From 8413dac87a3932114d26c23d93c35bd7f5a335f3 Mon Sep 17 00:00:00 2001 From: "Kevin Ransom (msft)" Date: Mon, 9 Sep 2019 16:43:34 -0700 Subject: [PATCH] Remove Dead code --- BigInteger (#7511) * Remove Dead code --- BigInteger * Put back FSharp.Math namespace ... even though it's empty * Improve empty namespace comment --- src/fsharp/FSharp.Core/FSharp.Core.fsproj | 6 - .../FSharp.Core/fslib-extra-pervasives.fsi | 1 - src/fsharp/FSharp.Core/math/n.fs | 1599 ----------------- src/fsharp/FSharp.Core/math/n.fsi | 59 - src/fsharp/FSharp.Core/math/z.fs | 356 +--- src/fsharp/FSharp.Core/math/z.fsi | 86 +- 6 files changed, 16 insertions(+), 2091 deletions(-) delete mode 100644 src/fsharp/FSharp.Core/math/n.fs delete mode 100644 src/fsharp/FSharp.Core/math/n.fsi diff --git a/src/fsharp/FSharp.Core/FSharp.Core.fsproj b/src/fsharp/FSharp.Core/FSharp.Core.fsproj index 588f72eae..03a83fca8 100644 --- a/src/fsharp/FSharp.Core/FSharp.Core.fsproj +++ b/src/fsharp/FSharp.Core/FSharp.Core.fsproj @@ -122,12 +122,6 @@ Reflection/reflect.fs - - Numerics/n.fsi - - - Numerics/n.fs - Numerics/z.fsi diff --git a/src/fsharp/FSharp.Core/fslib-extra-pervasives.fsi b/src/fsharp/FSharp.Core/fslib-extra-pervasives.fsi index 6cfbd860c..804d48bc3 100644 --- a/src/fsharp/FSharp.Core/fslib-extra-pervasives.fsi +++ b/src/fsharp/FSharp.Core/fslib-extra-pervasives.fsi @@ -11,7 +11,6 @@ module ExtraTopLevelOperators = open Microsoft.FSharp.Control open Microsoft.FSharp.Collections open Microsoft.FSharp.Text - open Microsoft.FSharp.Math #if !FX_NO_SYSTEM_CONSOLE /// Print to stdout using the given format. diff --git a/src/fsharp/FSharp.Core/math/n.fs b/src/fsharp/FSharp.Core/math/n.fs deleted file mode 100644 index f448940a8..000000000 --- a/src/fsharp/FSharp.Core/math/n.fs +++ /dev/null @@ -1,1599 +0,0 @@ -// Copyright (c) Microsoft Corporation. All Rights Reserved. See License.txt in the project root for license information. - -namespace Microsoft.FSharp.Math - -#if FX_NO_BIGINT -open System -open System.Diagnostics.CodeAnalysis -open Microsoft.FSharp.Core -open Microsoft.FSharp.Core.LanguagePrimitives.IntrinsicOperators -open Microsoft.FSharp.Core.Operators -open Microsoft.FSharp.Collections -open Microsoft.FSharp.Primitives.Basics - -type ints = int array - -[] -type internal BigNat = - - // Have n = sum (from i=0 to bound) a.[i] * baseN ^ i - // Have 0 <= a.[i] < baseN. - //------ - // Invariant: bound is least such, i.e. bound=0 or (a.[bound-1] is highest coeff). - // Zero is {bound=0,a=...}. - // Naturals are a normal form, - // but not structurally so, - // since arrays may have non-contributing cells at a.[bound] and beyond. - // - { mutable bound : int; // non-zero coeff must be 0...(bound-1) - digits : ints // must have at least elts 0...(bound-1), - // maybe more (which should be zero!). - // Actually, the "zero" condition may be relaxed. - // - } - - -module internal BigNatModule = - - //------------------------------------------------------------------------- - // misc - //----------------------------------------------------------------------- - - #if SELFTEST - let check b = if not b then failwith "assertion failwith" - #endif - - module FFT = - let rec pow32 x n = - if n=0 then 1 - elif n % 2 = 0 then pow32 (x*x) (n / 2) - else x* pow32 (x*x) (n / 2) - - let leastBounding2Power b = - let rec findBounding2Power b tp i = if b<=tp then tp,i else findBounding2Power b (tp*2) (i+1) in - findBounding2Power b 1 0 - - //------------------------------------------------------------------------- - // p = 2^k.m + 1 prime and w primitive 2^k root of 1 mod p - //----------------------------------------------------------------------- - - // Given p = 2^k.m + 1 prime and w a primitive 2^k root of unity (mod p). - // Required to define arithmetic ops for Fp = field modulo p. - // The following are possible choices for p. - - // p, k, m, g, w - // let p,k,m,g,w = 97L, 4, 6, 5, 8 // p is 7 bit - // let p,k,m,g,w = 769L, 8, 3, 7, 7 // p is 10 bit - // let p,k,m,g,w = 7681L, 8, 30, 13, 198 // p is 13 bit - // let p,k,m,g,w = 12289L, 10, 12, 11, 49 // p is 14 bit - // let p,k,m,g,w = 167772161L, 25, 5, 557092, 39162105 // p is 28 bit - // let p,k,m,g,w = 469762049L, 26, 7, 1226571, 288772249 // p is 29 bit - - - let p,k,m,g,w = 2013265921L, 27, 15, 31, 440564289 // p is 31 bit - let primeP = p - - let maxBitsInsideFp = 30 - - - //------------------------------------------------------------------------- - // Fp = finite field mod p - rep is uint32 - //----------------------------------------------------------------------- - - - type fp = uint32 - // operations in Fp (finite field size p) - module Fp = - //module I = UInt32 - let p = 2013265921ul : fp - let p64 = 2013265921UL : uint64 - let toInt (x:fp) : int = int32 x - let ofInt32 (x:int) : fp = uint32 x - - let mzero : fp = 0ul - let mone : fp = 1ul - let mtwo : fp = 2ul - let inline madd (x:fp) (y:fp) : fp = (x + y) % p - let inline msub (x:fp) (y:fp) : fp = (x + p - y) % p - let inline mmul (x:fp) (y:fp) : fp = uint32 ((uint64 x * uint64 y) % p64) - - let rec mpow x n = - if n=0 then mone - elif n % 2=0 then mpow (mmul x x) (n / 2) - else mmul x (mpow (mmul x x) (n / 2)) - - let rec mpowL x n = - if n = 0L then mone - elif n % 2L = 0L then mpowL (mmul x x) (n / 2L) - else mmul x (mpowL (mmul x x) (n / 2L)) - - // Have the w is primitive 2^kth root of 1 in Zp - let m2PowNthRoot n = - // Find x s.t. x is (2^n)th root of unity. - // - // pow w (pow 2 k) = 1 primitively. - // = pow w (pow 2 ((k-n)+n)) - // = pow w (pow 2 (k-n) * pow 2 n) - // = pow (pow w (pow 2 (k-n))) (pow 2 n) - // - // Take wn = pow (pow w (pow 2 (k-n))) - - mpow (uint32 w) (pow32 2 (k-n)) - - let minv x = mpowL x (primeP - 2L) - - - //------------------------------------------------------------------------- - // FFT - in place low garbage - //----------------------------------------------------------------------- - - open Fp - let rec computeFFT lambda mu n w (u: _[]) (res: _[]) offset = - // Given n a 2-power, - // w an nth root of 1 in Fp, and - // lambda, mu and u(x) defining - // poly(lambda,mu,x) = sum(i pow32 2 i) - - let computeFftPaddedPolynomialProduct bigK k u v = - // REQUIRES: bigK = 2^k - // REQUIRES: Array lengths of u and v = bigK. - // REQUIRES: degree(uv) <= bigK-1 - // --- - // Given u,v polynomials. - // Computes the product polynomial by FFT. - // For correctness, - // require the result coeff to be in range [0,p-1], for p defining Fp above. - - #if SELFTEST - check ( k <= maxTwoPower ); - check ( bigK = twoPowerTable.[k] ); - check ( u.Length = bigK ); - check ( v.Length = bigK ); - #endif - // Find 2^k primitive root of 1 - let w = m2PowNthRoot k - // FFT - let n = bigK - let uT = computFftInPlace n w u - let vT = computFftInPlace n w v - // Evaluate - let rT = Array.init n (fun i -> mmul uT.[i] vT.[i]) - // INV FFT - let r = computeInverseFftInPlace n w rT - r - - let padTo n (u: _ array) = - let uBound = u.Length - Array.init n (fun i -> if i mmul uT.[i] vT.[i]) - // INV FFT - let r = computeInverseFftInPlace n w rT - Array.map Fp.toInt r - - - //------------------------------------------------------------------------- - // fp exports - //----------------------------------------------------------------------- - - open Fp - let mzero = mzero - let mone = mone - let maxFp = msub Fp.p mone - - //------------------------------------------------------------------------- - // FFT - reference implementation - //----------------------------------------------------------------------- - - #if SELFTEST - open Fp - let rec computeFftReference n w u = - // Given n a 2-power, - // w an nth root of 1 in Fp, and - // u(x) = sum(i u.