506 lines
18 KiB
Zig
506 lines
18 KiB
Zig
const CHAR_BIT = 8;
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const du_int = u64;
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const di_int = i64;
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const si_int = c_int;
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const su_int = c_uint;
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const udwords = [2]su_int;
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const low = if (@compileVar("is_big_endian")) 1 else 0;
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const high = 1 - low;
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export fn __udivdi3(a: du_int, b: du_int) -> du_int {
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@setDebugSafety(this, false);
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return __udivmoddi4(a, b, null);
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}
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fn du_int_to_udwords(x: du_int) -> udwords {
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@setDebugSafety(this, false);
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return *@ptrcast(&udwords, &x);
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}
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export fn __udivmoddi4(a: du_int, b: du_int, maybe_rem: ?&du_int) -> du_int {
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@setDebugSafety(this, false);
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const n_uword_bits = @sizeOf(su_int) * CHAR_BIT;
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const n_udword_bits = @sizeOf(du_int) * CHAR_BIT;
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var n = du_int_to_udwords(a);
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var d = du_int_to_udwords(b);
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var q: udwords = undefined;
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var r: udwords = undefined;
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var sr: c_uint = undefined;
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// special cases, X is unknown, K != 0
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if (n[high] == 0) {
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if (d[high] == 0) {
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// 0 X
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// ---
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// 0 X
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if (const rem ?= maybe_rem) {
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*rem = n[low] % d[low];
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}
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return n[low] / d[low];
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}
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// 0 X
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// ---
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// K X
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if (const rem ?= maybe_rem) {
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*rem = n[low];
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}
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return 0;
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}
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// n[high] != 0
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if (d[low] == 0) {
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if (d[high] == 0) {
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// K X
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// ---
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// 0 0
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if (var rem ?= maybe_rem) {
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*rem = n[high] % d[low];
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}
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return n[high] / d[low];
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}
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// d[high] != 0
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if (n[low] == 0) {
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// K 0
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// ---
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// K 0
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if (var rem ?= maybe_rem) {
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r[high] = n[high] % d[high];
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r[low] = 0;
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*rem = *@ptrcast(&du_int, &r[0]);
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}
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return n[high] / d[high];
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}
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// K K
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// ---
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// K 0
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// if d is a power of 2
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if ((d[high] & (d[high] - 1)) == 0) {
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if (var rem ?= maybe_rem) {
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r[low] = n[low];
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r[high] = n[high] & (d[high] - 1);
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*rem = *@ptrcast(&du_int, &r[0]);
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}
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return n[high] >> @ctz(d[high]);
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}
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// K K
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// ---
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// K 0
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sr = @clz(su_int(d[high])) - @clz(su_int(n[high]));
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// 0 <= sr <= n_uword_bits - 2 or sr large
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if (sr > n_uword_bits - 2) {
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if (var rem ?= maybe_rem) {
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*rem = *@ptrcast(&du_int, &n[0]);
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}
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return 0;
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}
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sr += 1;
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// 1 <= sr <= n_uword_bits - 1
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// q.all = n.all << (n_udword_bits - sr);
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q[low] = 0;
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q[high] = n[low] << (n_uword_bits - sr);
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// r.all = n.all >> sr;
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r[high] = n[high] >> sr;
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r[low] = (n[high] << (n_uword_bits - sr)) | (n[low] >> sr);
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} else {
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// d[low] != 0
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if (d[high] == 0) {
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// K X
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// ---
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// 0 K
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// if d is a power of 2
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if ((d[low] & (d[low] - 1)) == 0) {
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if (var rem ?= maybe_rem) {
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*rem = n[low] & (d[low] - 1);
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}
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if (d[low] == 1) {
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return *@ptrcast(&du_int, &n[0]);
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}
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sr = @ctz(d[low]);
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q[high] = n[high] >> sr;
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q[low] = (n[high] << (n_uword_bits - sr)) | (n[low] >> sr);
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return *@ptrcast(&du_int, &q[0]);
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}
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// K X
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// ---
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// 0 K
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sr = 1 + n_uword_bits + @clz(su_int(d[low])) - @clz(su_int(n[high]));
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// 2 <= sr <= n_udword_bits - 1
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// q.all = n.all << (n_udword_bits - sr);
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// r.all = n.all >> sr;
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if (sr == n_uword_bits) {
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q[low] = 0;
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q[high] = n[low];
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r[high] = 0;
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r[low] = n[high];
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} else if (sr < n_uword_bits) {
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// 2 <= sr <= n_uword_bits - 1
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q[low] = 0;
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q[high] = n[low] << (n_uword_bits - sr);
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r[high] = n[high] >> sr;
