// Copyright (c) 1995-2009 Nokia Corporation and/or its subsidiary(-ies).

// All rights reserved.

// This component and the accompanying materials are made available

// which accompanies this distribution, and is available

//

// Initial Contributors:

// Nokia Corporation - initial contribution.

//

// Contributors:

//

// Description:

// e32\euser\maths\um_pow.cpp

// Raise to the power.

// 

//

#include "um_std.h"

#if defined(__USE_VFP_MATH) && !defined(__CPU_HAS_VFP)

#error	__USE_VFP_MATH was defined but not __CPU_HAS_VFP - impossible combination, check variant.mmh 

#endif

#ifndef __USE_VFP_MATH

LOCAL_D const TUint32 ArtanhCoeffs[] =

	{

	0x5C17F0BC,0xB8AA3B29,0x80010000,	// polynomial approximation to (4/ln2)artanh(x)

	0xD01FDDD8,0xF6384EE1,0x7FFF0000,	// for |x| <= (sqr2-1)/(sqr2+1)

	0x7D0DDC69,0x93BB6287,0x7FFF0000,

	0x6564D4F5,0xD30BB153,0x7FFE0000,

	0x1546C858,0xA4258A33,0x7FFE0000,

	0xCCE50DA9,0x864D28DF,0x7FFE0000,

	0x8E1A5DBB,0xE35271A0,0x7FFD0000,

	0xF5A67D92,0xC3A36B08,0x7FFD0000,

	0x62D53E02,0xC4A1FFAC,0x7FFD0000

	};

LOCAL_D const TUint32 TwoToxCoeffs[] =

	{

	0x00000000,0x80000000,0x7FFF0000,	// polynomial approximation to 2^(x/8) for

	0xD1CF79AC,0xB17217F7,0x7FFB0000,	// 0<=x<=1

	0x162CF72B,0xF5FDEFFC,0x7FF60000,

	0x23EC0D04,0xE35846B8,0x7FF10000,

	0xBDB408D7,0x9D955B7E,0x7FEC0000,

	0xFDD8A678,0xAEC3FE73,0x7FE60000,

	0xBD6E3950,0xA184E90A,0x7FE00000,

	0xC1054DA3,0xFFB259D8,0x7FD90000,

	0x70893DE4,0xB8BEDE2F,0x7FD30000

	};

LOCAL_D const TUint32 TwoToNover8[] =

	{

	0xEA8BD6E7,0x8B95C1E3,0x7FFF0000,	// 2^0.125

	0x8DB8A96F,0x9837F051,0x7FFF0000,	// 2^0.250

	0xB15138EA,0xA5FED6A9,0x7FFF0000,	// 2^0.375

	0xF9DE6484,0xB504F333,0x7FFF0000,	// 2^0.500

	0x5506DADD,0xC5672A11,0x7FFF0000,	// 2^0.625

	0xD69D6AF4,0xD744FCCA,0x7FFF0000,	// 2^0.750

	0xDD24392F,0xEAC0C6E7,0x7FFF0000	// 2^0.875

	};

LOCAL_D const TUint32 Sqr2data[] = {0xF9DE6484,0xB504F333,0x7FFF0000};		// sqr2

LOCAL_D const TUint32 Sqr2Invdata[] = {0xF9DE6484,0xB504F333,0x7FFE0000};	// 1/sqr2

LOCAL_D const TUint32 Onedata[] = {0x00000000,0x80000000,0x7FFF0000};		// 1.0

LOCAL_C void Log2(TRealX& y, TRealX& x)

	{

	// Calculate log2(x) and write to y

	// Result to 64-bit precision to allow accurate powers

	// Algorithm:

	//		log2(aSrc)=log2(2^e.m) e=exponent of aSrc, m=mantissa 1<=m<2

	//		log2(aSrc)=e+log2(m)

	//		If e=-1 (0.5<=aSrc<1), let x=aSrc else let x=mantissa(aSrc)

	//		If x>Sqr2, replace x with x/Sqr2

	//		If x<Sqr2/2, replace x with x*Sqr2

	//		Replace x with (x-1)/(x+1)

	//		Use polynomial to calculate artanh(x) for |x| <= (sqr2-1)/(sqr2+1)

	//			( use identity ln(x) = 2artanh((x-1)/(x+1)) )

	const TRealX& Sqr2=*(const TRealX*)Sqr2data;

	const TRealX& Sqr2Inv=*(const TRealX*)Sqr2Invdata;

	const TRealX& One=*(const TRealX*)Onedata;

