, 0.50, 0.50, "C", 0.00, 16.263193147074300000}, +{100.00, 100.00, 0.1000, 0.00, 0.50, 1.00, "C", 0.00, 23.926745214162700000}, +{100.00, 110.00, 0.1000, 0.00, 0.50, 0.10, "C", 0.00, 3.061909566605540000}, +{100.00, 110.00, 0.1000, 0.00, 0.50, 0.50, "C", 0.00, 12.155688815568700000}, +{100.00, 110.00, 0.1000, 0.00, 0.50, 1.00, "C", 0.00, 19.929858372066300000}, +{100.00, 90.00, 0.1000, 0.00, 0.10, 0.10, "P", 0.00, 0.000095752219082624}, +{100.00, 90.00, 0.1000, 0.00, 0.10, 0.50, "P", 0.00, 0.032219033907538300}, +{100.00, 90.00, 0.1000, 0.00, 0.10, 1.00, "P", 0.00, 0.066226743903883000}, +{100.00, 100.00, 0.1000, 0.00, 0.10, 0.10, "P", 0.00, 0.819967493295226000}, +{100.00, 100.00, 0.1000, 0.00, 0.10, 0.50, "P", 0.00, 0.973216054356396000}, +{100.00, 100.00, 0.1000, 0.00, 0.10, 1.00, "P", 0.00, 0.791889047262800000}, +{100.00, 110.00, 0.1000, 0.00, 0.10, 0.10, "P", 0.00, 8.909004787274070000}, +{100.00, 110.00, 0.1000, 0.00, 0.10, 0.50, "P", 0.00, 5.775959538905960000}, +{100.00, 110.00, 0.1000, 0.00, 0.10, 1.00, "P", 0.00, 3.748863004264400000}, +{100.00, 90.00, 0.1000, 0.00, 0.25, 0.10, "P", 0.00, 0.239729655771796000}, +{100.00, 90.00, 0.1000, 0.00, 0.25, 0.50, "P", 0.00, 1.703287049156570000}, +{100.00, 90.00, 0.1000, 0.00, 0.25, 1.00, "P", 0.00, 2.598822281716470000}, +{100.00, 100.00, 0.1000, 0.00, 0.25, 0.10, "P", 0.00, 2.664946035226810000}, +{100.00, 100.00, 0.1000, 0.00, 0.25, 0.50, "P", 0.00, 4.705173891158130000}, +{100.00, 100.00, 0.1000, 0.00, 0.25, 1.00, "P", 0.00, 5.459540245314840000}, +{100.00, 110.00, 0.1000, 0.00, 0.25, 0.10, "P", 0.00, 9.495094974443900000}, +{100.00, 110.00, 0.1000, 0.00, 0.25, 0.50, "P", 0.00, 9.758812111943870000}, +{100.00, 110.00, 0.1000, 0.00, 0.25, 1.00, "P", 0.00, 9.692171928472170000}, +{100.00, 90.00, 0.1000, 0.00, 0.50, 0.10, "P", 0.00, 2.023994656989830000}, +{100.00, 90.00, 0.1000, 0.00, 0.50, 0.50, "P", 0.00, 7.048928860788620000}, +{100.00, 90.00, 0.1000, 0.00, 0.50, 1.00, "P", 0.00, 10.079014887724600000}, +{100.00, 100.00, 0.1000, 0.00, 0.50, 0.10, "P", 0.00, 5.784920039208060000}, +{100.00, 100.00, 0.1000, 0.00, 0.50, 0.50, "P", 0.00, 11.386135597145700000}, +{100.00, 100.00, 0.1000, 0.00, 0.50, 1.00, "P", 0.00, 14.410487017758700000}, +{100.00, 110.00, 0.1000, 0.00, 0.50, 0.10, "P", 0.00, 11.967391279014000000}, +{100.00, 110.00, 0.1000, 0.00, 0.50, 0.50, "P", 0.00, 16.790925510647200000}, +{100.00, 110.00, 0.1000, 0.00, 0.50, 1.00, "P", 0.00, 19.461974356021900000}, +{50.00, 41.25, 0.1000, 0.00, 0.10, 0.10, "C", 0.00, 9.160444357863210000}, +{50.00, 41.25, 0.1000, 0.00, 0.10, 0.50, "C", 0.00, 10.762029464848100000}, +{50.00, 41.25, 0.1000, 0.00, 0.10, 1.00, "C", 0.00, 12.677609097740100000}, +{50.00, 50.00, 0.1000, 0.00, 0.10, 0.10, "C", 0.00, 0.907492059189209000}, +{50.00, 50.00, 0.1000, 0.00, 0.10, 0.50, "C", 0.00, 2.925136802142490000}, +{50.00, 50.00, 0.1000, 0.00, 0.10, 1.00, "C", 0.00, 5.154073621833420000}, +{50.00, 60.75, 0.1000, 0.00, 0.10, 0.10, "C", 0.00, 0.000000000717454849}, +{50.00, 60.75, 0.1000, 0.00, 0.10, 0.50, "C", 0.00, 0.028414779953288100}, +{50.00, 60.75, 0.1000, 0.00, 0.10, 1.00, "C", 0.00, 0.481908128709845000}, +{50.00, 41.25, 0.1000, 0.00, 0.25, 0.10, "C", 0.00, 9.166378741739160000}, +{50.00, 41.25, 0.1000, 0.00, 0.25, 0.50, "C", 0.00, 11.066856943917300000}, +{50.00, 41.25, 0.1000, 0.00, 0.25, 1.00, "C", 0.00, 13.316909764810900000}, +{50.00, 50.00, 0.1000, 0.00, 0.25, 0.10, "C", 0.00, 1.829981330155000000}, +{50.00, 50.00, 0.1000, 0.00, 0.25, 0.50, "C", 0.00, 4.791115720543370000}, +{50.00, 50.00, 0.1000, 0.00, 0.25, 1.00, "C", 0.00, 7.487899220859440000}, +{50.00, 60.75, 0.1000, 0.00, 0.25, 0.10, "C", 0.00, 0.014232371738726200}, +{50.00, 60.75, 0.1000, 0.00, 0.25, 0.50, "C", 0.00, 1.102318710852480000}, +{50.00, 60.75, 0.1000, 0.00, 0.25, 1.00, "C", 0.00, 3.104764376468200000}, +{50.00, 41.25, 0.1000, 0.00, 0.50, 0.10, "C", 0.00, 9.499149830045080000}, +{50.00, 41.25, 0.1000, 0.00, 0.50, 0.50, "C", 0.00, 13.034624930353100000}, +{50.00, 41.25, 0.1000, 0.00, 0.50, 1.00, "C", 0.00, 16.348279176395100000}, +{50.00, 50.00, 0.1000, 0.00, 0.50, 0.10, "C", 0.00, 3.389968332145630000}, +{50.00, 50.00, 0.1000, 0.00, 0.50, 0.50, "C", 0.00, 8.131596573537150000}, +{50.00, 50.00, 0.1000, 0.00, 0.50, 1.00, "C", 0.00, 11.963372607081400000}, +{50.00, 60.75, 0.1000, 0.00, 0.50, 0.10, "C", 0.00, 0.517721140543361000}, +{50.00, 60.75, 0.1000, 0.00, 0.50, 0.50, "C", 0.00, 4.285755504631100000}, +{50.00, 60.75, 0.1000, 0.00, 0.50, 1.00, "C", 0.00, 8.058110917563740000}, +{50.00, 41.25, 0.1000, 0.00, 0.10, 0.10, "P", 0.00, 0.000000000016396475}, +{50.00, 41.25, 0.1000, 0.00, 0.10, 0.50, "P", 0.00, 0.000243225502595658}, +{50.00, 41.25, 0.1000, 0.00, 0.10, 1.00, "P", 0.00, 0.002152591723420370}, +{50.00, 50.00, 0.1000, 0.00, 0.10, 0.10, "P", 0.00, 0.409983746647613000}, +{50.00, 50.00, 0.1000, 0.00, 0.10, 0.50, "P", 0.00, 0.486608027178198000}, +{50.00, 50.00, 0.1000, 0.00, 0.10, 1.00, "P", 0.00, 0.395944523631400000}, +{50.00, 60.75, 0.1000, 0.00, 0.10, 0.10, "P", 0.00, 10.145527400979400000}, +{50.00, 60.75, 0.1000, 0.00, 0.10, 0.50, "P", 0.00, 7.815602318371660000}, +{50.00, 60.75, 0.1000, 0.00, 0.10, 1.00, "P", 0.00, 5.450781274394380000}, +{50.00, 41.25, 0.1000, 0.00, 0.25, 0.10, "P", 0.00, 0.005934383892338090}, +{50.00, 41.25, 0.1000, 0.00, 0.25, 0.50, "P", 0.00, 0.305070704571745000}, +{50.00, 41.25, 0.1000, 0.00, 0.25, 1.00, "P", 0.00, 0.641453258794187000}, +{50.00, 50.00, 0.1000, 0.00, 0.25, 0.10, "P", 0.00, 1.332473017613400000}, +{50.00, 50.00, 0.1000, 0.00, 0.25, 0.50, "P", 0.00, 2.352586945579070000}, +{50.00, 50.00, 0.1000, 0.00, 0.25, 1.00, "P", 0.00, 2.729770122657420000}, +{50.00, 60.75, 0.1000, 0.00, 0.25, 0.10, "P", 0.00, 10.159759772000700000}, +{50.00, 60.75, 0.1000, 0.00, 0.25, 0.50, "P", 0.00, 8.889506249270860000}, +{50.00, 60.75, 0.1000, 0.00, 0.25, 1.00, "P", 0.00, 8.073637522152740000}, +{50.00, 41.25, 0.1000, 0.00, 0.50, 0.10, "P", 0.00, 0.338705472198261000}, +{50.00, 41.25, 0.1000, 0.00, 0.50, 0.50, "P", 0.00, 2.272838691007510000}, +{50.00, 41.25, 0.1000, 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2.892460019604030208 +50.00 50.00 0.1000 0.00 0.50 0.50 P 0.00 5.693067798572860383 +50.00 50.00 0.1000 0.00 0.50 1.00 P 0.00 7.205243508879349612 +50.00 60.75 0.1000 0.00 0.50 0.10 P 0.00 10.663248540805300379 +50.00 60.75 0.1000 0.00 0.50 0.50 P 0.00 12.072943043049500389 +50.00 60.75 0.1000 0.00 0.50 1.00 P 0.00 13.026984063248299606 +100.00 90.00 0.0275 0.00 0.10 0.10 C 0.00 10.247401000886400269 +100.00 90.00 0.0275 0.00 0.10 0.50 C 0.00 11.355496680087599159 +100.00 90.00 0.0275 0.00 0.10 1.00 C 0.00 12.841685844358700308 +100.00 100.00 0.0275 0.00 0.10 0.10 C 0.00 1.401851512188629911 +100.00 100.00 0.0275 0.00 0.10 0.50 C 0.00 3.536661968725869798 +100.00 100.00 0.0275 0.00 0.10 1.00 C 0.00 5.437616879373149636 +100.00 110.00 0.0275 0.00 0.10 0.10 C 0.00 0.001633213370202900 +100.00 110.00 0.0275 0.00 0.10 0.50 C 0.00 0.454070380213948022 +100.00 110.00 0.0275 0.00 0.10 1.00 C 0.00 1.532588879532599924 +100.00 90.00 0.0275 0.00 0.25 0.10 C 0.00 10.541889432392700598 +100.00 90.00 0.0275 0.00 0.25 0.50 C 0.00 13.710780949068899659 +100.00 90.00 0.0275 0.00 0.25 1.00 C 0.00 16.827677195009300704 +100.00 100.00 0.0275 0.00 0.25 0.10 C 0.00 3.287983325881400187 +100.00 100.00 0.0275 0.00 0.25 0.50 C 0.00 7.698994752653709917 +100.00 100.00 0.0275 0.00 0.25 1.00 C 0.00 11.227983057006399648 +100.00 110.00 0.0275 0.00 0.25 0.10 C 0.00 0.492789615196492004 +100.00 110.00 0.0275 0.00 0.25 0.50 C 0.00 3.858921644731479805 +100.00 110.00 0.0275 0.00 0.25 1.00 C 0.00 7.162832542185689988 +100.00 90.00 0.0275 0.00 0.50 0.10 C 0.00 12.443070129340599195 +100.00 90.00 0.0275 0.00 0.50 0.50 C 0.00 19.594067641915700051 +100.00 90.00 0.0275 0.00 0.50 1.00 C 0.00 25.369048485340599086 +100.00 100.00 0.0275 0.00 0.50 0.10 C 0.00 6.430883891711170364 +100.00 100.00 0.0275 0.00 0.50 0.50 C 0.00 14.629031944250099784 +100.00 100.00 0.0275 0.00 0.50 1.00 C 0.00 20.858610524946801235 +100.00 110.00 0.0275 0.00 0.50 0.10 C 0.00 2.855401894418239994 +100.00 110.00 0.0275 0.00 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1.00 C 0.00 19.485080840813399305 +100.00 100.00 0.0725 0.00 0.25 0.10 C 0.00 3.516086538379690207 +100.00 100.00 0.0725 0.00 0.25 0.50 C 0.00 8.842399982947430459 +100.00 100.00 0.0725 0.00 0.25 1.00 C 0.00 13.495077753475699822 +100.00 110.00 0.0725 0.00 0.25 0.10 C 0.00 0.551230670113857957 +100.00 110.00 0.0725 0.00 0.25 0.50 C 0.00 4.615616936834760153 +100.00 110.00 0.0725 0.00 0.25 1.00 C 0.00 8.950419705313610308 +100.00 90.00 0.0725 0.00 0.50 0.10 C 0.00 12.738053154952400092 +100.00 90.00 0.0725 0.00 0.50 0.50 C 0.00 20.731790057083298251 +100.00 90.00 0.0725 0.00 0.50 1.00 C 0.00 27.388177501336400610 +100.00 100.00 0.0725 0.00 0.50 0.10 C 0.00 6.646286959643459724 +100.00 100.00 0.0725 0.00 0.50 0.50 C 0.00 15.633506954311799930 +100.00 100.00 0.0725 0.00 0.50 1.00 C 0.00 22.743364795607099893 +100.00 110.00 0.0725 0.00 0.50 0.10 C 0.00 2.982365532654810192 +100.00 110.00 0.0725 0.00 0.50 0.50 C 0.00 11.615595844329000386 +100.00 110.00 0.0725 0.00 0.50 1.00 C 0.00 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0.10 C 0.00 0.825516063236723996 +50.00 50.00 0.0725 0.00 0.10 0.50 C 0.00 2.453126785293899825 +50.00 50.00 0.0725 0.00 0.10 1.00 C 0.00 4.156504194469899716 +50.00 60.75 0.0725 0.00 0.10 0.10 C 0.00 0.000000000418787169 +50.00 60.75 0.0725 0.00 0.10 0.50 C 0.00 0.016602183429001501 +50.00 60.75 0.0725 0.00 0.10 1.00 C 0.00 0.284483121731958999 +50.00 41.25 0.0725 0.00 0.25 0.10 C 0.00 9.054608341813459305 +50.00 41.25 0.0725 0.00 0.25 0.50 C 0.00 10.581658197115100251 +50.00 41.25 0.0725 0.00 0.25 1.00 C 0.00 12.444199535517000754 +50.00 50.00 0.0725 0.00 0.25 0.10 C 0.00 1.758043269189839997 +50.00 50.00 0.0725 0.00 0.25 0.50 C 0.00 4.421199991473709900 +50.00 50.00 0.0725 0.00 0.25 1.00 C 0.00 6.747538876737840141 +50.00 60.75 0.0725 0.00 0.25 0.10 C 0.00 0.012850834682157100 +50.00 60.75 0.0725 0.00 0.25 0.50 C 0.00 0.964632352153436012 +50.00 60.75 0.0725 0.00 0.25 1.00 C 0.00 2.663220686150450156 +50.00 41.25 0.0725 0.00 0.50 0.10 C 0.00 9.399799864285059314 +50.00 41.25 0.0725 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41.25 0.0500 0.00 0.10 0.50 P 0.00 0.000929484057595751 +50.00 41.25 0.0500 0.00 0.10 1.00 P 0.00 0.011203410830535001 +50.00 50.00 0.0500 0.00 0.10 0.10 P 0.00 0.512342316477927051 +50.00 50.00 0.0500 0.00 0.10 0.50 P 0.00 0.861631156783567054 +50.00 50.00 0.0500 0.00 0.10 1.00 P 0.00 0.963952709050059031 +50.00 60.75 0.0500 0.00 0.10 0.10 P 0.00 10.447008111223599514 +50.00 60.75 0.0500 0.00 0.10 0.50 P 0.00 9.260524025525999292 +50.00 60.75 0.0500 0.00 0.10 1.00 P 0.00 7.964423688129230072 +50.00 41.25 0.0500 0.00 0.25 0.10 P 0.00 0.007248461621002290 +50.00 41.25 0.0500 0.00 0.25 0.50 P 0.00 0.417326857948238983 +50.00 41.25 0.0500 0.00 0.25 1.00 P 0.00 0.972659576104396018 +50.00 50.00 0.0500 0.00 0.25 0.10 P 0.00 1.451070877482949939 +50.00 50.00 0.0500 0.00 0.25 0.50 P 0.00 2.895497904257770205 +50.00 50.00 0.0500 0.00 0.25 1.00 P 0.00 3.729464342569280166 +50.00 60.75 0.0500 0.00 0.25 0.10 P 0.00 10.458819940242900515 +50.00 60.75 0.0500 0.00 0.25 0.50 P 0.00 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0.0725 0.00 0.10 1.00 C 0.00 8.313008388939790549 +100.00 110.00 0.0725 0.00 0.10 0.10 C 0.00 0.002646197663476990 +100.00 110.00 0.0725 0.00 0.10 0.50 C 0.00 0.822087720719597015 +100.00 110.00 0.0725 0.00 0.10 1.00 C 0.00 2.984536842326119821 +100.00 90.00 0.0725 0.00 0.25 0.10 C 0.00 10.909604363485600587 +100.00 90.00 0.0725 0.00 0.25 0.50 C 0.00 15.175519060709600438 +100.00 90.00 0.0725 0.00 0.25 1.00 C 0.00 19.485080840813399305 +100.00 100.00 0.0725 0.00 0.25 0.10 C 0.00 3.516086538379690207 +100.00 100.00 0.0725 0.00 0.25 0.50 C 0.00 8.842399982947430459 +100.00 100.00 0.0725 0.00 0.25 1.00 C 0.00 13.495077753475699822 +100.00 110.00 0.0725 0.00 0.25 0.10 C 0.00 0.551230670113857957 +100.00 110.00 0.0725 0.00 0.25 0.50 C 0.00 4.615616936834760153 +100.00 110.00 0.0725 0.00 0.25 1.00 C 0.00 8.950419705313610308 +100.00 90.00 0.0725 0.00 0.50 0.10 C 0.00 12.738053154952400092 +100.00 90.00 0.0725 0.00 0.50 0.50 C 0.00 20.731790057083298251 +100.00 90.00 0.0725 0.00 0.50 1.00 C 0.00 27.388177501336400610 +100.00 100.00 0.0725 0.00 0.50 0.10 C 0.00 6.646286959643459724 +100.00 100.00 0.0725 0.00 0.50 0.50 C 0.00 15.633506954311799930 +100.00 100.00 0.0725 0.00 0.50 1.00 C 0.00 22.743364795607099893 +100.00 110.00 0.0725 0.00 0.50 0.10 C 0.00 2.982365532654810192 +100.00 110.00 0.0725 0.00 0.50 0.50 C 0.00 11.615595844329000386 +100.00 110.00 0.0725 0.00 0.50 1.00 C 0.00 18.835720450406999049 +100.00 90.00 0.0725 0.00 0.10 0.10 P 0.00 0.000136657478829508 +100.00 90.00 0.0725 0.00 0.10 0.50 P 0.00 0.055508124958985001 +100.00 90.00 0.0725 0.00 0.10 1.00 P 0.00 0.137680882868775001 +100.00 100.00 0.0725 0.00 0.10 0.10 P 0.00 0.928653911666423970 +100.00 100.00 0.0725 0.00 0.10 0.50 P 0.00 1.346169925812749968 +100.00 100.00 0.0725 0.00 0.10 1.00 P 0.00 1.319583054967649938 +100.00 110.00 0.0725 0.00 0.10 0.10 P 0.00 9.208030161375749145 +100.00 110.00 0.0725 0.00 0.10 0.50 P 0.00 6.905995711467039833 +100.00 110.00 0.0725 0.00 0.10 1.00 P 0.00 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0.50 P 0.00 0.000515507530913631 +50.00 41.25 0.0725 0.00 0.10 1.00 P 0.00 0.005477652449141430 +50.00 50.00 0.0725 0.00 0.10 0.10 P 0.00 0.464326955833211985 +50.00 50.00 0.0725 0.00 0.10 0.50 P 0.00 0.673084962906373985 +50.00 50.00 0.0725 0.00 0.10 1.00 P 0.00 0.659791527483822970 +50.00 60.75 0.0725 0.00 0.10 0.10 P 0.00 10.311155234923500501 +50.00 60.75 0.0725 0.00 0.10 0.50 P 0.00 8.603851369228159740 +50.00 60.75 0.0725 0.00 0.10 1.00 P 0.00 6.785977231343879978 +50.00 41.25 0.0725 0.00 0.25 0.10 P 0.00 0.006627328205560570 +50.00 41.25 0.0725 0.00 0.25 0.50 P 0.00 0.363123693645392986 +50.00 41.25 0.0725 0.00 0.25 1.00 P 0.00 0.809411585253517973 +50.00 50.00 0.0725 0.00 0.25 0.10 P 0.00 1.396854161786329929 +50.00 50.00 0.0725 0.00 