public static ULong BigSqrtRem(ULong lo, UInt hi, out ULong remainder)
{
unchecked {
if (0u == hi)
{
return(Mathematics.Elementary.Math.SqrtRem(lo, out remainder));
}
var old = (ULong)Math.Sqrt((0.0 + ((ULong)1u << (Misc.ULong.BitSize - 1)) + ((ULong)1u << (Misc.ULong.BitSize - 1))) * hi + lo);
ULong h;
var l = MathEx.BigSquare(old, out h);
l += lo;
h += hi;
if (l < lo)
{
++h;
}
var @new = MathEx.BigDivNoThrow(l, h, old) >> 1;
l = MathEx.BigSquare(@new, out h);
if ((h > hi) || ((h == hi) && (l > lo)))
{
remainder = lo - l - ((@new << 1) - 1u);
return(@new - (ULong)1u);
}
else
{
remainder = lo - l;
return(@new);
}
}
}
public static ULong BigSqrt(ULong lo, UInt hi)
{
unchecked {
if (0u == hi)
{
return(Mathematics.Elementary.Math.Sqrt(lo));
}
var old = (ULong)Math.Sqrt((0.0 + ((ULong)1u << (ULong_Misc.BitSizeAsIntUnchecked - 1)) + ((ULong)1u << (ULong_Misc.BitSizeAsIntUnchecked - 1))) * hi + lo);
ULong h;
var l = MathEx.BigSquare(old, out h);
l += lo;
h += hi;
if (l < lo)
{
++h;
}
var @new = MathEx.BigDivNoThrow(l, h, old) >> 1;
l = MathEx.BigSquare(@new, out h);
if ((h > hi) || ((h == hi) && (l > lo)))
{
return(@new - (ULong)1u);
}
else
{
return(@new);
}
}
}
// ~327. Cyc
public static ULong SqrtDouble(ULong radicand)
{
unchecked {
if (0u == radicand)
{
return(0u);
}
/*
* if (radicand <= ~(ULong)0 >> 2) {
* var old = (ULong)(((ULong)1u << (Misc.UInt.BitSize - 0)) * Math.Sqrt(radicand));
* ULong h;
* var l = MathEx.BigSquare(old, out h);
* h += radicand;
* var @new = MathEx.BigDivUnchecked(l, h, old) >> 1;
* l = MathEx.BigSquare(@new, out h);
* if ((h > radicand) || ((h == radicand) && (l > 0u))) {
* return @new - (ULong)1u;
* } else {
* return @new;
* }
* }
*/
{
if (radicand == ~(ULong)0)
{
return(~(ULong)0);
}
var old = (ULong)(((ULong)1u << (Misc.UInt.BitSize - 1)) * Math.Sqrt(radicand));
var a = (ULong)0u;
var lo = radicand << (Misc.ULong.BitSize - 2);
radicand = radicand >> 2;
ULong h;
var l = MathEx.BigSquare(old, out h);
l += lo;
h += radicand;
if (l < lo)
{
++h;
}
var @new = MathEx.BigDivNoThrow(l, h, old) >> 1;
l = MathEx.BigSquare(@new, out h);
if ((h > radicand) || ((h == radicand) && (l > lo)))
{
--@new;
@new <<= 1;
radicand = (radicand << 2) | (lo >> (Misc.ULong.BitSize - 2));
lo = a;
a = (@new << 1) + 1u;
var b = l;
l <<= 2;
h = (h << 2) + (ULong)(((l < a) ? -1 : 0) + ((0 > (Long)@new) ? -1 : 0) + ((int)(b >> (Misc.ULong.BitSize - 2))));
l -= a;
}
else
{
@new <<= 1;
radicand = (radicand << 2) | (lo >> (Misc.ULong.BitSize - 2));
lo = a;
a = (@new << 1) + 1u;
var b = l;
l <<= 2;
l += a;
h = (h << 2) + (((l < a) ? 1u : 0u) + ((0 > (Long)@new) ? 1u : 0u) + ((uint)(b >> (Misc.ULong.BitSize - 2))));
}
if ((h > radicand) || ((h == radicand) && (l > lo)))
{
}
else
{
++@new;
}
return(@new);
}
}
}
public static ULong BigSqrt(ULong lo, ULong hi)
{
unchecked {
if (0u == hi)
{
return(Mathematics.Elementary.Math.Sqrt(lo));
}
if (hi <= ~(ULong)0 >> 2)
{
var old = (ULong)Math.Sqrt((0.0 + ((ULong)1u << (Misc.ULong.BitSize - 1)) + ((ULong)1u << (Misc.ULong.BitSize - 1))) * hi + lo);
ULong h;
var l = MathEx.BigSquare(old, out h);
l += lo;
h += hi;
if (l < lo)
{
++h;
}
var @new = MathEx.BigDivNoThrow(l, h, old) >> 1;
l = MathEx.BigSquare(@new, out h);
if ((h > hi) || ((h == hi) && (l > lo)))
{
return(@new - (ULong)1u);
}
else
{
return(@new);
}
}
{
if (hi == ~(ULong)0)
{
return(~(ULong)0);
}
var old = (ULong)(((ULong)1u << (Misc.UInt.BitSize - 1)) * Math.Sqrt(hi));
var a = lo;
lo = (lo >> 2) | (hi << (Misc.ULong.BitSize - 2));
hi = hi >> 2;
ULong h;
var l = MathEx.BigSquare(old, out h);
l += lo;
h += hi;
if (l < lo)
{
++h;
}
var @new = MathEx.BigDivNoThrow(l, h, old) >> 1;
l = MathEx.BigSquare(@new, out h);
if ((h > hi) || ((h == hi) && (l > lo)))
{
--@new;
@new <<= 1;
hi = (hi << 2) | (lo >> (Misc.ULong.BitSize - 2));
lo = a;
a = (@new << 1) + 1u;
var b = l;
l <<= 2;
h = (h << 2) + (ULong)(((l < a) ? -1 : 0) + ((0 > (Long)@new) ? -1 : 0) + ((int)(b >> (Misc.ULong.BitSize - 2))));
l -= a;
}
else
{
@new <<= 1;
hi = (hi << 2) | (lo >> (Misc.ULong.BitSize - 2));
lo = a;
a = (@new << 1) + 1u;
var b = l;
l <<= 2;
l += a;
h = (h << 2) + (((l < a) ? 1u : 0u) + ((0 > (Long)@new) ? 1u : 0u) + ((uint)(b >> (Misc.ULong.BitSize - 2))));
}
if ((h > hi) || ((h == hi) && (l > lo)))
{
}
else
{
++@new;
}
return(@new);
}
}
}