Fix calculating an elliptical arc.
This commit is contained in:
Roman Telezhynskyi
parent
ab75b783b6
commit
1e344d6df0
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@ -20,6 +20,7 @@
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- Fix segmenting a simple curve.
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- Fix export tiled pdf on Mac OS.
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- Improve visualization for tools.
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- Fix calculating an elliptical arc.
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# Valentina 0.7.51 April 18, 2022
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- Z value change for a layout piece.
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@ -77,7 +77,6 @@ public:
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* @brief Clear Clears the carrousel (removes everything)
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*/
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void Clear();
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auto Layout() const -> VPLayoutWeakPtr;
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public slots:
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@ -37,9 +37,171 @@
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#include "../ifc/ifcdef.h"
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#include "../ifc/exception/vexception.h"
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#include "../vmisc/vabstractapplication.h"
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#include "../vmisc/fpm/fixed.hpp"
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#include "../vmisc/fpm/math.hpp"
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#include "../vmisc/compatibility.h"
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#include "vabstractcurve.h"
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#include "vellipticalarc_p.h"
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#include "../vmisc/vmath.h"
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namespace
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{
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constexpr qreal tolerance = accuracyPointOnLine/32;
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//---------------------------------------------------------------------------------------------------------------------
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auto VLen(fpm::fixed_16_16 x, fpm::fixed_16_16 y) -> fpm::fixed_16_16
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{
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x = fpm::abs(x);
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y = fpm::abs(y);
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if (x > y)
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{
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return x + qMax(y/8, y/2 - x/8);
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}
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return y + qMax(x/8, x/2 - y/8);
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}
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//---------------------------------------------------------------------------------------------------------------------
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auto AuxRadius(fpm::fixed_16_16 xP, fpm::fixed_16_16 yP, fpm::fixed_16_16 xQ, fpm::fixed_16_16 yQ) -> fpm::fixed_16_16
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{
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fpm::fixed_16_16 dP = VLen(xP, yP);
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fpm::fixed_16_16 dQ = VLen(xQ, yQ);
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fpm::fixed_16_16 dJ = VLen(xP + xQ, yP + yQ);
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fpm::fixed_16_16 dK = VLen(xP - xQ, yP - yQ);
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fpm::fixed_16_16 r1 = qMax(dP, dQ);
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fpm::fixed_16_16 r2 = qMax(dJ, dK);
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return qMax(r1 + r1/16, r2 - r2/4);
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}
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//---------------------------------------------------------------------------------------------------------------------
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auto AngularInc(fpm::fixed_16_16 xP, fpm::fixed_16_16 yP, fpm::fixed_16_16 xQ, fpm::fixed_16_16 yQ,
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fpm::fixed_16_16 flatness) -> int
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{
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fpm::fixed_16_16 r = AuxRadius(xP, yP, xQ, yQ);
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fpm::fixed_16_16 err2{r >> 3};
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// 2nd-order term
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fpm::fixed_16_16 err4{r >> 7};
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// 4th-order term
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const int kmax = qRound(0.5 * std::log2(maxSceneSize / (8. * tolerance)));
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for (int k = 0; k < kmax; ++k)
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{
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if (flatness >= err2 + err4)
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{
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return k;
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}
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err2 >>= 2;
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err4 >>= 4;
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}
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return kmax;
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}
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//---------------------------------------------------------------------------------------------------------------------
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inline void CircleGen(fpm::fixed_16_16& u, fpm::fixed_16_16& v, uint k)
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{
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u -= v >> k;
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v += u >> k;
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}
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//---------------------------------------------------------------------------------------------------------------------
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auto InitialValue(fpm::fixed_16_16 u0, fpm::fixed_16_16 v0, uint k) -> fpm::fixed_16_16
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{
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uint shift = 2*k + 3;
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fpm::fixed_16_16 w {u0 >> shift};
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fpm::fixed_16_16 U0 = u0 - w + (v0 >> (k + 1));
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w >>= (shift + 1);
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U0 -= w;
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w >>= shift;
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U0 -= w;
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return U0;
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}
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//---------------------------------------------------------------------------------------------------------------------
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auto EllipseCore(fpm::fixed_16_16 xC, fpm::fixed_16_16 yC, fpm::fixed_16_16 xP, fpm::fixed_16_16 yP,
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fpm::fixed_16_16 xQ, fpm::fixed_16_16 yQ, fpm::fixed_16_16 sweep,
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fpm::fixed_16_16 flatness) -> QVector<QPointF>
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{
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uint k = qMin(static_cast<uint>(AngularInc(xP, yP, xQ, yQ, flatness)), 16U);
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const uint count = static_cast<std::uint32_t>(sweep.raw_value()) >> (16 - k);
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QVector<QPointF> arc;
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arc.reserve(static_cast<int>(count) + 1);
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// Arc start point
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arc.append({static_cast<qreal>(xP + xC), static_cast<qreal>(yP + yC)});
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xQ = InitialValue(xQ, xP, k);
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yQ = InitialValue(yQ, yP, k);
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for (uint i = 0; i < count; ++i)
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{
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CircleGen(xQ, xP, k);
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CircleGen(yQ, yP, k);
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arc.append({static_cast<qreal>(xP + xC), static_cast<qreal>(yP + yC)});
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}
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return arc;
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}
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//---------------------------------------------------------------------------------------------------------------------
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auto EllipticArcPoints(QPointF c, qreal radius1, qreal radius2, qreal astart, qreal asweep,
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qreal approximationScale) -> QVector<QPointF>
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{
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fpm::fixed_16_16 xC{c.x()};
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fpm::fixed_16_16 yC{c.y()};
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fpm::fixed_16_16 xP{c.x() + radius1};
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fpm::fixed_16_16 yP{c.y()};
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fpm::fixed_16_16 xQ{c.x()};
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fpm::fixed_16_16 yQ{c.y() - radius2};
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xP -= xC;
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yP -= yC;
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xQ -= xC;
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yQ -= yC;
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if (not qFuzzyIsNull(astart))
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{
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// Set new conjugate diameter end points P’ and Q’
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fpm::fixed_16_16 cosa {cos(astart)};
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fpm::fixed_16_16 sina {sin(astart)};
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fpm::fixed_16_16 x {xP * cosa + xQ * sina};
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fpm::fixed_16_16 y {yP * cosa + yQ * sina};
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xQ = xQ * cosa - xP * sina;
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yQ = yQ * cosa - yP * sina;
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xP = x;
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yP = y;
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}
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// If sweep angle is negative, switch direction
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if (asweep < 0)
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{
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xQ = -xQ;
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yQ = -yQ;
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asweep = -asweep;
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}
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if(approximationScale < minCurveApproximationScale || approximationScale > maxCurveApproximationScale)
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{
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approximationScale = VAbstractApplication::VApp()->Settings()->GetCurveApproximationScale();
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}
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fpm::fixed_16_16 flatness {maxCurveApproximationScale / approximationScale * tolerance};
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fpm::fixed_16_16 swangle{asweep};
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QVector<QPointF> arc = EllipseCore(xC, yC, xP, yP, xQ, yQ, swangle, flatness);
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// Arc end point
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fpm::fixed_16_16 cosb {qCos(asweep)};
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fpm::fixed_16_16 sinb {qSin(asweep)};
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xP = xP*cosb + xQ*sinb;
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yP = yP*cosb + yQ*sinb;
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arc.append({static_cast<qreal>(xP+xC), static_cast<qreal>(yP+yC)});
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return arc;
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}
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} // namespace
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//---------------------------------------------------------------------------------------------------------------------
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/**
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@ -59,11 +221,11 @@ VEllipticalArc::VEllipticalArc()
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* @param f2 end angle (degree).