	TInt n=(x.iExp-0x7FFF)<<1;

	x.iExp=0x7FFF;

	if (n!=-2)

		{

		if (x>Sqr2)

			{

			x*=Sqr2Inv;

			n++;

			}

		}

	else 

		{

		n=0;

		x.iExp=0x7FFE;

		if (x<Sqr2Inv)

			{

			x*=Sqr2;

			n--;

			}

		}

	x=(x-One)/(x+One);	// ln(x)=2artanh((x-1)/(x+1))

	Math::PolyX(y,x*x,8,(const TRealX*)ArtanhCoeffs);

	y*=x;

	y+=TRealX(n);

	if (y.iExp>1)

		y.iExp--;

	else

		y.iExp=0;

	}

LOCAL_C TInt TwoTox(TRealX& y, TRealX& x)

	{

	// Calculate 2^x and write result to y. Result to 64 bit precision.

	// Algorithm:

	//		2^x = 2^int(x).2^frac(x)

	//		2^int(x) just adds int(x) to the final result exponent

	//		Reduce frac(x) to the range [0,0.125] (modulo 0.125)

	//		Use polynomial to calculate 2^x for 0<=x<=0.125

	//		Multiply by 2^(n/8) for n=0,1,2,3,4,5,6,7 to give 2^frac(x)

	if (x.iExp)

		x.iExp+=3;

	TInt n=(TInt)x;

	if (n<16384 && n>-16384)

		{

		if (x.iSign&1)

			n--;

		x-=TRealX(n);

		Math::PolyX(y,x,8,(const TRealX*)TwoToxCoeffs);

		y.iExp=TUint16(TInt(y.iExp)+(n>>3));

		n&=7;

		if (n)

			y*= (*(const TRealX*)(TwoToNover8+3*n-3));

		return KErrNone;

		}

	else

		{

		if (n<0)

			{

			y.SetZero();

			return KErrUnderflow;

			}

		else

			{

			y.SetInfinite(0);

			return KErrOverflow;

			}

		}

	}

EXPORT_C TInt Math::Pow(TReal &aTrg,const TReal &aSrc,const TReal &aPower)

/**

Calculates the value of x raised to the power of y.

The behaviour conforms to that specified for pow() in the

ISO C Standard ISO/IEC 9899 (Annex F), although floating-point exceptions

are not supported.

@param aTrg   A reference containing the result.

@param aSrc   The x argument of the function.

@param aPower The y argument of the function.

@return KErrNone if successful;

		KErrOverflow if the result is +/- infinity;

	   	KErrUnderflow if the result is too small to be represented;

		KErrArgument if the result is not a number (NaN).

*/

//

// Evaluates aSrc raised to the power aPower and places the result in aTrg.

// For non-special values algorithm is aTrg=2^(aPower*log2(aSrc))

//

	{

	TRealX x,p;

	TInt ret2=p.Set(aPower);

	// pow(x, +/-0) -> 1 for any x, even a NaN

	if (p.IsZero())

		{

		aTrg=1.0;

		return KErrNone;

		}

	TInt ret1=x.Set(aSrc);

	if (ret1==KErrArgument || ret2==KErrArgument)

		{

		// pow(+1, y) -> 1 for any y, even a NaN

		// XXX First test should not be necessary, but on WINS

		//     aSrc == 1.0 is true when aSrc is NaN.

		if (ret1 != KErrArgument && aSrc == 1.0)

			{

			aTrg=aSrc;

			return KErrNone;

			}

		SetNaN(aTrg);

		return KErrArgument;

		}

	// Infinite power

	if (ret2==KErrOverflow)

		{

		// figure out which of these cases we have:

		//

		// pow(x, -INF) -> +INF for |x| < 1  } flag = 0

		// pow(x, +INF) -> +INF for |x| > 1  }

		// pow(x, -INF) -> +0 for |x| > 1      } flag = 1

		// pow(x, +INF) -> +0 for |x| < 1      }

		//

		// flag = 2 => |x| == 1.0

		//

		TInt flag=2;

		if (Abs(aSrc)>1.0)

			flag=p.iSign&1;

		if (Abs(aSrc)<1.0)

			flag=1-(p.iSign&1);

		if (flag==0)

			{

			SetInfinite(aTrg,0);

			return KErrOverflow;

			}

		if (flag==1)