[2*i]) - let uodd = Array.init (n/2) (fun i -> u.[2*i+1]) - let uevenFT = computeFftReference (n/2) (mmul w w) ueven - let uoddFT = computeFftReference (n/2) (mmul w w) uodd - Array.init n - (fun j -> - if j < n/2 then - madd - (uevenFT.[j]) - (mmul - (mpow w j) - (uoddFT.[j])) - else - let j = j - (n/2) - msub - (uevenFT.[j]) - (mmul - (mpow w j) - (uoddFT.[j]))) - #endif - - open FFT - - type n = BigNat - - let bound (n: n) = n.bound - let setBound (n: n) (v:int32) = n.bound <- v - let coeff (n:n) i = n.digits.[i] - let coeff64 (n:n) i = int64 (coeff n i) - let setCoeff (n:n) i v = n.digits.[i] <- v - - let rec pow64 x n = - if n=0 then 1L - elif n % 2 = 0 then pow64 (x * x) (n / 2) - else x * (pow64 (x * x) (n / 2)) - - let rec pow32 x n = - if n=0 then 1 - elif n % 2 = 0 then pow32 (x*x) (n / 2) - else x* pow32 (x*x) (n / 2) - - let hash(n) = - let mutable res = 0 - for i = 0 to n.bound - 1 do // could stop soon, it's "hash" - res <- n.digits.[i] + (res <<< 3) - done; - res - - //---------------------------------------------------------------------------- - // misc - //-------------------------------------------------------------------------- - -#if CHECKED - let check b str = if not b then failwith ("check failed: " + str) -#endif - let maxInt a b = if a int32 - let inline div64base (x:int64) = int64 (uint64 x >>> baseBits) - - let divbase x = int32 (uint32 x >>> baseBits) - let modbase x = (x &&& baseMask) - - let inline index z i = if i < z.bound then z.digits.[i] else 0 - - let createN b = { bound = b; - digits = Array.zeroCreate b } - let copyN x = { bound = x.bound; - digits = Array.copy x.digits } // could copy just enough... - - let normN n = - // normalises bound - let rec findLeastBound (na:ints) i = if i = -1 || na.[i]<>0 then i+1 else findLeastBound na (i-1) - let bound = findLeastBound n.digits (n.bound-1) - n.bound <- bound; - n - - let boundInt = 2 // int will fit with bound=2 - let boundInt64 = 3 // int64 will fit with bound=3 - let boundBase = 1 // base will fit with bound=1 - obviously! - -//---------------------------------------------------------------------------- -// base, coefficients, poly -//-------------------------------------------------------------------------- - - let embed x = - let x = if x<0 then 0 else x // no -ve naturals - if x < baseN then - let r = createN 1 - r.digits.[0] <- x; - normN r - else - let r = createN boundInt - for i = 0 to boundInt - 1 do - r.digits.[i] <- (x / pow32 baseN i) % baseN - done; - normN r - - let embed64 x = - let x = if x<0L then 0L else x // no -ve naturals - let r = createN boundInt64 - for i = 0 to boundInt64-1 do - r.digits.[i] <- int32 ( (x / pow64 baseNi64 i) % baseNi64) - done; - normN r - - let eval n = - if n.bound = 1 - then n.digits.[0] - else - let mutable acc = 0 - for i = n.bound-1 downto 0 do - acc <- n.digits.[i] + baseN * acc - done; - acc - - let eval64 n = - if n.bound = 1 - then int64 n.digits.[0] - else - let mutable acc = 0L - for i = n.bound-1 downto 0 do - acc <- int64 (n.digits.[i]) + baseNi64 * acc - done; - acc - - let one = embed 1 - let zero = embed 0 - - let restrictTo d n = - { bound = minInt d n.bound; digits = n.digits} - - let shiftUp d n = - let m = createN (n.bound+d) - for i = 0 to n.bound-1 do - m.digits.[i+d] <- n.digits.[i] - done; - m - - let shiftDown d n = - if n.bound-d<=0 then - zero - else - let m = createN (n.bound-d) - for i = 0 to m.bound-1 do - m.digits.[i] <- n.digits.[i+d] - done; - m - - let degree n = n.bound-1 - - -//---------------------------------------------------------------------------- -// add, sub -//-------------------------------------------------------------------------- - - // addition - let rec addP i n c p q r = // p+q + c - if i0 then - r.digits.[i] <- modbase x; - let c = divbase x - // if p (or q) exhausted and c zero could switch to copying mode - subP (i+1) n c p q r - else - let x = x + baseN // add baseN - r.digits.[i] <- modbase x; - let c = divbase x - 1 // sub baseN - // if p (or q) exhausted and c zero could switch to copying mode - subP (i+1) n c p q r - else - let underflow = c<>0 - underflow - - let sub p q = - // NOTE: x-y=0 when x<=y, it is natural subtraction - let rbound = maxInt p.bound q.bound - let r = createN rbound - let carry = 0 - let underflow = subP 0 rbound carry p q r - if underflow then - embed 0 - else - normN r - - -//---------------------------------------------------------------------------- -// isZero, equal, ordering, sign, min, max -//-------------------------------------------------------------------------- - - let isZero p = p.bound=0 - let IsZero p = isZero p - let isOne p = p.bound=1 && p.digits.[0] = 1 - - let equal p q = - (p.bound = q.bound) && - (let rec check (pa:ints) (qa:ints) i = - // HAVE: pa.[j] = qa.[j] for i < j < p.bound - (i = -1) || (pa.[i]=qa.[i] && check pa qa (i-1)) - - check p.digits q.digits (p.bound-1)) - - let shiftCompare p pn q qn = - if p.bound + pn < q.bound + qn then -1 - elif p.bound + pn > q.bound + pn then 1 - else - let rec check (pa:ints) (qa:ints) i = - // HAVE: pa.[j-pn] = qa.[j-qn] for i < j < p.bound - // Looking for most significant differing coeffs to determine ordering - if i = -1 then - 0 - else - let pai = if i < pn then 0 else pa.[i-pn] - let qai = if i < qn then 0 else qa.[i-qn] - if pai = qai then check pa qa (i-1) - elif pai < qai then -1 - else 1 - - check p.digits q.digits (p.bound + pn - 1) - - let compare p q = - if p.bound < q.bound then -1 - elif p.bound > q.bound then 1 - else - let rec check (pa:ints) (qa:ints) i = - // HAVE: pa.[j] = qa.[j] for i < j < p.bound - // Looking for most significant differing coeffs to determine ordering - if i = -1 then 0 - elif pa.[i]=qa.[i] then check pa qa (i-1) - elif pa.[i]] - let lt p q = compare p q = -1 - [] - let gt p q = compare p q = 1 - [] - let lte p q = compare p q <> 1 - [] - let gte p q = compare p q <> -1 - - [] - let min a b = if lt a b then a else b - [] - let max a b = if lt a b then b else a - - -//---------------------------------------------------------------------------- -// scale -//-------------------------------------------------------------------------- - - // REQUIRE: baseN + baseN.2^32 < Int64.maxInt - let rec contributeArr (a:ints) i (c:int64) = - // Given c and require c < baseN.2^32 - // Compute: r <- r + c . B^i - // via r.digits.[i] <- r.digits.[i] + c and normalised - let x = int64 a.[i] + c - // HAVE: x < baseN + baseN.2^32 - let c = div64base x - let x = mod64base x - // HAVE: c < 1 + 2^32 < baseN.2^32, recursive call ok - // HAVE: x < baseN - a.[i] <- x; // store residue x - if c>0L then - contributeArr a (i+1) c // contribute carry next position - - let inline contribute r i c = contributeArr r.digits i c - - // REQUIRE: maxInt < 2^32 - [] - let rec scale (k:int) (p:n) = - // Given k and p and require k < 2^32 - // Computes "scalar" product k.p - // - let rbound = p.bound + boundInt - let r = createN rbound - let k = int64 k - for i = 0 to p.bound-1 do - let kpi = k * int64 p.digits.[i] - // HAVE: kpi < 2^32 * baseN which meets "contribute" requirement - contribute r i kpi - done; - normN r - - -//---------------------------------------------------------------------------- -// mulSchoolBook -//-------------------------------------------------------------------------- - - // multiplication: naively O(n^2) -(* - let mulSchoolBook' p q = - let rbound = p.bound + q.bound + boundBase*2 - let r = createN rbound - let pa = p.digits - let qa = q.digits - for i = 0 to p.bound-1 do - for j = 0 to q.bound-1 do - contribute r (i+j) (int64 pa.