mirror of
https://github.com/c64scene-ar/llvm-6502.git
synced 2024-12-13 04:30:23 +00:00
856361cb06
ScaledNumber has been cleaned up enough to pull out of BFI now. Still work to do there (tests for shifting, bloated printing code, etc.), but it seems clean enough for its new home. git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@211562 91177308-0d34-0410-b5e6-96231b3b80d8
320 lines
8.8 KiB
C++
320 lines
8.8 KiB
C++
//==- lib/Support/ScaledNumber.cpp - Support for scaled numbers -*- C++ -*-===//
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//
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// The LLVM Compiler Infrastructure
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//
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// This file is distributed under the University of Illinois Open Source
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// License. See LICENSE.TXT for details.
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//
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//===----------------------------------------------------------------------===//
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//
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// Implementation of some scaled number algorithms.
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//
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//===----------------------------------------------------------------------===//
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#include "llvm/Support/ScaledNumber.h"
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#include "llvm/ADT/APFloat.h"
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#include "llvm/Support/Debug.h"
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using namespace llvm;
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using namespace llvm::ScaledNumbers;
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std::pair<uint64_t, int16_t> ScaledNumbers::multiply64(uint64_t LHS,
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uint64_t RHS) {
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// Separate into two 32-bit digits (U.L).
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auto getU = [](uint64_t N) { return N >> 32; };
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auto getL = [](uint64_t N) { return N & UINT32_MAX; };
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uint64_t UL = getU(LHS), LL = getL(LHS), UR = getU(RHS), LR = getL(RHS);
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// Compute cross products.
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uint64_t P1 = UL * UR, P2 = UL * LR, P3 = LL * UR, P4 = LL * LR;
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// Sum into two 64-bit digits.
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uint64_t Upper = P1, Lower = P4;
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auto addWithCarry = [&](uint64_t N) {
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uint64_t NewLower = Lower + (getL(N) << 32);
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Upper += getU(N) + (NewLower < Lower);
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Lower = NewLower;
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};
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addWithCarry(P2);
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addWithCarry(P3);
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// Check whether the upper digit is empty.
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if (!Upper)
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return std::make_pair(Lower, 0);
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// Shift as little as possible to maximize precision.
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unsigned LeadingZeros = countLeadingZeros(Upper);
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int Shift = 64 - LeadingZeros;
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if (LeadingZeros)
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Upper = Upper << LeadingZeros | Lower >> Shift;
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return getRounded(Upper, Shift,
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Shift && (Lower & UINT64_C(1) << (Shift - 1)));
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}
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static uint64_t getHalf(uint64_t N) { return (N >> 1) + (N & 1); }
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std::pair<uint32_t, int16_t> ScaledNumbers::divide32(uint32_t Dividend,
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uint32_t Divisor) {
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assert(Dividend && "expected non-zero dividend");
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assert(Divisor && "expected non-zero divisor");
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// Use 64-bit math and canonicalize the dividend to gain precision.
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uint64_t Dividend64 = Dividend;
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int Shift = 0;
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if (int Zeros = countLeadingZeros(Dividend64)) {
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Shift -= Zeros;
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Dividend64 <<= Zeros;
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}
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uint64_t Quotient = Dividend64 / Divisor;
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uint64_t Remainder = Dividend64 % Divisor;
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// If Quotient needs to be shifted, leave the rounding to getAdjusted().
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if (Quotient > UINT32_MAX)
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return getAdjusted<uint32_t>(Quotient, Shift);
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// Round based on the value of the next bit.
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return getRounded<uint32_t>(Quotient, Shift, Remainder >= getHalf(Divisor));
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}
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std::pair<uint64_t, int16_t> ScaledNumbers::divide64(uint64_t Dividend,
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uint64_t Divisor) {
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assert(Dividend && "expected non-zero dividend");
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assert(Divisor && "expected non-zero divisor");
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// Minimize size of divisor.
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int Shift = 0;
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if (int Zeros = countTrailingZeros(Divisor)) {
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Shift -= Zeros;
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Divisor >>= Zeros;
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}
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// Check for powers of two.
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if (Divisor == 1)
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return std::make_pair(Dividend, Shift);
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// Maximize size of dividend.
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if (int Zeros = countLeadingZeros(Dividend)) {
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Shift -= Zeros;
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Dividend <<= Zeros;
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}
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// Start with the result of a divide.
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uint64_t Quotient = Dividend / Divisor;
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Dividend %= Divisor;
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// Continue building the quotient with long division.
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while (!(Quotient >> 63) && Dividend) {
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// Shift Dividend and check for overflow.
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bool IsOverflow = Dividend >> 63;
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Dividend <<= 1;
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--Shift;
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// Get the next bit of Quotient.
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Quotient <<= 1;
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if (IsOverflow || Divisor <= Dividend) {
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Quotient |= 1;
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Dividend -= Divisor;
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}
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}
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return getRounded(Quotient, Shift, Dividend >= getHalf(Divisor));
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}
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int ScaledNumbers::compareImpl(uint64_t L, uint64_t R, int ScaleDiff) {
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assert(ScaleDiff >= 0 && "wrong argument order");
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assert(ScaleDiff < 64 && "numbers too far apart");
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uint64_t L_adjusted = L >> ScaleDiff;
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if (L_adjusted < R)
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return -1;
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if (L_adjusted > R)
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return 1;
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return L > L_adjusted << ScaleDiff ? 1 : 0;
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}
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static void appendDigit(std::string &Str, unsigned D) {
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assert(D < 10);
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Str += '0' + D % 10;
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}
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static void appendNumber(std::string &Str, uint64_t N) {
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while (N) {
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appendDigit(Str, N % 10);
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N /= 10;
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}
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}
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static bool doesRoundUp(char Digit) {
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switch (Digit) {
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case '5':
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case '6':
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case '7':
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case '8':
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case '9':
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return true;
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default:
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return false;
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}
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}
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static std::string toStringAPFloat(uint64_t D, int E, unsigned Precision) {
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assert(E >= ScaledNumbers::MinScale);
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assert(E <= ScaledNumbers::MaxScale);
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// Find a new E, but don't let it increase past MaxScale.