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r[low] = (n[high] << (n_uword_bits - sr)) | (n[low] >> sr);
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} else {
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// n_uword_bits + 1 <= sr <= n_udword_bits - 1
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q[low] = n[low] << (n_udword_bits - sr);
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q[high] = (n[high] << (n_udword_bits - sr)) |
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(n[low] >> (sr - n_uword_bits));
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r[high] = 0;
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r[low] = n[high] >> (sr - n_uword_bits);
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}
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} else {
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// K X
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// ---
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// K K
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sr = @clz(su_int(d[high])) - @clz(su_int(n[high]));
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// 0 <= sr <= n_uword_bits - 1 or sr large
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if (sr > n_uword_bits - 1) {
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if (var rem ?= maybe_rem) {
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*rem = *@ptrcast(&du_int, &n[0]);
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}
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return 0;
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}
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sr += 1;
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// 1 <= sr <= n_uword_bits
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// q.all = n.all << (n_udword_bits - sr);
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q[low] = 0;
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if (sr == n_uword_bits) {
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q[high] = n[low];
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r[high] = 0;
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r[low] = n[high];
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} else {
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q[high] = n[low] << (n_uword_bits - sr);
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r[high] = n[high] >> sr;
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r[low] = (n[high] << (n_uword_bits - sr)) | (n[low] >> sr);
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}
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}
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}
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// Not a special case
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// q and r are initialized with:
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// q.all = n.all << (n_udword_bits - sr);
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// r.all = n.all >> sr;
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// 1 <= sr <= n_udword_bits - 1
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var carry: su_int = 0;
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while (sr > 0) {
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// r:q = ((r:q) << 1) | carry
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r[high] = (r[high] << 1) | (r[low] >> (n_uword_bits - 1));
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r[low] = (r[low] << 1) | (q[high] >> (n_uword_bits - 1));
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q[high] = (q[high] << 1) | (q[low] >> (n_uword_bits - 1));
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q[low] = (q[low] << 1) | carry;
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// carry = 0;
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// if (r.all >= d.all)
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// {
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// r.all -= d.all;
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// carry = 1;
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// }
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const s: di_int = (di_int)(*@ptrcast(&du_int, &d[0]) - *@ptrcast(&du_int, &r[0]) - 1) >> (n_udword_bits - 1);
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carry = su_int(s & 1);
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*@ptrcast(&du_int, &r[0]) -= *@ptrcast(&du_int, &d[0]) & u64(s);
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sr -= 1;
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}
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*@ptrcast(&du_int, &q[0]) = (*@ptrcast(&du_int, &q[0]) << 1) | u64(carry);
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if (var rem ?= maybe_rem) {
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*rem = *@ptrcast(&du_int, &r[0]);
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}
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return *@ptrcast(&du_int, &q[0]);
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}
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export fn __umoddi3(a: du_int, b: du_int) -> du_int {
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@setDebugSafety(this, false);
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var r: du_int = undefined;
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_ = __udivmoddi4(a, b, &r);
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return r;
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}
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fn isArmArch() -> bool {
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return switch (@compileVar("arch")) {
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Arch.armv8_2a,
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Arch.armv8_1a,
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Arch.armv8,
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Arch.armv8m_baseline,
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Arch.armv8m_mainline,
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Arch.armv7,
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Arch.armv7em,
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Arch.armv7m,
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Arch.armv7s,
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Arch.armv7k,
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Arch.armv6,
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Arch.armv6m,
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Arch.armv6k,
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Arch.armv6t2,
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Arch.armv5,
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Arch.armv5te,
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Arch.armv4t,
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Arch.armeb => true,
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else => false,
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};
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}
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export nakedcc fn __aeabi_uidivmod() {
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@setDebugSafety(this, false);
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if (comptime isArmArch()) {
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asm volatile (
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\\ push { lr }
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\\ sub sp, sp, #4
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\\ mov r2, sp
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\\ bl __udivmodsi4
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\\ ldr r1, [sp]
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\\ add sp, sp, #4
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\\ pop { pc }
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::: "r2", "r1");
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unreachable;
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}
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@setGlobalLinkage(__aeabi_uidivmod, GlobalLinkage.Internal);
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}
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export fn __udivmodsi4(a: su_int, b: su_int, rem: &su_int) -> su_int {
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@setDebugSafety(this, false);
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const d = __udivsi3(a, b);
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*rem = su_int(si_int(a) -% (si_int(d) * si_int(b)));
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return d;
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}
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// TODO make this an alias instead of an extra function call
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// https://github.com/andrewrk/zig/issues/256
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export fn __aeabi_uidiv(n: su_int, d: su_int) -> su_int {
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@setDebugSafety(this, false);
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return __udivsi3(n, d);
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}
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export fn __udivsi3(n: su_int, d: su_int) -> su_int {
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@setDebugSafety(this, false);
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const n_uword_bits: c_uint = @sizeOf(su_int) * CHAR_BIT;
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// special cases
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if (d == 0)
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return 0; // ?!