[i] * int64 qa.[j]) - done - done; - normN r -*) - - let mulSchoolBookBothSmall p q = - let r = createN 2 - let rak = int64 p * int64 q - setCoeff r 0 (mod64base rak); - setCoeff r 1 (int32 (div64base rak)) - normN r - - let rec mulSchoolBookCarry r c k = - if ( c > 0L ) then - // ToAdd = c.B^k - let rak = (coeff64 r k) + c - setCoeff r k (mod64base rak); - mulSchoolBookCarry r (div64base rak) (k + 1) - - let mulSchoolBookOneSmall p q = - let bp = bound(p) - let rbound = bp + 1 - let r = createN rbound - let q = int64 q - let mutable c = 0L - for i = 0 to bp-1 do - let rak = c + (coeff64 r i) + (coeff64 p i) * q - setCoeff r i (mod64base rak); - c <- div64base rak; - mulSchoolBookCarry r c bp - normN r - - - // multiplication: naively O(n^2) -- this version - unchecked - is faster - let mulSchoolBookNeitherSmall p q = - let rbound = p.bound + q.bound - let r = createN rbound - let ra = r.digits - let pa = p.digits - let qa = q.digits - // ToAdd p*q - for i = 0 to p.bound-1 do - // ToAdd p.[i] * q * B^i - let pai = int64 pa.[i] - let mutable c = 0L - let mutable k = i // k = i + j - // ToAdd = pi.qj.B^(i+j) for j = 0,j+1... - for j = 0 to q.bound-1 do - // ToAdd = c.B^k + pi.qj.B^(i+j) for j = j,j+1... and k = i+j - let qaj = int64 qa.[j] - let rak = int64 ra.[k] + c + pai * qaj - ra.[k] <- int32 (mod64base rak); - c <- div64base rak; - k <- k + 1; - mulSchoolBookCarry r c k - normN r - - let mulSchoolBook p q = - let pSmall = (bound(p) = 1) - let qSmall = (bound(q) = 1) - if (pSmall && qSmall) then mulSchoolBookBothSmall (coeff p 0) (coeff q 0) - elif pSmall then mulSchoolBookOneSmall q (coeff p 0) - elif qSmall then mulSchoolBookOneSmall p (coeff q 0) - else mulSchoolBookNeitherSmall p q - - -//---------------------------------------------------------------------------- -// quickMulUsingFft -//-------------------------------------------------------------------------- - - // The FFT polynomial multiplier requires the result coeffs fit inside Fp. - // - // OVERVIEW: - // The numbers are recoded as polynomials to be evaluated at (x=2^bigL). - // The polynomials are FFT multiplied, requiring result coeff to fit Fp. - // The result product is recovered by evaluating the poly at (x=2^bigL). - // - // REF: - // QuickMul: Practical FFT-base Integer Multiplication, - // Chee Yap and Chen Yi. - // - // There is choice of how to encode the nats polynomials. - // The choice is the (2^bigL) base to use. - // For bigL=1, the FFT will cater for a product of upto 256M bits. - // Larger bigL have less reach, but compute faster. - // So plan to choose bigL depending on the number of bits product. - // - // DETERMINING THE K,L BOUNDS. - // - // Given representing using K-vectors, K a power of 2, K=2^k, and - // If choosing inputs to have L-bit coefficients. - // - // The result coeff are: - // - // res(i) = sum (j] - type encoding = - { bigL : int; // bits per input coeff - twoToBigL : int; // 2^bigL - k : int; - bigK : int; // bigK = 2^k, number of terms polynomials - bigN : int; // bits result (under-estimate of limit) - split : int; // baseBits / bigL - splits : int array; - } - -#if CHECKED - let _ = check (baseBits=24) "24bit" -#endif - // Requiring baseN mod 2^bigL = 0 gave quick encoding, but... - // also a terrible drop performance when the bigK jumped by more than needed! - // Below, it choose a minimal bigK to hold the product. - - let mkEncoding (bigL,k,bigK,bigN) = -#if CHECKED - check (bigK = pow32 2 k) "bigK"; - check (bigN = bigK * bigL) "bigN"; - check (2 * bigL + k <= maxBitsInsideFp) "constraint"; -#endif - { bigL = bigL; - twoToBigL = pow32 2 bigL; - k = k; - bigK = bigK; - bigN = bigN; - split = baseBits/bigL; // should divide exactly - splits = Array.init (baseBits/bigL) (fun i -> pow32 2 (bigL*i)) - } - - let table = - [| // bigL , k , bigK , bigN // - mkEncoding ( 1 , 28 , 268435456 , 268435456 ) ; - mkEncoding ( 2 , 26 , 67108864 , 134217728 ) ; - mkEncoding ( 3 , 24 , 16777216 , 50331648 ) ; - mkEncoding ( 4 , 22 , 4194304 , 16777216 ) ; - mkEncoding ( 5 , 20 , 1048576 , 5242880 ) ; - mkEncoding ( 6 , 18 , 262144 , 1572864 ) ; - mkEncoding ( 7 , 16 , 65536 , 458752 ) ; - mkEncoding ( 8 , 14 , 16384 , 131072 ) ; - mkEncoding ( 9 , 12 , 4096 , 36864 ) ; - mkEncoding ( 10 , 10 , 1024 , 10240 ) ; - mkEncoding ( 11 , 8 , 256 , 2816 ) ; - mkEncoding ( 12 , 6 , 64 , 768 ) ; - mkEncoding ( 13 , 4 , 16 , 208 ) ; - |] - - let calculateTableTow bigL = - // Given L. - // Have L via "log2 K <= maxBitsInsideFp - 2L". - // Have N via "N = K.L" - // - let k = maxBitsInsideFp - 2*bigL - let bigK = pow64 2L k - let N = bigK * int64 bigL - bigL,k,bigK,N - - let encodingGivenResultBits bitsRes = - // choose maximum bigL s.t. bitsRes < bigN - // EXCEPTION: fails is bitsRes exceeds 2^28 (largest bigN table) - let rec selectFrom i = - if i+1 < table.Length && bitsRes < table.[i+1].bigN then - selectFrom (i+1) - else - table.[i] - - if bitsRes >= table.[0].bigN then - failwith "Product is huge, around 268435456 bits, beyond quickmul" - else - selectFrom 0 - - let bitmask = Array.init baseBits (fun i -> (pow32 2 i - 1)) - let twopowers = Array.init baseBits (fun i -> (pow32 2 i)) - let twopowersI64 = Array.init baseBits (fun i -> (pow64 2L i)) - // bitmask(k) = 2^k - 1 - // twopowers(k) = 2^k // - - let wordBits word = - let rec hi k = - if k=0 then 0 - elif (word &&& twopowers.[k-1]) <> 0 then k - else hi (k-1) - - hi baseBits - - let bits u = - if u.bound=0 then 0 - else degree u * baseBits + wordBits u.digits.[degree u] - - let extractBits n enc bi = - let bj = bi + enc.bigL - 1 // the last bit (inclusive) - let biw = bi / baseBits // first bit is this index pos - let bjw = bj / baseBits // last bit is this index pos - if biw <> bjw then - // two words - let x = index n biw - let y = index n bjw // bjw = biw+1 - let xbit = bi % baseBits // start bit x - let nxbits = baseBits - xbit // number of bitsin x - let x = x >>> xbit // shift down x so bit0 is first - let y = y <<< nxbits // shift up y so it starts where x finished - let x = x ||| y // combine them - let x = x &&& bitmask.[enc.bigL] // mask out (high y bits) to get required bits - x - else - // one word - let x = index n biw - let xbit = bi % baseBits // start bit x - let x = x >>> xbit - let x = x &&& bitmask.[enc.bigL] - x - - let encodePoly enc n = - // Find poly s.t. n = poly evaluated at x=2^bigL - // with 0 <= pi < 2^bigL. - // - let poly = Array.create enc.bigK (Fp.ofInt32 0) - let biMax = n.bound * baseBits - let rec encoder i bi = - // bi = i * bigL - if i=enc.bigK || bi > biMax then - () // done - else - ( let pi = extractBits n enc bi - poly.[i] <- Fp.ofInt32 pi; - let i = i + 1 - let bi = bi + enc.bigL - encoder i bi - ) - - encoder 0 0; - poly - - let decodeResultBits enc (poly : fp array) = - // Decoding evaluates poly(x) (coeff Fp) at X = 2^bigL. - // A bound on number of result bits is "enc.bigN + boundInt", but that takes HUGE STEPS. - // Garbage has a cost, so we minimize it by working out a tight bound. - // - // poly(X) = sum i=0..n coeff_i * X^i where n is highest non-zero coeff. - // <= 2^maxBitsInsideFp * (1 + X + ... X^n) - // <= 2^maxBitsInsideFp * (X^(n+1) - 1) / (X - 1) - // <= 2^maxBitsInsideFp * X^(n+1) / (X - 1) - // <= 2^maxBitsInsideFp * X^(n+1) / (X/2) provided X/2 <= X-1 - // <= 2^maxBitsInsideFp * X^n * 2 - // <= 2^maxBitsInsideFp * (2^bigL)^n * 2 - // <= 2^(maxBitsInsideFp + bigL.n + 1) - // - let mutable n = 0 - for i = 0 to poly.Length-1 do - if poly.