0.25 0.50 P 0.00 2.641158169086189833 +50.00 50.00 0.0725 0.00 0.25 1.00 P 0.00 3.250826209751759954 +50.00 60.75 0.0725 0.00 0.25 0.10 P 0.00 10.324006069186900447 +50.00 60.75 0.0725 0.00 0.25 0.50 P 0.00 9.551881537952599643 +50.00 60.75 0.0725 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0.25 0.10 C 0.00 3.287983325881400187 +100.00 100.00 0.0275 0.00 0.25 0.50 C 0.00 7.698994752653709917 +100.00 100.00 0.0275 0.00 0.25 1.00 C 0.00 11.227983057006399648 +100.00 110.00 0.0275 0.00 0.25 0.10 C 0.00 0.492789615196492004 +100.00 110.00 0.0275 0.00 0.25 0.50 C 0.00 3.858921644731479805 +100.00 110.00 0.0275 0.00 0.25 1.00 C 0.00 7.162832542185689988 +100.00 90.00 0.0275 0.00 0.50 0.10 C 0.00 12.443070129340599195 +100.00 90.00 0.0275 0.00 0.50 0.50 C 0.00 19.594067641915700051 +100.00 90.00 0.0275 0.00 0.50 1.00 C 0.00 25.369048485340599086 +100.00 100.00 0.0275 0.00 0.50 0.10 C 0.00 6.430883891711170364 +100.00 100.00 0.0275 0.00 0.50 0.50 C 0.00 14.629031944250099784 +100.00 100.00 0.0275 0.00 0.50 1.00 C 0.00 20.858610524946801235 +100.00 110.00 0.0275 0.00 0.50 0.10 C 0.00 2.855401894418239994 +100.00 110.00 0.0275 0.00 0.50 0.50 C 0.00 10.762095702746799830 +100.00 110.00 0.0275 0.00 0.50 1.00 C 0.00 17.109364250968301491 +100.00 90.00 0.0275 0.00 0.10 0.10 P 0.00 0.000241001647596191 +100.00 90.00 0.0275 0.00 0.10 0.50 P 0.00 0.126465632121558008 +100.00 90.00 0.0275 0.00 0.10 1.00 P 0.00 0.400407274169525984 +100.00 100.00 0.0275 0.00 0.10 0.10 P 0.00 1.127229290812219897 +100.00 100.00 0.0275 0.00 0.10 0.50 P 0.00 2.171071915430269783 +100.00 100.00 0.0275 0.00 0.10 1.00 P 0.00 2.725085134718539859 +100.00 110.00 0.0275 0.00 0.10 0.10 P 0.00 9.699548769856150443 +100.00 110.00 0.0275 0.00 0.10 0.50 P 0.00 8.951921321588779179 +100.00 110.00 0.0275 0.00 0.10 1.00 P 0.00 8.548803960412529435 +100.00 90.00 0.0275 0.00 0.25 0.10 P 0.00 0.294729433153973985 +100.00 90.00 0.0275 0.00 0.25 0.50 P 0.00 2.481749901102829892 +100.00 90.00 0.0275 0.00 0.25 1.00 P 0.00 4.386398624820129655 +100.00 100.00 0.0275 0.00 0.25 0.10 P 0.00 3.013361104504979959 +100.00 100.00 0.0275 0.00 0.25 0.50 P 0.00 6.333404699358100132 +100.00 100.00 0.0275 0.00 0.25 1.00 P 0.00 8.515451312351789426 +100.00 110.00 0.0275 0.00 0.25 0.10 P 0.00 10.190705171682399310 +100.00 110.00 0.0275 0.00 0.25 0.50 P 0.00 12.356772586106300693 +100.00 110.00 0.0275 0.00 0.25 1.00 P 0.00 14.179047623065599737 +100.00 90.00 0.0275 0.00 0.50 0.10 P 0.00 2.195910130101800029 +100.00 90.00 0.0275 0.00 0.50 0.50 P 0.00 8.365036593949600530 +100.00 90.00 0.0275 0.00 0.50 1.00 P 0.00 12.927769915151500868 +100.00 100.00 0.0275 0.00 0.50 0.10 P 0.00 6.156261670334750136 +100.00 100.00 0.0275 0.00 0.50 0.50 P 0.00 13.263441890954499769 +100.00 100.00 0.0275 0.00 0.50 1.00 P 0.00 18.146078780292199895 +100.00 110.00 0.0275 0.00 0.50 0.10 P 0.00 12.553317450904199148 +100.00 110.00 0.0275 0.00 0.50 0.50 P 0.00 19.259946644121601622 +100.00 110.00 0.0275 0.00 0.50 1.00 P 0.00 24.125579331848300058 +50.00 41.25 0.0275 0.00 0.10 0.10 C 0.00 8.863281666392300195 +50.00 41.25 0.0275 0.00 0.10 0.50 C 0.00 9.314944657044039289 +50.00 41.25 0.0275 0.00 0.10 1.00 C 0.00 9.890867970305359691 +50.00 50.00 0.0275 0.00 0.10 0.10 C 0.00 0.700925756094316954 +50.00 50.00 0.0275 0.00 0.10 0.50 C 0.00 1.768330984362940006 +50.00 50.00 0.0275 0.00 0.10 1.00 C 0.00 2.718808439686569933 +50.00 60.75 0.0275 0.00 0.10 0.10 C 0.00 0.000000000170861147 +50.00 60.75 0.0275 0.00 0.10 0.50 C 0.00 0.006433878180657690 +50.00 60.75 0.0275 0.00 0.10 1.00 C 0.00 0.106190314866699997 +50.00 41.25 0.0275 0.00 0.25 0.10 C 0.00 8.871203986520360019 +50.00 41.25 0.0275 0.00 0.25 0.50 C 0.00 9.791475497647290638 +50.00 41.25 0.0275 0.00 0.25 1.00 C 0.00 11.030984382704700053 +50.00 50.00 0.0275 0.00 0.25 0.10 C 0.00 1.643991662940700094 +50.00 50.00 0.0275 0.00 0.25 0.50 C 0.00 3.849497376326850073 +50.00 50.00 0.0275 0.00 0.25 1.00 C 0.00 5.613991528503190054 +50.00 60.75 0.0275 0.00 0.25 0.10 C 0.00 0.010849363947345101 +50.00 60.75 0.0275 0.00 0.25 0.50 C 0.00 0.768274495718032968 +50.00 60.75 0.0275 0.00 0.25 1.00 C 0.00 2.036957925438520167 +50.00 41.25 0.0275 0.00 0.50 0.10 C 0.00 9.237479294160509724 +50.00 41.25 0.0275 0.00 0.50 0.50 C 0.00 12.055228107416699146 +50.00 41.25 0.0275 0.00 0.50 1.00 C 0.00 14.655915985561399850 +50.00 50.00 0.0275 0.00 0.50 0.10 C 0.00 3.215441945855579853 +50.00 50.00 0.0275 0.00 0.50 0.50 C 0.00 7.314515972125059662 +50.00 50.00 0.0275 0.00 0.50 1.00 C 0.00 10.429305262473400617 +50.00 60.75 0.0275 0.00 0.50 0.10 C 0.00 0.473089228156816977 +50.00 60.75 0.0275 0.00 0.50 0.50 C 0.00 3.727049105818879937 +50.00 60.75 0.0275 0.00 0.50 1.00 C 0.00 6.800854032435259988 +50.00 41.25 0.0275 0.00 0.10 0.10 P 0.00 0.000000000074528552 +50.00 41.25 0.0275 0.00 0.10 0.50 P 0.00 0.001638760059608080 +50.00 41.25 0.0275 0.00 0.10 1.00 P 0.00 0.021948625635337300 +50.00 50.00 0.0275 0.00 0.10 0.10 P 0.00 0.563614645406108949 +50.00 50.00 0.0275 0.00 0.10 0.50 P 0.00 1.085535957715130007 +50.00 50.00 0.0275 0.00 0.10 1.00 P 0.00 1.362542567359269929 +50.00 60.75 0.0275 0.00 0.10 0.10 P 0.00 10.583167000684699843 +50.00 60.75 0.0275 0.00 0.10 0.50 P 0.00 9.926837920803579962 +50.00 60.75 0.0275 0.00 0.10 1.00 P 0.00 9.208327279989029890 +50.00 41.25 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0.25 0.50 C 0.00 8.260004605682269130 +100.00 100.00 0.0500 0.00 0.25 1.00 C 0.00 12.335986235067199601 +100.00 110.00 0.0500 0.00 0.25 0.10 C 0.00 0.521347622182002035 +100.00 110.00 0.0500 0.00 0.25 0.50 C 0.00 4.225788960901319946 +100.00 110.00 0.0500 0.00 0.25 1.00 C 0.00 8.026371324891460546 +100.00 90.00 0.0500 0.00 0.50 0.10 C 0.00 12.590255331551100326 +100.00 90.00 0.0500 0.00 0.50 0.50 C 0.00 20.159976068200698762 +100.00 90.00 0.0500 0.00 0.50 1.00 C 0.00 26.372713127990198956 +100.00 100.00 0.0500 0.00 0.50 0.10 C 0.00 6.538072233170310277 +100.00 100.00 0.0500 0.00 0.50 0.50 C 0.00 15.127170180011800582 +100.00 100.00 0.0500 0.00 0.50 1.00 C 0.00 21.792596179591701144 +100.00 110.00 0.0500 0.00 0.50 0.10 C 0.00 2.918389335831479858 +100.00 110.00 0.0500 0.00 0.50 0.50 C 0.00 11.184108264097899266 +100.00 110.00 0.0500 0.00 0.50 1.00 C 0.00 17.962314921602001050 +100.00 90.00 0.0500 0.00 0.10 0.10 P 0.00 0.000181894142655793 +100.00 90.00 0.0500 0.00 0.10 0.50 P 0.00 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0.00 3.402481484014360014 +50.00 60.75 0.0500 0.00 0.10 0.10 C 0.00 0.000000000268144541 +50.00 60.75 0.0500 0.00 0.10 0.50 C 0.00 0.010446869804788600 +50.00 60.75 0.0500 0.00 0.10 1.00 C 0.00 0.177236149710852997 +50.00 41.25 0.0500 0.00 0.25 0.10 C 0.00 8.962983694922849409 +50.00 41.25 0.0500 0.00 0.25 0.50 C 0.00 10.185792986779500069 +50.00 41.25 0.0500 0.00 0.25 1.00 C 0.00 11.734445815449900508 +50.00 50.00 0.0500 0.00 0.25 0.10 C 0.00 1.700446917848839945 +50.00 50.00 0.0500 0.00 0.25 0.50 C 0.00 4.130002302841130124 +50.00 50.00 0.0500 0.00 0.25 1.00 C 0.00 6.167993117533580261 +50.00 60.75 0.0500 0.00 0.25 0.10 C 0.00 0.011811829287480400 +50.00 60.75 0.0500 0.00 0.25 0.50 C 0.00 0.862122715911548987 +50.00 60.75 0.0500 0.00 0.25 1.00 C 0.00 2.335403007584940127 +50.00 41.25 0.0500 0.00 0.50 0.10 C 0.00 9.318598550815249126 +50.00 41.25 0.0500 0.00 0.50 0.50 C 0.00 12.357234669808299543 +50.00 41.25 0.0500 0.00 0.50 1.00 C 0.00 15.177352941362299177 +50.00 50.00 0.0500 0.00 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0.10 C 0.00 0.000000000418787169 +50.00 60.75 0.0725 0.00 0.10 0.50 C 0.00 0.016602183429001501 +50.00 60.75 0.0725 0.00 0.10 1.00 C 0.00 0.284483121731958999 +50.00 41.25 0.0725 0.00 0.25 0.10 C 0.00 9.054608341813459305 +50.00 41.25 0.0725 0.00 0.25 0.50 C 0.00 10.581658197115100251 +50.00 41.25 0.0725 0.00 0.25 1.00 C 0.00 12.444199535517000754 +50.00 50.00 0.0725 0.00 0.25 0.10 C 0.00 1.758043269189839997 +50.00 50.00 0.0725 0.00 0.25 0.50 C 0.00 4.421199991473709900 +50.00 50.00 0.0725 0.00 0.25 1.00 C 0.00 6.747538876737840141 +50.00 60.75 0.0725 0.00 0.25 0.10 C 0.00 0.012850834682157100 +50.00 60.75 0.0725 0.00 0.25 0.50 C 0.00 0.964632352153436012 +50.00 60.75 0.0725 0.00 0.25 1.00 C 0.00 2.663220686150450156 +50.00 41.25 0.0725 0.00 0.50 0.10 C 0.00 9.399799864285059314 +50.00 41.25 0.0725 0.00 0.50 0.50 C 0.00 12.661052853996299206 +50.00 41.25 0.0725 0.00 0.50 1.00 C 0.00 15.702432182518300863 +50.00 50.00 0.0725 0.00 0.50 0.10 C 0.00 3.323143479821729862 +50.00 50.00 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9.047981013637180325 +50.00 41.25 0.0725 0.00 0.10 0.50 C 0.00 10.219050011000600620 +50.00 41.25 0.0725 0.00 0.10 1.00 C 0.00 11.640265602712700499 +50.00 50.00 0.0725 0.00 0.10 0.10 C 0.00 0.825516063236723996 +50.00 50.00 0.0725 0.00 0.10 0.50 C 0.00 2.453126785293899825 +50.00 50.00 0.0725 0.00 0.10 1.00 C 0.00 4.156504194469899716 +50.00 60.75 0.0725 0.00 0.10 0.10 C 0.00 0.000000000418787169 +50.00 60.75 0.0725 0.00 0.10 0.50 C 0.00 0.016602183429001501 +50.00 60.75 0.0725 0.00 0.10 1.00 C 0.00 0.284483121731958999 +50.00 41.25 0.0725 0.00 0.25 0.10 C 0.00 9.054608341813459305 +50.00 41.25 0.0725 0.00 0.25 0.50 C 0.00 10.581658197115100251 +50.00 41.25 0.0725 0.00 0.25 1.00 C 0.00 12.444199535517000754 +50.00 50.00 0.0725 0.00 0.25 0.10 C 0.00 1.758043269189839997 +50.00 50.00 0.0725 0.00 0.25 0.50 C 0.00 4.421199991473709900 +50.00 50.00 0.0725 0.00 0.25 1.00 C 0.00 6.747538876737840141 +50.00 60.75 0.0725 0.00 0.25 0.10 C 0.00 0.012850834682157100 +50.00 60.75 0.0725 0.00 0.25 0.50 C 0.00 0.964632352153436012 +50.00 60.75 0.0725 0.00 0.25 1.00 C 0.00 2.663220686150450156 +50.00 41.25 0.0725 0.00 0.50 0.10 C 0.00 9.399799864285059314 +50.00 41.25 0.0725 0.00 0.50 0.50 C 0.00 12.661052853996299206 +50.00 41.25 0.0725 0.00 0.50 1.00 C 0.00 15.702432182518300863 +50.00 50.00 0.0725 0.00 0.50 0.10 C 0.00 3.323143479821729862 +50.00 50.00 0.0725 0.00 0.50 0.50 C 0.00 7.816753477155890195 +50.00 50.00 0.0725 0.00 0.50 1.00 C 0.00 11.371682397803500209 +50.00 60.75 0.0725 0.00 0.50 0.10 C 0.00 0.500408614730963985 +50.00 60.75 0.0725 0.00 0.50 0.50 C 0.00 4.067835234635260200 +50.00 60.75 0.0725 0.00 0.50 1.00 C 0.00 7.567318237821569760 +50.00 41.25 0.0725 0.00 0.10 0.10 P 0.00 0.000000000029292149 +50.00 41.25 0.0725 0.00 0.10 0.50 P 0.00 0.000515507530913631 +50.00 41.25 0.0725 0.00 0.10 1.00 P 0.00 0.005477652449141430 +50.00 50.00 0.0725 0.00 0.10 0.10 P 0.00 0.464326955833211985 +50.00 50.00 0.0725 0.00 0.10 0.50 P 0.00 0.673084962906373985 +50.00 50.00 0.0725 0.00 0.10 1.00 P 0.00 0.659791527483822970 +50.00 60.75 0.0725 0.00 0.10 0.10 P 0.00 10.311155234923500501 +50.00 60.75 0.0725 0.00 0.10 0.50 P 0.00 8.603851369228159740 +50.00 60.75 0.0725 0.00 0.10 1.00 P 0.00 6.785977231343879978 +50.00 41.25 0.0725 0.00 0.25 0.10 P 0.00 0.006627328205560570 +50.00 41.25 0.0725 0.00 0.25 0.50 P 0.00 0.363123693645392986 +50.00 41.25 0.0725 0.00 0.25 1.00 P 0.00 0.809411585253517973 +50.00 50.00 0.0725 0.00 0.25 0.10 P 0.00 1.396854161786329929 +50.00 50.00 0.0725 0.00 0.25 0.50 P 0.00 2.641158169086189833 +50.00 50.00 0.0725 0.00 0.25 1.00 P 0.00 3.250826209751759954 +50.00 60.75 0.0725 0.00 0.25 0.10 P 0.00 10.324006069186900447 +50.00 60.75 0.0725 0.00 0.25 0.50 P 0.00 9.551881537952599643 +50.00 60.75 0.0725 0.00 0.25 1.00 P 0.00 9.164714795762359145 +50.00 41.25 0.0725 0.00 0.50 0.10 P 0.00 0.351818850677170003 +50.00 41.25 0.0725 0.00 0.50 0.50 P 0.00 2.442518350526630133 +50.00 41.25 0.0725 0.00 0.50 1.00 P 0.00 4.067644232254740366 +50.00 50.00 0.0725 0.00 0.50 0.10 P 0.00 2.961954372418219794 +50.00 50.00 0.0725 0.00 0.50 0.50 P 0.00 6.036711654768369684 +50.00 50.00 0.0725 0.00 0.50 1.00 P 0.00 7.874969730817450220 +50.00 60.75 0.0725 0.00 0.50 0.10 P 0.00 10.811563849235700019 +50.00 60.75 0.0725 0.00 0.50 0.50 P 0.00 12.655084420434400627 +50.00 60.75 0.0725 0.00 0.50 1.00 P 0.00 14.068812347433500065 +100.00 90.00 0.0825 0.00 0.10 0.10 C 0.00 10.739565764427599248 +100.00 90.00 0.0825 0.00 0.10 0.50 C 0.00 13.682682955061700625 +100.00 90.00 0.0825 0.00 0.10 1.00 C 0.00 17.233234434950201575 +100.00 100.00 0.0825 0.00 0.10 0.10 C 0.00 1.709643173779020087 +100.00 100.00 0.0825 0.00 0.10 0.50 C 0.00 5.240956408279039636 +100.00 100.00 0.0825 0.00 0.10 1.00 C 0.00 9.021567470247120468 +100.00 110.00 0.0825 0.00 0.10 0.10 C 0.00 0.002938681227336320 +100.00 110.00 0.0825 0.00 0.10 0.50 C 0.00 0.928877789383869001 +100.00 110.00 0.0825 0.00 0.10 1.00 C 0.00 3.401688909911659842 +100.00 90.00 0.0825 0.00 0.25 0.10 C 0.00 10.991579413464499737 +100.00 90.00 0.0825 0.00 0.25 0.50 C 0.00 15.507256193857399396 +100.00 90.00 0.0825 0.00 0.25 1.00 C 0.00 20.091308227254799590 +100.00 100.00 0.0825 0.00 0.25 0.10 C 0.00 3.568013775180880032 +100.00 100.00 0.0825 0.00 0.25 0.50 C 0.00 9.107927694355590020 +100.00 100.00 0.0825 0.00 0.25 1.00 C 0.00 14.025694755963399984 +100.00 110.00 0.0825 0.00 0.25 0.10 C 0.00 0.564947997341127994 +100.00 110.00 0.0825 0.00 0.25 0.50 C 0.00 4.796306777823869716 +100.00 110.00 0.0825 0.00 0.25 1.00 C 0.00 9.380215666129899432 +100.00 90.00 0.0825 0.00 0.50 0.10 C 0.00 12.803934625179900664 +100.00 90.00 0.0825 0.00 0.50 0.50 C 0.00 20.987751407192000386 +100.00 90.00 0.0825 0.00 0.50 1.00 C 0.00 27.842982610886100048 +100.00 100.00 0.0825 0.00 0.50 0.10 C 0.00 6.694710681788889950 +100.00 100.00 0.0825 0.00 0.50 0.50 C 0.00 15.861123252603299250 +100.00 100.00 0.0825 0.00 0.50 1.00 C 0.00 23.171055823976999477 +100.00 110.00 0.0825 0.00 0.50 0.10 C 0.00 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0.50 P 0.00 0.000515507530913631 +50.00 41.25 0.0725 0.00 0.10 1.00 P 0.00 0.005477652449141430 +50.00 50.00 0.0725 0.00 0.10 0.10 P 0.00 0.464326955833211985 +50.00 50.00 0.0725 0.00 0.10 0.50 P 0.00 0.673084962906373985 +50.00 50.00 0.0725 0.00 0.10 1.00 P 0.00 0.659791527483822970 +50.00 60.75 0.0725 0.00 0.10 0.10 P 0.00 10.311155234923500501 +50.00 60.75 0.0725 0.00 0.10 0.50 P 0.00 8.603851369228159740 +50.00 60.75 0.0725 0.00 0.10 1.00 P 0.00 6.785977231343879978 +50.00 41.25 0.0725 0.00 0.25 0.10 P 0.00 0.006627328205560570 +50.00 41.25 0.0725 