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*/
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VEllipticalArc::VEllipticalArc (const VPointF ¢er, qreal radius1, qreal radius2, const QString &formulaRadius1,
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const QString &formulaRadius2, qreal f1, const QString &formulaF1, qreal f2,
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const QString &formulaF2, qreal rotationAngle, const QString &formulaRotationAngle,
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quint32 idObject, Draw mode)
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const QString &formulaRadius2, qreal f1, const QString &formulaF1, qreal f2,
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const QString &formulaF2, qreal rotationAngle, const QString &formulaRotationAngle,
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quint32 idObject, Draw mode)
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: VAbstractArc(GOType::EllipticalArc, center, f1, formulaF1, f2, formulaF2, idObject, mode),
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d (new VEllipticalArcData(radius1, radius2, formulaRadius1, formulaRadius2, rotationAngle, formulaRotationAngle))
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d (new VEllipticalArcData(radius1, radius2, formulaRadius1, formulaRadius2, rotationAngle, formulaRotationAngle))
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{
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CreateName();
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}
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@ -72,7 +234,7 @@ VEllipticalArc::VEllipticalArc (const VPointF ¢er, qreal radius1, qreal radi
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VEllipticalArc::VEllipticalArc(const VPointF ¢er, qreal radius1, qreal radius2, qreal f1, qreal f2,
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qreal rotationAngle)
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: VAbstractArc(GOType::EllipticalArc, center, f1, f2, NULL_ID, Draw::Calculation),
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d (new VEllipticalArcData(radius1, radius2, rotationAngle))
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d (new VEllipticalArcData(radius1, radius2, rotationAngle))
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{
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CreateName();
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}
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@ -83,7 +245,7 @@ VEllipticalArc::VEllipticalArc(qreal length, const QString &formulaLength, const
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const QString &formulaF1, qreal rotationAngle, const QString &formulaRotationAngle,
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quint32 idObject, Draw mode)
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: VAbstractArc(GOType::EllipticalArc, formulaLength, center, f1, formulaF1, idObject, mode),
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d (new VEllipticalArcData(radius1, radius2, formulaRadius1, formulaRadius2, rotationAngle, formulaRotationAngle))
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d (new VEllipticalArcData(radius1, radius2, formulaRadius1, formulaRadius2, rotationAngle, formulaRotationAngle))
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{
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CreateName();
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FindF2(length);
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@ -93,7 +255,7 @@ VEllipticalArc::VEllipticalArc(qreal length, const QString &formulaLength, const
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VEllipticalArc::VEllipticalArc(qreal length, const VPointF ¢er, qreal radius1, qreal radius2, qreal f1,
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qreal rotationAngle)
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: VAbstractArc(GOType::EllipticalArc, center, f1, NULL_ID, Draw::Calculation),
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d (new VEllipticalArcData(radius1, radius2, rotationAngle))
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d (new VEllipticalArcData(radius1, radius2, rotationAngle))
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{
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CreateName();
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FindF2(length);
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@ -193,7 +355,7 @@ auto VEllipticalArc::Move(qreal length, qreal angle, const QString &prefix) cons
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const VPointF center = oldCenter.Move(length, angle);
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const QPointF position = d->m_transform.inverted().map(center.toQPointF()) -
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d->m_transform.inverted().map(oldCenter.toQPointF());
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d->m_transform.inverted().map(oldCenter.toQPointF());
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QTransform t = d->m_transform;
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t.translate(position.x(), position.y());
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@ -285,45 +447,19 @@ auto VEllipticalArc::GetCenter() const -> VPointF
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auto VEllipticalArc::GetPoints() const -> QVector<QPointF>
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{
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const QPointF center = VAbstractArc::GetCenter().toQPointF();
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QRectF box(center.x() - d->radius1, center.y() - d->radius2, d->radius1*2, d->radius2*2);
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QLineF startLine(center.x(), center.y(), center.x() + d->radius1, center.y());
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QLineF endLine = startLine;
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startLine.setAngle(VAbstractArc::GetStartAngle());
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endLine.setAngle(RealEndAngle());
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qreal sweepAngle = startLine.angleTo(endLine);
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if (qFuzzyIsNull(sweepAngle))
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{
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sweepAngle = 360;
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}
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QPainterPath path;
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path.moveTo(GetP1());
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path.arcTo(box, VAbstractArc::GetStartAngle(), sweepAngle);
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path.moveTo(GetP2());
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// Generate complete ellipse because angles are not correct and have to be fixed manually
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QVector<QPointF> points = EllipticArcPoints(center, d->radius1, d->radius2, 0.0, M_2PI, GetApproximationScale());
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points = ArcPoints(points);
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QTransform t = d->m_transform;
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t.translate(center.x(), center.y());
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t.rotate(-GetRotationAngle());
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t.translate(-center.x(), -center.y());
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path = t.map(path);
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std::transform(points.begin(), points.end(), points.begin(), [t](const QPointF &point) { return t.map(point); });
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QPolygonF polygon;
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const QList<QPolygonF> sub = path.toSubpathPolygons();
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if (not sub.isEmpty())
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{
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polygon = ConstFirst (path.toSubpathPolygons());
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if (not polygon.isEmpty() && not VFuzzyComparePoints(GetP1(), ConstFirst<QPointF> (polygon)))
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{
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polygon.removeFirst(); // remove point (0;0)
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}
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}
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return static_cast<QVector<QPointF>>(polygon);
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return points;
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}
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//---------------------------------------------------------------------------------------------------------------------
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@ -360,7 +496,7 @@ auto VEllipticalArc::CutArc(const qreal &length, VEllipticalArc &arc1, VElliptic
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const QString errorMsg = QObject::tr("Unable to cut curve '%1'. The curve is too short.").arg(name());
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VAbstractApplication::VApp()->IsPedantic() ? throw VException(errorMsg) :
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qWarning() << VAbstractApplication::warningMessageSignature + errorMsg;
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qWarning() << VAbstractApplication::warningMessageSignature + errorMsg;
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return {};
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}
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@ -380,10 +516,10 @@ auto VEllipticalArc::CutArc(const qreal &length, VEllipticalArc &arc1, VElliptic
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else
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{
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errorMsg = QObject::tr("Curve '%1'. Length of a cut segment is too small. Optimize it to minimal value.")
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.arg(name());
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.arg(name());
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}
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VAbstractApplication::VApp()->IsPedantic() ? throw VException(errorMsg) :
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qWarning() << VAbstractApplication::warningMessageSignature + errorMsg;
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qWarning() << VAbstractApplication::warningMessageSignature + errorMsg;
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}
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else if (length > maxLength)
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{
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@ -393,15 +529,15 @@ auto VEllipticalArc::CutArc(const qreal &length, VEllipticalArc &arc1, VElliptic
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if (not pointName.isEmpty())
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{
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errorMsg = QObject::tr("Curve '%1'. Length of a cut segment (%2) is too big. Optimize it to maximal value.")
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.arg(name(), pointName);
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.arg(name(), pointName);
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}
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else
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{
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errorMsg = QObject::tr("Curve '%1'. Length of a cut segment is too big. Optimize it to maximal value.")
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.arg(name());
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.arg(name());
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}
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VAbstractApplication::VApp()->IsPedantic() ? throw VException(errorMsg) :
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qWarning() << VAbstractApplication::warningMessageSignature + errorMsg;
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qWarning() << VAbstractApplication::warningMessageSignature + errorMsg;
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}
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else
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{
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@ -410,13 +546,13 @@ auto VEllipticalArc::CutArc(const qreal &length, VEllipticalArc &arc1, VElliptic
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// the first arc has given length and startAngle just like in the origin arc
