/*==LICENSE==* CyanWorlds.com Engine - MMOG client, server and tools Copyright (C) 2011 Cyan Worlds, Inc. This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see . Additional permissions under GNU GPL version 3 section 7 If you modify this Program, or any covered work, by linking or combining it with any of RAD Game Tools Bink SDK, Autodesk 3ds Max SDK, NVIDIA PhysX SDK, Microsoft DirectX SDK, OpenSSL library, Independent JPEG Group JPEG library, Microsoft Windows Media SDK, or Apple QuickTime SDK (or a modified version of those libraries), containing parts covered by the terms of the Bink SDK EULA, 3ds Max EULA, PhysX SDK EULA, DirectX SDK EULA, OpenSSL and SSLeay licenses, IJG JPEG Library README, Windows Media SDK EULA, or QuickTime SDK EULA, the licensors of this Program grant you additional permission to convey the resulting work. Corresponding Source for a non-source form of such a combination shall include the source code for the parts of OpenSSL and IJG JPEG Library used as well as that of the covered work. You can contact Cyan Worlds, Inc. by email legal@cyan.com or by snail mail at: Cyan Worlds, Inc. 14617 N Newport Hwy Mead, WA 99021 *==LICENSE==*/ #include "hsWide.h" ///////////////////////////////////////////////////////////////////////// inline bool OverflowAdd(uint32_t* sum, uint32_t a, uint32_t b) { *sum = a + b; return (a | b) > *sum; // true if overflow } /* Return the overflow from adding the three longs into a signed-wide wide = (high << 32) + (middle << 16) + low */ inline bool SetWide3(hsWide* target, int32_t high, uint32_t middle, uint32_t low) { hsAssert(high >= 0, "high is neg"); target->fLo = low + (middle << 16); target->fHi = high + (middle >> 16) + (((low >> 16) + (uint16_t)middle) >> 16); return target->fHi < 0; // true if overflow } ///////////////////////////////////////////////////////////////////////// hsWide* hsWide::Mul(int32_t src1, int32_t src2) { int neg = 0; if (src1 < 0) { src1 = -src1; neg = ~0; } if (src2 < 0) { src2 = -src2; neg = ~neg; } uint32_t a = src1 >> 16; uint32_t b = (uint16_t)src1; uint32_t c = src2 >> 16; uint32_t d = (uint16_t)src2; (void)SetWide3(this, a * c, a * d + c * b, b * d); if (neg) this->Negate(); return this; } hsWide* hsWide::Mul(int32_t A) { int neg = 0; uint32_t B = fLo; int32_t C = fHi; int32_t tmp; uint32_t clo,blo,bhi,alo; if (A < 0) { A = -A; neg = ~0; } if (WIDE_ISNEG(C, B)) { WIDE_NEGATE(C, B); neg = ~neg; } uint32_t ahi = A >> 16; uint32_t chi = C >> 16; if (ahi != 0 && chi != 0) goto OVER_FLOW; alo = (uint16_t)A; bhi = B >> 16; blo = (uint16_t)B; clo = (uint16_t)C; tmp = alo * clo; if (tmp < 0 || SetWide3(this, tmp, alo * bhi, alo * blo)) goto OVER_FLOW; if (chi != 0) { uint32_t Vh = alo * chi; if (Vh >> 15) goto OVER_FLOW; if (((this->fHi >> 16) + (uint16_t)Vh) >> 15) goto OVER_FLOW; this->fHi += Vh << 16; } else // ahi != 0 && chi == 0 { hsWide w; uint32_t Vh = ahi * clo; if (Vh >> 16) goto OVER_FLOW; tmp = ahi * bhi; if (tmp < 0 || SetWide3(&w, tmp, ahi * blo, 0)) goto OVER_FLOW; if (((w.fHi >> 16) + (uint16_t)Vh) >> 15) goto OVER_FLOW; w.fHi += Vh << 16; this->Add(&w); } if (neg) this->Negate(); return this; OVER_FLOW: *this = neg ? kNegInfinity64 : kPosInfinity64; return this; } hsWide* hsWide::Div(int32_t denom) { if (denom == 0) { if (this->IsNeg()) { hsSignalMathUnderflow(); *this = kNegInfinity64; } else { hsSignalMathOverflow(); *this = kPosInfinity64; } return this; } int neg = 0; int32_t resultH = 0; uint32_t resultL = 0; int32_t numerH = this->fHi; uint32_t numerL = this->fLo; if (denom < 0) { denom = -denom; neg = ~0; } if (WIDE_ISNEG(numerH, numerL)) { WIDE_NEGATE(numerH, numerL); neg = ~neg; } WIDE_ADDPOS(numerH, numerL, denom >> 1); // add denom/2 to get a round result uint32_t curr = (uint32_t)numerH >> 31; for (int i = 0; i < 64; i++) { WIDE_SHIFTLEFT(resultH, resultL, resultH, resultL, 1); if (uint32_t(denom) <= curr) { resultL |= 1; curr -= denom; } WIDE_SHIFTLEFT(numerH, numerL, numerH, numerL, 1); curr = (curr << 1) | ((uint32_t)numerH >> 31); } if (neg) WIDE_NEGATE(resultH, resultL); return this->Set(resultH, resultL); } hsWide* hsWide::Div(const hsWide* denom) { hsWide d = *denom; int shift = 0; while (d.IsWide()) { (void)d.ShiftRight(1); shift += 1; } if (shift) { d = *denom; (void)this->RoundRight(shift); (void)d.RoundRight(shift); } return this->Div(d.AsLong()); } inline int MaxLeftShift(const hsWide* w) { int32_t hi = w->fHi; if (hi == 0) return 31; else { int shift = -1; if (hi < 0) hi = -hi; do { hi <<= 1; shift += 1; } while (hi > 0); return shift; } } int32_t hsWide::FixDiv(const hsWide* denom) const { hsWide num = *this; hsWide den = *denom; int maxShift = MaxLeftShift(this); if (maxShift >= 16) // easy case (void)num.ShiftLeft(16); else { (void)num.ShiftLeft(maxShift); (void)den.RoundRight(16 - maxShift); } return num.Div(&den)->AsLong(); } int32_t hsWide::FracDiv(const hsWide* denom) const { hsWide num = *this; hsWide den = *denom; int maxShift = MaxLeftShift(this); if (maxShift >= 30) // easy case (void)num.ShiftLeft(30); else { (void)num.ShiftLeft(maxShift); (void)den.RoundRight(30 - maxShift); } return num.Div(&den)->AsLong(); } //////////////////////////////////////////////////////////////////////////////////// int32_t hsWide::Sqrt() const { int bits = 32; uint32_t root = 0; uint32_t valueH = (uint32_t)fHi; uint32_t valueL = fLo; uint32_t currH = 0; uint32_t currL = 0; uint32_t guessH, guessL; do { WIDE_SHIFTLEFT(currH, currL, currH, currL, 2); currL |= TOP2BITS(valueH); WIDE_SHIFTLEFT(valueH, valueL, valueH, valueL, 2); WIDE_SHIFTLEFT(guessH, guessL, 0, root, 2); root <<= 1; if (WIDE_LESSTHAN(guessH, guessL, currH, currL)) { WIDE_ADDPOS(guessH, guessL, 1); WIDE_SUBWIDE(currH, currL, guessH, guessL); root |= 1; } } while (--bits); return (int32_t)root; } int32_t hsWide::CubeRoot() const { int bits = 21; uint32_t root = 0; uint32_t valueH = (uint32_t)fHi; uint32_t valueL = fLo; uint32_t currH, currL; uint32_t guessH, guessL; bool neg = false; if (WIDE_ISNEG(valueH, valueL)) { neg = true; WIDE_NEGATE(valueH, valueL); } currH = currL = 0; WIDE_SHIFTLEFT(valueH, valueL, valueH, valueL, 1); do { WIDE_SHIFTLEFT(currH, currL, currH, currL, 3); currL |= TOP3BITS(valueH); WIDE_SHIFTLEFT(valueH, valueL, valueH, valueL, 3); root <<= 1; hsWide w; w.Mul(root, root)->Add(root); #if 0 w.Mul(3); #else hsWide w2 = w; w.ShiftLeft(1)->Add(&w2); #endif guessH = (uint32_t)w.fHi; guessL = w.fLo; if (WIDE_LESSTHAN(guessH, guessL, currH, currL)) { WIDE_ADDPOS(guessH, guessL, 1); WIDE_SUBWIDE(currH, currL, guessH, guessL); root |= 1; } } while (--bits); if (neg) root = -int32_t(root); return (int32_t)root; }