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int LeadingZeros = ScaledNumberBase::countLeadingZeros64(D);
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int NewE = std::min(ScaledNumbers::MaxScale, E + 63 - LeadingZeros);
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int Shift = 63 - (NewE - E);
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assert(Shift <= LeadingZeros);
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assert(Shift == LeadingZeros || NewE == ScaledNumbers::MaxScale);
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D <<= Shift;
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E = NewE;
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// Check for a denormal.
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unsigned AdjustedE = E + 16383;
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if (!(D >> 63)) {
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assert(E == ScaledNumbers::MaxScale);
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AdjustedE = 0;
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}
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// Build the float and print it.
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uint64_t RawBits[2] = {D, AdjustedE};
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APFloat Float(APFloat::x87DoubleExtended, APInt(80, RawBits));
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SmallVector<char, 24> Chars;
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Float.toString(Chars, Precision, 0);
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return std::string(Chars.begin(), Chars.end());
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}
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static std::string stripTrailingZeros(const std::string &Float) {
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size_t NonZero = Float.find_last_not_of('0');
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assert(NonZero != std::string::npos && "no . in floating point string");
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if (Float[NonZero] == '.')
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++NonZero;
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return Float.substr(0, NonZero + 1);
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}
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std::string ScaledNumberBase::toString(uint64_t D, int16_t E, int Width,
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unsigned Precision) {
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if (!D)
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return "0.0";
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// Canonicalize exponent and digits.
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uint64_t Above0 = 0;
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uint64_t Below0 = 0;
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uint64_t Extra = 0;
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int ExtraShift = 0;
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if (E == 0) {
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Above0 = D;
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} else if (E > 0) {
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if (int Shift = std::min(int16_t(countLeadingZeros64(D)), E)) {
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D <<= Shift;
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E -= Shift;
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if (!E)
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Above0 = D;
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}
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} else if (E > -64) {
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Above0 = D >> -E;
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Below0 = D << (64 + E);
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} else if (E > -120) {
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Below0 = D >> (-E - 64);
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Extra = D << (128 + E);
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ExtraShift = -64 - E;
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}
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// Fall back on APFloat for very small and very large numbers.
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if (!Above0 && !Below0)
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return toStringAPFloat(D, E, Precision);
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// Append the digits before the decimal.
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std::string Str;
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size_t DigitsOut = 0;
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if (Above0) {
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appendNumber(Str, Above0);
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DigitsOut = Str.size();
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} else
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appendDigit(Str, 0);
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std::reverse(Str.begin(), Str.end());
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// Return early if there's nothing after the decimal.
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if (!Below0)
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return Str + ".0";
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// Append the decimal and beyond.
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Str += '.';
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uint64_t Error = UINT64_C(1) << (64 - Width);
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// We need to shift Below0 to the right to make space for calculating
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// digits. Save the precision we're losing in Extra.
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Extra = (Below0 & 0xf) << 56 | (Extra >> 8);
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Below0 >>= 4;
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size_t SinceDot = 0;
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size_t AfterDot = Str.size();
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do {
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if (ExtraShift) {
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--ExtraShift;
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Error *= 5;
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} else
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Error *= 10;
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Below0 *= 10;
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Extra *= 10;
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Below0 += (Extra >> 60);
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Extra = Extra & (UINT64_MAX >> 4);
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appendDigit(Str, Below0 >> 60);
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Below0 = Below0 & (UINT64_MAX >> 4);
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if (DigitsOut || Str.back() != '0')
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++DigitsOut;
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++SinceDot;
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} while (Error && (Below0 << 4 | Extra >> 60) >= Error / 2 &&
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(!Precision || DigitsOut <= Precision || SinceDot < 2));
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// Return early for maximum precision.
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if (!Precision || DigitsOut <= Precision)
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return stripTrailingZeros(Str);
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// Find where to truncate.
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size_t Truncate =
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std::max(Str.size() - (DigitsOut - Precision), AfterDot + 1);
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// Check if there's anything to truncate.
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if (Truncate >= Str.size())
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return stripTrailingZeros(Str);
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bool Carry = doesRoundUp(Str[Truncate]);
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if (!Carry)
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return stripTrailingZeros(Str.substr(0, Truncate));
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// Round with the first truncated digit.
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for (std::string::reverse_iterator I(Str.begin() + Truncate), E = Str.rend();
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I != E; ++I) {
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if (*I == '.')
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continue;
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if (*I == '9') {
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*I = '0';
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continue;
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}
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++*I;
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Carry = false;
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break;
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}
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// Add "1" in front if we still need to carry.
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return stripTrailingZeros(std::string(Carry, '1') + Str.substr(0, Truncate));
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}
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raw_ostream &ScaledNumberBase::print(raw_ostream &OS, uint64_t D, int16_t E,
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int Width, unsigned Precision) {
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return OS << toString(D, E, Width, Precision);
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}
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void ScaledNumberBase::dump(uint64_t D, int16_t E, int Width) {
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print(dbgs(), D, E, Width, 0) << "[" << Width << ":" << D << "*2^" << E
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<< "]";
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}
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