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arc1 = VEllipticalArc (len, QString().setNum(length), GetCenter(), d->radius1, d->radius2,
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d->formulaRadius1, d->formulaRadius2, GetStartAngle(), GetFormulaF1(), d->rotationAngle,
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GetFormulaRotationAngle(), getIdObject(), getMode());
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d->formulaRadius1, d->formulaRadius2, GetStartAngle(), GetFormulaF1(), d->rotationAngle,
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GetFormulaRotationAngle(), getIdObject(), getMode());
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// the second arc has startAngle just like endAngle of the first arc
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// and it has endAngle just like endAngle of the origin arc
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arc2 = VEllipticalArc (GetCenter(), d->radius1, d->radius2, d->formulaRadius1, d->formulaRadius2,
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arc1.GetEndAngle(), arc1.GetFormulaF2(), GetEndAngle(), GetFormulaF2(), d->rotationAngle,
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GetFormulaRotationAngle(), getIdObject(), getMode());
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arc1.GetEndAngle(), arc1.GetFormulaF2(), GetEndAngle(), GetFormulaF2(), d->rotationAngle,
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GetFormulaRotationAngle(), getIdObject(), getMode());
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return arc1.GetP1();
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}
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@ -432,7 +568,7 @@ auto VEllipticalArc::CutArc(const qreal &length, const QString &pointName) const
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//---------------------------------------------------------------------------------------------------------------------
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void VEllipticalArc::CreateName()
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{
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QString name = ELARC_ + QString("%1").arg(this->GetCenter().name());
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QString name = ELARC_ + QStringLiteral("%1").arg(this->GetCenter().name());
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const QString nameStr = QStringLiteral("_%1");
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if (getMode() == Draw::Modeling && getIdObject() != NULL_ID)
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@ -555,23 +691,101 @@ auto VEllipticalArc::GetP(qreal angle) const -> QPointF
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}
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//---------------------------------------------------------------------------------------------------------------------
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auto VEllipticalArc::RealEndAngle() const -> qreal
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auto VEllipticalArc::ArcPoints(QVector<QPointF> points) const -> QVector<QPointF>
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{
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qreal endAngle = VEllipticalArc::OptimizeAngle(VAbstractArc::GetEndAngle());
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if (qFuzzyIsNull(endAngle) ||
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VFuzzyComparePossibleNulls(endAngle, 90) ||
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VFuzzyComparePossibleNulls(endAngle, 180) ||
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VFuzzyComparePossibleNulls(endAngle, 270) ||
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VFuzzyComparePossibleNulls(endAngle, 360))
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if (points.size() < 2 || VFuzzyComparePossibleNulls(VAbstractArc::GetStartAngle(), VAbstractArc::GetEndAngle()))
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{
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return endAngle;
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return points;
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}
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endAngle = qRadiansToDegrees(qAtan2(d->radius1 * qSin(qDegreesToRadians(endAngle)),
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d->radius2 * qCos(qDegreesToRadians(endAngle))));
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QPointF center = static_cast<QPointF>(GetCenter());
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qreal radius = qMax(d->radius1, d->radius2) * 2;
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return endAngle;
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QLineF start(center.x(), center.y(), center.x() + radius, center.y());
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start.setAngle(VAbstractArc::GetStartAngle());
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QLineF end(center.x(), center.y(), center.x() + radius, center.y());
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end.setAngle(VAbstractArc::GetEndAngle());
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if (VFuzzyComparePossibleNulls(start.angle(), end.angle()))
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{
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return points;
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}
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|
||||
auto IsBoundedIntersection = [](QLineF::IntersectType type, QPointF p, const QLineF &segment1,
|
||||
const QLineF &segment2)
|
||||
{
|
||||
return type == QLineF::BoundedIntersection ||
|
||||
(VGObject::IsPointOnLineSegment (p, segment1.p1(), segment2.p1()) &&
|
||||
VGObject::IsPointOnLineSegment (p, segment2.p1(), segment2.p2()));
|
||||
};
|
||||
|
||||
bool begin = true;
|
||||
|
||||
if (start.angle() > end.angle())
|
||||
{
|
||||
for (int i=0; i < points.size()-1; ++i)
|
||||
{
|
||||
QLineF edge(points.at(i), points.at(i+1));
|
||||
|
||||
QPointF p;
|
||||
QLineF::IntersectType type = Intersects(start, edge, &p);
|
||||
|
||||
// QLineF::intersects not always accurate on edge cases
|
||||
if (IsBoundedIntersection(type, p, edge, start))
|
||||
{
|
||||
QVector<QPointF> head = points.mid(0, i+1);
|
||||
QVector<QPointF> tail = points.mid(i+1, -1);
|
||||
tail.prepend(p);
|
||||
points = tail + head;
|
||||
begin = false;
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
QVector<QPointF> arc;
|
||||
arc.reserve(points.size());
|
||||
|
||||
for (int i=0; i < points.size()-1; ++i)
|
||||
{
|
||||
QLineF edge(points.at(i), points.at(i+1));
|
||||
|
||||
if (begin)
|
||||
{
|
||||
QPointF p;
|
||||
QLineF::IntersectType type = Intersects(start, edge, &p);
|
||||
|
||||
// QLineF::intersects not always accurate on edge cases
|
||||
if (IsBoundedIntersection(type, p, edge, start))
|
||||
{
|
||||
arc.append(p);
|
||||
begin = false;
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
QPointF p;
|
||||
QLineF::IntersectType type = Intersects(end, edge, &p);
|
||||
|
||||
// QLineF::intersects not always accurate on edge cases
|
||||
if (IsBoundedIntersection(type, p, edge, end))
|
||||
{
|
||||
arc.append(points.at(i));
|
||||
arc.append(p);
|
||||
break;
|
||||
}
|
||||
|
||||
arc.append(points.at(i));
|
||||
}
|
||||
}
|
||||
|
||||
if (arc.isEmpty())
|
||||
{
|
||||
return points;
|
||||
}
|
||||
|
||||
return arc;
|
||||
}
|
||||
|
||||
//---------------------------------------------------------------------------------------------------------------------
|
||||
|
|
|
|||
|
|
@ -114,10 +114,8 @@ private:
|
|||
QSharedDataPointer<VEllipticalArcData> d;
|
||||
|
||||
auto MaxLength() const -> qreal;
|
||||
|
||||
auto GetP(qreal angle) const -> QPointF;
|
||||
|
||||
auto RealEndAngle() const -> qreal;
|
||||
auto ArcPoints(QVector<QPointF> points) const -> QVector<QPointF>;
|
||||
};
|
||||
|
||||
Q_DECLARE_METATYPE(VEllipticalArc) // NOLINT
|
||||
|
|
|
|||
|
|
@ -64,13 +64,6 @@
|
|||
#include "../ifc/exception/vexception.h"
|
||||
#include "literals.h"
|
||||
|
||||
const qreal defCurveApproximationScale = 0.5;
|
||||
const qreal minCurveApproximationScale = 0.2;
|
||||
const qreal maxCurveApproximationScale = 10.0;
|
||||
|
||||
const int minLabelFontSize = 5;
|
||||
const int maxLabelFontSize = 100;
|
||||
|
||||
//---------------------------------------------------------------------------------------------------------------------
|
||||
QPixmap QPixmapFromCache(const QString &pixmapPath)
|
||||
{
|
||||
|
|
|
|||
|
|
@ -74,13 +74,14 @@ class QMarginsF;
|
|||
class VTranslateMeasurements;
|
||||
class QGraphicsItem;
|
||||
|
||||
#define SceneSize 50000
|
||||
extern const qreal defCurveApproximationScale;
|
||||
extern const qreal minCurveApproximationScale;
|
||||
extern const qreal maxCurveApproximationScale;
|
||||
constexpr qreal maxSceneSize = ((20.0 * 1000.0) / 25.4) * PrintDPI; // 20 meters in pixels
|
||||
|
||||
extern const int minLabelFontSize;
|
||||
extern const int maxLabelFontSize;
|
||||
constexpr qreal defCurveApproximationScale = 0.5;
|
||||
constexpr qreal minCurveApproximationScale = 0.2;
|
||||
constexpr qreal maxCurveApproximationScale = 10.0;
|
||||
|
||||
constexpr int minLabelFontSize = 5;
|
||||
constexpr int maxLabelFontSize = 100;
|
||||
|
||||
enum class NodeDetail : qint8 { Contour, Modeling };
|
||||
enum class SceneObject : qint8 { Point, Line, Spline, Arc, ElArc, SplinePath, Detail, Unknown };
|
||||
|
|
|
|||
21
src/libs/vmisc/fpm/LICENSE
Normal file
21
src/libs/vmisc/fpm/LICENSE
Normal file
|
|
@ -0,0 +1,21 @@
|
|||
MIT License
|
||||
|
||||
Copyright (c) 2019 Mike Lankamp
|
||||
|
||||
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.
|
||||
497
src/libs/vmisc/fpm/fixed.hpp
Normal file
497
src/libs/vmisc/fpm/fixed.hpp
Normal file
|
|
@ -0,0 +1,497 @@
|
|||
#ifndef FPM_FIXED_HPP
|
||||
#define FPM_FIXED_HPP
|
||||
|
||||
#include <cassert>
|
||||
#include <cmath>
|
||||
#include <cstdint>
|
||||
#include <functional>
|
||||
#include <limits>
|
||||
#include <type_traits>
|
||||
#include <QtGlobal>
|
||||
|
||||
#if QT_VERSION < QT_VERSION_CHECK(5, 5, 0)
|
||||
#include "../diagnostic.h"
|
||||
#endif // QT_VERSION < QT_VERSION_CHECK(5, 5, 0)
|
||||
|
||||
namespace fpm
|
||||
{
|
||||
|
||||
//! Fixed-point number type
|
||||
//! \tparam BaseType the base integer type used to store the fixed-point number. This can be a signed or
|
||||
//! unsigned type.
|
||||
//! \tparam IntermediateType the integer type used to store intermediate results during calculations.
|
||||
//! \tparam FractionBits the number of bits of the BaseType used to store the fraction
|
||||
template <typename BaseType, typename IntermediateType, unsigned int FractionBits>
|
||||
class fixed
|
||||
{
|
||||
static_assert(std::is_integral<BaseType>::value, "BaseType must be an integral type");
|
||||
static_assert(FractionBits > 0, "FractionBits must be greater than zero");
|
||||
static_assert(FractionBits <= sizeof(BaseType) * 8 - 1, "BaseType must at least be able to contain entire "
|
||||
"fraction, with space for at least one integral bit");
|
||||
static_assert(sizeof(IntermediateType) > sizeof(BaseType), "IntermediateType must be larger than BaseType");
|
||||
static_assert(std::is_signed<IntermediateType>::value == std::is_signed<BaseType>::value,
|
||||
"IntermediateType must have same signedness as BaseType");
|
||||
|
||||
// Although this value fits in the BaseType in terms of bits, if there's only one integral bit, this value
|
||||
// is incorrect (flips from positive to negative), so we must extend the size to IntermediateType.
|
||||
static constexpr IntermediateType FRACTION_MULT = IntermediateType(1) << FractionBits;
|
||||
|
||||
struct raw_construct_tag {};
|
||||
constexpr inline fixed(BaseType val, raw_construct_tag /*unused*/) noexcept : m_value(val) {}
|
||||
|
||||
public:
|
||||
inline fixed() noexcept = default;
|
||||
|
||||
// Converts an integral number to the fixed-point type.
|
||||
// Like static_cast, this truncates bits that don't fit.
|
||||
template <typename T, typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
|
||||
constexpr inline explicit fixed(T val) noexcept
|
||||
: m_value(static_cast<BaseType>(val * FRACTION_MULT))
|
||||
{}
|
||||
|
||||
// Converts an floating-point number to the fixed-point type.
|
||||
// Like static_cast, this truncates bits that don't fit.
|
||||
template <typename T, typename std::enable_if<std::is_floating_point<T>::value>::type* = nullptr>
|
||||
constexpr inline explicit fixed(T val) noexcept
|
||||
: m_value(static_cast<BaseType>((val >= 0.0) ? (val * FRACTION_MULT + T{0.5}) : (val * FRACTION_MULT - T{0.5})))
|
||||
{}
|
||||
|
||||
// Constructs from another fixed-point type with possibly different underlying representation.
|
||||
// Like static_cast, this truncates bits that don't fit.