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if (n == 0)
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return 0;
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var sr: c_uint = @clz(d) - @clz(n);
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// 0 <= sr <= n_uword_bits - 1 or sr large
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if (sr > n_uword_bits - 1) // d > r
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return 0;
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if (sr == n_uword_bits - 1) // d == 1
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return n;
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sr += 1;
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// 1 <= sr <= n_uword_bits - 1
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// Not a special case
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var q: su_int = n << (n_uword_bits - sr);
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var r: su_int = n >> sr;
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var carry: su_int = 0;
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while (sr > 0; sr -= 1) {
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// r:q = ((r:q) << 1) | carry
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r = (r << 1) | (q >> (n_uword_bits - 1));
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q = (q << 1) | carry;
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// carry = 0;
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// if (r.all >= d.all)
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// {
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// r.all -= d.all;
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// carry = 1;
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// }
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const s = si_int(d - r - 1) >> si_int(n_uword_bits - 1);
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carry = su_int(s & 1);
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r -= d & su_int(s);
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}
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q = (q << 1) | carry;
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return q;
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}
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test "test_umoddi3" {
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test_one_umoddi3(0, 1, 0);
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test_one_umoddi3(2, 1, 0);
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test_one_umoddi3(0x8000000000000000, 1, 0x0);
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test_one_umoddi3(0x8000000000000000, 2, 0x0);
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test_one_umoddi3(0xFFFFFFFFFFFFFFFF, 2, 0x1);
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}
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fn test_one_umoddi3(a: du_int, b: du_int, expected_r: du_int) {
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const r = __umoddi3(a, b);
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assert(r == expected_r);
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}
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test "test_udivmoddi4" {
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const cases = [][4]du_int {
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[]du_int{0x0000000000000000, 0x0000000000000001, 0x0000000000000000, 0x0000000000000000},
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[]du_int{0x0000000080000000, 0x0000000100000001, 0x0000000000000000, 0x0000000080000000},
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[]du_int{0x7FFFFFFF00000001, 0x0000000000000001, 0x7FFFFFFF00000001, 0x0000000000000000},
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[]du_int{0x7FFFFFFF7FFFFFFF, 0xFFFFFFFFFFFFFFFF, 0x0000000000000000, 0x7FFFFFFF7FFFFFFF},
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[]du_int{0x8000000000000002, 0xFFFFFFFFFFFFFFFE, 0x0000000000000000, 0x8000000000000002},
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[]du_int{0x80000000FFFFFFFD, 0xFFFFFFFFFFFFFFFD, 0x0000000000000000, 0x80000000FFFFFFFD},
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[]du_int{0xFFFFFFFD00000010, 0xFFFFFFFF80000000, 0x0000000000000000, 0xFFFFFFFD00000010},
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[]du_int{0xFFFFFFFDFFFFFFFF, 0xFFFFFFFF7FFFFFFF, 0x0000000000000000, 0xFFFFFFFDFFFFFFFF},
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[]du_int{0xFFFFFFFE0747AE14, 0xFFFFFFFF0747AE14, 0x0000000000000000, 0xFFFFFFFE0747AE14},
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[]du_int{0xFFFFFFFF00000001, 0xFFFFFFFF078644FA, 0x0000000000000000, 0xFFFFFFFF00000001},
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[]du_int{0xFFFFFFFF80000000, 0xFFFFFFFF00000010, 0x0000000000000001, 0x000000007FFFFFF0},
