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const builtin = @import("builtin");
const is_test = builtin.is_test;
const native_endian = builtin.cpu.arch.endian();
const std = @import("std");
const low = switch (native_endian) {
.Big => 1,
.Little => 0,
};
const high = 1 - low;
pub fn udivmod(comptime DoubleInt: type, a: DoubleInt, b: DoubleInt, maybe_rem: ?*DoubleInt) DoubleInt {
@setRuntimeSafety(is_test);
const double_int_bits = @typeInfo(DoubleInt).Int.bits;
const single_int_bits = @divExact(double_int_bits, 2);
const SingleInt = std.meta.Int(.unsigned, single_int_bits);
const SignedDoubleInt = std.meta.Int(.signed, double_int_bits);
const Log2SingleInt = std.math.Log2Int(SingleInt);
const n = @ptrCast(*const [2]SingleInt, &a).*; // TODO issue #421
const d = @ptrCast(*const [2]SingleInt, &b).*; // TODO issue #421
var q: [2]SingleInt = undefined;
var r: [2]SingleInt = undefined;
var sr: c_uint = undefined;
// special cases, X is unknown, K != 0
if (n[high] == 0) {
if (d[high] == 0) {
// 0 X
// ---
// 0 X
if (maybe_rem) |rem| {
rem.* = n[low] % d[low];
}
return n[low] / d[low];
}
// 0 X
// ---
// K X
if (maybe_rem) |rem| {
rem.* = n[low];
}
return 0;
}
// n[high] != 0
if (d[low] == 0) {
if (d[high] == 0) {
// K X
// ---
// 0 0
if (maybe_rem) |rem| {
rem.* = n[high] % d[low];
}
return n[high] / d[low];
}
// d[high] != 0
if (n[low] == 0) {
// K 0
// ---
// K 0
if (maybe_rem) |rem| {
r[high] = n[high] % d[high];
r[low] = 0;
rem.* = @ptrCast(*align(@alignOf(SingleInt)) DoubleInt, &r[0]).*; // TODO issue #421
}
return n[high] / d[high];
}
// K K
// ---
// K 0
if ((d[high] & (d[high] - 1)) == 0) {
// d is a power of 2
if (maybe_rem) |rem| {
r[low] = n[low];
r[high] = n[high] & (d[high] - 1);
rem.* = @ptrCast(*align(@alignOf(SingleInt)) DoubleInt, &r[0]).*; // TODO issue #421
}
return n[high] >> @intCast(Log2SingleInt, @ctz(d[high]));
}
// K K
// ---
// K 0
sr = @bitCast(c_uint, @as(c_int, @clz(d[high])) - @as(c_int, @clz(n[high])));
// 0 <= sr <= single_int_bits - 2 or sr large
if (sr > single_int_bits - 2) {
if (maybe_rem) |rem| {
rem.* = a;
}
return 0;
}
sr += 1;
// 1 <= sr <= single_int_bits - 1
// q.all = a << (double_int_bits - sr);
q[low] = 0;
q[high] = n[low] << @intCast(Log2SingleInt, single_int_bits - sr);
// r.all = a >> sr;
r[high] = n[high] >> @intCast(Log2SingleInt, sr);
r[low] = (n[high] << @intCast(Log2SingleInt, single_int_bits - sr)) | (n[low] >> @intCast(Log2SingleInt, sr));
} else {
// d[low] != 0
if (d[high] == 0) {
// K X
// ---
// 0 K
if ((d[low] & (d[low] - 1)) == 0) {
// d is a power of 2
if (maybe_rem) |rem| {
rem.* = n[low] & (d[low] - 1);
}
if (d[low] == 1) {
return a;
}
sr = @ctz(d[low]);
q[high] = n[high] >> @intCast(Log2SingleInt, sr);
q[low] = (n[high] << @intCast(Log2SingleInt, single_int_bits - sr)) | (n[low] >> @intCast(Log2SingleInt, sr));