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline explicit fixed(fixed<B,I,F> val) noexcept
|
||||
: m_value(from_fixed_point<F>(val.raw_value()).raw_value())
|
||||
{}
|
||||
|
||||
// Explicit conversion to a floating-point type
|
||||
template <typename T, typename std::enable_if<std::is_floating_point<T>::value>::type* = nullptr>
|
||||
constexpr inline explicit operator T() const noexcept
|
||||
{
|
||||
return static_cast<T>(m_value) / FRACTION_MULT;
|
||||
}
|
||||
|
||||
// Explicit conversion to an integral type
|
||||
template <typename T, typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
|
||||
constexpr inline explicit operator T() const noexcept
|
||||
{
|
||||
return static_cast<T>(m_value / FRACTION_MULT);
|
||||
}
|
||||
|
||||
// Returns the raw underlying value of this type.
|
||||
// Do not use this unless you know what you're doing.
|
||||
constexpr inline auto raw_value() const noexcept -> BaseType
|
||||
{
|
||||
return m_value;
|
||||
}
|
||||
|
||||
//! Constructs a fixed-point number from another fixed-point number.
|
||||
//! \tparam NumFractionBits the number of bits used by the fraction in \a value.
|
||||
//! \param value the integer fixed-point number
|
||||
template <unsigned int NumFractionBits, typename T,
|
||||
typename std::enable_if<(NumFractionBits > FractionBits)>::type* = nullptr>
|
||||
static constexpr inline auto from_fixed_point(T value) noexcept -> fixed
|
||||
{
|
||||
// To correctly round the last bit in the result, we need one more bit of information.
|
||||
// We do this by multiplying by two before dividing and adding the LSB to the real result.
|
||||
return fixed(static_cast<BaseType>(
|
||||
value / (T(1) << (NumFractionBits - FractionBits)) +
|
||||
(value / (T(1) << (NumFractionBits - FractionBits - 1)) % 2)),
|
||||
raw_construct_tag{});
|
||||
}
|
||||
|
||||
template <unsigned int NumFractionBits, typename T,
|
||||
typename std::enable_if<(NumFractionBits <= FractionBits)>::type* = nullptr>
|
||||
static constexpr inline auto from_fixed_point(T value) noexcept -> fixed
|
||||
{
|
||||
return fixed(static_cast<BaseType>(
|
||||
value * (T(1) << (FractionBits - NumFractionBits))),
|
||||
raw_construct_tag{});
|
||||
}
|
||||
|
||||
// Constructs a fixed-point number from its raw underlying value.
|
||||
// Do not use this unless you know what you're doing.
|
||||
static constexpr inline auto from_raw_value(BaseType value) noexcept -> fixed
|
||||
{
|
||||
return fixed(value, raw_construct_tag{});
|
||||
}
|
||||
|
||||
//
|
||||
// Constants
|
||||
//
|
||||
static constexpr auto e() -> fixed { return from_fixed_point<61>(6267931151224907085LL); }
|
||||
static constexpr auto pi() -> fixed { return from_fixed_point<61>(7244019458077122842LL); }
|
||||
static constexpr auto half_pi() -> fixed { return from_fixed_point<62>(7244019458077122842LL); }
|
||||
static constexpr auto two_pi() -> fixed { return from_fixed_point<60>(7244019458077122842LL); }
|
||||
|
||||
//
|
||||
// Arithmetic member operators
|
||||
//
|
||||
|
||||
constexpr inline auto operator-() const noexcept -> fixed
|
||||
{
|
||||
return fixed::from_raw_value(-m_value);
|
||||
}
|
||||
|
||||
inline auto operator+=(const fixed& y) noexcept -> fixed&
|
||||
{
|
||||
m_value += y.m_value;
|
||||
return *this;
|
||||
}
|
||||
|
||||
template <typename I, typename std::enable_if<std::is_integral<I>::value>::type* = nullptr>
|
||||
inline auto operator+=(I y) noexcept -> fixed&
|
||||
{
|
||||
m_value += y * FRACTION_MULT;
|
||||
return *this;
|
||||
}
|
||||
|
||||
inline auto operator-=(const fixed& y) noexcept -> fixed&
|
||||
{
|
||||
m_value -= y.m_value;
|
||||
return *this;
|
||||
}
|
||||
|
||||
template <typename I, typename std::enable_if<std::is_integral<I>::value>::type* = nullptr>
|
||||
inline auto operator-=(I y) noexcept -> fixed&
|
||||
{
|
||||
m_value -= y * FRACTION_MULT;
|
||||
return *this;
|
||||
}
|
||||
|
||||
inline auto operator*=(const fixed& y) noexcept -> fixed&
|
||||
{
|
||||
// Normal fixed-point multiplication is: x * y / 2**FractionBits.
|
||||
// To correctly round the last bit in the result, we need one more bit of information.
|
||||
// We do this by multiplying by two before dividing and adding the LSB to the real result.
|
||||
auto value = static_cast<IntermediateType>(
|
||||
static_cast<double>(static_cast<IntermediateType>(m_value) * y.m_value) / (FRACTION_MULT / 2));
|
||||
m_value = static_cast<BaseType>((value / 2) + (value % 2));
|
||||
return *this;
|
||||
}
|
||||
|
||||
template <typename I, typename std::enable_if<std::is_integral<I>::value>::type* = nullptr>
|
||||
inline auto operator*=(I y) noexcept -> fixed&
|
||||
{
|
||||
m_value *= y;
|
||||
return *this;
|
||||
}
|
||||
|
||||
inline auto operator/=(const fixed& y) noexcept -> fixed&
|
||||
{
|
||||
assert(y.m_value != 0);
|
||||
// Normal fixed-point division is: x * 2**FractionBits / y.
|
||||
// To correctly round the last bit in the result, we need one more bit of information.
|
||||
// We do this by multiplying by two before dividing and adding the LSB to the real result.