[i] <> mzero then n <- i - done; - let rbits = maxBitsInsideFp + enc.bigL * n + 1 - rbits + 1 // +1 since 2^1 requires 2 bits not 1 - - // REQUIRE: bigL <= baseBits - let decodePoly enc poly = - // Find n = poly evaluated at x=2^bigL - // Note, 0 <= pi < maxFp. - // - let rbound = (decodeResultBits enc poly) / baseBits + 1 - let r = createN rbound - let rec evaluate i j d = - // HAVE: bigL.i = j * baseBits + d and d= rbound then -#if CHECKED - check (poly.[i] = mzero) "decodePoly"; -#endif - () - else ( - let x = int64 (Fp.toInt poly.[i]) * twopowersI64.[d] - // HAVE: x < 2^32 . 2^baseBits = 2^32.baseN - contribute r j x - ); - let i = i + 1 - let d = d + enc.bigL - let j,d = if d >= baseBits then j+1 , d-baseBits else j,d - // HAVE: d < baseBits, note: bigL minDigitsKaratsuba then - let k = bmax / 2 - let a0 = restrictTo k p - let a1 = shiftDown k p - let b0 = restrictTo k q - let b1 = shiftDown k q - let q0 = mul a0 b0 - let q1 = mul (add a0 a1) (add b0 b1) - let q2 = mul a1 b1 - let p0 = q0 - let p1 = sub q1 (add q0 q2) - let p2 = q2 - let r = add p0 (shiftUp k (add p1 (shiftUp k p2))) - r - else - mulSchoolBook p q - - let rec mulKaratsuba x y = recMulKaratsuba mulKaratsuba x y - - -//---------------------------------------------------------------------------- -// mul - composite -//-------------------------------------------------------------------------- - - let productDigitsUpperSchoolBook = (64000 / baseBits) - // When is it worth switching away from SchoolBook? - // SchoolBook overhead is low, so although it's O(n^2) it remains competitive. - // - // 28/3/2006: - // The FFT can take over from SchoolBook at around 64000 bits. - // Note, FFT performance is stepwise, according to enc from table. - // The steps are big steps (meaning sudden jumps/drops perf). - // - - let singleDigitForceSchoolBook = (32000 / baseBits) - // If either argument is "small" then stay with SchoolBook. - // - - let productDigitsUpperFft = (table.[0].bigN / baseBits) - // QuickMul is good upto a finite (but huge) limit: - // Limit 268,435,456 bits product. - // - // From the code: - // let bitsRes = bits u + bits v - // fails when bitsRes >= table.[0].bigN - // So, not applicable when: - // P1: table.[0].bigN <= bits(u) + bits(v) - // P2: table.[0].bigN <= .. <= baseBits * (u.bound + v.bound) - // P3: table.[0].bigN <= .. <= baseBits * (u.bound + v.bound) - // P4: table.[0].bigN / baseBits <= u.bound + v.bound - // - - // Summary of mul algorithm choice: - // 0 <= uv_bound < upper_school_book - Schoolbook - // upper_school_book <= uv_bound < upper_fft - QuickMul - // upper_fft <= uv_bound < ... - Karatsuba - // - // NOTE: - // - Karatsuba current implementation has high garbage cost. - // - However, a linear space cost is possible... - // - Meantime, switch to Karatsuba only beyond FFT range. - // - - let rec mul p q = - let pqBound = p.bound + q.bound - if pqBound < productDigitsUpperSchoolBook || - p.bound < singleDigitForceSchoolBook || - q.bound < singleDigitForceSchoolBook - then - // Within school-book initial range: - mulSchoolBook p q - else - if pqBound < productDigitsUpperFft then - // Inside QuickMul FFT range: - quickMulUsingFft p q - else - // Beyond QuickMul FFT range, or maybe between Schoolbook and QuickMul (no!): - // Use karatsuba method, with "mul" as recursive multiplier, - // so will reduce sizes of products on recursive calls, - // and QuickMul will take over if they fall within it's range. - // - recMulKaratsuba mul p q - - -//---------------------------------------------------------------------------- -// division - scaleSubInPlace -//-------------------------------------------------------------------------- - - let scaleSubInPlace x f a n = - // Have x = sumR 0 xd (\i.xi.B^i) where xd = degree x - // a = sumR 0 ad (\i.digitsi.B^i) where ad = degree a - // f < B - // n < xd - // Assumes "f.digits.B^n < x". - // Required to remove f.digits.B^n from x place. - //------ - // Result = x_initial - f.digits.B^n - // = x_initial - f.[sumR 0 ad (\i.digitsi.B^(i+n))] - // State: j = 0 - // z = f * a0 - // Invariant(x,z,j,n): - // P1: x_result = x - z.B^(j+n) - f.[sumR (j+1) ad (\i.digitsi.B^i+n)] - // P2: z < B^2 - 1, and so has form z = zHi.B + zLo for zHi,zLo < B. - // Base: Invariant holds initially. - // Step: (a) Remove zLo from x: - // If zLo <= x_(j+n) then zLo <- 0 - // x_(j+n) <- x_(j+n) - zLo - // else zLo <- 0 - // x_(j+n) <- x_(j+n) + (B - zLo) - // = x_(j+n) - zLo + B - // zHi <- zHi + 1 - // Here, invariant P1 still holds, P2 may break. - // (b) Advance j: - // Have z = zHi.B since zLo = 0. - // j <- j + 1 - // z <- zHi + f * a_(j+1) - // P2 holds: - // Have z <= B + (B-1)*(B-1) = B + B^2 - 2B + 1 = B^2 - B + 1 - // Have z <= B^2 - 1 when B >= 2 which is required for B being a base. - // P1 holds, - // moved f.digits_(j+1).B^(j+1+n) factor over. - // - // Once j+1 exceeds ad, summation is zero and it contributes no more terms (b). - // Continue until z = 0, which happens since z decreases towards 0. - // Done. - // - let invariant (_,_,_) = () - #if CHECKED - let x_initial = copyN x - let x_result = sub x_initial (shiftUp n (scale f a)) - let invariant (z,j,n) = - let P1 = - equal - x_result - (sub x (add (shiftUp (j+n) (embed64 z)) - (mul (embed f) - (shiftUp (j+1+n) (shiftDown (j+1) a))))) - let P2 = z < baseNi64 * baseNi64 - 1L - check P1 "P1"; - check P2 "P2" - - #endif - let xres = x - let x,xd = x.digits,degree x - let a,ad = a.digits,degree a - let f = int64 f - let mutable j = 0 - let mutable z = f * int64 a.[0] - while( z > 0L || j < ad ) do - if j > xd then failwith "scaleSubInPlace: pre-condition did not apply, result would be -ve"; - invariant(z,j,n); // P1,P2 hold - let mutable zLo = mod64base z |> int32 - let mutable zHi = div64base z - if zLo <= x.[j+n] then - x.[j+n] <- x.[j+n] - zLo - else ( - x.[j+n] <- x.[j+n] + (baseN - zLo); - zHi <- zHi + 1L - ); - // P1 holds - if j < ad then - z <- zHi + f * int64 a.[j+1] - else - z <- zHi; - j <- j + 1; - // P1,P2 hold - done; - ignore (normN xres) - - // - let scaleSub x f a n = - let freshx = add x zero - scaleSubInPlace freshx f a n; - normN freshx -(* - - let scaleSub2 x f a n = sub x (shiftUp n (mul (embed f) a)) - - let x = (mul (embed 234234234) (pow (embed 10) (embed 20))) - let f = 2 - let a = (embed 1231231231) - let n = 2 - let res = scaleSub x f a n - let res2 = scaleSub2 x f a n - - let x, xd, f, a, ad, n = freshx.digits, freshx.bound, f, a.digits, a.bound, n - *) - - -//---------------------------------------------------------------------------- -// division - scaleAddInPlace -//-------------------------------------------------------------------------- - - let scaleAddInPlace x f a n = - // Have x = sumR 0 xd (\i.xi.B^i) - // a = sumR 0 ad (\i.digitsi.B^i) - // f < B - // n < xd - // Required to add f.digits.B^n to x place. - // Assumes result will fit with x (0...xd). - //------ - // Result = x_initial + f.digits.B^n - // = x_initial + f.[sumR 0 ad (\i.digitsi.B^i+n)] - // State: j = 0 - // z = f * a0 - // Invariant(x,z,j,n): - // P1: x_result = x + z.B^(j+n) + f.