// umagic computes the constants needed to strength reduce unsigned n-bit divides by the constant uint64(c).
// The return values satisfy for all 0 <= x < 2^n
// floor(x / uint64(c)) = x * (m + 2^n) >> (n+s)
private static umagicData umagic(ulong n, long c) => func((_, panic, __) =>
{
// Convert from ConstX auxint values to the real uint64 constant they represent.
var d = uint64(c) << (int)((64L - n)) >> (int)((64L - n));
ptr <object> C = @new <big.Int>().SetUint64(d);
var s = C.BitLen();
var M = big.NewInt(1L);
M.Lsh(M, n + uint(s)); // 2^(n+s)
M.Add(M, C); // 2^(n+s)+c
M.Sub(M, big.NewInt(1L)); // 2^(n+s)+c-1
M.Div(M, C); // ⎡2^(n+s)/c⎤
if (M.Bit(int(n)) != 1L)
{
panic("n+1st bit isn't set");
}
M.SetBit(M, int(n), 0L);
var m = M.Uint64();
return(new umagicData(s: int64(s), m: m));
});
// magic computes the constants needed to strength reduce signed n-bit divides by the constant c.
// Must have c>0.
// The return values satisfy for all -2^(n-1) <= x < 2^(n-1)
// trunc(x / c) = x * m >> (n+s) + (x < 0 ? 1 : 0)
private static smagicData smagic(ulong n, long c) => func((_, panic, __) =>
{
ptr <object> C = @new <big.Int>().SetInt64(c);
var s = C.BitLen() - 1L;
var M = big.NewInt(1L);
M.Lsh(M, n + uint(s)); // 2^(n+s)
M.Add(M, C); // 2^(n+s)+c
M.Sub(M, big.NewInt(1L)); // 2^(n+s)+c-1
M.Div(M, C); // ⎡2^(n+s)/c⎤
if (M.Bit(int(n)) != 0L)
{
panic("n+1st bit is set");
}
if (M.Bit(int(n - 1L)) == 0L)
{
panic("nth bit is not set");
}
var m = M.Uint64();
return(new smagicData(s: int64(s), m: m));
});