|
||||
auto value = (static_cast<IntermediateType>(m_value) * FRACTION_MULT * 2) / y.m_value;
|
||||
m_value = static_cast<BaseType>((value / 2) + (value % 2));
|
||||
return *this;
|
||||
}
|
||||
|
||||
template <typename I, typename std::enable_if<std::is_integral<I>::value>::type* = nullptr>
|
||||
inline auto operator/=(I y) noexcept -> fixed&
|
||||
{
|
||||
m_value /= y;
|
||||
return *this;
|
||||
}
|
||||
|
||||
//
|
||||
// Shift operators
|
||||
//
|
||||
|
||||
template <typename I, typename std::enable_if<std::is_integral<I>::value>::type* = nullptr>
|
||||
inline auto operator>>=(I y) noexcept -> fixed&
|
||||
{
|
||||
m_value >>= y;
|
||||
return *this;
|
||||
}
|
||||
|
||||
template <typename I, typename std::enable_if<std::is_integral<I>::value>::type* = nullptr>
|
||||
inline auto operator<<=(I y) noexcept -> fixed&
|
||||
{
|
||||
m_value <<= y;
|
||||
return *this;
|
||||
}
|
||||
|
||||
private:
|
||||
BaseType m_value;
|
||||
};
|
||||
|
||||
//
|
||||
// Convenience typedefs
|
||||
//
|
||||
|
||||
using fixed_16_16 = fixed<std::int32_t, std::int64_t, 16>;
|
||||
using fixed_24_8 = fixed<std::int32_t, std::int64_t, 8>;
|
||||
using fixed_8_24 = fixed<std::int32_t, std::int64_t, 24>;
|
||||
|
||||
//
|
||||
// Addition
|
||||
//
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto operator+(const fixed<B, I, F>& x, const fixed<B, I, F>& y) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
return fixed<B, I, F>(x) += y;
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F, typename T,
|
||||
typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
|
||||
constexpr inline auto operator+(const fixed<B, I, F>& x, T y) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
return fixed<B, I, F>(x) += y;
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F, typename T,
|
||||
typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
|
||||
constexpr inline auto operator+(T x, const fixed<B, I, F>& y) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
return fixed<B, I, F>(y) += x;
|
||||
}
|
||||
|
||||
//
|
||||
// Subtraction
|
||||
//
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto operator-(const fixed<B, I, F>& x, const fixed<B, I, F>& y) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
return fixed<B, I, F>(x) -= y;
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F, typename T,
|
||||
typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
|
||||
constexpr inline auto operator-(const fixed<B, I, F>& x, T y) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
return fixed<B, I, F>(x) -= y;
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F, typename T,
|
||||
typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
|
||||
constexpr inline auto operator-(T x, const fixed<B, I, F>& y) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
return fixed<B, I, F>(x) -= y;
|
||||
}
|
||||
|
||||
//
|
||||
// Multiplication
|
||||
//
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto operator*(const fixed<B, I, F>& x, const fixed<B, I, F>& y) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
return fixed<B, I, F>(x) *= y;
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F, typename T,
|
||||
typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
|
||||
constexpr inline auto operator*(const fixed<B, I, F>& x, T y) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
return fixed<B, I, F>(x) *= y;
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F, typename T,
|
||||
typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
|
||||
constexpr inline auto operator*(T x, const fixed<B, I, F>& y) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
return fixed<B, I, F>(y) *= x;
|
||||
}
|
||||
|
||||
//
|
||||
// Division
|
||||
//
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto operator/(const fixed<B, I, F>& x, const fixed<B, I, F>& y) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
return fixed<B, I, F>(x) /= y;
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F, typename T,
|
||||
typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
|
||||
constexpr inline auto operator/(const fixed<B, I, F>& x, T y) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
return fixed<B, I, F>(x) /= y;
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F, typename T,
|
||||
typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
|
||||
constexpr inline auto operator/(T x, const fixed<B, I, F>& y) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
return fixed<B, I, F>(x) /= y;
|
||||
}
|
||||
|
||||
//
|
||||
// Shift operators
|
||||
//
|
||||
|
||||
template <typename B, typename I, unsigned int F, typename T,
|
||||
typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
|
||||
constexpr inline auto operator>>(const fixed<B, I, F>& x, T y) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
return fixed<B, I, F>(x) >>= y;
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F, typename T,
|
||||
typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
|
||||
constexpr inline auto operator<<(const fixed<B, I, F>& x, T y) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
return fixed<B, I, F>(x) <<= y;
|
||||
}
|
||||
|
||||
//
|
||||
// Comparison operators
|
||||
//
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto operator==(const fixed<B, I, F>& x, const fixed<B, I, F>& y) noexcept -> bool
|
||||
{
|
||||
return x.raw_value() == y.raw_value();
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto operator!=(const fixed<B, I, F>& x, const fixed<B, I, F>& y) noexcept -> bool
|
||||
{
|
||||
return x.raw_value() != y.raw_value();
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto operator<(const fixed<B, I, F>& x, const fixed<B, I, F>& y) noexcept -> bool
|
||||
{
|
||||
return x.raw_value() < y.raw_value();
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto operator>(const fixed<B, I, F>& x, const fixed<B, I, F>& y) noexcept -> bool
|
||||
{
|
||||
return x.raw_value() > y.raw_value();
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto operator<=(const fixed<B, I, F>& x, const fixed<B, I, F>& y) noexcept -> bool
|
||||
{
|
||||
return x.raw_value() <= y.raw_value();
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto operator>=(const fixed<B, I, F>& x, const fixed<B, I, F>& y) noexcept -> bool
|
||||
{
|
||||
return x.raw_value() >= y.raw_value();
|
||||
}
|
||||
|
||||
namespace detail
|
||||
{
|
||||
|
||||
QT_WARNING_PUSH
|
||||
QT_WARNING_DISABLE_CLANG("-Wunneeded-internal-declaration")
|
||||
|
||||
// Number of base-10 digits required to fully represent a number of bits
|
||||
static constexpr auto max_digits10(int bits) -> int
|
||||
{
|
||||
// 8.24 fixed-point equivalent of (int)ceil(bits * std::log10(2));
|
||||
using T = long long; // NOLINT(google-runtime-int)
|
||||
return static_cast<int>((T{bits} * 5050445 + (T{1} << 24) - 1) >> 24); // NOLINT(hicpp-signed-bitwise)
|
||||
}
|
||||
|
||||
// Number of base-10 digits that can be fully represented by a number of bits
|
||||
static constexpr auto digits10(int bits) -> int
|
||||
{
|
||||
// 8.24 fixed-point equivalent of (int)(bits * std::log10(2));
|
||||
using T = long long; // NOLINT(google-runtime-int)
|
||||
return static_cast<int>((T{bits} * 5050445) >> 24); //NOLINT(hicpp-signed-bitwise)
|
||||
}
|
||||
|
||||
QT_WARNING_POP
|
||||
|
||||
} // namespace detail
|
||||
} // namespace fpm
|
||||
|
||||
// Specializations for customization points
|
||||
namespace std // NOLINT(cert-dcl58-cpp)
|
||||
{
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
struct hash<fpm::fixed<B,I,F>>
|
||||
{
|
||||
using argument_type = fpm::fixed<B, I, F>;
|
||||
using result_type = std::size_t;
|
||||
|
||||
auto operator()(const argument_type &arg) const noexcept(noexcept(std::declval<std::hash<B>>()(arg.raw_value())))
|
||||
-> result_type
|
||||
{
|
||||
return m_hash(arg.raw_value());
|
||||
}
|
||||
|
||||
private:
|
||||
std::hash<B> m_hash;
|
||||
};
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
struct numeric_limits<fpm::fixed<B,I,F>>
|
||||
{
|
||||
static constexpr bool is_specialized = true;
|
||||
static constexpr bool is_signed = std::numeric_limits<B>::is_signed;
|
||||
static constexpr bool is_integer = false;
|
||||
static constexpr bool is_exact = true;
|
||||
static constexpr bool has_infinity = false;
|
||||
static constexpr bool has_quiet_NaN = false;
|
||||
static constexpr bool has_signaling_NaN = false;
|
||||
static constexpr bool has_denorm = std::denorm_absent;
|
||||
static constexpr bool has_denorm_loss = false;
|
||||
static constexpr std::float_round_style round_style = std::round_to_nearest;
|
||||
static constexpr bool is_iec_559 = false;
|
||||
static constexpr bool is_bounded = true;
|
||||
static constexpr bool is_modulo = std::numeric_limits<B>::is_modulo;
|
||||
static constexpr int digits = std::numeric_limits<B>::digits;
|
||||
|
||||
// Any number with `digits10` significant base-10 digits (that fits in
|
||||
// the range of the type) is guaranteed to be convertible from text and
|
||||
// back without change. Worst case, this is 0.000...001, so we can only
|
||||
// guarantee this case. Nothing more.
|
||||
static constexpr int digits10 = 1;
|
||||
|
||||
// This is equal to max_digits10 for the integer and fractional part together.