return @ptrCast(*align(@alignOf(SingleInt)) DoubleInt, &q[0]).*; // TODO issue #421
}
// K X
// ---
// 0 K
sr = 1 + single_int_bits + @as(c_uint, @clz(d[low])) - @as(c_uint, @clz(n[high]));
// 2 <= sr <= double_int_bits - 1
// q.all = a << (double_int_bits - sr);
// r.all = a >> sr;
if (sr == single_int_bits) {
q[low] = 0;
q[high] = n[low];
r[high] = 0;
r[low] = n[high];
} else if (sr < single_int_bits) {
// 2 <= sr <= single_int_bits - 1
q[low] = 0;
q[high] = n[low] << @intCast(Log2SingleInt, single_int_bits - sr);
r[high] = n[high] >> @intCast(Log2SingleInt, sr);
r[low] = (n[high] << @intCast(Log2SingleInt, single_int_bits - sr)) | (n[low] >> @intCast(Log2SingleInt, sr));
} else {
// single_int_bits + 1 <= sr <= double_int_bits - 1
q[low] = n[low] << @intCast(Log2SingleInt, double_int_bits - sr);
q[high] = (n[high] << @intCast(Log2SingleInt, double_int_bits - sr)) | (n[low] >> @intCast(Log2SingleInt, sr - single_int_bits));
r[high] = 0;
r[low] = n[high] >> @intCast(Log2SingleInt, sr - single_int_bits);
}
} else {
// K X
// ---
// K K
sr = @bitCast(c_uint, @as(c_int, @clz(d[high])) - @as(c_int, @clz(n[high])));
// 0 <= sr <= single_int_bits - 1 or sr large
if (sr > single_int_bits - 1) {
if (maybe_rem) |rem| {
rem.* = a;
}
return 0;
}
sr += 1;
// 1 <= sr <= single_int_bits
// q.all = a << (double_int_bits - sr);
// r.all = a >> sr;
q[low] = 0;
if (sr == single_int_bits) {
q[high] = n[low];
r[high] = 0;
r[low] = n[high];
} else {
r[high] = n[high] >> @intCast(Log2SingleInt, sr);
r[low] = (n[high] << @intCast(Log2SingleInt, single_int_bits - sr)) | (n[low] >> @intCast(Log2SingleInt, sr));
q[high] = n[low] << @intCast(Log2SingleInt, single_int_bits - sr);
}
}
}
// Not a special case
// q and r are initialized with:
// q.all = a << (double_int_bits - sr);
// r.all = a >> sr;
// 1 <= sr <= double_int_bits - 1
var carry: u32 = 0;
var r_all: DoubleInt = undefined;
while (sr > 0) : (sr -= 1) {
// r:q = ((r:q) << 1) | carry
r[high] = (r[high] << 1) | (r[low] >> (single_int_bits - 1));
r[low] = (r[low] << 1) | (q[high] >> (single_int_bits - 1));
q[high] = (q[high] << 1) | (q[low] >> (single_int_bits - 1));
q[low] = (q[low] << 1) | carry;
// carry = 0;
// if (r.all >= b)
// {
// r.all -= b;
// carry = 1;
// }
r_all = @ptrCast(*align(@alignOf(SingleInt)) DoubleInt, &r[0]).*; // TODO issue #421
const s: SignedDoubleInt = @bitCast(SignedDoubleInt, b -% r_all -% 1) >> (double_int_bits - 1);
carry = @intCast(u32, s & 1);
r_all -= b & @bitCast(DoubleInt, s);
r = @ptrCast(*[2]SingleInt, &r_all).*; // TODO issue #421
}
const q_all = ((@ptrCast(*align(@alignOf(SingleInt)) DoubleInt, &q[0]).*) << 1) | carry; // TODO issue #421
if (maybe_rem) |rem| {
rem.* = r_all;
}
return q_all;
}
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