0.00 0.25 0.50 P 0.00 0.363123693645392986 +50.00 41.25 0.0725 0.00 0.25 1.00 P 0.00 0.809411585253517973 +50.00 50.00 0.0725 0.00 0.25 0.10 P 0.00 1.396854161786329929 +50.00 50.00 0.0725 0.00 0.25 0.50 P 0.00 2.641158169086189833 +50.00 50.00 0.0725 0.00 0.25 1.00 P 0.00 3.250826209751759954 +50.00 60.75 0.0725 0.00 0.25 0.10 P 0.00 10.324006069186900447 +50.00 60.75 0.0725 0.00 0.25 0.50 P 0.00 9.551881537952599643 +50.00 60.75 0.0725 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110.00 0.0275 0.00 0.25 0.50 P 0.00 12.356772586106300693 +100.00 110.00 0.0275 0.00 0.25 1.00 P 0.00 14.179047623065599737 +100.00 90.00 0.0275 0.00 0.50 0.10 P 0.00 2.195910130101800029 +100.00 90.00 0.0275 0.00 0.50 0.50 P 0.00 8.365036593949600530 +100.00 90.00 0.0275 0.00 0.50 1.00 P 0.00 12.927769915151500868 +100.00 100.00 0.0275 0.00 0.50 0.10 P 0.00 6.156261670334750136 +100.00 100.00 0.0275 0.00 0.50 0.50 P 0.00 13.263441890954499769 +100.00 100.00 0.0275 0.00 0.50 1.00 P 0.00 18.146078780292199895 +100.00 110.00 0.0275 0.00 0.50 0.10 P 0.00 12.553317450904199148 +100.00 110.00 0.0275 0.00 0.50 0.50 P 0.00 19.259946644121601622 +100.00 110.00 0.0275 0.00 0.50 1.00 P 0.00 24.125579331848300058 +50.00 41.25 0.0275 0.00 0.10 0.10 C 0.00 8.863281666392300195 +50.00 41.25 0.0275 0.00 0.10 0.50 C 0.00 9.314944657044039289 +50.00 41.25 0.0275 0.00 0.10 1.00 C 0.00 9.890867970305359691 +50.00 50.00 0.0275 0.00 0.10 0.10 C 0.00 0.700925756094316954 +50.00 50.00 0.0275 0.00 0.10 0.50 C 0.00 1.768330984362940006 +50.00 50.00 0.0275 0.00 0.10 1.00 C 0.00 2.718808439686569933 +50.00 60.75 0.0275 0.00 0.10 0.10 C 0.00 0.000000000170861147 +50.00 60.75 0.0275 0.00 0.10 0.50 C 0.00 0.006433878180657690 +50.00 60.75 0.0275 0.00 0.10 1.00 C 0.00 0.106190314866699997 +50.00 41.25 0.0275 0.00 0.25 0.10 C 0.00 8.871203986520360019 +50.00 41.25 0.0275 0.00 0.25 0.50 C 0.00 9.791475497647290638 +50.00 41.25 0.0275 0.00 0.25 1.00 C 0.00 11.030984382704700053 +50.00 50.00 0.0275 0.00 0.25 0.10 C 0.00 1.643991662940700094 +50.00 50.00 0.0275 0.00 0.25 0.50 C 0.00 3.849497376326850073 +50.00 50.00 0.0275 0.00 0.25 1.00 C 0.00 5.613991528503190054 +50.00 60.75 0.0275 0.00 0.25 0.10 C 0.00 0.010849363947345101 +50.00 60.75 0.0275 0.00 0.25 0.50 C 0.00 0.768274495718032968 +50.00 60.75 0.0275 0.00 0.25 1.00 C 0.00 2.036957925438520167 +50.00 41.25 0.0275 0.00 0.50 0.10 C 0.00 9.237479294160509724 +50.00 41.25 0.0275 0.00 0.50 0.50 C 0.00 12.055228107416699146 +50.00 41.25 0.0275 0.00 0.50 1.00 C 0.00 14.655915985561399850 +50.00 50.00 0.0275 0.00 0.50 0.10 C 0.00 3.215441945855579853 +50.00 50.00 0.0275 0.00 0.50 0.50 C 0.00 7.314515972125059662 +50.00 50.00 0.0275 0.00 0.50 1.00 C 0.00 10.429305262473400617 +50.00 60.75 0.0275 0.00 0.50 0.10 C 0.00 0.473089228156816977 +50.00 60.75 0.0275 0.00 0.50 0.50 C 0.00 3.727049105818879937 +50.00 60.75 0.0275 0.00 0.50 1.00 C 0.00 6.800854032435259988 +50.00 41.25 0.0275 0.00 0.10 0.10 P 0.00 0.000000000074528552 +50.00 41.25 0.0275 0.00 0.10 0.50 P 0.00 0.001638760059608080 +50.00 41.25 0.0275 0.00 0.10 1.00 P 0.00 0.021948625635337300 +50.00 50.00 0.0275 0.00 0.10 0.10 P 0.00 0.563614645406108949 +50.00 50.00 0.0275 0.00 0.10 0.50 P 0.00 1.085535957715130007 +50.00 50.00 0.0275 0.00 0.10 1.00 P 0.00 1.362542567359269929 +50.00 60.75 0.0275 0.00 0.10 0.10 P 0.00 10.583167000684699843 +50.00 60.75 0.0275 0.00 0.10 0.50 P 0.00 9.926837920803579962 +50.00 60.75 0.0275 0.00 0.10 1.00 P 0.00 9.208327279989029890 +50.00 41.25 0.0275 0.00 0.25 0.10 P 0.00 0.007922320202584000 +50.00 41.25 0.0275 0.00 0.25 0.50 P 0.00 0.478169600662851024 +50.00 41.25 0.0275 0.00 0.25 1.00 P 0.00 1.162065038034679976 +50.00 50.00 0.0275 0.00 0.25 0.10 P 0.00 1.506680552252489980 +50.00 50.00 0.0275 0.00 0.25 0.50 P 0.00 3.166702349679050066 +50.00 50.00 0.0275 0.00 0.25 1.00 P 0.00 4.257725656175890272 +50.00 60.75 0.0275 0.00 0.25 0.10 P 0.00 10.594016364461200652 +50.00 60.75 0.0275 0.00 0.25 0.50 P 0.00 10.688678538340999680 +50.00 60.75 0.0275 0.00 0.25 1.00 P 0.00 11.139094890560899742 +50.00 41.25 0.0275 0.00 0.50 0.10 P 0.00 0.374197627842735026 +50.00 41.25 0.0275 0.00 0.50 0.50 P 0.00 2.741922210432270024 +50.00 41.25 0.0275 0.00 0.50 1.00 P 0.00 4.786996640891410415 +50.00 50.00 0.0275 0.00 0.50 0.10 P 0.00 3.078130835167379953 +50.00 50.00 0.0275 0.00 0.50 0.50 P 0.00 6.631720945477259654 +50.00 50.00 0.0275 0.00 0.50 1.00 P 0.00 9.073039390146110605 +50.00 60.75 0.0275 0.00 0.50 0.10 P 0.00 11.056256228670600095 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0.25 0.50 C 0.00 8.260004605682269130 +100.00 100.00 0.0500 0.00 0.25 1.00 C 0.00 12.335986235067199601 +100.00 110.00 0.0500 0.00 0.25 0.10 C 0.00 0.521347622182002035 +100.00 110.00 0.0500 0.00 0.25 0.50 C 0.00 4.225788960901319946 +100.00 110.00 0.0500 0.00 0.25 1.00 C 0.00 8.026371324891460546 +100.00 90.00 0.0500 0.00 0.50 0.10 C 0.00 12.590255331551100326 +100.00 90.00 0.0500 0.00 0.50 0.50 C 0.00 20.159976068200698762 +100.00 90.00 0.0500 0.00 0.50 1.00 C 0.00 26.372713127990198956 +100.00 100.00 0.0500 0.00 0.50 0.10 C 0.00 6.538072233170310277 +100.00 100.00 0.0500 0.00 0.50 0.50 C 0.00 15.127170180011800582 +100.00 100.00 0.0500 0.00 0.50 1.00 C 0.00 21.792596179591701144 +100.00 110.00 0.0500 0.00 0.50 0.10 C 0.00 2.918389335831479858 +100.00 110.00 0.0500 0.00 0.50 0.50 C 0.00 11.184108264097899266 +100.00 110.00 0.0500 0.00 0.50 1.00 C 0.00 17.962314921602001050 +100.00 90.00 0.0500 0.00 0.10 0.10 P 0.00 0.000181894142655793 +100.00 90.00 0.0500 0.00 0.10 0.50 P 0.00 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110.00 0.0500 0.00 0.25 1.00 P 0.00 12.661608019970000072 +100.00 90.00 0.0500 0.00 0.50 0.10 P 0.00 2.141378458892469805 +100.00 90.00 0.0500 0.00 0.50 0.50 P 0.00 7.937868150750600371 +100.00 90.00 0.0500 0.00 0.50 1.00 P 0.00 11.983361333054400433 +100.00 100.00 0.0500 0.00 0.50 0.10 P 0.00 6.039320152438549805 +100.00 100.00 0.0500 0.00 0.50 0.50 P 0.00 12.658161382844999920 +100.00 100.00 0.0500 0.00 0.50 1.00 P 0.00 16.915538629663100068 +100.00 110.00 0.0500 0.00 0.50 0.10 P 0.00 12.369762047026499729 +100.00 110.00 0.0500 0.00 0.50 0.50 P 0.00 18.468198587214498474 +100.00 110.00 0.0500 0.00 0.50 1.00 P 0.00 22.597551616680501496 +50.00 41.25 0.0500 0.00 0.10 0.10 C 0.00 8.955735233348690372 +50.00 41.25 0.0500 0.00 0.10 0.50 C 0.00 9.769395612888869707 +50.00 41.25 0.0500 0.00 0.10 1.00 C 0.00 10.772989650176100440 +50.00 50.00 0.0500 0.00 0.10 0.10 C 0.00 0.761718356843805955 +50.00 50.00 0.0500 0.00 0.10 0.50 C 0.00 2.096135555366939851 +50.00 50.00 0.0500 0.00 0.10 1.00 C 0.00 3.402481484014360014 +50.00 60.75 0.0500 0.00 0.10 0.10 C 0.00 0.000000000268144541 +50.00 60.75 0.0500 0.00 0.10 0.50 C 0.00 0.010446869804788600 +50.00 60.75 0.0500 0.00 0.10 1.00 C 0.00 0.177236149710852997 +50.00 41.25 0.0500 0.00 0.25 0.10 C 0.00 8.962983694922849409 +50.00 41.25 0.0500 0.00 0.25 0.50 C 0.00 10.185792986779500069 +50.00 41.25 0.0500 0.00 0.25 1.00 C 0.00 11.734445815449900508 +50.00 50.00 0.0500 0.00 0.25 0.10 C 0.00 1.700446917848839945 +50.00 50.00 0.0500 0.00 0.25 0.50 C 0.00 4.130002302841130124 +50.00 50.00 0.0500 0.00 0.25 1.00 C 0.00 6.167993117533580261 +50.00 60.75 0.0500 0.00 0.25 0.10 C 0.00 0.011811829287480400 +50.00 60.75 0.0500 0.00 0.25 0.50 C 0.00 0.862122715911548987 +50.00 60.75 0.0500 0.00 0.25 1.00 C 0.00 2.335403007584940127 +50.00 41.25 0.0500 0.00 0.50 0.10 C 0.00 9.318598550815249126 +50.00 41.25 0.0500 0.00 0.50 0.50 C 0.00 12.357234669808299543 +50.00 41.25 0.0500 0.00 0.50 1.00 C 0.00 15.177352941362299177 +50.00 50.00 0.0500 0.00 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9.047981013637180325 +50.00 41.25 0.0725 0.00 0.10 0.50 C 0.00 10.219050011000600620 +50.00 41.25 0.0725 0.00 0.10 1.00 C 0.00 11.640265602712700499 +50.00 50.00 0.0725 0.00 0.10 0.10 C 0.00 0.825516063236723996 +50.00 50.00 0.0725 0.00 0.10 0.50 C 0.00 2.453126785293899825 +50.00 50.00 0.0725 0.00 0.10 1.00 C 0.00 4.156504194469899716 +50.00 60.75 0.0725 0.00 0.10 0.10 C 0.00 0.000000000418787169 +50.00 60.75 0.0725 0.00 0.10 0.50 C 0.00 0.016602183429001501 +50.00 60.75 0.0725 0.00 0.10 1.00 C 0.00 0.284483121731958999 +50.00 41.25 0.0725 0.00 0.25 0.10 C 0.00 9.054608341813459305 +50.00 41.25 0.0725 0.00 0.25 0.50 C 0.00 10.581658197115100251 +50.00 41.25 0.0725 0.00 0.25 1.00 C 0.00 12.444199535517000754 +50.00 50.00 0.0725 0.00 0.25 0.10 C 0.00 1.758043269189839997 +50.00 50.00 0.0725 0.00 0.25 0.50 C 0.00 4.421199991473709900 +50.00 50.00 0.0725 0.00 0.25 1.00 C 0.00 6.747538876737840141 +50.00 60.75 0.0725 0.00 0.25 0.10 C 0.00 0.012850834682157100 +50.00 60.75 0.0725 0.00 0.25 0.50 C 0.00 0.964632352153436012 +50.00 60.75 0.0725 0.00 0.25 1.00 C 0.00 2.663220686150450156 +50.00 41.25 0.0725 0.00 0.50 0.10 C 0.00 9.399799864285059314 +50.00 41.25 0.0725 0.00 0.50 0.50 C 0.00 12.661052853996299206 +50.00 41.25 0.0725 0.00 0.50 1.00 C 0.00 15.702432182518300863 +50.00 50.00 0.0725 0.00 0.50 0.10 C 0.00 3.323143479821729862 +50.00 50.00 0.0725 0.00 0.50 0.50 C 0.00 7.816753477155890195 +50.00 50.00 0.0725 0.00 0.50 1.00 C 0.00 11.371682397803500209 +50.00 60.75 0.0725 0.00 0.50 0.10 C 0.00 0.500408614730963985 +50.00 60.75 0.0725 0.00 0.50 0.50 C 0.00 4.067835234635260200 +50.00 60.75 0.0725 0.00 0.50 1.00 C 0.00 7.567318237821569760 +50.00 41.25 0.0725 0.00 0.10 0.10 P 0.00 0.000000000029292149 +50.00 41.25 0.0725 0.00 0.10 0.50 P 0.00 0.000515507530913631 +50.00 41.25 0.0725 0.00 0.10 1.00 P 0.00 0.005477652449141430 +50.00 50.00 0.0725 0.00 0.10 0.10 P 0.00 0.464326955833211985 +50.00 50.00 0.0725 0.00 0.10 0.50 P 0.00 0.673084962906373985 +50.00 50.00 0.0725 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0.00 10.991579413464499737 +100.00 90.00 0.0825 0.00 0.25 0.50 C 0.00 15.507256193857399396 +100.00 90.00 0.0825 0.00 0.25 1.00 C 0.00 20.091308227254799590 +100.00 100.00 0.0825 0.00 0.25 0.10 C 0.00 3.568013775180880032 +100.00 100.00 0.0825 0.00 0.25 0.50 C 0.00 9.107927694355590020 +100.00 100.00 0.0825 0.00 0.25 1.00 C 0.00 14.025694755963399984 +100.00 110.00 0.0825 0.00 0.25 0.10 C 0.00 0.564947997341127994 +100.00 110.00 0.0825 0.00 0.25 0.50 C 0.00 4.796306777823869716 +100.00 110.00 0.0825 0.00 0.25 1.00 C 0.00 9.380215666129899432 +100.00 90.00 0.0825 0.00 0.50 0.10 C 0.00 12.803934625179900664 +100.00 90.00 0.0825 0.00 0.50 0.50 C 0.00 20.987751407192000386 +100.00 90.00 0.0825 0.00 0.50 1.00 C 0.00 27.842982610886100048 +100.00 100.00 0.0825 0.00 0.50 0.10 C 0.00 6.694710681788889950 +100.00 100.00 0.0825 0.00 0.50 0.50 C 0.00 15.861123252603299250 +100.00 100.00 0.0825 0.00 0.50 1.00 C 0.00 23.171055823976999477 +100.00 110.00 0.0825 0.00 0.50 0.10 C 0.00 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0.50 C 0.00 10.417339221247599923 +50.00 41.25 0.0825 0.00 0.10 1.00 C 0.00 12.020458260573199993 +50.00 50.00 0.0825 0.00 0.10 0.10 C 0.00 0.854821586889512042 +50.00 50.00 0.0825 0.00 0.10 0.50 C 0.00 2.620478204139519818 +50.00 50.00 0.0825 0.00 0.10 1.00 C 0.00 4.510783735123560234 +50.00 60.75 0.0825 0.00 0.10 0.10 C 0.00 0.000000000509770462 +50.00 60.75 0.0825 0.00 0.10 0.50 C 0.00 0.020258714482434301 +50.00 60.75 0.0825 0.00 0.10 1.00 C 0.00 0.346802700406623976 +50.00 41.25 0.0825 0.00 0.25 0.10 C 0.00 9.095279779656779695 +50.00 41.25 0.0825 0.00 0.25 0.50 C 0.00 10.757961410313800599 +50.00 41.25 0.0825 0.00 0.25 1.00 C 0.00 12.761066081739599554 +50.00 50.00 0.0825 0.00 0.25 0.10 C 0.00 1.784006887590440016 +50.00 50.00 0.0825 0.00 0.25 0.50 C 0.00 4.553963847177789681 +50.00 50.00 0.0825 0.00 0.25 1.00 C 0.00 7.012847377981679564 +50.00 60.75 0.0825 0.00 0.25 0.10 C 0.00 0.013338549021010599 +50.00 60.75 0.0825 0.00 0.25 0.50 C 0.00 1.013087068903510080 +50.00 60.75 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0.35 P 0.00 11.317468853380699301 +50.00 60.75 0.0275 0.00 0.45 0.40 P 0.00 12.513285685081099174 +50.00 60.75 0.0275 0.00 0.65 0.75 P 0.00 17.450036828799401434 +50.00 60.75 0.0275 0.00 0.25 0.25 P 0.00 10.533352432665900267 +50.00 60.75 0.0275 0.00 0.35 0.35 P 0.00 11.317468853380699301 +50.00 60.75 0.0275 0.00 0.45 0.40 P 0.00 12.513285685081099174 +100.00 110.00 0.1000 0.00 0.25 0.50 C 0.00 5.123575416865319809 +100.00 110.00 0.1000 0.00 0.25 1.00 C 0.00 10.160055944516599880 +100.00 90.00 0.1000 0.00 0.50 0.10 C 0.00 12.919509619564699676 +100.00 90.00 0.1000 0.00 0.50 0.50 C 0.00 21.438280655724401669 +100.00 90.00 0.1000 0.00 0.50 1.00 C 0.00 28.643647264488201643 +100.00 100.00 0.1000 0.00 0.50 0.10 C 0.00 6.779936664291260406 +100.00 100.00 0.1000 0.00 0.50 0.50 C 0.00 16.263193147074300526 +100.00 100.00 0.1000 0.00 0.50 1.00 C 0.00 23.926745214162700393 +100.00 110.00 0.1000 0.00 0.50 0.10 C 0.00 3.061909566605539812 +100.00 110.00 0.1000 0.00 0.50 0.50 C 0.00 12.155688815568700178 +100.00 110.00 0.1000 0.00 0.50 1.00 C 0.00 19.929858372066298955 +100.00 90.00 0.1000 0.00 0.10 0.10 P 0.00 0.000095752219082624 +100.00 90.00 0.1000 0.00 0.10 0.50 P 0.00 0.032219033907538303 +100.00 90.00 0.1000 0.00 0.10 1.00 P 0.00 0.066226743903883001 +100.00 100.00 0.1000 0.00 0.10 0.10 P 0.00 0.819967493295226002 +100.00 100.00 0.1000 0.00 0.10 0.50 P 0.00 0.973216054356396021 +100.00 100.00 0.1000 0.00 0.10 1.00 P 0.00 0.791889047262799961 +100.00 110.00 0.1000 0.00 0.10 0.10 P 0.00 8.909004787274069415 +100.00 110.00 0.1000 0.00 0.10 0.50 P 0.00 5.775959538905960144 +100.00 110.00 0.1000 0.00 0.10 1.00 P 0.00 3.748863004264400001 diff --git a/constantine/platforms/threadpool/benchmarks/black_scholes/threadpool_black_scholes.nim b/constantine/platforms/threadpool/benchmarks/black_scholes/threadpool_black_scholes.nim new file mode 100644 index 0000000..07bc4b3 --- /dev/null +++ b/constantine/platforms/threadpool/benchmarks/black_scholes/threadpool_black_scholes.nim @@ -0,0 +1,372 @@ +# Weave +# Copyright (c) 2019 Mamy André-Ratsimbazafy +# Licensed and distributed under either of +# * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT). +# * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0). +# at your option. This file may not be copied, modified, or distributed except according to those terms. + +# Reference implementation from +# // Copyright (c) 2007 Intel Corp. +# +# // Black-Scholes +# // Analytical method for calculating European Options +# // +# // +# // Reference Source: Options, Futures, and Other Derivatives, 3rd Edition, Prentice +# // Hall, John C. Hull, +# +# File manipulation routines ported from C++-Taskflow + +import + # Stdlib + system/ansi_c, std/[strformat, os, strutils, math, cpuinfo, streams, strscans], + # Constantine + ../../threadpool + +when defined(linux): + # bench + import ../wtime, ../resources + +# Types +# -------------------------------- + +type + OptionKind = enum + Put + Call + + OptionData[T: SomeFloat] = object + spot: T # Spot price + strike: T # Strike price + riskfree: T # risk-free rate + divrate: T # dividend rate + vol: T # volatility + expiry: T # expiry to maturity or option expiration in years + # (1 year = 1.0, 6 months = 0.5) + kind: OptionKind + divvals: T # Dividend values (not used in this test) + dgrefval: T # DerivaGem reference value + + Context[T: SomeFloat] = object + data: ptr UncheckedArray[OptionData[T]] + prices: ptr UncheckedArray[T] + numOptions: int + numRuns: int + + otype: ptr UncheckedArray[OptionKind] + spot: ptr UncheckedArray[T] + strike: ptr UncheckedArray[T] + riskFreeRate: ptr UncheckedArray[T] + volatility: ptr UncheckedArray[T] + expiry: ptr UncheckedArray[T] + numErrors: int + +# Helpers +# --------------------------------------------------- + +proc wv_alloc*(T: typedesc): ptr T {.inline.