[sumR (j+1) ad (\i.digitsi.B^i+n)] - // P2: z < B^2 - 1, and so has form z = zHi.B + zLo for zHi,zLo < B. - // Base: Invariant holds initially. - // Step: (a) Add zLo to x: - // If zLo < B - x_(j+n) then zLo <- 0 - // x_(j+n) <- x_(j+n) + zLo - // else zLo <- 0 - // x_(j+n) <- zLo - (B - x_(j+n)) - // = x_(j+n) + zLo - B - // zHi <- zHi + 1 - // Here, invariant P1 still holds, P2 may break. - // (b) Advance j: - // Have z = zHi.B since zLo = 0. - // j <- j + 1 - // z <- zHi + f * a_(j+1) - // P2 holds: - // Have z <= B + (B-1)*(B-1) = B + B^2 - 2B + 1 = B^2 - B + 1 - // Have z <= B^2 - 1 when B >= 2 which is required for B being a base. - // P1 holds, - // moved f.digits_(j+1).B^(j+1+n) factor over. - // - // Once j+1 exceeds ad, summation is zero and it contributes no more terms (b). - // Continue until z = 0, which happens since z decreases towards 0. - // Done. - // - let invariant (_,_,_) = () -#if CHECKED - let x_initial = copyN x - let x_result = add x_initial (shiftUp n (scale f a)) - let invariant (z,j,n) = - let P1 = - equal - x_result - (add x (add (shiftUp (j+n) (embed64 z)) - (mul (embed f) - (shiftUp (j+1+n) (shiftDown (j+1) a))))) - let P2 = z < baseNi64 * baseNi64 - 1L - check P1 "P1"; - check P2 "P2" - -#endif - let xres = x - let x,xd = x.digits,degree x - let a,ad = a.digits,degree a - let f = int64 f - let mutable j = 0 - let mutable z = f * int64 a.[0] - while( z > 0L || j < ad ) do - if j > xd then failwith "scaleSubInPlace: pre-condition did not apply, result would be -ve"; - invariant(z,j,n); // P1,P2 hold - let mutable zLo = mod64base z |> int32 - let mutable zHi = div64base z - if zLo < baseN - x.[j+n] then - x.[j+n] <- x.[j+n] + zLo - else ( - x.[j+n] <- zLo - (baseN - x.[j+n]); - zHi <- zHi + 1L - ); - // P1 holds - if j < ad then - z <- zHi + f * int64 a.[j+1] - else - z <- zHi; - j <- j + 1; - // P1,P2 hold - done; - ignore (normN xres) - - // - let scaleAdd x f a n = - let freshx = add x zero - scaleAddInPlace freshx f a n; - normN freshx - -(* - let scaleAdd2 x f a n = add x (shiftUp n (mul (embed f) a)) - - let x = (mul (embed 234234234) (pow (embed 10) (embed 20))) - let f = 2 - let a = (embed 1231231231) - let n = 2 - let res = scaleAdd x f a n - let res2 = scaleAdd2 x f a n - - let x, xd, f, a, ad, n = freshx.digits, freshx.bound, f, a.digits, a.bound, n -*) - -//---------------------------------------------------------------------------- -// division - removeFactor -//-------------------------------------------------------------------------- - - (* - let removeFactorReference x a n = - let ff = div x (shiftUp n a) - toInt ff - *) - - let removeFactor x a n = - // Assumes x < a.B^(n+1) - // Choose f s.t. - // (a) f.digits.B^n <= x - // (b) f=0 iff x < a.B^n - // - let dega,degx = degree a,degree x - if degx < dega + n then 0 else // possible with "normalisation" - let aa,xa = a.digits,x.digits - let f = - if dega = 0 then // a = a0 - if degx = n then - xa.[n] / aa.[0] - else ( -#if CHECKED - check (degx = n+1) "removeFactor degx#1"; -#endif - let f64 = (int64 xa.[degx] * baseNi64 + int64 xa.[degx-1]) / int64 aa.[0] - int32 f64 - ) - else // a = sumR 0 dega (\i.digitsi.B^i) - if degx = dega + n then - xa.[degx] / (aa.[dega] + 1) // +1 to bound above a - else ( -#if CHECKED - check (degx = dega+n+1) "removeFactor degx#2"; -#endif - let f64 = (int64 xa.[degx] * baseNi64 + int64 xa.[degx-1]) - / (int64 aa.[dega] + 1L) // +1 to bound above a - int32 f64 - ) - - if f = 0 then - let lte = (shiftCompare a n x 0) <> 1 - if lte then 1 else 0 - else - f - - -//---------------------------------------------------------------------------- -// division - divmod -//-------------------------------------------------------------------------- - - let divmod b a = - // Returns d,r where b = d.digits + r and r0 then - scaleSubInPlace x f a n; - scaleAddInPlace d f one n; - Invariant(d,x,n,p) - else - finished <- f=0 && n=0; - if not finished then - if p = m+n then - Invariant(d,x,n-1,p); - n <- n-1 - else - Invariant(d,x,n-1,p-1); - n <- n-1; - p <- p-1 - // Have: "b = d.digits + x" return d,x - normN d,normN x - - //---------------------------------------------------------------------------- - // div, mod - //-------------------------------------------------------------------------- - - [] - let div b a = fst (divmod b a) - [] - let rem b a = snd (divmod b a) - // rem b a, for small a can do (base mod a) trick - O(N) - - - //---------------------------------------------------------------------------- - // hcf - //-------------------------------------------------------------------------- - - let hcf a b = - // Have: 0 <= a,b since naturals - let rec hcfloop a b = // Require: 0 <= a <= b - if equal zero a then b - else - // Have: 0 < a <= b - let _,r = divmod b a - // Have: r < a from divmod - hcfloop r a // Have: 0 <= r < a - - if lt a b then hcfloop a b // Have: 0 <= a < b - else hcfloop b a // Have: 0 <= b <= a - - //---------------------------------------------------------------------------- - // pow - //-------------------------------------------------------------------------- - - let two = embed 2 - let powi x n = - let rec power acc x n = - if n=0 then acc - elif n % 2=0 then power acc (mul x x) (n / 2) - else power (mul x acc) (mul x x) (n / 2) - - power one x n - - let pow x n = - let rec power acc x n = - if isZero n then acc - else - let ndiv2,nmod2 = divmod n two // use: intdivmod when available - if isZero nmod2 then power acc (mul x x) ndiv2 - else power (mul x acc) (mul x x) ndiv2 - - power one x n - -//---------------------------------------------------------------------------- -// float n -//-------------------------------------------------------------------------- - - let toFloat n = - let basef = float baseN - let rec evalFloat acc k i = - if i = n.bound then - acc - else - evalFloat (acc + k * float n.digits.[i]) (k * basef) (i+1) - evalFloat 0.0 1.0 0 - -//---------------------------------------------------------------------------- -// n <-> int -//-------------------------------------------------------------------------- - - let ofInt32 n = embed n - let ofInt64 n = embed64 n - - /// Convert BigNat to uint32 otherwise OverflowException. - let toUInt32 n = - match n.bound with - | 0 -> 0u - | 1 -> n.digits.[0] |> uint32 - | 2 -> let xA,xB = n.digits.[0],n.digits.[1] - if xB > baseMask32B then raise (System.OverflowException()) - ( uint32 (xA &&& baseMask32A)) + - ((uint32 (xB &&& baseMask32B)) <<< baseShift32B) - | _ -> raise (System.OverflowException()) - - /// Convert BigNat to uint64 otherwise OverflowException. - let toUInt64 n = - match n.bound with - | 0 -> 0UL - | 1 -> n.digits.[0] |> uint64 - | 2 -> let xA,xB = n.digits.[0],n.digits.[1] - ( uint64 (xA &&& baseMask64A)) + - ((uint64 (xB &&& baseMask64B)) <<< baseShift64B) - | 3 -> let xA,xB,xC = n.digits.[0],n.digits.[1],n.digits.[2] - if xC > baseMask64C then raise (System.OverflowException()) - ( uint64 (xA &&& baseMask64A)) + - ((uint64 (xB &&& baseMask64B)) <<< baseShift64B) + - ((uint64 (xC &&& baseMask64C)) <<< baseShift64C) - | _ -> raise (System.OverflowException()) - - -//---------------------------------------------------------------------------- -// n -> string -//-------------------------------------------------------------------------- - - -#if CHECKED - let checks = false -#endif - let toString n = - // Much better complexity than naive_string_of_z. - // It still does "nDigit" calls to (int)divmod, - // but the degree on which it is called halves (not decrements) each time. - // - let degn = degree n - let rec route prior k ten2k = - if degree ten2k > degn - then (k,ten2k) :: prior - else route ((k,ten2k) :: prior) (k+1) (mul ten2k ten2k) - let kten2ks = route [] 0 (embed 10) - let rec collect isLeading digits n = function - | [] -> - // Have 0 <= n < 10^1, so collect a single digit (if needed) - let n = eval n -#if CHECKED - if checks then check (0 <= n) "toString: digit0"; - if checks then check (n <= 9) "toString: digit9"; -#endif - if isLeading && n=0 then digits // suppress leading 0 - else string n :: digits - | (_,ten2k) :: prior -> -#if CHECKED - if checks then check (lt n (mul ten2k ten2k)) "string_of_int: bound n"; -#endif - // Have 0 <= n < (ten2k)^2 and ten2k = 10^(2^k) - let nH,nL = divmod n ten2k -#if CHECKED - if checks then check (lt nH ten2k) "string_of_int: bound nH"; - if checks then check (lt nL ten2k) "string_of_int: bound nL"; -#endif - // Have 0 <= nH,nL < (ten2k) and ten2k = 10^(2^k) - if isLeading && isZero nH then - // suppress leading 0s - let digits = collect isLeading digits nL prior - digits - else - let digits = collect false digits nL prior - let digits = collect isLeading digits nH prior - digits - - let prior = kten2ks - let digits = collect true [] n prior - match digits with - | [] -> "0" - | _ -> digits |> Array.ofList |> System.String.Concat - -//---------------------------------------------------------------------------- -// n <- string -//-------------------------------------------------------------------------- - - let ofString (str:string) = - // Would it be better to split string half and combine results? - let len = str.Length - if System.String.IsNullOrEmpty str then invalidArg "str" "empty string"; - let ten = embed 10 - let rec build acc i = - if i=len then - acc - else - let c = str.[i] - let d = int c - int '0' - if 0 <= d && d <= 9 then - build (add (mul ten acc) (embed d)) (i+1) - else - raise (new System.FormatException(SR.GetString(SR.badFormatString))) - - build (embed 0) 0 - - let isSmall n = (n.bound <= 1) - let getSmall n = index n 0 - - //---------------------------------------------------------------------------- - // factorial - //-------------------------------------------------------------------------- - - let factorial n = - //***** - // Factorial(n) = 1.2.3.....(n-1).n - // - // Factorial is sometimes used as a test for multiplication. - // The QuickMul FFT multiplier takes over only when both operands reach a given size. - // How to compute factorial? - // - // (a) Factorial(n) = factorial(n-1).n - // This is unlikely to make use of the FFT (n never large enough). - // (b) Factorial(n) = (1.2.3.4....k) . (k.[k+1]...(n-1).n) - // Applied recursively QuickMul FFT will take over on large products. - // - //**** - let rec productR a b = - if equal a b then a - else - let m = div (add a b) (ofInt32 2) - mul (productR a m) (productR (add m one) b) - - productR one n - - -#endif diff --git a/src/fsharp/FSharp.Core/math/n.fsi b/src/fsharp/FSharp.Core/math/n.fsi deleted file mode 100644 index 78f44e6d4..000000000 --- a/src/fsharp/FSharp.Core/math/n.fsi +++ /dev/null @@ -1,59 +0,0 @@ -// Copyright (c) Microsoft Corporation. All Rights Reserved. See License.txt in the project root for license information. - -namespace Microsoft.FSharp.Math - -#if FX_NO_BIGINT -open Microsoft.FSharp.Collections -open Microsoft.FSharp.Core - -/// Abstract internal type -[] -type internal BigNat - -module internal BigNatModule = - - val zero : BigNat - val one : BigNat - val two : BigNat - - val add : BigNat -> BigNat -> BigNat - val sub : BigNat -> BigNat -> BigNat - val mul : BigNat -> BigNat -> BigNat - val divmod : BigNat -> BigNat -> BigNat * BigNat - val div : BigNat -> BigNat -> BigNat - val rem : BigNat -> BigNat -> BigNat - val hcf : BigNat -> BigNat -> BigNat - - val min : BigNat -> BigNat -> BigNat - val max : BigNat -> BigNat -> BigNat - val scale : int -> BigNat -> BigNat - val powi : BigNat -> int -> BigNat - val pow : BigNat -> BigNat -> BigNat - - val IsZero : BigNat -> bool - val isZero : BigNat -> bool - val isOne : BigNat -> bool - val equal : BigNat -> BigNat -> bool - val compare : BigNat -> BigNat -> int - val lt : BigNat -> BigNat -> bool - val gt : BigNat -> BigNat -> bool - val lte : BigNat -> BigNat -> bool - val gte : BigNat -> BigNat -> bool - - val hash : BigNat -> int - val toFloat : BigNat -> float - val ofInt32 : int -> BigNat - val ofInt64 : int64 -> BigNat - val toString : BigNat -> string - val ofString : string -> BigNat - - val toUInt32 : BigNat -> uint32 - val toUInt64 : BigNat -> uint64 - - val factorial : BigNat -> BigNat - // val randomBits : int -> BigNat - val bits : BigNat -> int - val isSmall : BigNat -> bool (* will fit in int32 (but not nec all int32) *) - val getSmall : BigNat -> int32 (* get the value, if it satisfies isSmall *) - -#endif diff --git a/src/fsharp/FSharp.Core/math/z.fs b/src/fsharp/FSharp.Core/math/z.fs index c9e9614b3..fa6599431 100644 --- a/src/fsharp/FSharp.Core/math/z.fs +++ b/src/fsharp/FSharp.Core/math/z.fs @@ -1,337 +1,19 @@ // Copyright (c) Microsoft Corporation. All Rights Reserved. See License.txt in the project root for license information. #nowarn "44" // This construct is deprecated. This function is for use by compiled F# code and should not be used directly -namespace System.Numerics -#if FX_NO_BIGINT - open Microsoft.FSharp.Collections - open Microsoft.FSharp.Core - open Microsoft.FSharp.Core.Operators - open Microsoft.FSharp.Core.LanguagePrimitives.IntrinsicOperators - open Microsoft.FSharp.Primitives.Basics - open Microsoft.FSharp.Math - open System - open System.Globalization - - - // INVARIANT: signInt = 1 or -1 - // value(z) = signInt * v - // NOTE: 0 has two repns (+1,0) or (-1,0). - [] - [] -#if !NETSTANDARD - [] -#endif - type BigInteger(signInt:int, v : BigNat) = - - static let smallLim = 4096 - static let smallPosTab = Array.init smallLim BigNatModule.ofInt32 - static let one = BigInteger(1) - static let zero = BigInteger(0) - - static member internal nat n = - if BigNatModule.isSmall n && BigNatModule.getSmall n < smallLim - then smallPosTab.[BigNatModule.getSmall n] - else n - - static member internal create (s,n) = BigInteger(s,BigInteger.nat n) - - static member internal posn n = BigInteger(1,BigInteger.nat n) - - static member internal negn n = BigInteger(-1,BigInteger.nat n) - - member x.Sign = if x.IsZero then 0 else signInt - - member x.SignInt = signInt - - member internal x.V = v - - static member op_Equality (x:BigInteger, y:BigInteger) = - //System.Console.WriteLine("x = {0}",box x) - //System.Console.WriteLine("y = {0}",box y) - match x.SignInt,y.SignInt with - | 1, 1 -> BigNatModule.equal x.V y.V // +1.xv = +1.yv iff xv = yv - | -1, -1 -> BigNatModule.equal x.V y.V // -1.xv = -1.yv iff xv = yv - | 1,-1 -> BigNatModule.isZero x.V && BigNatModule.isZero y.V // 1.xv = -1.yv iff xv=0 and yv=0 - | -1, 1 -> BigNatModule.isZero x.V && BigNatModule.isZero y.V // -1.xv = 1.yv iff xv=0 and yv=0 - | 0, 0 -> true - | 0, 1 -> BigNatModule.isZero y.V - | 0, -1 -> BigNatModule.isZero y.V - | 1, 0 -> BigNatModule.isZero x.V - | -1, 0 -> BigNatModule.isZero x.V - | _ -> invalidArg "x" "signs should be +/- 1 or 0" - - static member op_Inequality (x:BigInteger, y:BigInteger) = not (BigInteger.op_Equality(x,y)) // CA2226: OperatorsShouldHaveSymmetricalOverloads - - static member op_LessThan (x:BigInteger, y:BigInteger) = - match x.SignInt,y.SignInt with - | 1, 1 -> BigNatModule.lt x.V y.V // 1.xv < 1.yv iff xv < yv - | -1,-1 -> BigNatModule.lt y.V x.V // -1.xv < -1.yv iff yv < xv - | 1,-1 -> false // 1.xv < -1.yv iff 0 <= 1.xv < -1.yv <= 0 iff false - | -1, 1 -> not (BigNatModule.isZero x.V) || not (BigNatModule.isZero y.V) - // -1.xv < 1.yv - // (a) xv=0 and yv=0, then false - // (b) xv<>0, -1.xv < 0 <= 1.yv, so true - // (c) yv<>0, -1.xv <= 0 < 1.yv, so true - | 0, 0 -> false - | 0, 1 -> not (BigNatModule.isZero y.V) - | 0,-1 -> false - | 1, 0 -> false - | -1, 0 -> not (BigNatModule.isZero x.V) - | _ -> invalidArg "x" "signs should be +/- 1 or 0" - - static member op_GreaterThan (x:BigInteger, y:BigInteger) = // Follow