|
||||
static constexpr int max_digits10 =
|
||||
fpm::detail::max_digits10(std::numeric_limits<B>::digits - F) + fpm::detail::max_digits10(F);
|
||||
|
||||
static constexpr int radix = 2;
|
||||
static constexpr int min_exponent = 1 - F;
|
||||
static constexpr int min_exponent10 = -fpm::detail::digits10(F);
|
||||
static constexpr int max_exponent = std::numeric_limits<B>::digits - F;
|
||||
static constexpr int max_exponent10 = fpm::detail::digits10(std::numeric_limits<B>::digits - F);
|
||||
static constexpr bool traps = true;
|
||||
static constexpr bool tinyness_before = false;
|
||||
|
||||
static constexpr auto lowest() noexcept -> fpm::fixed<B,I,F>
|
||||
{
|
||||
return fpm::fixed<B,I,F>::from_raw_value(std::numeric_limits<B>::lowest());
|
||||
}
|
||||
|
||||
static constexpr auto min() noexcept -> fpm::fixed<B,I,F>
|
||||
{
|
||||
return lowest();
|
||||
}
|
||||
|
||||
static constexpr auto max() noexcept -> fpm::fixed<B,I,F>
|
||||
{
|
||||
return fpm::fixed<B,I,F>::from_raw_value(std::numeric_limits<B>::max());
|
||||
}
|
||||
|
||||
static constexpr auto epsilon() noexcept -> fpm::fixed<B,I,F>
|
||||
{
|
||||
return fpm::fixed<B,I,F>::from_raw_value(1);
|
||||
}
|
||||
|
||||
static constexpr auto round_error() noexcept -> fpm::fixed<B,I,F>
|
||||
{
|
||||
return fpm::fixed<B,I,F>(1) / 2;
|
||||
}
|
||||
|
||||
static constexpr auto denorm_min() noexcept -> fpm::fixed<B,I,F>
|
||||
{
|
||||
return min();
|
||||
}
|
||||
};
|
||||
|
||||
} // namespace std
|
||||
|
||||
#endif
|
||||
700
src/libs/vmisc/fpm/math.hpp
Normal file
700
src/libs/vmisc/fpm/math.hpp
Normal file
|
|
@ -0,0 +1,700 @@
|
|||
#ifndef FPM_MATH_HPP
|
||||
#define FPM_MATH_HPP
|
||||
|
||||
#include "fixed.hpp"
|
||||
#include <cmath>
|
||||
|
||||
#ifdef _MSC_VER
|
||||
#include <intrin.h>
|
||||
#endif
|
||||
|
||||
#include <QtGlobal>
|
||||
|
||||
#if QT_VERSION < QT_VERSION_CHECK(5, 5, 0)
|
||||
#include "../diagnostic.h"
|
||||
#endif // QT_VERSION < QT_VERSION_CHECK(5, 5, 0)
|
||||
|
||||
namespace fpm
|
||||
{
|
||||
|
||||
//
|
||||
// Helper functions
|
||||
//
|
||||
namespace detail
|
||||
{
|
||||
|
||||
QT_WARNING_PUSH
|
||||
QT_WARNING_DISABLE_CLANG("-Wsign-conversion")
|
||||
|
||||
// Returns the index of the most-signifcant set bit
|
||||
inline auto find_highest_bit(unsigned long long value) noexcept -> long
|
||||
{
|
||||
assert(value != 0);
|
||||
#if defined(_MSC_VER)
|
||||
unsigned long index;
|
||||
#if defined(_WIN64)
|
||||
_BitScanReverse64(&index, value);
|
||||
#else
|
||||
if (_BitScanReverse(&index, static_cast<unsigned long>(value >> 32)) != 0) {
|
||||
index += 32;
|
||||
} else {
|
||||
_BitScanReverse(&index, static_cast<unsigned long>(value & 0xfffffffflu));
|
||||
}
|
||||
#endif
|
||||
return index;
|
||||
#elif defined(__GNUC__) || defined(__clang__)
|
||||
return sizeof(value) * 8 - 1 - __builtin_clzll(value); // NOLINT
|
||||
#else
|
||||
# error "your platform does not support find_highest_bit()"
|
||||
#endif
|
||||
}
|
||||
|
||||
QT_WARNING_POP
|
||||
|
||||
} // namespace detail
|
||||
|
||||
//
|
||||
// Classification methods
|
||||
//
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto fpclassify(fixed<B, I, F> x) noexcept -> int
|
||||
{
|
||||
return (x.raw_value() == 0) ? FP_ZERO : FP_NORMAL;
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto isfinite(fixed<B, I, F> /*unused*/) noexcept -> bool
|
||||
{
|
||||
return true;
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto isinf(fixed<B, I, F> /*unused*/) noexcept -> bool
|
||||
{
|
||||
return false;
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto isnan(fixed<B, I, F> /*unused*/) noexcept -> bool
|
||||
{
|
||||
return false;
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto isnormal(fixed<B, I, F> x) noexcept -> bool
|
||||
{
|
||||
return x.raw_value() != 0;
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto signbit(fixed<B, I, F> x) noexcept -> bool
|
||||
{
|
||||
return x.raw_value() < 0;
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto isgreater(fixed<B, I, F> x, fixed<B, I, F> y) noexcept -> bool
|
||||
{
|
||||
return x > y;
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto isgreaterequal(fixed<B, I, F> x, fixed<B, I, F> y) noexcept -> bool
|
||||
{
|
||||
return x >= y;
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto isless(fixed<B, I, F> x, fixed<B, I, F> y) noexcept -> bool
|
||||
{
|
||||
return x < y;
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto islessequal(fixed<B, I, F> x, fixed<B, I, F> y) noexcept -> bool
|
||||
{
|
||||
return x <= y;
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto islessgreater(fixed<B, I, F> x, fixed<B, I, F> y) noexcept -> bool
|
||||
{
|
||||
return x != y;
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto isunordered(fixed<B, I, F> /*x*/, fixed<B, I, F> /*y*/) noexcept -> bool
|
||||
{
|
||||
return false;
|
||||
}
|
||||
|
||||
//
|
||||
// Nearest integer operations
|
||||
//
|
||||
template <typename B, typename I, unsigned int F>
|
||||
inline auto ceil(fixed<B, I, F> x) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
constexpr auto FRAC = B(1) << F;
|
||||
auto value = x.raw_value();
|
||||
if (value > 0)
|
||||
{
|
||||
value += FRAC - 1;
|
||||
}
|
||||
return fixed<B, I, F>::from_raw_value(value / FRAC * FRAC);
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
inline auto floor(fixed<B, I, F> x) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
constexpr auto FRAC = B(1) << F;
|
||||
auto value = x.raw_value();
|
||||
if (value < 0)
|
||||
{
|
||||
value -= FRAC - 1;
|
||||
}
|
||||
return fixed<B, I, F>::from_raw_value(value / FRAC * FRAC);
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
inline auto trunc(fixed<B, I, F> x) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
constexpr auto FRAC = B(1) << F;
|
||||
return fixed<B, I, F>::from_raw_value(x.raw_value() / FRAC * FRAC);
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
inline auto round(fixed<B, I, F> x) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
constexpr auto FRAC = B(1) << F;
|
||||
auto value = x.raw_value() / (FRAC / 2);
|
||||
return fixed<B, I, F>::from_raw_value(((value / 2) + (value % 2)) * FRAC);
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
auto nearbyint(fixed<B, I, F> x) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
// Rounding mode is assumed to be FE_TONEAREST
|
||||
constexpr auto FRAC = B(1) << F;
|
||||
auto value = x.raw_value();
|
||||
const bool is_half = std::abs(value % FRAC) == FRAC / 2;
|
||||
value /= FRAC / 2;
|
||||
value = (value / 2) + (value % 2);
|
||||
value -= (value % 2) * is_half;
|
||||
return fixed<B, I, F>::from_raw_value(value * FRAC);
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto rint(fixed<B, I, F> x) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
// Rounding mode is assumed to be FE_TONEAREST
|
||||
return nearbyint(x);
|
||||
}
|
||||
|
||||
//
|
||||
// Mathematical functions
|
||||
//
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto abs(fixed<B, I, F> x) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
return (x >= fixed<B, I, F>{0}) ? x : -x;
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto fmod(fixed<B, I, F> x, fixed<B, I, F> y) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
return
|
||||
assert(y.raw_value() != 0),
|
||||
fixed<B, I, F>::from_raw_value(x.raw_value() % y.raw_value());
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto remainder(fixed<B, I, F> x, fixed<B, I, F> y) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
return
|
||||
assert(y.raw_value() != 0),
|
||||
x - nearbyint(x / y) * y;
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
inline auto remquo(fixed<B, I, F> x, fixed<B, I, F> y, int* quo) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
assert(y.raw_value() != 0);
|
||||
assert(quo != nullptr);
|
||||
*quo = x.raw_value() / y.raw_value();
|
||||
return fixed<B, I, F>::from_raw_value(x.raw_value() % y.raw_value());
|
||||
}
|
||||
|
||||
//
|
||||
// Manipulation functions
|
||||
//
|
||||
|
||||
template <typename B, typename I, unsigned int F, typename C, typename J, unsigned int G>
|
||||
constexpr inline auto copysign(fixed<B, I, F> x, fixed<C, J, G> y) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
return
|
||||
x = abs(x),
|
||||
(y >= fixed<C, J, G>{0}) ? x : -x;
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto nextafter(fixed<B, I, F> from, fixed<B, I, F> to) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
return from == to ? to :
|
||||
to > from ? fixed<B, I, F>::from_raw_value(from.raw_value() + 1)
|
||||
: fixed<B, I, F>::from_raw_value(from.raw_value() - 1);
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
constexpr inline auto nexttoward(fixed<B, I, F> from, fixed<B, I, F> to) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
return nextafter(from, to);
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
inline auto modf(fixed<B, I, F> x, fixed<B, I, F>* iptr) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
const auto raw = x.raw_value();
|
||||
constexpr auto FRAC = B{1} << F;
|
||||
*iptr = fixed<B, I, F>::from_raw_value(raw / FRAC * FRAC);
|
||||
return fixed<B, I, F>::from_raw_value(raw % FRAC);
|
||||
}
|
||||
|
||||
|
||||
//
|
||||
// Power functions
|
||||
//
|
||||
|
||||
template <typename B, typename I, unsigned int F, typename T,
|
||||
typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
|
||||
auto pow(fixed<B, I, F> base, T exp) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
using Fixed = fixed<B, I, F>;
|
||||
|
||||
if (base == Fixed(0)) {
|
||||
assert(exp > 0);
|
||||
return Fixed(0);
|
||||
}
|
||||
|
||||
Fixed result {1};
|
||||
if (exp < 0)
|
||||
{
|
||||
for (Fixed intermediate = base; exp != 0; exp /= 2, intermediate *= intermediate)
|
||||
{
|
||||
if ((exp % 2) != 0)
|
||||
{
|
||||
result /= intermediate;
|
||||
}
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
for (Fixed intermediate = base; exp != 0; exp /= 2, intermediate *= intermediate)
|
||||
{
|
||||
if ((exp % 2) != 0)
|
||||
{
|
||||
result *= intermediate;
|
||||
}
|
||||
}
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
auto pow(fixed<B, I, F> base, fixed<B, I, F> exp) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
using Fixed = fixed<B, I, F>;
|
||||
|
||||
if (base == Fixed(0)) {
|
||||
assert(exp > Fixed(0));
|
||||
return Fixed(0);
|
||||
}
|
||||
|
||||
if (exp < Fixed(0))
|
||||
{
|
||||
return 1 / pow(base, -exp);
|
||||
}
|
||||
|
||||
constexpr auto FRAC = B(1) << F;
|
||||
if (exp.raw_value() % FRAC == 0)
|
||||
{
|
||||
// Non-fractional exponents are easier to calculate
|
||||
return pow(base, exp.raw_value() / FRAC);
|
||||
}
|
||||
|
||||
// For negative bases we do not support fractional exponents.