}= + ## Default allocator for the Picasso library + ## This allocates memory to hold the type T + ## and returns a pointer to it + ## + ## Can use Nim allocator to measure the overhead of its lock + ## Memory is not zeroed + when defined(WV_useNimAlloc): + createSharedU(T) + else: + cast[ptr T](c_malloc(csize_t sizeof(T))) + +proc wv_alloc*(T: typedesc, len: SomeInteger): ptr UncheckedArray[T] {.inline.} = + ## Default allocator for the Picasso library. + ## This allocates a contiguous chunk of memory + ## to hold ``len`` elements of type T + ## and returns a pointer to it. + ## + ## Can use Nim allocator to measure the overhead of its lock + ## Memory is not zeroed + when defined(WV_useNimAlloc): + cast[type result](createSharedU(T, len)) + else: + cast[type result](c_malloc(csize_t len*sizeof(T))) + +proc wv_free*[T: ptr](p: T) {.inline.} = + when defined(WV_useNimAlloc): + freeShared(p) + else: + c_free(p) + +proc initialize[T](ctx: var Context[T], numOptions: int) = + ctx.numOptions = numOptions + + ctx.data = wv_alloc(OptionData[T], numOptions) + ctx.prices = wv_alloc(T, numOptions) + ctx.otype = wv_alloc(OptionKind, numOptions) + ctx.spot = wv_alloc(T, numOptions) + ctx.strike = wv_alloc(T, numOptions) + ctx.riskFreeRate = wv_alloc(T, numOptions) + ctx.volatility = wv_alloc(T, numOptions) + ctx.expiry = wv_alloc(T, numOptions) + +proc delete[T](ctx: sink Context[T]) = + + wv_free ctx.data + wv_free ctx.prices + wv_free ctx.otype + wv_free ctx.spot + wv_free ctx.strike + wv_free ctx.riskFreeRate + wv_free ctx.volatility + wv_free ctx.expiry + +# Cumulative Normal Distribution Function +# --------------------------------------------------- +# See Hull, Section 11.8, P.243-244 + +const InvSqrt2xPI = 0.39894228040143270286 + +func cumulNormalDist[T: SomeFloat](inputX: T): T = + + # Check for negative value of inputX + var isNegative = false + var inputX = inputX + if inputX < 0.T: + inputX = -inputX + isNegative = true + + let xInput = inputX + + # Compute NPrimeX term common to both four & six decimal accuracy calcs + let expValues = exp(-0.5.T * inputX * inputX) + let xNPrimeofX = expValues * InvSqrt2xPI + + let + xK2 = 1.0 / (1.0 + 0.2316419*xInput) + xK2_2 = xK2 * xK2 + xK2_3 = xK2_2 * xK2 + xK2_4 = xK2_3 * xK2 + xK2_5 = xK2_4 * xK2 + + var + xLocal_1 = xK2 * 0.319381530 + xLocal_2 = xK2_2 * -0.356563782 + xLocal_3 = xK2_3 * 1.781477937 + xLocal_2 += xLocal_3 + xLocal_3 = xK2_4 * -1.821255978 + xLocal_2 += xLocal_3 + xLocal_3 = xK2_5 * 1.330274429 + xLocal_2 += xLocal_3 + + xLocal_1 += xLocal_2 + result = 1.T - xLocal_1 * xNPrimeofX + + if isNegative: + result = 1.T - result + +# Black & Scholes +# --------------------------------------------------- + +func blackScholesEqEuroNoDiv[T]( + spot, strike, riskFreeRate, volatility, expiry: T, + otype: OptionKind, + timet: float32 + ): T = + + var xD1 = riskFreeRate + 0.5.T * volatility * volatility + xD1 *= expiry + xD1 += ln(spot / strike) + + var xDen = volatility * sqrt(expiry) + xD1 /= xDen + + let xD2 = xD1 - xDen + + let nofXd1 = cumulNormalDist(xD1) + let nofXd2 = cumulNormalDist(xD2) + + let futureValueX = strike * exp(-riskFreeRate*expiry) + if otype == Call: + result = spot * nofXd1 - futureValueX * nofXd2 + else: + let negNofxd1 = 1.T - nofXd1 + let negNofxd2 = 1.T - nofXd2 + result = futureValueX * negNofxd2 - spot * negNofXd1 + +func checkErrors[T](ctx: var Context[T], i: int, price: T) = + let priceDelta = ctx.data[i].dgrefval - price + if abs(priceDelta) >= 1e-4: + c_printf("Error on %d. Computed=%.5f, Ref=%.5f, Delta=%.5f\n", + i.int, price, ctx.data[i].dgrefval, priceDelta + ) + ctx.numErrors += 1 + +func blackScholesSequential(ctx: var Context) = + + for j in 0 ..< ctx.numRuns: + for i in 0 ..< ctx.numOptions: + let price = blackScholesEqEuroNoDiv( + ctx.spot[i], ctx.strike[i], + ctx.riskFreeRate[i], ctx.volatility[i], + ctx.expiry[i], ctx.otype[i], 0 + ) + ctx.prices[i] = price + + when defined(check): + checkErrors(ctx, i, price) + +proc blackScholesConstantine(tp: Threadpool, ctx: ptr Context) = + + for j in 0 ..< ctx.numRuns: + tp.parallelFor i in 0 ..< ctx.numOptions: + captures: {ctx} + let price = blackScholesEqEuroNoDiv( + ctx.spot[i], ctx.strike[i], + ctx.riskFreeRate[i], ctx.volatility[i], + ctx.expiry[i], ctx.otype[i], 0 + ) + ctx.prices[i] = price + + when defined(check): + checkErrors(ctx[], i, price) + + tp.syncAll() + +proc dump[T](ctx: Context[T], file: string) = + + let stream = openFileStream(file, fmWrite) + defer: stream.close() + + stream.write($ctx.numOptions) + stream.write("\n") + + for i in 0 ..< ctx.numOptions: + stream.write($ctx.prices[i]) + stream.write("\n") + +proc parseOptions[T](ctx: var Context[T], optFile: string) = + + let stream = openFileStream(optFile, fmRead) + defer: stream.close() + + var line: string + discard stream.readLine(line) + + # Allocate the buffers + # Note sure why the original bench uses a struct of arrays + let numOptions = line.parseInt() + ctx.initialize(numOptions) + echo "Reading ", numOptions, " options" + + # For parsing Nim uses float64 by default + var + spot, strike, riskfree, divrate, vol, expiry: float64 + optKind: string + divvals, dgrefval: float64 + + for i in 0 ..< ctx.numOptions: + discard stream.readLine(line) + let isLineParsed = scanf(line, "$f $f $f $f $f $f $w $f $f", + spot, strike, riskFree, + divrate, vol, expiry, + optKind, divvals, dgrefval + ) + doAssert isLineParsed + + ctx.data[i].spot = spot.T + ctx.data[i].strike = strike.T + ctx.data[i].riskfree = riskfree.T + ctx.data[i].divrate = divrate.T + ctx.data[i].vol = vol.T + ctx.data[i].expiry = expiry.T + ctx.data[i].divvals = divvals.T + ctx.data[i].dgrefval = dgrefval.T + + if optKind == "C": + ctx.data[i].kind = Call + elif optKind == "P": + ctx.data[i].kind = Put + else: + raise newException(ValueError, "Invalid option kind: \"" & optKind & '"') + + ctx.otype[i] = ctx.data[i].kind + ctx.spot[i] = ctx.data[i].spot + ctx.strike[i] = ctx.data[i].strike + ctx.riskFreeRate[i] = ctx.data[i].riskfree + ctx.volatility[i] = ctx.data[i].vol + ctx.expiry[i] = ctx.data[i].expiry + +proc main() = + + var + input = "" + output = "" + numRounds = 2000 + + if paramCount() == 0: + let exeName = getAppFilename().extractFilename() + echo &"Usage: {exeName} " + quit 0 + elif paramCount() == 1: + input = paramStr(1) + elif paramCount() == 2: + input = paramStr(1) + output = paramStr(2) + elif paramCount() == 3: + input = paramStr(1) + output = paramStr(2) + numRounds = paramStr(3).parseInt() + else: + let exeName = getAppFilename().extractFilename() + echo &"Usage: {exeName} " + quit 1 + + var ctx: Context[float32] + ctx.numRuns = numRounds + ctx.parseOptions(input) + + var nthreads: int + if existsEnv"CTT_NUM_THREADS": + nthreads = getEnv"CTT_NUM_THREADS".parseInt() + else: + nthreads = countProcessors() + + when not defined(windows): + var ru: Rusage + getrusage(RusageSelf, ru) + var + rss = ru.ru_maxrss + flt = ru.ru_minflt + + let start = wtime_msec() + var tp = Threadpool.new(numThreads = nthreads) + tp.blackScholesConstantine(ctx.addr) + tp.shutdown() + + when not defined(windows): + let stop = wtime_msec() + + getrusage(RusageSelf, ru) + rss = ru.ru_maxrss - rss + flt = ru.ru_minflt - flt + + echo "--------------------------------------------------------------------------" + echo "Scheduler: Constantine" + echo "Benchmark: Black & Scholes Option Pricing (including init+shutdown)" + echo "Threads: ", nthreads + when not defined(windows): + echo "Time(ms) ", round(stop - start, 3) + echo "Max RSS (KB): ", ru.ru_maxrss + echo "Runtime RSS (KB): ", rss + echo "# of page faults: ", flt + echo "--------------------------------------------------------------------------" + echo "# of rounds: ", numRounds + echo "# of options: ", ctx.numOptions + + if output != "": + echo "\nDumping prices to \"", output, '"' + dump(ctx, output) + + delete(ctx) + + quit 0 + +main() diff --git a/constantine/platforms/threadpool/benchmarks/dfs/threadpool_dfs.nim b/constantine/platforms/threadpool/benchmarks/dfs/threadpool_dfs.nim index afe0e48..8b7bede 100644 --- a/constantine/platforms/threadpool/benchmarks/dfs/threadpool_dfs.nim +++ b/constantine/platforms/threadpool/benchmarks/dfs/threadpool_dfs.nim @@ -10,7 +10,7 @@ import system/ansi_c, std/[strformat, os, strutils, cpuinfo], # Library ../../threadpool - + when not defined(windows): # bench import ../wtime @@ -63,22 +63,31 @@ proc main() = # Staccato benches runtime init and exit as well when not defined(windows): - let start = wtime_usec() + let startRuntime = wtime_usec() tp = Threadpool.new() + + when not defined(windows): + let startBench = wtime_usec() + answer = test(depth, breadth) + + when not defined(windows): + let stopBench = wtime_usec() + tp.shutdown() when not defined(windows): - let stop = wtime_usec() + let stopRuntime = wtime_usec() echo "--------------------------------------------------------------------------" - echo "Scheduler: Constantine's Threadpool" - echo "Benchmark: dfs" - echo "Threads: ", nthreads + echo "Scheduler: Constantine's Threadpool" + echo "Benchmark: dfs" + echo "Threads: ", nthreads when not defined(windows): - echo "Time(us) ", stop - start - echo "Output: ", answer + echo "Time(us) runtime: ", stopRuntime - startRuntime + echo "Time(us) bench: ", stopBench - startBench + echo "Output: ", answer echo "--------------------------------------------------------------------------" quit 0 diff --git a/constantine/platforms/threadpool/benchmarks/histogram_2D/README.md b/constantine/platforms/threadpool/benchmarks/histogram_2D/README.md new file mode 100644 index 0000000..3f40827 --- /dev/null +++ b/constantine/platforms/threadpool/benchmarks/histogram_2D/README.md @@ -0,0 +1,10 @@ +# Histogram 2D + +This is a very interesting benchmark to test map-reduce style of computation and nested parallelism. + +It needs: +- 2 loops over a 2D matrix +- A reduction + +OpenMP is unable to deal intuitively with nesting +2 parallel loops and a custom reduction operation diff --git a/constantine/platforms/threadpool/benchmarks/histogram_2D/openmp_histogram.c b/constantine/platforms/threadpool/benchmarks/histogram_2D/openmp_histogram.c new file mode 100644 index 0000000..06790f7 --- /dev/null +++ b/constantine/platforms/threadpool/benchmarks/histogram_2D/openmp_histogram.c @@ -0,0 +1,162 @@ +// Source: https://stackoverflow.com/questions/16751445/parallelize-nested-for-loop-with-openmp + +#include +#include +#include +#include +#define float_t float +#include +#include + +// This was the original function to optimize +// where the reader had issues with OpenMP nested parallelism +float_t generate_histogram(float_t **matrix, int *histogram, int mat_size, int hist_size) +{ +int i,j,k,count; +float_t max = 0.; +float_t sum; + +//set histogram to zero everywhere +for(i = 0; i < hist_size; i++) + histogram[i] = 0; + + +//matrix computations +//#pragma omp parallel for schedule(runtime) +for (i = 1; i < (mat_size-1); i++) +{ + //pragma omp prallel for schedule(dynamic) + for(j = 1; j < (mat_size-1); j++) + { + + //assign current matrix[i][j] to element in order to reduce memory access + sum = fabs(matrix[i][j]-matrix[i-1][j]) + fabs(matrix[i][j] - matrix[i+1][j]) + + fabs(matrix[i][j]-matrix[i][j-1]) + fabs(matrix[i][j] - matrix[i][j+1]); + + //compute index of histogram bin + k = (int)(sum * (float)mat_size); + histogram[k] += 1; + + //keep track of largest element + if(sum > max) + max = sum; + + }//end inner for +}//end outer for + +return max; +} + +// This is the proposed alternative +float_t generate_histogram_omp(float_t **matrix, int *histogram, int mat_size, int hist_size) { + float_t max = 0.; + //set histogram to zero everywhere + int i; + for(i = 0; i < hist_size; i++) + histogram[i] = 0; + + //matrix computations + #pragma omp parallel + { + int *histogram_private = (int*)malloc(hist_size * sizeof(int)); + int i; + for(i = 0; i < hist_size; i++) + histogram_private[i] = 0; + float_t max_private = 0.; + int n; + int j; + #pragma omp for + for (i = 1; i < (mat_size-1); i++) { + for(j = 1; j < (mat_size-1); j++) { + // for (n=0; n < (mat_size-2)*(mat_size-2); n++) { + // int i = n/(mat_size-2)+1; + // int j = n%(mat_size-2)+1; + + float_t sum = fabs(matrix[i][j]-matrix[i-1][j]) + fabs(matrix[i][j] - matrix[i+1][j]) + + fabs(matrix[i][j]-matrix[i][j-1]) + fabs(matrix[i][j] - matrix[i][j+1]); + + //compute index of histogram bin + int k = (int)(sum * (float)mat_size); + histogram_private[k] += 1; + + //keep track of largest element + if(sum > max_private) + max_private = sum; + } + } + #pragma omp critical + { + + for(i = 0; i < hist_size; i++) + histogram[i] += histogram_private[i]; + if(max_private>max) + max = max_private; + } + + free(histogram_private); + } + return max; +} + +int compare_hists(int *hist1, int *hist2, int N) { + int i; + int diff = 0; + for(i =0; i < N; i++) { + int tmp = hist1[i] - hist2[i]; + diff += tmp; + if(tmp!