(Mod64 x y) => (MODD x y)
(Mod64u ...) => (MODDU ...)
// MODW/MODWU has a 64-bit dividend and a 32-bit divisor,
// so a sign/zero extension of the dividend is required.
(Mod32  x y) => (MODW  (MOVWreg x) y)
(Mod32u x y) => (MODWU (MOVWZreg x) y)
(Mod16  x y) => (MODW  (MOVHreg x) (MOVHreg y))
(Mod16u x y) => (MODWU (MOVHZreg x) (MOVHZreg y))
(Mod8   x y) => (MODW  (MOVBreg x) (MOVBreg y))
(Mod8u  x y) => (MODWU (MOVBZreg x) (MOVBZreg y))

		return
	case m == 0:
		q = z[:0] // result is 0
		return
	}
	// m > 0
	z = z.make(m)
	r = divWVW(z, 0, x, y)
	q = z.norm()
	return
}

// modW returns x % d.
func (x nat) modW(d Word) (r Word) {
	// TODO(agl): we don't actually need to store the q value.
	var q nat
	q = q.make(len(x))
	return divWVW(q, 0, x, d)
}

// explicit requirements of the modules in mods.
func spotCheckRoots(ctx context.Context, rs *Requirements, mods map[module.Version]bool) bool {
	ctx, cancel := context.WithCancel(ctx)
	defer cancel()

	work := par.NewQueue(runtime.GOMAXPROCS(0))
	for m := range mods {
		m := m
		work.Add(func() {
			if ctx.Err() != nil {
				return
			}

	for i, test := range tests {
		in, _ := new(Int).SetString(test.in, 10)
		d, _ := new(Int).SetString(test.dividend, 10)
		out, _ := new(Int).SetString(test.out, 10)

		r := in.abs.modW(d.abs[0])
		if r != out.abs[0] {
			t.Errorf("#%d failed: got %d want %s", i, r, out)
		}
	}
}

func TestModW(t *testing.T) {
	if _W >= 32 {
		runModWTests(t, modWTests32)
	}
	if _W >= 64 {

		{name: "AVGLU", argLength: 2, reg: gp21, commutative: true, resultInArg0: true, clobberFlags: true}, // (arg0 + arg1) / 2 as unsigned, all 32 result bits

		// For DIVL, DIVW, MODL and MODW, AuxInt non-zero means that the divisor has been proved to be not -1.
		{name: "DIVL", argLength: 2, reg: gp11div, asm: "IDIVL", aux: "Bool", clobberFlags: true}, // arg0 / arg1

	var mods = []struct {
		name string
		val  string
	}{
		{"Odd", "0x82828282828200FFFF28FF2B218281FF82828282828200FFFF28FF2B218281FF82828282828200FFFF28FF2B218281FF"},

		{name: "MODD", argLength: 2, reg: gp21tmp, asm: "MODD", resultInArg0: true, clobberFlags: true}, // arg0 % arg1
		{name: "MODW", argLength: 2, reg: gp21tmp, asm: "MODW", resultInArg0: true, clobberFlags: true}, // arg0 % arg1

		{name: "MODDU", argLength: 2, reg: gp21tmp, asm: "MODDU", resultInArg0: true, clobberFlags: true}, // arg0 % arg1

func (ld *loader) checkMultiplePaths() {
	mods := ld.requirements.rootModules
	if cached := ld.requirements.graph.Load(); cached != nil {
		if mg := cached.mg; mg != nil {
			mods = mg.BuildList()
		}
	}

	firstPath := map[module.Version]string{}
	for _, mod := range mods {
		src := resolveReplacement(mod)
		if prev, ok := firstPath[src]; !ok {

	"VPDEPD",
	"VMULOUD",
	"VMULOSD",
	"VMULLD",
	"VMULHUW",
	"VMULHUD",
	"VMULHSW",
	"VMULHSD",
	"VMULEUD",
	"VMULESD",
	"VMSUMCUD",
	"VMODUW",
	"VMODUQ",
	"VMODUD",
	"VMODSW",
	"VMODSQ",
	"VMODSD",
	"VINSWVRX",
	"VINSWVLX",
	"VINSWRX",
	"VINSWLX",
	"VINSW",
	"VINSHVRX",
	"VINSHVLX",
	"VINSHRX",
	"VINSHLX",
	"VINSDRX",
	"VINSDLX",
	"VINSD",

(Div64u ...) => (UDIV  ...)
(Div32u ...) => (UDIVW ...)
(Div32F ...) => (FDIVS ...)
(Div64F ...) => (FDIVD ...)

(Mod64 x y) => (MOD x y)
(Mod32 x y) => (MODW x y)
(Mod64u ...) => (UMOD ...)
(Mod32u ...) => (UMODW ...)
(Mod(16|8)  x y) => (MODW  (SignExt(16|8)to32 x) (SignExt(16|8)to32 y))
(Mod(16|8)u x y) => (UMODW (ZeroExt(16|8)to32 x) (ZeroExt(16|8)to32 y))

// (x + y) / 2 with x>=y    =>    (x - y) / 2 + y