|
||||
// Technically fractions with odd denominators could work,
|
||||
// but that's too much work to figure out.
|
||||
assert(base > Fixed(0));
|
||||
return exp2(log2(base) * exp);
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
auto exp(fixed<B, I, F> x) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
using Fixed = fixed<B, I, F>;
|
||||
if (x < Fixed(0)) {
|
||||
return 1 / exp(-x);
|
||||
}
|
||||
constexpr auto FRAC = B(1) << F;
|
||||
const B x_int = x.raw_value() / FRAC;
|
||||
x -= x_int;
|
||||
assert(x >= Fixed(0) && x < Fixed(1));
|
||||
|
||||
constexpr auto fA = Fixed::template from_fixed_point<63>( 128239257017632854LL); // 1.3903728105644451e-2
|
||||
constexpr auto fB = Fixed::template from_fixed_point<63>( 320978614890280666LL); // 3.4800571158543038e-2
|
||||
constexpr auto fC = Fixed::template from_fixed_point<63>(1571680799599592947LL); // 1.7040197373796334e-1
|
||||
constexpr auto fD = Fixed::template from_fixed_point<63>(4603349000587966862LL); // 4.9909609871464493e-1
|
||||
constexpr auto fE = Fixed::template from_fixed_point<62>(4612052447974689712LL); // 1.0000794567422495
|
||||
constexpr auto fF = Fixed::template from_fixed_point<63>(9223361618412247875LL); // 9.9999887043019773e-1
|
||||
return pow(Fixed::e(), x_int) * (((((fA * x + fB) * x + fC) * x + fD) * x + fE) * x + fF);
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
auto exp2(fixed<B, I, F> x) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
using Fixed = fixed<B, I, F>;
|
||||
if (x < Fixed(0)) {
|
||||
return 1 / exp2(-x);
|
||||
}
|
||||
constexpr auto FRAC = B(1) << F;
|
||||
const B x_int = x.raw_value() / FRAC;
|
||||
x -= x_int;
|
||||
assert(x >= Fixed(0) && x < Fixed(1));
|
||||
|
||||
constexpr auto fA = Fixed::template from_fixed_point<63>( 17491766697771214LL); // 1.8964611454333148e-3
|
||||
constexpr auto fB = Fixed::template from_fixed_point<63>( 82483038782406547LL); // 8.9428289841091295e-3
|
||||
constexpr auto fC = Fixed::template from_fixed_point<63>( 515275173969157690LL); // 5.5866246304520701e-2
|
||||
constexpr auto fD = Fixed::template from_fixed_point<63>(2214897896212987987LL); // 2.4013971109076949e-1
|
||||
constexpr auto fE = Fixed::template from_fixed_point<63>(6393224161192452326LL); // 6.9315475247516736e-1
|
||||
constexpr auto fF = Fixed::template from_fixed_point<63>(9223371050976163566LL); // 9.9999989311082668e-1
|
||||
return Fixed(1 << x_int) * (((((fA * x + fB) * x + fC) * x + fD) * x + fE) * x + fF);
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
auto expm1(fixed<B, I, F> x) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
return exp(x) - 1; // cppcheck-suppress unpreciseMathCall
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
auto log2(fixed<B, I, F> x) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
using Fixed = fixed<B, I, F>;
|
||||
assert(x > Fixed(0));
|
||||
|
||||
// Normalize input to the [1:2] domain
|
||||
B value = x.raw_value();
|
||||
const long highest = detail::find_highest_bit(value);
|
||||
if (highest >= F)
|
||||
{
|
||||
value >>= (highest - F);
|
||||
}
|
||||
else
|
||||
{
|
||||
value <<= (F - highest);
|
||||
}
|
||||
x = Fixed::from_raw_value(value);
|
||||
assert(x >= Fixed(1) && x < Fixed(2));
|
||||
|
||||
constexpr auto fA = Fixed::template from_fixed_point<63>( 413886001457275979LL); // 4.4873610194131727e-2
|
||||
constexpr auto fB = Fixed::template from_fixed_point<63>(-3842121857793256941LL); // -4.1656368651734915e-1
|
||||
constexpr auto fC = Fixed::template from_fixed_point<62>( 7522345947206307744LL); // 1.6311487636297217
|
||||
constexpr auto fD = Fixed::template from_fixed_point<61>(-8187571043052183818LL); // -3.5507929249026341
|
||||
constexpr auto fE = Fixed::template from_fixed_point<60>( 5870342889289496598LL); // 5.0917108110420042
|
||||
constexpr auto fF = Fixed::template from_fixed_point<61>(-6457199832668582866LL); // -2.8003640347009253
|
||||
return Fixed(highest - F) + (((((fA * x + fB) * x + fC) * x + fD) * x + fE) * x + fF);
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
auto log(fixed<B, I, F> x) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
using Fixed = fixed<B, I, F>;
|
||||
return log2(x) / log2(Fixed::e());
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
auto log10(fixed<B, I, F> x) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
using Fixed = fixed<B, I, F>;
|
||||
return log2(x) / log2(Fixed(10));
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
auto log1p(fixed<B, I, F> x) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
return log(1 + x); // cppcheck-suppress unpreciseMathCall
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
auto cbrt(fixed<B, I, F> x) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
using Fixed = fixed<B, I, F>;
|
||||
|
||||
if (x == Fixed(0))
|
||||
{
|
||||
return x;
|
||||
}
|
||||
if (x < Fixed(0))
|
||||
{
|
||||
return -cbrt(-x);
|
||||
}
|
||||
assert(x >= Fixed(0));
|
||||
|
||||
// Finding the cube root of an integer, taken from Hacker's Delight,
|
||||
// based on the square root algorithm.
|
||||
|
||||
// We start at the greatest power of eight that's less than the argument.
|
||||
int ofs = ((detail::find_highest_bit(x.raw_value()) + 2*F) / 3 * 3);
|
||||
I num = I{x.raw_value()};
|
||||
I res = 0;
|
||||
|
||||
const auto do_round = [&]
|
||||
{
|
||||
for (; ofs >= 0; ofs -= 3)
|
||||
{
|
||||
res += res;
|
||||
const I val = (3*res*(res + 1) + 1) << ofs;
|
||||
if (num >= val)
|
||||
{
|
||||
num -= val;
|
||||
res++;
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
// We should shift by 2*F (since there are two multiplications), but that
|
||||
// could overflow even the intermediate type, so we have to split the
|
||||
// algorithm up in two rounds of F bits each. Each round will deplete
|
||||
// 'num' digit by digit, so after a round we can shift it again.
|
||||
num <<= F;
|
||||
ofs -= F;
|
||||
do_round();
|
||||
|
||||
num <<= F;
|
||||
ofs += F;
|
||||
do_round();
|
||||
|
||||
return Fixed::from_raw_value(static_cast<B>(res));
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
auto sqrt(fixed<B, I, F> x) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
using Fixed = fixed<B, I, F>;
|
||||
|
||||
assert(x >= Fixed(0));
|
||||
if (x == Fixed(0))
|
||||
{
|
||||
return x;
|
||||
}
|
||||
|
||||
// Finding the square root of an integer in base-2, from:
|
||||
// https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Binary_numeral_system_.28base_2.29
|
||||
|
||||
// Shift by F first because it's fixed-point.
|
||||
I num = I{x.raw_value()} << F;
|
||||
I res = 0;
|
||||
|
||||
// "bit" starts at the greatest power of four that's less than the argument.
|
||||
for (I bit = I{1} << ((detail::find_highest_bit(x.raw_value()) + F) / 2 * 2); bit != 0; bit >>= 2)
|
||||
{
|
||||
const I val = res + bit;
|
||||
res >>= 1;
|
||||
if (num >= val)
|
||||
{
|
||||
num -= val;
|
||||
res += bit;
|
||||
}
|
||||
}
|
||||
|
||||
// Round the last digit up if necessary
|
||||
if (num > res)
|
||||
{
|
||||
res++;
|
||||
}
|
||||
|
||||
return Fixed::from_raw_value(static_cast<B>(res));
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
auto hypot(fixed<B, I, F> x, fixed<B, I, F> y) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
assert(x != 0 || y != 0);
|
||||
return sqrt(x*x + y*y);
|
||||
}
|
||||
|
||||
//
|
||||
// Trigonometry functions
|
||||
//
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
auto sin(fixed<B, I, F> x) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
// This sine uses a fifth-order curve-fitting approximation originally
|
||||
// described by Jasper Vijn on coranac.com which has a worst-case
|
||||
// relative error of 0.07% (over [-pi:pi]).