=0) { + printf("i %d, hist1 %d, hist2 %d\n", i, hist1[i], hist2[i]); + } + } + return diff; +} + +int main() { + int i,j,N,boxes; + + // Original values + // N = 10000; + // boxes = N / 2; + + N = 25000; + boxes = 1000; + + float_t **matrix; + int* histogram1; + int* histogram2; + + //allocate a matrix with some numbers + matrix = (float_t**)calloc(N, sizeof(float_t **)); + for(i = 0; i < N; i++) + matrix[i] = (float_t*)calloc(N, sizeof(float_t *)); + for(i = 0; i < N; i++) + for(j = 0; j < N; j++) + matrix[i][j] = 1./(float_t) N * (float_t) i * 100.0; + + + histogram1 = (int*)malloc(boxes * sizeof(int)); + histogram2 = (int*)malloc(boxes * sizeof(int)); + + for(i = 0; i result: + result = sum + +proc generateHistogramThreadpoolReduce[T](tp: Threadpool, matrix: Matrix[T], hist: Histogram): T = + # We await reduce max only, sending the histogram across threads + # is too costly so the temporary histogram are freed in their allocating threads + + # In generic proc, Nim tries to resolve symbol earlier than when the reduce macros creates them + # so we need to tell Nim that the symbol will exist in time. + mixin distributedMax + + let boxes = hist.len + + for i in 0 ..< boxes: + hist[i] = 0 + + # Parallel reduction + tp.parallelFor i in 1 ..< matrix.ld-1: + captures: {hist, matrix, boxes} + reduceInto(distributedMax: T): + prologue: + let threadHist = newHistogram(boxes) + var max = T(-Inf) + forLoop: + # with inner for loop + for j in 1 ..< matrix.ld-1: + let sum = abs(matrix[i, j] - matrix[i-1, j]) + abs(matrix[i,j] - matrix[i+1, j]) + + abs(matrix[i, j] - matrix[i, j-1] + abs(matrix[i, j] - matrix[i, j+1])) + let k = int(sum * T(matrix.ld)) + + threadHist[k] += 1 + if sum > max: + max = sum + merge(remoteMax: FlowVar[T]): + block: + let remoteMax = sync(remoteMax) # Await max from other thread + if remoteMax > max: + max = remoteMax + for k in 0 ..< boxes: + discard hist[k].addr.atomicFetchAdd(threadHist[k], ATOMIC_RELAXED) + epilogue: + wv_free(threadHist.buffer) + return max + + return sync(distributedMax) + +# proc generateHistogramThreadpoolStaged[T](matrix: Matrix[T], hist: Histogram): T = + +# var max = T(-Inf) +# let maxAddr = max.addr + +# var lock: Lock +# lock.initLock() +# let lockAddr = lock.addr + +# let boxes = hist.len + +# for i in 0 ..< boxes: +# hist[i] = 0 + +# # Parallel reduction +# parallelForStaged i in 1 ..< matrix.ld-1: +# captures: {maxAddr, lockAddr, hist, matrix, boxes} +# awaitable: histoLoop +# prologue: +# let threadHist = newHistogram(boxes) +# var threadMax = T(-Inf) +# forLoop: +# # with inner for loop +# for j in 1 ..< matrix.ld-1: +# let sum = abs(matrix[i, j] - matrix[i-1, j]) + abs(matrix[i,j] - matrix[i+1, j]) + +# abs(matrix[i, j] - matrix[i, j-1] + abs(matrix[i, j] - matrix[i, j+1])) +# let k = int(sum * T(matrix.ld)) + +# threadHist[k] += 1 +# if sum > threadMax: +# threadMax = sum +# epilogue: +# lockAddr[].acquire() +# maxAddr[] = max(maxAddr[], threadMax) +# if threadMax > maxAddr[]: +# maxAddr[] = threadMax +# for k in 0 ..< boxes: +# hist[k] += threadHist[k] +# lockAddr[].release() +# wv_free(threadHist.buffer) + +# let waslastThread = sync(histoLoop) +# lock.deinitLock() +# return max + +proc main() = + + if sizeof(int) == 4: + echo "Running on 32-bit. This benchmark is requires 64-bit." + return + + var + matrixSize = 25000 + boxes = 1000 + + if paramCount() == 0: + let exeName = getAppFilename().extractFilename() + echo &"Usage: {exeName} " + echo &"Running with default matrixSize={matrixSize}, boxes={boxes}" + elif paramCount() == 2: + matrixSize = paramStr(1).parseInt() + boxes = paramStr(2).parseInt() + else: + let exeName = getAppFilename().extractFilename() + echo &"Usage: {exeName} " + echo &"Default \"{exeName} {matrixSize} {boxes}\"" + quit 1 + + var nthreads: int + if existsEnv"CTT_NUM_THREADS": + nthreads = getEnv"CTT_NUM_THREADS".parseInt() + else: + nthreads = countProcessors() + + var tp: Threadpool + var matrix: Matrix[float32] + # The reference code zero-out the histogram in the bench as well + prepareMatrix(matrix, matrixSize) + + reportConfig("Sequential", 1, matrixSize, boxes) + runBench(tp, generateHistogramSerial, matrix, boxes, parallel = false) + reportConfig("Constantine's threadpool - Parallel Reduce", nthreads, matrixSize, boxes) + runBench(tp, generateHistogramThreadpoolReduce, matrix, boxes) + # reportConfig("Constantine's threadpool - Parallel For Staged", nthreads, matrixSize, boxes) + # runBench(generateHistogramThreadpoolStaged, matrix, boxes) + + wv_free(matrix.buffer) + + +main() diff --git a/constantine/platforms/threadpool/benchmarks/logsumexp/README.md b/constantine/platforms/threadpool/benchmarks/logsumexp/README.md new file mode 100644 index 0000000..ecf5600 --- /dev/null +++ b/constantine/platforms/threadpool/benchmarks/logsumexp/README.md @@ -0,0 +1,28 @@ +# Log-Sum-Exp + +Log-Sum-Exp computes `ln ∑i exp(xi)` by using the trick: + +``` +log ∑i exp(xi) = α + log ∑i exp(xi−α) +with α = max(xi) for xi in x +``` + +Log-Sum-Exp is a key algorithm behind the Softmax Cross-Entropy loss function, +which is used in almost all deep learning classification problems. + +Furthermore this is a huge bottleneck in NLP and research in fast softmax +approximation is active. + +We are interested in testing parallel reductions +so we do first a parallel max and then a parallel exponential sum. + +However note that there exist a streaming version +at http://www.nowozin.net/sebastian/blog/streaming-log-sum-exp-computation.html +which is similar to Welford algorithm for streaming mean and variance in statistics. + +Given that exponential is a very heavy operation all framework should see a linear speedup. +The main challenge is the framework syntax for complex reduction operation. + +Note that `` exponential can be significantly improved (10x) +by using vectorization techniques from Laser +https://github.com/numforge/laser/blob/d1e6ae6106564bfb350d4e566261df97dbb578b3/benchmarks/vector_math/bench_exp_avx2.nim#L373-L379 diff --git a/constantine/platforms/threadpool/benchmarks/logsumexp/threadpool_logsumexp.nim b/constantine/platforms/threadpool/benchmarks/logsumexp/threadpool_logsumexp.nim new file mode 100644 index 0000000..99afdab --- /dev/null +++ b/constantine/platforms/threadpool/benchmarks/logsumexp/threadpool_logsumexp.nim @@ -0,0 +1,402 @@ +# Weave +# Copyright (c) 2019 Mamy André-Ratsimbazafy +# Licensed and distributed under either of +# * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT). +# * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0). +# at your option. This file may not be copied, modified, or distributed except according to those terms. + +import + # Stdlib + system/ansi_c, std/[strformat, os, strutils, cpuinfo, math, random, locks], + # Constantine + ../../threadpool + +when not defined(windows): + # bench + import ../wtime, ../resources + +# TODO: there is an overflow on Linux32 or MacOS for MaxRSS but not Linux or Windows +# This test is quite important to ensure parallel reductions work within a generic proc. +{.push checks: off.} + +# Helpers +# ------------------------------------------------------- + +# We need a thin wrapper around raw pointers for matrices, +# Note that matrices for log-sum-exp are usually in the following shapes: +# - Classification of a batch of 256 images in 3 categories: 256x3 +# - Classification of a batch of words from a 50000 words dictionary: 256x50000 + +# Helpers +# ------------------------------------------------------- + +proc wv_alloc*(T: typedesc): ptr T {.inline.}= + cast[ptr T](c_malloc(csize_t sizeof(T))) + +proc wv_alloc*(T: typedesc, len: SomeInteger): ptr UncheckedArray[T] {.inline.} = + cast[type result](c_malloc(csize_t len*sizeof(T))) + +proc wv_free*[T: ptr](p: T) {.inline.} = + c_free(p) + +# We need a thin wrapper around raw pointers for matrices, +# we can't pass "var" to other threads +type + Matrix[T: SomeFloat] = object + buffer: ptr UncheckedArray[T] + nrows, ncols: int # int64 on x86-64 + +func newMatrix[T](rows, cols: Natural): Matrix[T] {.inline.} = + # Create a rows x cols Matrix + result.buffer = cast[ptr UncheckedArray[T]](c_malloc(csize_t rows*cols*sizeof(T))) + result.nrows = rows + result.ncols = cols + +template `[]`[T](M: Matrix[T], row, col: Natural): T = + # row-major storage + assert row < M.nrows + assert col < M.ncols + M.buffer[row * M.ncols + col] + +template `[]=`[T](M: Matrix[T], row, col: Natural, value: T) = + assert row < M.nrows + assert col < M.ncols + M.buffer[row * M.ncols + col] = value + +proc initialize[T](M: Matrix[T]) = + randomize(1234) # Seed + for i in 0 ..< M.nrows: + for j in 0 ..< M.ncols: + M[i, j] = T(rand(1.0)) + +func rowView*[T](M: Matrix[T], rowPos, size: Natural): Matrix[T]{.inline.}= + ## Returns a new view offset by the row and column stride + result.buffer = cast[ptr UncheckedArray[T]]( + addr M.buffer[rowPos * M.ncols] + ) + result.nrows = size + result.ncols = M.ncols + +# Reports +# ------------------------------------------------------- + +template memUsage(maxRSS, runtimeRSS, pageFaults: untyped{ident}, body: untyped) = + var maxRSS, runtimeRSS, pageFaults: int32 + block: + var ru: Rusage + getrusage(RusageSelf, ru) + runtimeRSS = ru.ru_maxrss + pageFaults = ru.ru_minflt + + body + + getrusage(RusageSelf, ru) + runtimeRSS = ru.ru_maxrss - runtimeRSS + pageFaults = ru.ru_minflt - pageFaults + maxRss = ru.ru_maxrss + +proc reportConfig( + scheduler: string, + nthreads: int, datasetSize, batchSize, imageLabels, textVocabulary: int64 + ) = + + echo "--------------------------------------------------------------------------" + echo "Scheduler: ", scheduler + echo "Benchmark: Log-Sum-Exp (Machine Learning) " + echo "Threads: ", nthreads + echo "datasetSize: ", datasetSize + echo "batchSize: ", batchSize + echo "# of full batches: ", datasetSize div batchSize + echo "# of image labels: ", imageLabels + echo "Text vocabulary size: ", textVocabulary + +proc reportBench( + batchSize, numLabels: int64, + time: float64, maxRSS, runtimeRss, pageFaults: int32, + logSumExp: float32 + ) = + echo "--------------------------------------------------------------------------" + echo "Dataset: ", batchSize,'x',numLabels + echo "Time(ms): ", round(time, 3) + echo "Max RSS (KB): ", maxRss + echo "Runtime RSS (KB): ", runtimeRSS + echo "# of page faults: ", pageFaults + echo "Logsumexp: ", logsumexp + +template runBench(procName: untyped, datasetSize, batchSize, numLabels: int64) = + let data = newMatrix[float32](datasetSize, numLabels) + data.initialize() + + when not defined(windows): + let start = wtime_msec() + + var lse = 0'f32 + memUsage(maxRSS, runtimeRSS, pageFaults): + # For simplicity we ignore the last few data points + for batchIdx in 0 ..< datasetSize div batchSize: + let X = data.rowView(batchIdx*batchSize, batchSize) + lse += procName(X) + + let stop = wtime_msec() + + reportBench(batchSize, numlabels, stop-start, maxRSS, runtimeRSS, pageFaults, lse) + else: + # For simplicity we ignore the last few data points + var lse = 0'f32 + for batchIdx in 0 ..< datasetSize div batchSize: + let X = data.rowView(batchIdx*batchSize, batchSize) + lse += procName(X) + + +template runBench(tp: Threadpool, procName: untyped, datasetSize, batchSize, numLabels: int64) = + let data = newMatrix[float32](datasetSize, numLabels) + data.initialize() + + when not defined(windows): + let start = wtime_msec() + + var lse = 0'f32 + memUsage(maxRSS, runtimeRSS, pageFaults): + # For simplicity we ignore the last few data points + for batchIdx in 0 ..< datasetSize div batchSize: + let X = data.rowView(batchIdx*batchSize, batchSize) + lse += procName(tp, X) + + let stop = wtime_msec() + + reportBench(batchSize, numlabels, stop-start, maxRSS, runtimeRSS, pageFaults, lse) + else: + var lse = 0'f32 + for batchIdx in 0 ..< datasetSize div batchSize: + let X = data.rowView(batchIdx*batchSize, batchSize) + lse += procName(tp, X) + +# Algo - Serial +# ------------------------------------------------------- + +proc maxSerial[T: SomeFloat](M: Matrix[T]) : T = + result = T(-Inf) + + for i in 0 ..< M.nrows: + for j in 0 ..< M.ncols: + result = max(result, M[i, j]) + +proc logsumexpSerial[T: SomeFloat](M: Matrix[T]): T = + let alpha = M.maxSerial() + + result = 0 + + for i in 0 ..< M.nrows: + for j in 0 ..< M.ncols: + result += exp(M[i, j] - alpha) + + result = alpha + ln(result) + +# Algo - parallel reduction +# ------------------------------------------------------- + +proc maxThreadpoolReduce[T: SomeFloat](tp: Threadpool, M: Matrix[T]) : T = + mixin globalMax + + tp.parallelFor i in 0 ..< M.nrows: + captures:{M} + reduceInto(globalMax: T): + prologue: + var localMax = T(-Inf) + forLoop: + for j in 0 ..< M.ncols: + localMax = max(localMax, M[i, j]) + merge(remoteMax: Flowvar[T]): + localMax = max(localMax, sync(remoteMax)) + epilogue: + return localMax + + result = sync(globalMax) + +proc logsumexpThreadpoolReduce[T: SomeFloat](tp: Threadpool, M: Matrix[T]): T = + mixin lse + + let alpha = tp.maxThreadpoolReduce(M) + tp.parallelFor i in 0 ..< M.nrows: + captures:{alpha, M} + reduceInto(lse: T): + prologue: + var localLSE = 0.T + forLoop: + for j in 0 ..< M.ncols: + localLSE += exp(M[i, j] - alpha) + merge(remoteLSE: Flowvar[T]): + localLSE += sync(remoteLSE) + epilogue: + return localLSE + + result = alpha + ln(sync(lse)) + +# Algo - parallel reduction collapsed +# ------------------------------------------------------- + +proc maxThreadpoolCollapsed[T: SomeFloat](tp: Threadpool, M: Matrix[T]) : T = + mixin globalMax + + tp.parallelFor ij in 0 ..