## How are drives used for Erasure Code?

MinIO divides the drives you provide into erasure-coding sets of *2 to 16* drives.  Therefore, the number of drives you present must be a multiple of one of these numbers.  Each object is written to a single erasure-coding set.

// umagicOK reports whether we should strength reduce a n-bit divide by c.
func umagicOK(n uint, c int64) bool {
	// Convert from ConstX auxint values to the real uint64 constant they represent.
	d := uint64(c) << (64 - n) >> (64 - n)

	// Doesn't work for 0.
	// Don't use for powers of 2.
	return d&(d-1) != 0
}

// umagicOKn reports whether we should strength reduce an unsigned n-bit divide by c.

	if scale >= 18 {
		return 0, base, false
	}
	divisor := pow10Int64(int64(scale))
	return base / divisor, base % divisor, true
}

// removeInt64Factors divides in a loop; the return values have the property that
// value == result * base ^ scale
func removeInt64Factors(value int64, base int64) (result int64, times int32) {
	times = 0
	result = value
	negative := result < 0

		const (
			eosCode    = 0x3fffffff
			eosNBits   = 30
			eosPadByte = eosCode >> (eosNBits - 8)
		)
		pad := 8 - over
		x = (x << pad) | (eosPadByte >> over)
		n += pad // 8 now divides into n exactly
	}
	// n in (0, 8, 16, 24, 32)
	switch n / 8 {
	case 0:
		return dst
	case 1:
		return append(dst, byte(x))
	case 2:
		y := uint16(x)
		return append(dst, byte(y>>8), byte(y))

    int bytesToCopy = bufferSize - buffer.position();
    for (int i = 0; i < bytesToCopy; i++) {
      buffer.put(readBuffer.get());
    }
    munch(); // buffer becomes empty here, since chunkSize divides bufferSize

    // Now process directly from the rest of the input buffer
    while (readBuffer.remaining() >= chunkSize) {
      process(readBuffer);
    }

  • u/v < B^(n+m) / B^(n-1)   [divide bounds for u, v]
  • u/v < B^(m+1)             [simplify]

The first step is special: it takes the top n digits of u and divides them by
the n digits of v, producing the first quotient digit and an n-digit remainder.
In the example, q₂ = ⌊u₄u₃u₂ / v⌋.

The first step divides n digits by n digits to ensure that it produces only a
single digit.

    int bytesToCopy = bufferSize - buffer.position();
    for (int i = 0; i < bytesToCopy; i++) {
      buffer.put(readBuffer.get());
    }
    munch(); // buffer becomes empty here, since chunkSize divides bufferSize

    // Now process directly from the rest of the input buffer
    while (readBuffer.remaining() >= chunkSize) {
      process(readBuffer);
    }

	return NewAllocationMapWithOffset(max, rangeSpec, 0)
}

// NewAllocationMapWithOffset creates an allocation bitmap using a random scan strategy that
// allows to pass an offset that divides the allocation bitmap in two blocks.
// The first block of values will not be used for random value assigned by the AllocateNext()
// method until the second block of values has been exhausted.

// decimal and rounding.
//
// The key observation and some code (shr) is borrowed from
// strconv/decimal.go: conversion of binary fractional values can be done
// precisely in multi-precision decimal because 2 divides 10 (required for
// >> of mantissa); but conversion of decimal floating-point values cannot
// be done precisely in binary representation.
//
// In contrast to strconv/decimal.go, only right shift is implemented in

func (addrs addrList) first(strategy func(Addr) bool) Addr {
	for _, addr := range addrs {
		if strategy(addr) {
			return addr
		}
	}
	return addrs[0]
}

// partition divides an address list into two categories, using a
// strategy function to assign a boolean label to each address.
// The first address, and any with a matching label, are returned as