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[]du_int{0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0x0000000000000001, 0x0000000000000000},
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};
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for (cases) |case| {
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test_one_udivmoddi4(case[0], case[1], case[2], case[3]);
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}
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}
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fn test_one_udivmoddi4(a: du_int, b: du_int, expected_q: du_int, expected_r: du_int) {
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var r: du_int = undefined;
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const q = __udivmoddi4(a, b, &r);
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assert(q == expected_q);
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assert(r == expected_r);
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}
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test "test_udivsi3" {
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const cases = [][3]su_int {
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[]su_int{0x00000000, 0x00000001, 0x00000000},
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[]su_int{0x00000000, 0x00000002, 0x00000000},
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[]su_int{0x00000000, 0x00000003, 0x00000000},
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[]su_int{0x00000000, 0x00000010, 0x00000000},
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[]su_int{0x00000000, 0x078644FA, 0x00000000},
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[]su_int{0x00000000, 0x0747AE14, 0x00000000},
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[]su_int{0x00000000, 0x7FFFFFFF, 0x00000000},
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[]su_int{0x00000000, 0x80000000, 0x00000000},
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[]su_int{0x00000000, 0xFFFFFFFD, 0x00000000},
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[]su_int{0x00000000, 0xFFFFFFFE, 0x00000000},
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[]su_int{0x00000000, 0xFFFFFFFF, 0x00000000},
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[]su_int{0x00000001, 0x00000001, 0x00000001},
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[]su_int{0x00000001, 0x00000002, 0x00000000},
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[]su_int{0x00000001, 0x00000003, 0x00000000},
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[]su_int{0x00000001, 0x00000010, 0x00000000},
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[]su_int{0x00000001, 0x078644FA, 0x00000000},
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[]su_int{0x00000001, 0x0747AE14, 0x00000000},
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[]su_int{0x00000001, 0x7FFFFFFF, 0x00000000},
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[]su_int{0x00000001, 0x80000000, 0x00000000},
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[]su_int{0x00000001, 0xFFFFFFFD, 0x00000000},
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[]su_int{0x00000001, 0xFFFFFFFE, 0x00000000},
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[]su_int{0x00000001, 0xFFFFFFFF, 0x00000000},
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[]su_int{0x00000002, 0x00000001, 0x00000002},
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[]su_int{0x00000002, 0x00000002, 0x00000001},
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[]su_int{0x00000002, 0x00000003, 0x00000000},
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[]su_int{0x00000002, 0x00000010, 0x00000000},
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[]su_int{0x00000002, 0x078644FA, 0x00000000},
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[]su_int{0x00000002, 0x0747AE14, 0x00000000},
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[]su_int{0x00000002, 0x7FFFFFFF, 0x00000000},
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[]su_int{0x00000002, 0x80000000, 0x00000000},
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[]su_int{0x00000002, 0xFFFFFFFD, 0x00000000},
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[]su_int{0x00000002, 0xFFFFFFFE, 0x00000000},
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[]su_int{0x00000002, 0xFFFFFFFF, 0x00000000},
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[]su_int{0x00000003, 0x00000001, 0x00000003},
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[]su_int{0x00000003, 0x00000002, 0x00000001},
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[]su_int{0x00000003, 0x00000003, 0x00000001},
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[]su_int{0x00000003, 0x00000010, 0x00000000},
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[]su_int{0x00000003, 0x078644FA, 0x00000000},