< M.nrows * M.ncols: + captures:{M} + reduceInto(globalMax: T): + prologue: + var localMax = T(-Inf) + forLoop: + localMax = max(localMax, M.buffer[ij]) + merge(remoteMax: FlowVar[T]): + localMax = max(localMax, sync(remoteMax)) + epilogue: + return localMax + + result = sync(globalMax) + +proc logsumexpThreadpoolCollapsed[T: SomeFloat](tp: Threadpool, M: Matrix[T]): T = + mixin lse + let alpha = tp.maxThreadpoolCollapsed(M) + + tp.parallelFor ij in 0 ..< M.nrows * M.ncols: + captures:{alpha, M} + reduceInto(lse: T): + prologue: + var localLSE = 0.T + forLoop: + localLSE += exp(M.buffer[ij] - alpha) + merge(remoteLSE: Flowvar[T]): + localLSE += sync(remoteLSE) + epilogue: + return localLSE + + result = alpha + ln(sync(lse)) + +# proc maxThreadpoolStaged[T: SomeFloat](tp: Threadpool, M: Matrix[T]) : T = +# mixin maxLoop +# +# var max = T(-Inf) +# let maxAddr = max.addr +# +# var lock: Lock +# lock.initLock() +# let lockAddr = lock.addr +# +# tp.parallelForStaged i in 0 ..< M.nrows: +# captures:{maxAddr, lockAddr, M} +# awaitable: maxLoop +# prologue: +# var localMax = T(-Inf) +# forLoop: +# for j in 0 ..< M.ncols: +# localMax = max(localMax, M[i, j]) +# epilogue: +# lockAddr[].acquire() +# maxAddr[] = max(maxAddr[], localMax) +# lockAddr[].release() +# +# let waslastThread = sync(maxLoop) +# lock.deinitLock() +# +# proc logsumexpThreadpoolStaged[T: SomeFloat](tp: Threadpool, M: Matrix[T]): T = +# mixin logSumExpLoop +# let alpha = M.maxThreadpoolStaged() +# +# var lse = T(0) +# let lseAddr = lse.addr +# +# # Atomic increment for float is done with a Compare-And-Swap loop usually. +# # Due to lazy splitting, load distribution is unbalanced between threads so they shouldn't +# # finish at the same time in general and lock contention would be low +# var lock: Lock +# lock.initLock() +# let lockAddr = lock.addr +# +# tp.parallelForStaged i in 0 ..< M.nrows: +# captures:{lseAddr, lockAddr, alpha, M} +# awaitable: logSumExpLoop +# prologue: +# var localLSE = 0.T +# loop: +# for j in 0 ..< M.ncols: +# localLSE += exp(M[i, j] - alpha) +# epilogue: +# lockAddr[].acquire() +# lseAddr[] += localLSE +# lockAddr[].release() +# +# let wasLastThread = sync(logSumExpLoop) +# result = alpha + ln(lse) +# lock.deinitLock() + +# Main +# ------------------------------------------------------- + +proc main() = + echo "Note that a text vocabulary is often in the 50000-15000 words\n" + + var + datasetSize = 20000'i64 + batchSize = 256'i64 + imagelabels = 1000'i64 + textVocabulary = 10000'i64 + + if paramCount() == 0: + let exeName = getAppFilename().extractFilename() + echo &"Usage: {exeName} " + echo &"Running with default datasetSize={datasetSize}, batchSize={batchSize}, imagelabels={imagelabels}, textVocabulary={textVocabulary}" + elif paramCount() == 4: + datasetSize = paramStr(1).parseBiggestInt().int64 + batchSize = paramStr(2).parseBiggestInt().int64 + imagelabels = paramStr(3).parseBiggestInt().int64 + textVocabulary = paramStr(4).parseBiggestInt().int64 + else: + let exeName = getAppFilename().extractFilename() + echo &"Usage: {exeName} " + echo &"Default \"{datasetSize} {batchSize} {imagelabels} {textVocabulary}\"" + quit 1 + + var nthreads: int + if existsEnv"CTT_NUM_THREADS": + nthreads = getEnv"CTT_NUM_THREADS".parseInt() + else: + nthreads = countProcessors() + + let sanityM = newMatrix[float32](1, 9) + for i in 0'i32 ..< 9: + sanityM[0, i] = i.float32 + 1 + + echo "Sanity check, logSumExp(1..<10) should be 9.4585514 (numpy logsumexp): ", logsumexpSerial(sanityM) + echo '\n' + wv_free(sanityM.buffer) + + reportConfig("Sequential", 1, datasetSize, batchSize, imageLabels, textVocabulary) + block: + runBench(logsumexpSerial, datasetSize, batchSize, imageLabels) + block: + runBench(logsumexpSerial, datasetSize, batchSize, textVocabulary) + + # TODO: Placing the threadpool before the sequential bench makes it take ~85 ms instead of ~48 ms + var tp = Threadpool.new(nthreads) + + # TODO: The parallel algorithm is slower than Weave AND slower than serial + + reportConfig("Constantine's Threadpool Reduce", nthreads, datasetSize, batchSize, imageLabels, textVocabulary) + block: + tp.runBench(logsumexpThreadpoolReduce, datasetSize, batchSize, imageLabels) + block: + tp.runBench(logsumexpThreadpoolReduce, datasetSize, batchSize, textVocabulary) + + reportConfig("Constantine's Threadpool (Collapsed)", nthreads, datasetSize, batchSize, imageLabels, textVocabulary) + block: + tp.runBench(logsumexpThreadpoolCollapsed, datasetSize, batchSize, imageLabels) + block: + tp.runBench(logsumexpThreadpoolCollapsed, datasetSize, batchSize, textVocabulary) + + # reportConfig("Constantine's Threadpool (Staged)", nthreads, datasetSize, batchSize, imageLabels, textVocabulary) + # block: + # tp.runBench(logsumexpThreadpoolStaged, datasetSize, batchSize, imageLabels) + # block: + # tp.runBench(logsumexpThreadpoolStaged, datasetSize, batchSize, textVocabulary) + + tp.shutdown() + +main() \ No newline at end of file diff --git a/constantine/platforms/threadpool/benchmarks/matrix_transposition/README.md b/constantine/platforms/threadpool/benchmarks/matrix_transposition/README.md new file mode 100644 index 0000000..e30e34d --- /dev/null +++ b/constantine/platforms/threadpool/benchmarks/matrix_transposition/README.md @@ -0,0 +1,14 @@ +# Matrix transposition + +This benchmark extract from [Laser](https://github.com/numforge/laser) +stresses the ability for a runtime to support nested loops. + +A matrix is being copied to another buffer with transposition. +For one buffer or the other the accesses will not be linear +so it is important to do tiling. As dimensions might be skewed, +the ideal tiling should be 2D with nested parallel for loops that properly find +work for all cores even if a matrix is tall and skinny or short and fat. + +Note that as OpenMP nested loop support is very problematic +we use the `collapse` clause for OpenMP which is only usable +in a restricted number of scenarios. diff --git a/constantine/platforms/threadpool/benchmarks/matrix_transposition/openmp_transposes.nim b/constantine/platforms/threadpool/benchmarks/matrix_transposition/openmp_transposes.nim new file mode 100644 index 0000000..43bc783 --- /dev/null +++ b/constantine/platforms/threadpool/benchmarks/matrix_transposition/openmp_transposes.nim @@ -0,0 +1,294 @@ +# Weave +# Copyright (c) 2019 Mamy André-Ratsimbazafy +# Licensed and distributed under either of +# * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT). +# * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0). +# at your option. This file may not be copied, modified, or distributed except according to those terms. + +# Original transposition codes from Laser project +# (c) Mamy André Ratsimbazafy, Apache License version 2 + +import + # Stdlib + strformat, os, strutils, math, system/ansi_c, + cpuinfo, streams, strscans, + # Third-party + cligen, + # bench + ../wtime, ../resources + +# OpenMP +# --------------------------------------------------- + +{.passC:"-fopenmp".} +{.passL:"-fopenmp".} +{.pragma: omp, header:"omp.h".} +proc omp_get_num_threads*(): cint {.omp.} + +# Memory +# --------------------------------------------------- + +proc wv_alloc*(T: typedesc): ptr T {.inline.}= + ## Default allocator for the Picasso library + ## This allocates memory to hold the type T + ## and returns a pointer to it + ## + ## Can use Nim allocator to measure the overhead of its lock + ## Memory is not zeroed + when defined(WV_useNimAlloc): + createSharedU(T) + else: + cast[ptr T](c_malloc(csize_t sizeof(T))) + +proc wv_alloc*(T: typedesc, len: SomeInteger): ptr UncheckedArray[T] {.inline.} = + ## Default allocator for the Picasso library. + ## This allocates a contiguous chunk of memory + ## to hold ``len`` elements of type T + ## and returns a pointer to it. + ## + ## Can use Nim allocator to measure the overhead of its lock + ## Memory is not zeroed + when defined(WV_useNimAlloc): + cast[type result](createSharedU(T, len)) + else: + cast[type result](c_malloc(csize_t len*sizeof(T))) + +proc wv_free*[T: ptr](p: T) {.inline.} = + when defined(WV_useNimAlloc): + freeShared(p) + else: + c_free(p) + +# Transpose implementations +# --------------------------------------------------- + +type TransposeStrategy = enum + Sequential + Naive + Collapsed + TiledCollapsed + +# Question: do we need __restrict to avoid the compiler generating +# defensive aliasing robust code? + +proc sequentialTranspose(M, N: int, bufIn, bufOut: ptr UncheckedArray[float32]) = + for j in 0 ..< N: + for i in 0 ..< M: + bufOut[j*M+i] = bufIn[i*N+j] + +proc ompNaiveTranspose(M, N: int, bufIn, bufOut: ptr UncheckedArray[float32]) = + ## Transpose a MxN matrix into a NxM matrix + + # Write are more expensive than read so we keep i accesses linear for writes + {.push stacktrace:off.} + for j in 0||(N-1): + for i in 0 ..< M: + bufOut[j*M+i] = bufIn[i*N+j] + {.pop.} + +proc ompCollapsedTranspose(M, N: int, bufIn, bufOut: ptr UncheckedArray[float32]) = + ## Transpose a MxN matrix into a NxM matrix + + # We need to go down to C level for the collapsed clause + # This relies on M, N, bfIn, bufOut symbols being the same in C and Nim + # The proper interpolation syntax is a bit busy otherwise + {.emit: """ + + #pragma omp parallel for collapse(2) + for (int i = 0; i < `M`; ++i) + for (int j = 0; j < `N`; ++j) + `bufOut`[j*M+i] = `bufIn`[i*N+j]; + """.} + +proc omp2DTiledCollapsedTranspose(M, N: int, bufIn, bufOut: ptr UncheckedArray[float32]) = + ## Transpose with 2D tiling and collapsed + + const blck = 64 + + {.emit: """ + + #define min(a,b) (((a)<(b))?(a):(b)) + + #pragma omp parallel for collapse(2) + for (int j = 0; j < `N`; j+=`blck`) + for (int i = 0; i < `M`; i+=`blck`) + for (int jj = j; jj ", N, 'x', M + echo "Time(ms): ", round(mxnTime, 3) + echo "Max RSS (KB): ", mxnMaxRss + echo "Runtime RSS (KB): ", mxnRuntimeRSS + echo "# of page faults: ", mxnPageFaults + echo "Perf (GMEMOPs/s ~ GigaMemory Operations/s) ", round(mxnPerf, 3) + echo "--------------------------------------------------------------------------" + echo "Transposition: ", N,'x',M, " --> ", M, 'x', N + echo "Time(ms): ", round(nxmTime, 3) + echo "Max RSS (KB): ", nxmMaxRss + echo "Runtime RSS (KB): ", nxmRuntimeRSS + echo "# of page faults: ", nxmPageFaults + echo "Perf (GMEMOPs/s ~ GigaMemory Operations/s) ", round(nxmPerf, 3) + else: + echo "Transposition: ", N,'x',M, " --> ", M, 'x', N + echo "Time(ms): ", round(nxmTime, 3) + echo "Max RSS (KB): ", nxmMaxRss + echo "Runtime RSS (KB): ", nxmRuntimeRSS + echo "# of page faults: ", nxmPageFaults + echo "Perf (GMEMOPs/s ~ GigaMemory Operations/s) ", round(mxnPerf, 3) + echo "--------------------------------------------------------------------------" + echo "Transposition: ", M,'x',N, " --> ", N, 'x', M + echo "Time(ms): ", round(mxnTime, 3) + echo "Max RSS (KB): ", mxnMaxRss + echo "Runtime RSS (KB): ", mxnRuntimeRSS + echo "# of page faults: ", mxnPageFaults + echo "Perf (GMEMOPs/s ~ GigaMemory Operations/s) ", round(nxmPerf, 3) + +template runBench(transposeName: typed, reorderCompute: bool): untyped = + if not reorderCompute: + memUsage(mxnMaxRss, mxnRuntimeRss, mxnPageFaults): + let start = wtime_msec() + for _ in 0 ..< nrounds: + transposeName(M, N, bufIn, bufOut) + let stop = wtime_msec() + mxnTime = stop - start + + memUsage(nxmMaxRss, nxmRuntimeRss, nxmPageFaults): + let start = wtime_msec() + for _ in 0 ..< nrounds: + transposeName(N, M, bufIn, bufOut) + let stop = wtime_msec() + nxmTime = stop - start + + report(M, N, nthreads, nrounds, reorderCompute, + transposeStrat, reqOps, reqBytes, + mxnTime, mxnMaxRSS, mxnRuntimeRss, mxnPageFaults, + nxmTime, nxmMaxRSS, nxmRuntimeRss, nxmPageFaults + ) + else: + memUsage(nxmMaxRss, nxmRuntimeRss, nxmPageFaults): + let start = wtime_msec() + for _ in 0 ..< nrounds: + transposeName(N, M, bufIn, bufOut) + let stop = wtime_msec() + nxmTime = stop - start + + memUsage(mxnMaxRss, mxnRuntimeRss, mxnPageFaults): + let start = wtime_msec() + for _ in 0 ..< nrounds: + transposeName(M, N, bufIn, bufOut) + let stop = wtime_msec() + mxnTime = stop - start + + report(M, N, nthreads, nrounds, reorderCompute, + transposeStrat, reqOps, reqBytes, + mxnTime, mxnMaxRSS, mxnRuntimeRss, mxnPageFaults, + nxmTime, nxmMaxRSS, nxmRuntimeRss, nxmPageFaults + ) + +# Interface +# --------------------------------------------------- + +proc main() = + + var + M = 400 + N = 4000 + nrounds = 1000 + transposeStrat = TiledCollapsed + reorderCompute = false + + if paramCount() == 0: + let exeName = getAppFilename().extractFilename() + echo &"Usage: {exeName} " + echo &"Running with default M={M}, N={N}, rounds={nrounds}, transposeStrategy={transposeStrat}, reorderCompute={reorderCompute}" + elif paramCount() == 5: + M = paramStr(1).parseInt() + N = paramStr(2).parseInt() + nrounds = paramStr(3).parseInt() + transposeStrat = paramStr(4).parseEnum[:TransposeStrategy]() + reorderCompute = paramStr(5).parseBool() + else: + let exeName = getAppFilename().extractFilename() + echo &"Usage: {exeName} " + echo &"Default \"{exeName} {M} {N} {nrounds} {transposeStrat} {reorderCompute}\"" + quit 1 + + echo "Inverting the transpose order may favor one transposition heavily for non-tiled strategies" + + let nthreads = if transposeStrat == Sequential: 1'i32 + else: omp_get_num_threads() + + let (reqOps, reqBytes, bufSize) = computeMeta(M, N) + + let bufOut = wv_alloc(float32, bufSize) + let bufIn = wv_alloc(float32, bufSize) + + bufIn.initialize(bufSize) + + var mxnTime, nxmTime: float64 + + case transposeStrat + of Sequential: runBench(sequentialTranspose, reorderCompute) + of Naive: runBench(ompNaiveTranspose, reorderCompute) + of Collapsed: runBench(ompCollapsedTranspose, reorderCompute) + of TiledCollapsed: runBench(omp2DTiledCollapsedTranspose, reorderCompute) + + wv_free(bufOut) + wv_free(bufIn) + +dispatch(main) diff --git a/constantine/platforms/threadpool/benchmarks/matrix_transposition/threadpool_transposes.nim b/constantine/platforms/threadpool/benchmarks/matrix_transposition/threadpool_transposes.nim new file mode 100644 index 0000000..a960c48 --- /dev/null +++ b/constantine/platforms/threadpool/benchmarks/matrix_transposition/threadpool_transposes.nim @@ -0,0 +1,319 @@ +# Weave +# Copyright (c) 2019 Mamy André-Ratsimbazafy +# Licensed and distributed under either of +# * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT). +# * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0). +# at your option. This file may not be copied, modified, or distributed except according to those terms. + +# Original transposition codes from Laser project +# (c) Mamy André Ratsimbazafy, Apache License version 2 + +import + # Stdlib + system/ansi_c, std/[strformat, os, strutils, math, cpuinfo], + # Constantine + ../../threadpool + +when not defined(windows): + # bench + import ../wtime, ../resources + + +# Memory +# --------------------------------------------------- + +proc wv_alloc*(T: typedesc): ptr T {.inline.