lt by +/- symmetry - match x.SignInt,y.SignInt with - | 1, 1 -> BigNatModule.gt x.V y.V - | -1,-1 -> BigNatModule.gt y.V x.V - | 1,-1 -> not (BigNatModule.isZero x.V) || not (BigNatModule.isZero y.V) - | -1, 1 -> false - | 0, 0 -> false - | 0, 1 -> false - | 0,-1 -> not (BigNatModule.isZero y.V) - | 1, 0 -> not (BigNatModule.isZero x.V) - | -1, 0 -> false - | _ -> invalidArg "x" "signs should be +/- 1 or 0" - - static member internal compare(n,nn) = if BigInteger.op_LessThan(n,nn) then -1 elif BigInteger.op_Equality(n,nn) then 0 else 1 - - static member internal hash (z:BigInteger) = - if z.SignInt = 0 then 1 // 1 is hashcode for initialized BigInteger.Zero - else z.SignInt + BigNatModule.hash(z.V) - - override x.ToString() = - match x.SignInt with - | 1 -> BigNatModule.toString x.V // positive - | -1 -> - if BigNatModule.isZero x.V - then "0" // not negative in fact, but zero. - else "-" + BigNatModule.toString x.V // negative - | 0 -> "0" - | _ -> invalidOp "signs should be +/- 1 or 0" - - member x.StructuredDisplayString = x.ToString() - - interface System.IComparable with - member this.CompareTo(obj:obj) = - match obj with - | :? BigInteger as that -> BigInteger.compare(this,that) - | _ -> invalidArg "obj" "the objects are not comparable" - - override this.Equals(obj) = - match obj with - | :? BigInteger as that -> BigInteger.op_Equality(this, that) - | _ -> false - - override x.GetHashCode() = BigInteger.hash(x) - - new (n:int) = - if n>=0 - then BigInteger (1,BigInteger.nat(BigNatModule.ofInt32 n)) - elif (n = System.Int32.MinValue) - then BigInteger(-1,BigInteger.nat(BigNatModule.ofInt64 (-(int64 n)))) - else BigInteger(-1,BigInteger.nat(BigNatModule.ofInt32 (-n))) - - new (n:int64) = - if n>=0L - then BigInteger(1,BigInteger.nat (BigNatModule.ofInt64 n)) - elif (n = System.Int64.MinValue) - then BigInteger(-1,BigInteger.nat (BigNatModule.add (BigNatModule.ofInt64 System.Int64.MaxValue) BigNatModule.one) ) - else BigInteger(-1,BigInteger.nat (BigNatModule.ofInt64 (-n))) - - static member One = one +namespace Microsoft.FSharp.Math - static member Zero = zero - - static member (~-) (z:BigInteger) = - match z.SignInt with - | 0 -> BigInteger.Zero - | i -> BigInteger.create(-i, z.V) - - static member Scale(k, z:BigInteger) = - if z.SignInt = 0 then BigInteger.Zero else - if k<0 - then BigInteger.create(-z.SignInt, (BigNatModule.scale (-k) z.V)) // k.zsign.zv = -zsign.(-k.zv) - else BigInteger.create(z.SignInt, (BigNatModule.scale k z.V)) // k.zsign.zv = zsign.k.zv - - // Result: 1.nx - 1.ny (integer subtraction) - static member internal subnn (nx,ny) = - if BigNatModule.gte nx ny - then BigInteger.posn (BigNatModule.sub nx ny) // nx >= ny, result +ve, +1.(nx - ny) - else BigInteger.negn (BigNatModule.sub ny nx) // nx < ny, result -ve, -1.(ny - nx) - - static member internal addnn (nx,ny) = - BigInteger.posn (BigNatModule.add nx ny) // Compute "nx + ny" to be integer - - member x.IsZero = x.SignInt = 0 || BigNatModule.isZero x.V - - member x.IsOne = (x.SignInt = 1) && BigNatModule.isOne x.V // signx.xv = 1 iff signx = +1 and xv = 1 - - static member (+) (x:BigInteger,y:BigInteger) = - if y.IsZero then x else - if x.IsZero then y else - match x.SignInt,y.SignInt with - | 1, 1 -> BigInteger.addnn(x.V,y.V) // 1.xv + 1.yv = (xv + yv) - | -1,-1 -> -(BigInteger.addnn(x.V,y.V)) // -1.xv + -1.yv = -(xv + yv) - | 1,-1 -> BigInteger.subnn (x.V,y.V) // 1.xv + -1.yv = (xv - yv) - | -1, 1 -> BigInteger.subnn(y.V,x.V) // -1.xv + 1.yv = (yv - xv) - | _ -> invalidArg "x" "signs should be +/- 1" - - static member (-) (x:BigInteger,y:BigInteger) = - if y.IsZero then x else - if x.IsZero then -y else - match x.SignInt,y.SignInt with - | 1, 1 -> BigInteger.subnn(x.V,y.V) // 1.xv - 1.yv = (xv - yv) - | -1,-1 -> BigInteger.subnn(y.V,x.V) // -1.xv - -1.yv = (yv - xv) - | 1,-1 -> BigInteger.addnn(x.V,y.V) // 1.xv - -1.yv = (xv + yv) - | -1, 1 -> -(BigInteger.addnn(x.V,y.V)) // -1.xv - 1.yv = -(xv + yv) - | _ -> invalidArg "x" "signs should be +/- 1" - - static member ( * ) (x:BigInteger,y:BigInteger) = - if x.IsZero then x - elif y.IsZero then y - elif x.IsOne then y - elif y.IsOne then x - else - let m = (BigNatModule.mul x.V y.V) - BigInteger.create (x.SignInt * y.SignInt,m) // xsign.xv * ysign.yv = (xsign.ysign).(xv.yv) - - static member DivRem (x:BigInteger, y:BigInteger, []rem:BigInteger byref) = - if y.IsZero then raise (new System.DivideByZeroException()) - if x.IsZero then - rem <- BigInteger.Zero - BigInteger.Zero - else - let d,r = BigNatModule.divmod x.V y.V - // HAVE: |x| = d.|y| + r and 0 <= r < |y| - // HAVE: xv = d.yv + r and 0 <= r < yv - match x.SignInt,y.SignInt with - | 1, 1 -> rem <- BigInteger.posn r ; BigInteger.posn d // 1.xv = 1.d.( 1.yv) + ( 1.r) - | -1,-1 -> rem <- BigInteger.negn r ; BigInteger.posn d // -1.xv = 1.d.(-1.yv) + (-1.r) - | 1,-1 -> rem <- BigInteger.posn r ; BigInteger.negn d // 1.xv = -1.d.(-1.yv) + ( 1.r) - | -1, 1 -> rem <- BigInteger.negn r ; BigInteger.negn d // -1.xv = -1.d.( 1.yv) + (-1.r) - | _ -> invalidArg "x" "signs should be +/- 1" - - static member (/) (x:BigInteger,y:BigInteger) = - let mutable rem = new BigInteger(0) - BigInteger.DivRem(x,y,&rem) - - static member (%) (x:BigInteger,y:BigInteger) = - let mutable rem = new BigInteger(0) - BigInteger.DivRem(x,y,&rem) |> ignore ; rem - - static member GreatestCommonDivisor (x:BigInteger,y:BigInteger) = - match x.SignInt,y.SignInt with - | 0, 0 -> BigInteger.Zero - | 0, _ -> BigInteger.posn y.V - | _, 0 -> BigInteger.posn x.V - | _ -> BigInteger.posn (BigNatModule.hcf x.V y.V) // hcf (xsign.xv,ysign.yv) = hcf (xv,yv) - - member x.IsNegative = x.SignInt = -1 && not (x.IsZero) // signx.xv < 0 iff signx = -1 and xv<>0 - - member x.IsPositive = x.SignInt = 1 && not (x.IsZero) // signx.xv > 0 iff signx = +1 and xv<>0 - - static member Abs (x:BigInteger) = if x.SignInt = -1 then -x else x - - static member op_LessThanOrEqual (x:BigInteger,y:BigInteger) = - match x.SignInt,y.SignInt with - | 1, 1 -> BigNatModule.lte x.V y.V // 1.xv <= 1.yv iff xv <= yv - | -1,-1 -> BigNatModule.lte y.V x.V // -1.xv <= -1.yv iff yv <= xv - | 1,-1 -> BigNatModule.isZero x.V && BigNatModule.isZero y.V // 1.xv <= -1.yv, - // (a) if xv=0 and yv=0 then true - // (b) otherwise false, only meet at zero. - - | -1, 1 -> true // -1.xv <= 1.yv, true - | 0, 0 -> true - | 1, 0 -> BigNatModule.isZero x.V - | -1, 0 -> true - | 0, 1 -> true - | 0,-1 -> BigNatModule.isZero y.V - | _ -> invalidArg "x" "signs should be +/- 1 or 0" - - static member op_GreaterThanOrEqual (x:BigInteger,y:BigInteger) = // Follow lte by +/- symmetry - match x.SignInt,y.SignInt with - | 1, 1 -> BigNatModule.gte x.V y.V - | -1,-1 -> BigNatModule.gte y.V x.V - | 1,-1 -> true - | -1, 1 -> BigNatModule.isZero x.V && BigNatModule.isZero y.V - | 0, 0 -> true - | 1, 0 -> true - | -1, 0 -> BigNatModule.isZero x.V - | 0, 1 -> BigNatModule.isZero y.V - | 0,-1 -> true - | _ -> invalidArg "x" "signs should be +/- 1 or 0" - - static member Pow (x:BigInteger,y:int32) = - if y < 0 then raise (new System.ArgumentOutOfRangeException("y", (SR.GetString(SR.inputMustBeNonNegative)))) - match x.IsZero, y with - | true, 0 -> BigInteger.One - | true, _ -> BigInteger.Zero - | _ -> - let yval = BigInteger(y) - BigInteger.create ((if BigNatModule.isZero (BigNatModule.rem yval.V BigNatModule.two) then 1 else x.SignInt), BigNatModule.pow x.V yval.V) - - static member op_Explicit (x:BigInteger) = - if x.IsZero then 0 else - let u = BigNatModule.toUInt32 x.V - if u <= uint32 System.Int32.MaxValue then - // Handle range [-MaxValue,MaxValue] - x.SignInt * int32 u - elif x.SignInt = -1 && u = uint32 (System.Int32.MaxValue + 1) then - //assert(System.Int32.MinValue = 0 - System.Int32.MaxValue - 1) - // Handle MinValue = -(MaxValue+1) special case not covered by the above - System.Int32.MinValue - else - raise (System.OverflowException()) - - static member op_Explicit (x:BigInteger) = - if x.IsZero then 0L else - let u = BigNatModule.toUInt64 x.V - if u <= uint64 System.Int64.MaxValue then - (* Handle range [-MaxValue,MaxValue] *) - int64 x.SignInt * int64 u - elif x.SignInt = -1 && u = uint64 (System.Int64.MaxValue + 1L) then - //assert(System.Int64.MinValue = 0 - System.Int64.MaxValue - 1L) - (* Handle MinValue = -(MaxValue+1) special case not covered by the above *) - System.Int64.MinValue - else - raise (System.OverflowException()) - - static member op_Explicit (x:BigInteger) = - match x.SignInt with - | 1 -> BigNatModule.toFloat x.V // float (1.xv) = float (xv) - | -1 -> - (BigNatModule.toFloat x.V) // float (-1.xv) = - float (xv) - | 0 -> 0. - | _ -> invalidArg "x" "signs should be +/- 1 or 0" - - static member Parse(text:string) = - if isNull text then raise (new ArgumentNullException("text")) - let text = text.Trim() - let len = text.Length - if len = 0 then raise (new System.FormatException(SR.GetString(SR.badFormatString))) - match text.[0], len with - | '-', 1 -> raise (new System.FormatException(SR.GetString(SR.badFormatString))) - | '-', _ -> BigInteger.negn (BigNatModule.ofString text.[1..len-1]) - | '+', 1 -> raise (new System.FormatException(SR.GetString(SR.badFormatString))) - | '+', _ -> BigInteger.posn (BigNatModule.ofString text.[1..len-1]) - | _ -> BigInteger.posn (BigNatModule.ofString text) - - member internal x.IsSmall = x.IsZero || BigNatModule.isSmall (x.V) - - static member Factorial (x:BigInteger) = - if x.IsNegative then invalidArg "x" (SR.GetString(SR.inputMustBeNonNegative)) - if x.IsPositive then BigInteger.posn (BigNatModule.factorial x.V) - else BigInteger.One - - static member ( ~+ )(n1:BigInteger) = n1 - - static member FromInt64(x:int64) = new BigInteger(x) - - static member FromInt32(x:int32) = new BigInteger(x) -#endif +// Deliberately left empty +// +// FSharp.Core previously exposed the namespace Microsoft.FSharp.Math even though there were no types in it. +// This retains that. +// Existing programs could, and did contain the line: +// open FSharp.Math +// namespace Microsoft.FSharp.Core - type bigint = System.Numerics.BigInteger open System @@ -341,22 +23,6 @@ namespace Microsoft.FSharp.Core open Microsoft.FSharp.Core.LanguagePrimitives.IntrinsicOperators open System.Numerics -#if FX_NO_BIGINT - // FxCop suppressions - [] - [] - [] - [] - [] - [] - [] - [] - [] - [] - [] - do() -#endif - [] module NumericLiterals = @@ -402,14 +68,10 @@ namespace Microsoft.FSharp.Core res else let v = -#if FX_NO_BIGINT - BigInteger.Parse s -#else if isOX s then BigInteger.Parse (s.[2..],NumberStyles.AllowHexSpecifier,CultureInfo.InvariantCulture) else BigInteger.Parse (s,NumberStyles.AllowLeadingSign,CultureInfo.InvariantCulture) -#endif res <- v tabParse.[s] <- res res) @@ -421,5 +83,3 @@ namespace Microsoft.FSharp.Core (FromStringDynamic text :?> 'T) when 'T : BigInteger = getParse text - - diff --git a/src/fsharp/FSharp.Core/math/z.fsi b/src/fsharp/FSharp.Core/math/z.fsi index 3ea632763..e49b1b3d5 100644 --- a/src/fsharp/FSharp.Core/math/z.fsi +++ b/src/fsharp/FSharp.Core/math/z.fsi @@ -1,82 +1,14 @@ // Copyright (c) Microsoft Corporation. All Rights Reserved. See License.txt in the project root for license information. -namespace System.Numerics -#if FX_NO_BIGINT - - open System - open Microsoft.FSharp.Collections - open Microsoft.FSharp.Core - - /// The type of arbitrary-sized integers - [] - [] - type BigInteger = - /// Return the sum of two big integers - static member ( + ) : x:BigInteger * y:BigInteger -> BigInteger - /// Return the modulus of big integers - static member ( % ) : x:BigInteger * y:BigInteger -> BigInteger - /// Return the product of big integers - static member ( * ) : x:BigInteger * y:BigInteger -> BigInteger - /// Return the difference of two big integers - static member ( - ) : x:BigInteger * y:BigInteger -> BigInteger - /// Return the ratio of two big integers - static member ( / ) : x:BigInteger * y:BigInteger -> BigInteger - /// Return the negation of a big integer - static member (~-) : x:BigInteger -> BigInteger - /// Return the given big integer - static member (~+) : x:BigInteger -> BigInteger - /// Convert a big integer to a floating point number - static member op_Explicit : x:BigInteger -> float - /// Convert a big integer to a 64-bit signed integer - static member op_Explicit : x:BigInteger -> int64 - /// Convert a big integer to a 32-bit signed integer - static member op_Explicit : x:BigInteger -> int32 - /// Parse a big integer from a string format - static member Parse : text:string -> BigInteger - /// Return the sign of a big integer: 0, +1 or -1 - member Sign : int - /// Compute the ratio and remainder of two big integers - static member DivRem : x:BigInteger * y:BigInteger * []rem:BigInteger byref -> BigInteger - - /// This operator is for consistency when this type be used from other CLI languages - static member op_LessThan : x:BigInteger * y:BigInteger -> bool - /// This operator is for consistency when this type be used from other CLI languages - static member op_LessThanOrEqual : x:BigInteger * y:BigInteger -> bool - /// This operator is for consistency when this type be used from other CLI languages - static member op_GreaterThan : x:BigInteger * y:BigInteger -> bool - /// This operator is for consistency when this type be used from other CLI languages - static member op_GreaterThanOrEqual : x:BigInteger * y:BigInteger -> bool - /// This operator is for consistency when this type be used from other CLI languages - static member op_Equality : x:BigInteger * y:BigInteger -> bool - /// This operator is for consistency when this type be used from other CLI languages - static member op_Inequality : x:BigInteger * y:BigInteger -> bool - - /// Return the greatest common divisor of two big integers - static member GreatestCommonDivisor : x:BigInteger * y:BigInteger -> BigInteger - /// Return n^m for two big integers - static member Pow : x:BigInteger * y:int32 -> BigInteger - /// Compute the absolute value of a big integer - static member Abs : x:BigInteger -> BigInteger - /// Get the big integer for zero - static member Zero : BigInteger - /// Get the big integer for one - static member One : BigInteger - - /// Return true if a big integer is 'zero' - member IsZero : bool - /// Return true if a big integer is 'one' - member IsOne : bool - interface System.IComparable - override Equals : obj -> bool - override GetHashCode : unit -> int - override ToString : unit -> string - - /// Construct a BigInteger value for the given integer - new : x:int -> BigInteger - /// Construct a BigInteger value for the given 64-bit integer - new : x:int64 -> BigInteger -#endif +namespace Microsoft.FSharp.Math +// Deliberately left empty +// +// FSharp.Core previously exposed the namespace Microsoft.FSharp.Math even though there were no types in it. +// This retains that. +// Existing programs could, and did contain the line: +// open FSharp.Math +// namespace Microsoft.FSharp.Core @@ -104,5 +36,3 @@ namespace Microsoft.FSharp.Core val FromInt64Dynamic : value:int64 -> obj /// Provides a default implementations of F# numeric literal syntax for literals of the form 'dddI' val FromStringDynamic : text:string -> obj - - -- GitLab