|
||||
using Fixed = fixed<B, I, F>;
|
||||
|
||||
// Turn x from [0..2*PI] domain into [0..4] domain
|
||||
x = fmod(x, Fixed::two_pi());
|
||||
x = x / Fixed::half_pi();
|
||||
|
||||
// Take x modulo one rotation, so [-4..+4].
|
||||
if (x < Fixed(0)) {
|
||||
x += Fixed(4);
|
||||
}
|
||||
|
||||
int sign = +1;
|
||||
if (x > Fixed(2)) {
|
||||
// Reduce domain to [0..2].
|
||||
sign = -1;
|
||||
x -= Fixed(2);
|
||||
}
|
||||
|
||||
if (x > Fixed(1)) {
|
||||
// Reduce domain to [0..1].
|
||||
x = Fixed(2) - x;
|
||||
}
|
||||
|
||||
const Fixed x2 = x*x;
|
||||
return sign * x * (Fixed::pi() - x2*(Fixed::two_pi() - 5 - x2*(Fixed::pi() - 3)))/2;
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
inline auto cos(fixed<B, I, F> x) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
return sin(fixed<B, I, F>::half_pi() + x);
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
inline auto tan(fixed<B, I, F> x) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
auto cx = cos(x);
|
||||
|
||||
// Tangent goes to infinity at 90 and -90 degrees.
|
||||
// We can't represent that with fixed-point maths.
|
||||
assert(abs(cx).raw_value() > 1);
|
||||
|
||||
return sin(x) / cx;
|
||||
}
|
||||
|
||||
namespace detail {
|
||||
|
||||
// Calculates atan(x) assuming that x is in the range [0,1]
|
||||
template <typename B, typename I, unsigned int F>
|
||||
auto atan_sanitized(fixed<B, I, F> x) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
using Fixed = fixed<B, I, F>;
|
||||
assert(x >= Fixed(0) && x <= Fixed(1));
|
||||
|
||||
constexpr auto fA = Fixed::template from_fixed_point<63>( 716203666280654660LL); // 0.0776509570923569
|
||||
constexpr auto fB = Fixed::template from_fixed_point<63>(-2651115102768076601LL); // -0.287434475393028
|
||||
constexpr auto fC = Fixed::template from_fixed_point<63>( 9178930894564541004LL); // 0.995181681698119 (PI/4 - A - B)
|
||||
|
||||
const auto xx = x * x;
|
||||
return ((fA*xx + fB)*xx + fC)*x;
|
||||
}
|
||||
|
||||
// Calculate atan(y / x), assuming x != 0.
|
||||
//
|
||||
// If x is very, very small, y/x can easily overflow the fixed-point range.
|
||||
// If q = y/x and q > 1, atan(q) would calculate atan(1/q) as intermediate step
|
||||
// anyway. We can shortcut that here and avoid the loss of information, thus
|
||||
// improving the accuracy of atan(y/x) for very small x.
|
||||
template <typename B, typename I, unsigned int F>
|
||||
auto atan_div(fixed<B, I, F> y, fixed<B, I, F> x) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
using Fixed = fixed<B, I, F>;
|
||||
assert(x != Fixed(0));
|
||||
|
||||
// Make sure y and x are positive.
|
||||
// If y / x is negative (when y or x, but not both, are negative), negate the result to
|
||||
// keep the correct outcome.
|
||||
if (y < Fixed(0)) {
|
||||
if (x < Fixed(0)) {
|
||||
return atan_div(-y, -x);
|
||||
}
|
||||
return -atan_div(-y, x);
|
||||
}
|
||||
if (x < Fixed(0)) {
|
||||
return -atan_div(y, -x);
|
||||
}
|
||||
assert(y >= Fixed(0));
|
||||
assert(x > Fixed(0));
|
||||
|
||||
if (y > x) {
|
||||
return Fixed::half_pi() - detail::atan_sanitized(x / y);
|
||||
}
|
||||
return detail::atan_sanitized(y / x);
|
||||
}
|
||||
|
||||
} // namespace detail
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
auto atan(fixed<B, I, F> x) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
using Fixed = fixed<B, I, F>;
|
||||
if (x < Fixed(0))
|
||||
{
|
||||
return -atan(-x);
|
||||
}
|
||||
|
||||
if (x > Fixed(1))
|
||||
{
|
||||
return Fixed::half_pi() - detail::atan_sanitized(Fixed(1) / x);
|
||||
}
|
||||
|
||||
return detail::atan_sanitized(x);
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
auto asin(fixed<B, I, F> x) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
using Fixed = fixed<B, I, F>;
|
||||
assert(x >= Fixed(-1) && x <= Fixed(+1));
|
||||
|
||||
const auto yy = Fixed(1) - x * x;
|
||||
if (yy == Fixed(0))
|
||||
{
|
||||
return copysign(Fixed::half_pi(), x);
|
||||
}
|
||||
return detail::atan_div(x, sqrt(yy));
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
auto acos(fixed<B, I, F> x) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
using Fixed = fixed<B, I, F>;
|
||||
assert(x >= Fixed(-1) && x <= Fixed(+1));
|
||||
|
||||
if (x == Fixed(-1))
|
||||
{
|
||||
return Fixed::pi();
|
||||
}
|
||||
const auto yy = Fixed(1) - x * x;
|
||||
return Fixed(2)*detail::atan_div(sqrt(yy), Fixed(1) + x);
|
||||
}
|
||||
|
||||
template <typename B, typename I, unsigned int F>
|
||||
auto atan2(fixed<B, I, F> y, fixed<B, I, F> x) noexcept -> fixed<B, I, F>
|
||||
{
|
||||
using Fixed = fixed<B, I, F>;
|
||||
if (x == Fixed(0))
|
||||
{
|
||||
assert(y != Fixed(0));
|
||||
return (y > Fixed(0)) ? Fixed::half_pi() : -Fixed::half_pi();
|
||||
}
|
||||
|
||||
auto ret = detail::atan_div(y, x);
|
||||
|
||||
if (x < Fixed(0))
|
||||
{
|
||||
return (y >= Fixed(0)) ? ret + Fixed::pi() : ret - Fixed::pi();
|
||||
}
|
||||
return ret;
|
||||
}
|
||||
|
||||
} // namespace fpm
|
||||
|
||||
#endif
|
||||
|
|
@ -55,7 +55,9 @@ HEADERS += \
|
|||
$$PWD/vmodifierkey.h \
|
||||
$$PWD/typedef.h \
|
||||
$$PWD/backport/qscopeguard.h \
|
||||
$$PWD/dialogs/dialogselectlanguage.h
|
||||
$$PWD/dialogs/dialogselectlanguage.h \
|
||||
$$PWD/fpm/fixed.hpp \
|
||||
$$PWD/fpm/math.hpp
|
||||
|
||||
contains(DEFINES, APPIMAGE) {
|
||||
SOURCES += \
|
||||
|
|
|
|||
|
|
@ -53,8 +53,8 @@ DialogSinglePoint::DialogSinglePoint(const VContainer *data, quint32 toolId, QWi
|
|||
|
||||
ui->lineEditName->setClearButtonEnabled(true);
|
||||
|
||||
ui->doubleSpinBoxX->setRange(0, VAbstractValApplication::VApp()->fromPixel(SceneSize));
|
||||
ui->doubleSpinBoxY->setRange(0, VAbstractValApplication::VApp()->fromPixel(SceneSize));
|
||||
ui->doubleSpinBoxX->setRange(0, VAbstractValApplication::VApp()->fromPixel(maxSceneSize));
|
||||
ui->doubleSpinBoxY->setRange(0, VAbstractValApplication::VApp()->fromPixel(maxSceneSize));
|
||||
InitOkCancel(ui);
|
||||
|
||||
connect(ui->lineEditName, &QLineEdit::textChanged, this, [this]()
|
||||
|
|
|
|||
|
|
@ -51,21 +51,18 @@
|
|||
#include <QOpenGLWidget>
|
||||
#include <QMimeData>
|
||||
#include <QMimeDatabase>
|
||||
#include <QtMath>
|
||||
|
||||
#include "../vmisc/def.h"
|
||||
#include "../vmisc/vmath.h"
|
||||
#include "vmaingraphicsscene.h"
|
||||
#include "vsimplecurve.h"
|
||||
#include "vcontrolpointspline.h"
|
||||
#include "../vmisc/vabstractapplication.h"
|
||||
#include "../vmisc/vcommonsettings.h"
|
||||
#include "../vmisc/literals.h"
|
||||
#include "vabstractmainwindow.h"
|
||||
#include "global.h"
|
||||
#include "../ifc/xml/utils.h"
|
||||
|
||||
const qreal maxSceneSize = ((20.0 * 1000.0) / 25.4) * PrintDPI; // 20 meters in pixels
|
||||
|
||||
namespace
|
||||
{
|
||||
qreal ScrollingSteps(QWheelEvent* wheel_event)
|
||||
|
|
|
|||
Loading…
Reference in New Issue
Block a user