}= + ## Default allocator for the Picasso library + ## This allocates memory to hold the type T + ## and returns a pointer to it + ## + ## Can use Nim allocator to measure the overhead of its lock + ## Memory is not zeroed + when defined(WV_useNimAlloc): + createSharedU(T) + else: + cast[ptr T](c_malloc(csize_t sizeof(T))) + +proc wv_alloc*(T: typedesc, len: SomeInteger): ptr UncheckedArray[T] {.inline.} = + ## Default allocator for the Picasso library. + ## This allocates a contiguous chunk of memory + ## to hold ``len`` elements of type T + ## and returns a pointer to it. + ## + ## Can use Nim allocator to measure the overhead of its lock + ## Memory is not zeroed + when defined(WV_useNimAlloc): + cast[type result](createSharedU(T, len)) + else: + cast[type result](c_malloc(csize_t len*sizeof(T))) + +proc wv_free*[T: ptr](p: T) {.inline.} = + when defined(WV_useNimAlloc): + freeShared(p) + else: + c_free(p) + +# Transpose implementations +# --------------------------------------------------- + +type TransposeStrategy = enum + Sequential + Naive + Nested + TiledNested + +# Question: do we need __restrict to avoid the compiler generating +# defensive aliasing robust code? + +proc sequentialTranspose(tp: Threadpool, M, N: int, bufIn, bufOut: ptr UncheckedArray[float32]) = + for j in 0 ..< N: + for i in 0 ..< M: + bufOut[j*M+i] = bufIn[i*N+j] + +proc cttNaiveTranspose(tp: Threadpool, M, N: int, bufIn, bufOut: ptr UncheckedArray[float32]) = + ## Transpose a MxN matrix into a NxM matrix + + # Write are more expensive than read so we keep i accesses linear for writes + tp.parallelFor j in 0 ..< N: + captures: {M, N, bufIn, bufOut} + for i in 0 ..< M: + bufOut[j*M+i] = bufIn[i*N+j] + +proc cttNestedTranspose(tp: Threadpool, M, N: int, bufIn, bufOut: ptr UncheckedArray[float32]) = + ## Transpose a MxN matrix into a NxM matrix with nested for loops + + tp.parallelFor j in 0 ..< N: + captures: {tp, M, N, bufIn, bufOut} + tp.parallelFor i in 0 ..< M: + captures: {j, M, N, bufIn, bufOut} + bufOut[j*M+i] = bufIn[i*N+j] + +proc ctt2DTiledNestedTranspose(tp: Threadpool, M, N: int, bufIn, bufOut: ptr UncheckedArray[float32]) = + ## Transpose with 2D tiling and nested + + const blck = 64 # const do not need to be captured + + tp.parallelFor j in 0 ..< N: + stride: blck + captures: {tp, M, N, bufIn, bufOut} + tp.parallelFor i in 0 ..< M: + stride: blck + captures: {j, M, N, bufIn, bufOut} + for jj in j ..< min(j+blck, N): + for ii in i ..< min(i+blck, M): + bufOut[jj*M+ii] = bufIn[ii*N+jj] + +# Meta +# --------------------------------------------------- + +func computeMeta(height, width: int): tuple[reqOps, reqBytes, bufSize: int] = + + result.reqOps = height * width + result.reqBytes = sizeof(float32) * height * width + result.bufSize = height * width + +func initialize(buffer: ptr UncheckedArray[float32], len: int) = + for i in 0 ..< len: + buffer[i] = i.float32 + +# Bench +# --------------------------------------------------- + +template memUsage(maxRSS, runtimeRSS, pageFaults: untyped{ident}, body: untyped) = + var maxRSS, runtimeRSS, pageFaults: int32 + block: + when not defined(windows): + var ru: Rusage + getrusage(RusageSelf, ru) + runtimeRSS = ru.ru_maxrss + pageFaults = ru.ru_minflt + + body + + when not defined(windows): + getrusage(RusageSelf, ru) + runtimeRSS = ru.ru_maxrss - runtimeRSS + pageFaults = ru.ru_minflt - pageFaults + maxRss = ru.ru_maxrss + +proc report( + M, N: int, nthreads: int32, nrounds: int, reordered: bool, + transposeStrategy: TransposeStrategy, reqOps, reqBytes: int, + mxnTime: float64, mxnMaxRSS, mxnRuntimeRss, mxnPageFaults: int32, + nxmTime: float64, nxmMaxRSS, nxmRuntimeRss, nxmPageFaults: int32, + ) = + + let arithIntensity = reqOps.float / reqBytes.float + let mxnPerf = reqOps.float/(mxnTime*1e-3 / nrounds.float) * 1e-9 # Gops per second + let nxmPerf = reqOps.float/(nxmTime*1e-3 / nrounds.float) * 1e-9 # Gops per second + + echo "--------------------------------------------------------------------------" + echo "Scheduler: Constantine's threadpool" + echo "Benchmark: Transpose - ", $transposeStrategy + echo "Threads: ", nthreads + echo "# of rounds: ", nrounds + echo "# of operations: ", reqOps + echo "# of bytes: ", reqBytes + echo "Arithmetic Intensity: ", round(arithIntensity, 3) + echo "--------------------------------------------------------------------------" + if not reordered: + echo "Transposition: ", M,'x',N, " --> ", N, 'x', M + when not defined(windows): + echo "Time(ms): ", round(mxnTime, 3) + echo "Max RSS (KB): ", mxnMaxRss + echo "Runtime RSS (KB): ", mxnRuntimeRSS + echo "# of page faults: ", mxnPageFaults + echo "Perf (GMEMOPs/s ~ GigaMemory Operations/s) ", round(mxnPerf, 3) + echo "--------------------------------------------------------------------------" + echo "Transposition: ", N,'x',M, " --> ", M, 'x', N + when not defined(windows): + echo "Time(ms): ", round(nxmTime, 3) + echo "Max RSS (KB): ", nxmMaxRss + echo "Runtime RSS (KB): ", nxmRuntimeRSS + echo "# of page faults: ", nxmPageFaults + echo "Perf (GMEMOPs/s ~ GigaMemory Operations/s) ", round(nxmPerf, 3) + else: + echo "Transposition: ", N,'x',M, " --> ", M, 'x', N + when not defined(windows): + echo "Time(ms): ", round(nxmTime, 3) + echo "Max RSS (KB): ", nxmMaxRss + echo "Runtime RSS (KB): ", nxmRuntimeRSS + echo "# of page faults: ", nxmPageFaults + echo "Perf (GMEMOPs/s ~ GigaMemory Operations/s) ", round(mxnPerf, 3) + echo "--------------------------------------------------------------------------" + echo "Transposition: ", M,'x',N, " --> ", N, 'x', M + when not defined(windows): + echo "Time(ms): ", round(mxnTime, 3) + echo "Max RSS (KB): ", mxnMaxRss + echo "Runtime RSS (KB): ", mxnRuntimeRSS + echo "# of page faults: ", mxnPageFaults + echo "Perf (GMEMOPs/s ~ GigaMemory Operations/s) ", round(nxmPerf, 3) + +template runBench(tp: Threadpool, transposeName: typed, reorderCompute, isSequential: bool): untyped = + if not reorderCompute: + if not isSequential: + tp = Threadpool.new() + memUsage(mxnMaxRss, mxnRuntimeRss, mxnPageFaults): + when not defined(windows): + let start = wtime_msec() + for _ in 0 ..< nrounds: + tp.transposeName(M, N, bufIn, bufOut) + if not isSequential: + tp.syncAll() + when not defined(windows): + let stop = wtime_msec() + mxnTime = stop - start + + memUsage(nxmMaxRss, nxmRuntimeRss, nxmPageFaults): + when not defined(windows): + let start = wtime_msec() + for _ in 0 ..< nrounds: + tp.transposeName(N, M, bufIn, bufOut) + if not isSequential: + tp.syncAll() + when not defined(windows): + let stop = wtime_msec() + nxmTime = stop - start + + if not isSequential: + tp.shutdown() + + report(M, N, nthreads, nrounds, reorderCompute, + transposeStrat, reqOps, reqBytes, + mxnTime, mxnMaxRSS, mxnRuntimeRss, mxnPageFaults, + nxmTime, nxmMaxRSS, nxmRuntimeRss, nxmPageFaults + ) + + else: + if not isSequential: + tp = Threadpool.new() + memUsage(nxmMaxRss, nxmRuntimeRss, nxmPageFaults): + when not defined(windows): + let start = wtime_msec() + for _ in 0 ..< nrounds: + tp.transposeName(N, M, bufIn, bufOut) + if not isSequential: + tp.syncAll() + when not defined(windows): + let stop = wtime_msec() + nxmTime = stop - start + + memUsage(mxnMaxRss, mxnRuntimeRss, mxnPageFaults): + when not defined(windows): + let start = wtime_msec() + for _ in 0 ..< nrounds: + tp.transposeName(M, N, bufIn, bufOut) + if not isSequential: + tp.syncAll() + when not defined(windows): + let stop = wtime_msec() + mxnTime = stop - start + + if not isSequential: + tp.shutdown() + + report(M, N, nthreads, nrounds, reorderCompute, + transposeStrat, reqOps, reqBytes, + mxnTime, mxnMaxRSS, mxnRuntimeRss, mxnPageFaults, + nxmTime, nxmMaxRSS, nxmRuntimeRss, nxmPageFaults + ) + +# Interface +# --------------------------------------------------- + +proc main() = + + var + M = 400 + N = 4000 + nrounds = 1000 + transposeStrat = TiledNested + reorderCompute = false + + if paramCount() == 0: + let exeName = getAppFilename().extractFilename() + echo &"Usage: {exeName} " + echo &"Running with default M={M}, N={N}, rounds={nrounds}, transposeStrategy={transposeStrat}, reorderCompute={reorderCompute}" + elif paramCount() == 5: + M = paramStr(1).parseInt() + N = paramStr(2).parseInt() + nrounds = paramStr(3).parseInt() + transposeStrat = paramStr(4).parseEnum[:TransposeStrategy]() + reorderCompute = paramStr(5).parseBool() + else: + let exeName = getAppFilename().extractFilename() + echo &"Usage: {exeName} " + echo &"Default \"{exeName} {M} {N} {nrounds} {transposeStrat} {reorderCompute}\"" + quit 1 + + echo "Inverting the transpose order may favor one transposition heavily for non-tiled strategies" + + let isSequential = transposeStrat == Sequential + var nthreads: int32 + if transposeStrat == Sequential: + nthreads = 1 + elif existsEnv"CTT_NUM_THREADS": + nthreads = getEnv"CTT_NUM_THREADS".parseInt().int32 + else: + nthreads = countProcessors().int32 + + let (reqOps, reqBytes, bufSize) = computeMeta(M, N) + + let bufOut = wv_alloc(float32, bufSize) + let bufIn = wv_alloc(float32, bufSize) + + bufIn.initialize(bufSize) + + var mxnTime, nxmTime: float64 + + var tp: Threadpool + case transposeStrat + of Sequential: tp.runBench(sequentialTranspose, reorderCompute, isSequential) + of Naive: tp.runBench(cttNaiveTranspose, reorderCompute, isSequential) + of Nested: tp.runBench(cttNestedTranspose, reorderCompute, isSequential) + of TiledNested: tp.runBench(ctt2DTiledNestedTranspose, reorderCompute, isSequential) + + wv_free(bufOut) + wv_free(bufIn) + +main() \ No newline at end of file diff --git a/constantine/platforms/threadpool/benchmarks/nqueens/threadpool_nqueens.nim b/constantine/platforms/threadpool/benchmarks/nqueens/threadpool_nqueens.nim index 93fcd0b..146743a 100644 --- a/constantine/platforms/threadpool/benchmarks/nqueens/threadpool_nqueens.nim +++ b/constantine/platforms/threadpool/benchmarks/nqueens/threadpool_nqueens.nim @@ -218,7 +218,7 @@ proc main() = echo "Benchmark: N-queens" echo "Threads: ", nthreads when not defined(windows): - echo "Time(us) ", stop - start + echo "Time(ms) ", stop - start echo "Max RSS (KB): ", ru.ru_maxrss echo "Runtime RSS (KB): ", rss echo "# of page faults: ", flt diff --git a/constantine/platforms/threadpool/crossthread/backoff.nim b/constantine/platforms/threadpool/crossthread/backoff.nim index bf0a387..471126e 100644 --- a/constantine/platforms/threadpool/crossthread/backoff.nim +++ b/constantine/platforms/threadpool/crossthread/backoff.nim @@ -45,7 +45,7 @@ func initialize*(en: var EventNotifier) {.inline.} = func `=destroy`*(en: var EventNotifier) {.inline.} = en.futex.teardown() -func `=`*(dst: var EventNotifier, src: EventNotifier) {.error: "An event notifier cannot be copied".} +func `=copy`*(dst: var EventNotifier, src: EventNotifier) {.error: "An event notifier cannot be copied".} func `=sink`*(dst: var EventNotifier, src: EventNotifier) {.error: "An event notifier cannot be moved".} func prepareToPark*(en: var EventNotifier) {.inline.} = @@ -176,7 +176,7 @@ func initialize*(ec: var EventCount) {.inline.} = func `=destroy`*(ec: var EventCount) {.inline.} = ec.futex.teardown() -proc sleepy*(ec: var Eventcount): ParkingTicket {.inline.} = +proc sleepy*(ec: var Eventcount): ParkingTicket {.noInit, inline.} = ## To be called before checking if the condition to not sleep is met. ## Returns a ticket to be used when committing to sleep let prevState = ec.state.fetchAdd(kPreWait, moAcquireRelease) @@ -209,11 +209,11 @@ proc wakeAll*(ec: var EventCount) {.inline.} = if (prev and kAnyWaiterMask) != 0: ec.futex.wakeAll() -proc getNumWaiters*(ec: var EventCount): tuple[preSleep, committedSleep: uint32] {.inline.} = +proc getNumWaiters*(ec: var EventCount): tuple[preSleep, committedSleep: int32] {.noInit, inline.} = ## Get the number of idle threads: ## (planningToSleep, committedToSleep) let waiters = ec.state.load(moAcquire) - result.preSleep = uint32((waiters and kPreWaitMask) shr kPreWaitShift) - result.committedSleep = uint32(waiters and kWaitMask) + result.preSleep = cast[int32]((waiters and kPreWaitMask) shr kPreWaitShift) + result.committedSleep = cast[int32](waiters and kWaitMask) {.pop.} # {.push raises:[], checks:off.