			{

			SetZero(aTrg,0);

			return KErrNone;

			}

		if (Abs(aSrc)==1.0)

			{

			// pow(-1, +/-INF) -> 1

			aTrg=1.0;

			return KErrNone;

			}

		// This should never happen (i.e. aSrc is NaN, which

		// should be taken care of above)

		SetNaN(aTrg);

		return KErrArgument;

		}

	// Negative Base raised to a power

	TInt odd=1;

	if (x.iSign & 1)

		{

		TReal pint;

		Math::Int(pint,aPower);

		if (aPower-pint) // Checks that if aSrc is less than zero, then aPower is integral

			{

			// pow(-INF, y) -> +0 for y < 0 and not an odd integer

			// pow(-INF, y) -> +INF for y > 0 and not an odd integer

			// Since we're here, aPower is not integral, so can't be odd, either

			if (ret1 == KErrOverflow)

				{

				if (aPower < 0)

					{

					SetZero(aTrg);

					return KErrNone;

					}

				else

					{

					SetInfinite(aTrg,0);

					return KErrOverflow;

					}

				}

			SetNaN(aTrg);

			return KErrArgument;

			}

		TReal powerby2=aPower*0.5;

		Math::Int(pint,powerby2);

		if (powerby2-pint)

			odd=(-1);

		x.iSign=0;

		}

	// Zero or infinity raised to a power

	if (x.IsZero() || ret1==KErrOverflow)

		{

		if (x.IsZero() && p.IsZero())

			{

			aTrg=1.0;

			return KErrNone;

			}

		TInt sign=(odd==-1 ? 1 : 0);

		if ((x.IsZero() && (p.iSign&1)==0) || (ret1==KErrOverflow && (p.iSign&1)))

			{

			SetZero(aTrg,sign);				

			return KErrNone;

			}

		else

			{

			SetInfinite(aTrg,sign);

			return KErrOverflow;

			}

		}

	TRealX y;

	Log2(y,x);

	x=y*p;			// this cannot overflow or underflow

	TInt r=TwoTox(y,x);

	if (odd<0)

		y.iSign=1;

	TInt r2=y.GetTReal(aTrg);

	return (r==KErrNone)?r2:r;

	}

#else // __USE_VFP_MATH

// definitions come from RVCT math library

extern "C" TReal pow(TReal,TReal);

EXPORT_C TInt Math::Pow(TReal &aTrg,const TReal &aSrc,const TReal &aPower)

	{

	aTrg = pow(aSrc,aPower);

	if (Math::IsZero(aTrg) && !Math::IsZero(aSrc) && !Math::IsInfinite(aSrc) && !Math::IsInfinite(aPower))

		return KErrUnderflow;

	if (Math::IsFinite(aTrg))

		return KErrNone;

	if (Math::IsZero(aPower))	// pow(x, +/-0) -> 1 for any x, even a NaN

		{

		aTrg = 1.0;

		return KErrNone;

		}

	if (Math::IsInfinite(aTrg))

		return KErrOverflow;

	if (aSrc==1.0)				// pow(+1, y) -> 1 for any y, even a NaN

		{

		aTrg=aSrc;

		return KErrNone;

		}

	if (Math::IsInfinite(aPower))

		{

		if (aSrc == -1.0)		// pow(-1, +/-INF) -> 1

			{

			aTrg = 1.0;

			return KErrNone;

			}

		if (((Abs(aSrc) < 1) && (aPower < 0)) ||	// pow(x, -INF) -> +INF for |x| < 1

		    ((Abs(aSrc) > 1) && (aPower > 0)))		// pow(x, +INF) -> +INF for |x| > 1

			{

			SetInfinite(aTrg,0);

			return KErrOverflow;

			}

		}

	// pow(-INF, y) -> +INF for y > 0 and not an odd integer

	if (Math::IsInfinite(aSrc) && (aSrc < 0) && (aPower > 0))

		{

		TBool odd = EFalse;

		TReal pint;

		Math::Int(pint, aPower);

		if (aPower == pint)

			{

			TReal halfPower = aPower * 0.5;

			Math::Int(pint, halfPower);

			if (halfPower != pint)

				odd = ETrue;

			}

		if (odd == EFalse)

			{

			SetInfinite(aTrg,0);

			return KErrOverflow;

			}

		}

	// Otherwise...

	SetNaN(aTrg);

	return KErrArgument;

	}

#endif