} \ No newline at end of file diff --git a/constantine/platforms/threadpool/crossthread/taskqueues.nim b/constantine/platforms/threadpool/crossthread/taskqueues.nim index 68dd310..55fa387 100644 --- a/constantine/platforms/threadpool/crossthread/taskqueues.nim +++ b/constantine/platforms/threadpool/crossthread/taskqueues.nim @@ -76,7 +76,7 @@ proc peek*(tq: var Taskqueue): int = ## ## This is a non-locking operation. let # Handle race conditions - b = tq.back.load(moAcquire) + b = tq.back.load(moRelaxed) # Only the producer peeks in the threadpool so moRelaxed is enough f = tq.front.load(moAcquire) if b >= f: @@ -199,7 +199,7 @@ proc pop*(tq: var Taskqueue): ptr Task = # Empty queue, no thieves can have a pointer to an old retired buffer tq.garbageCollect() -proc steal*(thiefID: uint32, tq: var Taskqueue): ptr Task = +proc steal*(thiefID: int32, tq: var Taskqueue): ptr Task = ## Dequeue an item at the front. Takes ownership of the item ## This is intended for consumers. var f = tq.front.load(moAcquire) @@ -244,7 +244,7 @@ proc stealHalfImpl(dst: var Buf, dstBack: int, src: var Taskqueue): int = if compareExchange(src.front, f, f+n, moSequentiallyConsistent, moRelaxed): return n -proc stealHalf*(thiefID: uint32, dst: var Taskqueue, src: var Taskqueue): ptr Task = +proc stealHalf*(thiefID: int32, dst: var Taskqueue, src: var Taskqueue): ptr Task = ## Dequeue up to half of the items in the `src` tq, fom the front. ## Return the last of those, or nil if none found diff --git a/constantine/platforms/threadpool/crossthread/tasks_flowvars.nim b/constantine/platforms/threadpool/crossthread/tasks_flowvars.nim index 7b24960..959092f 100644 --- a/constantine/platforms/threadpool/crossthread/tasks_flowvars.nim +++ b/constantine/platforms/threadpool/crossthread/tasks_flowvars.nim @@ -9,7 +9,7 @@ import std/atomics, ../instrumentation, - ../../allocs, + ../../allocs, ../../primitives, ./backoff # Tasks have an efficient design so that a single heap allocation @@ -29,9 +29,9 @@ type Task* = object # Intrusive metadata # ------------------ - parent*: ptr Task # When a task is awaiting, a thread can quickly prioritize the direct child of a task + parent*: ptr Task # When a task is awaiting, a thread can quickly prioritize the direct child of a task - thiefID*: Atomic[uint32] # ID of the worker that stole and run the task. For leapfrogging. + thiefID*: Atomic[int32] # ID of the worker that stole and run the task. For leapfrogging. # Result sync # ------------------ @@ -39,21 +39,50 @@ type completed*: Atomic[bool] waiter*: Atomic[ptr EventNotifier] + # Data parallelism + # ------------------ + isFirstIter*: bool # Awaitable for-loops return true for first iter. Loops are split before first iter. + loopStart*: int + loopStop*: int + loopStride*: int + loopStepsLeft*: int + reductionDAG*: ptr ReductionDagNode # For parallel loop reduction, merge with other range result + + # Dataflow parallelism + # -------------------- + dependsOnEvent: bool # We cannot leapfrog a task triggered by an event + # Execution # ------------------ - fn*: proc (param: pointer) {.nimcall, gcsafe, raises: [].} - # destroy*: proc (param: pointer) {.nimcall, gcsafe.} # Constantine only deals with plain old data - data*{.align:sizeof(int).}: UncheckedArray[byte] + fn*: proc (env: pointer) {.nimcall, gcsafe, raises: [].} + # destroy*: proc (env: pointer) {.nimcall, gcsafe.} # Constantine only deals with plain old data + envSize*: int32 + env*{.align:sizeof(int).}: UncheckedArray[byte] Flowvar*[T] = object + ## A Flowvar is a placeholder for a future result that may be computed in parallel task: ptr Task -const SentinelThief* = 0xFACADE'u32 + ReductionDagNode* = object + ## In a parallel reduction, when a loop a split the worker + ## keeps track of the tasks to gather results from in a private task-local linked-list. + ## Those forms a global computation directed acyclic graph + ## with the initial parallel reduction task as root. + # Note: While this requires an extra allocation per split + # the alternative, making an intrusive linked-list of reduction tasks + # require synchronization between threads. + task*: ptr Task + next*: ptr ReductionDagNode -proc new*( +# Tasks +# ------------------------------------------------------------------------- + +const SentinelThief* = 0xFACADE'i32 + +proc newSpawn*( T: typedesc[Task], parent: ptr Task, - fn: proc (param: pointer) {.nimcall, gcsafe.}): ptr Task {.inline.} = + fn: proc (env: pointer) {.nimcall, gcsafe, raises: [].}): ptr Task = const size = sizeof(T) @@ -64,15 +93,25 @@ proc new*( result.completed.store(false, moRelaxed) result.waiter.store(nil, moRelaxed) result.fn = fn + result.envSize = 0 -proc new*( + result.isFirstIter = false + result.loopStart = 0 + result.loopStop = 0 + result.loopStride = 0 + result.loopStepsLeft = 0 + result.reductionDAG = nil + + result.dependsOnEvent = false + +proc newSpawn*( T: typedesc[Task], parent: ptr Task, - fn: proc (param: pointer) {.nimcall, gcsafe, raises: [].}, - params: auto): ptr Task {.inline.} = + fn: proc (env: pointer) {.nimcall, gcsafe, raises: [].}, + env: auto): ptr Task = const size = sizeof(T) + # size without Unchecked - sizeof(params) + sizeof(env) result = allocHeapUnchecked(T, size) result.parent = parent @@ -81,7 +120,78 @@ proc new*( result.completed.store(false, moRelaxed) result.waiter.store(nil, moRelaxed) result.fn = fn - cast[ptr[type params]](result.data)[] = params + result.envSize = int32 sizeof(env) + cast[ptr[type env]](result.env)[] = env + + result.isFirstIter = false + result.loopStart = 0 + result.loopStop = 0 + result.loopStride = 0 + result.loopStepsLeft = 0 + result.reductionDAG = nil + + result.dependsOnEvent = false + +proc newLoop*( + T: typedesc[Task], + parent: ptr Task, + start, stop, stride: int, + isFirstIter: bool, + fn: proc (env: pointer) {.nimcall, gcsafe, raises: [].}): ptr Task = + const size = sizeof(T) + preCondition: start < stop + + result = allocHeapUnchecked(T, size) + result.parent = parent + result.thiefID.store(SentinelThief, moRelaxed) + result.hasFuture = false + result.completed.store(false, moRelaxed) + result.waiter.store(nil, moRelaxed) + result.fn = fn + result.envSize = 0 + + result.isFirstIter = isFirstIter + result.loopStart = start + result.loopStop = stop + result.loopStride = stride + result.loopStepsLeft = ceilDiv_vartime(stop-start, stride) + result.reductionDAG = nil + + result.dependsOnEvent = false + +proc newLoop*( + T: typedesc[Task], + parent: ptr Task, + start, stop, stride: int, + isFirstIter: bool, + fn: proc (env: pointer) {.nimcall, gcsafe, raises: [].}, + env: auto): ptr Task = + + const size = sizeof(T) + # size without Unchecked + sizeof(env) + preCondition: start < stop + + result = allocHeapUnchecked(T, size) + result.parent = parent + result.thiefID.store(SentinelThief, moRelaxed) + result.hasFuture = false + result.completed.store(false, moRelaxed) + result.waiter.store(nil, moRelaxed) + result.fn = fn + result.envSize = int32(sizeof(env)) + cast[ptr[type env]](result.env)[] = env + + result.isFirstIter = isFirstIter + result.loopStart = start + result.loopStop = stop + result.loopStride = stride + result.loopStepsLeft = ceilDiv_vartime(stop-start, stride) + result.reductionDAG = nil + + result.dependsOnEvent = false + +# Flowvars +# ------------------------------------------------------------------------- # proc `=copy`*[T](dst: var Flowvar[T], src: Flowvar[T]) {.error: "Futures/Flowvars cannot be copied".} @@ -91,9 +201,9 @@ proc newFlowVar*(T: typedesc, task: ptr Task): Flowvar[T] {.inline.} = # Task with future references themselves so that readyWith can be called # within the constructed - # proc async_fn(param: pointer) {.nimcall.} - # that can only access data - cast[ptr ptr Task](task.data.addr)[] = task + # proc threadpoolSpawn_fn(env: pointer) {.nimcall.} + # that can only access env + cast[ptr ptr Task](task.env.addr)[] = task proc cleanup*(fv: var Flowvar) {.inline.} = fv.task.freeHeap() @@ -117,13 +227,24 @@ func readyWith*[T](task: ptr Task, childResult: T) {.inline.} = ## Send the Flowvar result from the child thread processing the task ## to its parent thread. precondition: not task.completed.load(moAcquire) - cast[ptr (ptr Task, T)](task.data.addr)[1] = childResult + cast[ptr (ptr Task, T)](task.env.addr)[1] = childResult task.completed.store(true, moRelease) -proc sync*[T](fv: sink Flowvar[T]): T {.inline, gcsafe.} = +proc sync*[T](fv: sink Flowvar[T]): T {.noInit, inline, gcsafe.} = ## Blocks the current thread until the flowvar is available ## and returned. ## The thread is not idle and will complete pending tasks. mixin completeFuture + if fv.task.isNil: + zeroMem(result.addr, sizeof(T)) + return completeFuture(fv, result) cleanup(fv) + +# ReductionDagNodes +# ------------------------------------------------------------------------- + +proc newReductionDagNode*(task: ptr Task, next: ptr ReductionDagNode): ptr ReductionDagNode {.inline.} = + result = allocHeap(ReductionDagNode) + result.next = next + result.task = task \ No newline at end of file diff --git a/constantine/platforms/threadpool/demos/raytracing/README.md b/constantine/platforms/threadpool/demos/raytracing/README.md new file mode 100644 index 0000000..d60a48c --- /dev/null +++ b/constantine/platforms/threadpool/demos/raytracing/README.md @@ -0,0 +1,142 @@ +# Raytracing + +This is a port to Nim and Weave of +SmallPT by Kevin Beason https://www.kevinbeason.com/smallpt/ + +The original C++ version is also provided (with 4 extra lines to highlight original code quirks when porting). + +## Showcase + +The Nim version has can use a single parallel-for loop +or nested parallel-for loop for better load balancing (important when the inner loop .is actually larget than the outer loop) + +At the moment, there is no random number generator that can deal with +the dynamic thread migration of Weave so we get interesting artifacts +compared to the single-threaded or the single parallel-for versions. + +**Single-thread or single parallel-for** + +![ray_trace_300samples_nim_threaded](ray_trace_300samples_nim_threaded.png) + +**Nested parallel-for** + +![ray_trace_300samples_nim_nested](ray_trace_300samples_nim_nested.png) + +## Benchmark + +Note: except for the nested parallelism which has RNG issue, +the Nim and C++ versions are pixel equivalent. + +### Setup + +CPU: i9-9980XE, 18 cores, overclocked at 4.1GHz all-core turbo (from 3.0 nominal) +The code was compiled with default flag, hence x86-64, hence SSE2. + +- Nim devel (1.3.5 2020-05-16) + GCC v10.1.0 + - `nim c --threads:off -d:danger` + - `nim c --threads:on -d:danger` +- GCC v10.1.0 + - `-O3` + - `-O3 -fopenmp` +- GCC v8.4.0 + - `-O3` + - `-O3 -fopenmp` +- Clang v10.0.0 + - `-O3` + - `-O3 -fopenmp` + +### Commands + + +```bash +git clone https://github.com/mratsim/weave +cd weave +nimble install -y # install Weave dependencies, here synthesis, overwriting if asked. + +nim -v # Ensure you have nim 1.2.0 or more recent + +# Threads on (by default in this repo) +nim c -d:danger -o:build/ray_threaded demos/raytracing/smallpt.nim + +# Threads off +nim c -d:danger --threads:off -o:build/ray_single demos/raytracing/smallpt.nim + +g++ -O3 -o build/ray_gcc_single demos/raytracing/smallpt.cpp +g++ -O3 -fopenmp -o build/ray_gcc_omp demos/raytracing/smallpt.cpp + +clang++ -O3 -o build/ray_clang_single demos/raytracing/smallpt.cpp +clang++ -O3 -fopenmp -o build/ray_clang_omp demos/raytracing/smallpt.cpp +``` + +Then run for 300 samples with + +``` +build/ray_threaded 300 +# ... +build/ray_clang_omp 300 +``` + +### Results & Analysis + +GCC 10 has a significant OpenMP regression + +| Bench | Nim | Clang C++ OpenMP | GCC 10 C++ OpenMP | GCC 8 C++ OpenMP | +| ---------------- | ----------: | ---------------: | ----------------: | ---------------: | +| Single-threaded | 4min43.369s | 4m51.052s | 4min50.934s | 4m50.648s | +| Multithreaded | 12.977s | 14.428s | 2min14.616s | 12.244s | +| Nested-parallel | 12.981s | | | | +| Parallel speedup | 21.83x | 20.17x | 2.16x | 23.74x | + +Single-threaded Nim is 2.7% faster than Clang C++. +Multithreaded Nim via Weave is 11.1% faster Clang C++. + +GCC 8 despite a simpler OpenMP design (usage of a global task queue instead of work-stealing) +achieves a better speedup than both Weave and Clang. +In that case, I expect it's because the tasks are so big that there is minimal contention +on the task queue, furthermore the OpenMP schedule is "Dynamic" so we avoid the worst case scenario +with static scheduling where a bunch of threads are assigned easy rays that never collide with a surface +and a couple of threads are drowned in complex rays. + +I have absolutely no idea of what happened to OpenMP in GCC 10. + +Note: I only have 18 cores but we observe speedups in the 20x +with Weave and LLVM. This is probably due to 2 factors: +- Raytracing is pure compute, in particular contrary to high-performance computing + and machine learning workloads which are also very memory-intensive (matrices and tensors with thousands to millions of elements) + The scene has only 10 objects and a camera to keep track off. + Memory is extremely slow, you can do 100 additions while waiting for data + in the L2 cache. +- A CPU has a certain number of execution ports and can use instruction-level parallelism (we call that superscalar). Hyperthreading is a way to + use those extra execution ports. However in many computing workloads + the sibling cores are also competing for memory bandwidth. + From the previous point, this is not true for raytracing + and so we enjoy super linear speedup. + +## License + +Kevin Beason code is licensed under (mail redacted to avoid spam) + +``` +LICENSE + +Copyright (c) 2006-2008 Kevin Beason (.@gmail.com) + +Permission is hereby granted, free of charge, to any person obtaining +a copy of this software and associated documentation files (the +"Software"), to deal in the Software without restriction, including +without limitation the rights to use, copy, modify, merge, publish, +distribute, sublicense, and/or sell copies of the Software, and to +permit persons to whom the Software is furnished to do so, subject to +the following conditions: + +The above copyright notice and this permission notice shall be included +in all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, +EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF +MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. +IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY +CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, +TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE +SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. +``` diff --git a/constantine/platforms/threadpool/demos/raytracing/ray_trace_300samples_nim_nested.png b/constantine/platforms/threadpool/demos/raytracing/ray_trace_300samples_nim_nested.png new file mode 100644 index 0000000000000000000000000000000000000000..0cc99574857bdd7b437d792bf628ffd4714df050 GIT binary patch literal 1755775 zcmV)dK&QWnP)004R>004l5008;`004mK004C`008P>0026e000+ooVrmw00006 zVoOIv0RI600RN!9r;`8xfB;EEK~#7F1mVZCtxcXNX8qDK@bWJrC`o~M{qF`SL(i1)%CgKwpn|b*Qd|qdC>piKl?v(lmrAJ zOHR<+cqvK2iYjMY2!0tCRTS5GK>&3j3Bvt&%|t?qTLx=HRUvgkdR+r#(4nM|GY&br 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