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[]su_int{0x00000003, 0x0747AE14, 0x00000000},
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[]su_int{0x00000003, 0x7FFFFFFF, 0x00000000},
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[]su_int{0x00000003, 0x80000000, 0x00000000},
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[]su_int{0x00000003, 0xFFFFFFFD, 0x00000000},
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[]su_int{0x00000003, 0xFFFFFFFE, 0x00000000},
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[]su_int{0x00000003, 0xFFFFFFFF, 0x00000000},
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[]su_int{0x00000010, 0x00000001, 0x00000010},
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[]su_int{0x00000010, 0x00000002, 0x00000008},
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[]su_int{0x00000010, 0x00000003, 0x00000005},
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[]su_int{0x00000010, 0x00000010, 0x00000001},
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[]su_int{0x00000010, 0x078644FA, 0x00000000},
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[]su_int{0x00000010, 0x0747AE14, 0x00000000},
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[]su_int{0x00000010, 0x7FFFFFFF, 0x00000000},
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[]su_int{0x00000010, 0x80000000, 0x00000000},
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[]su_int{0x00000010, 0xFFFFFFFD, 0x00000000},
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[]su_int{0x00000010, 0xFFFFFFFE, 0x00000000},
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[]su_int{0x00000010, 0xFFFFFFFF, 0x00000000},
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[]su_int{0x078644FA, 0x00000001, 0x078644FA},
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[]su_int{0x078644FA, 0x00000002, 0x03C3227D},
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[]su_int{0x078644FA, 0x00000003, 0x028216FE},
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[]su_int{0x078644FA, 0x00000010, 0x0078644F},
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[]su_int{0x078644FA, 0x078644FA, 0x00000001},
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[]su_int{0x078644FA, 0x0747AE14, 0x00000001},
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[]su_int{0x078644FA, 0x7FFFFFFF, 0x00000000},
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[]su_int{0x078644FA, 0x80000000, 0x00000000},
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[]su_int{0x078644FA, 0xFFFFFFFD, 0x00000000},
|
|
[]su_int{0x078644FA, 0xFFFFFFFE, 0x00000000},
|
|
[]su_int{0x078644FA, 0xFFFFFFFF, 0x00000000},
|
|
[]su_int{0x0747AE14, 0x00000001, 0x0747AE14},
|
|
[]su_int{0x0747AE14, 0x00000002, 0x03A3D70A},
|
|
[]su_int{0x0747AE14, 0x00000003, 0x026D3A06},
|
|
[]su_int{0x0747AE14, 0x00000010, 0x00747AE1},
|
|
[]su_int{0x0747AE14, 0x078644FA, 0x00000000},
|
|
[]su_int{0x0747AE14, 0x0747AE14, 0x00000001},
|
|
[]su_int{0x0747AE14, 0x7FFFFFFF, 0x00000000},
|
|
[]su_int{0x0747AE14, 0x80000000, 0x00000000},
|
|
[]su_int{0x0747AE14, 0xFFFFFFFD, 0x00000000},
|
|
[]su_int{0x0747AE14, 0xFFFFFFFE, 0x00000000},
|
|
[]su_int{0x0747AE14, 0xFFFFFFFF, 0x00000000},
|
|
[]su_int{0x7FFFFFFF, 0x00000001, 0x7FFFFFFF},
|
|
[]su_int{0x7FFFFFFF, 0x00000002, 0x3FFFFFFF},
|
|
[]su_int{0x7FFFFFFF, 0x00000003, 0x2AAAAAAA},
|
|
[]su_int{0x7FFFFFFF, 0x00000010, 0x07FFFFFF},
|
|
[]su_int{0x7FFFFFFF, 0x078644FA, 0x00000011},
|
|
[]su_int{0x7FFFFFFF, 0x0747AE14, 0x00000011},
|
|
[]su_int{0x7FFFFFFF, 0x7FFFFFFF, 0x00000001},
|
|
[]su_int{0x7FFFFFFF, 0x80000000, 0x00000000},
|
|
[]su_int{0x7FFFFFFF, 0xFFFFFFFD, 0x00000000},
|
|
[]su_int{0x7FFFFFFF, 0xFFFFFFFE, 0x00000000},
|
|
[]su_int{0x7FFFFFFF, 0xFFFFFFFF, 0x00000000},
|
|
[]su_int{0x80000000, 0x00000001, 0x80000000},
|
|
[]su_int{0x80000000, 0x00000002, 0x40000000},
|
|
[]su_int{0x80000000, 0x00000003, 0x2AAAAAAA},
|
|
[]su_int{0x80000000, 0x00000010, 0x08000000},
|
|
[]su_int{0x80000000, 0x078644FA, 0x00000011},
|
|
[]su_int{0x80000000, 0x0747AE14, 0x00000011},
|
|
[]su_int{0x80000000, 0x7FFFFFFF, 0x00000001},
|
|
[]su_int{0x80000000, 0x80000000, 0x00000001},
|
|
[]su_int{0x80000000, 0xFFFFFFFD, 0x00000000},
|
|
[]su_int{0x80000000, 0xFFFFFFFE, 0x00000000},
|
|
[]su_int{0x80000000, 0xFFFFFFFF, 0x00000000},
|
|
[]su_int{0xFFFFFFFD, 0x00000001, 0xFFFFFFFD},
|
|
[]su_int{0xFFFFFFFD, 0x00000002, 0x7FFFFFFE},
|
|
[]su_int{0xFFFFFFFD, 0x00000003, 0x55555554},
|
|
[]su_int{0xFFFFFFFD, 0x00000010, 0x0FFFFFFF},
|
|
[]su_int{0xFFFFFFFD, 0x078644FA, 0x00000022},
|
|
[]su_int{0xFFFFFFFD, 0x0747AE14, 0x00000023},
|
|
[]su_int{0xFFFFFFFD, 0x7FFFFFFF, 0x00000001},
|
|
[]su_int{0xFFFFFFFD, 0x80000000, 0x00000001},
|
|
[]su_int{0xFFFFFFFD, 0xFFFFFFFD, 0x00000001},
|
|
[]su_int{0xFFFFFFFD, 0xFFFFFFFE, 0x00000000},
|
|
[]su_int{0xFFFFFFFD, 0xFFFFFFFF, 0x00000000},
|
|
[]su_int{0xFFFFFFFE, 0x00000001, 0xFFFFFFFE},
|
|
[]su_int{0xFFFFFFFE, 0x00000002, 0x7FFFFFFF},
|
|
[]su_int{0xFFFFFFFE, 0x00000003, 0x55555554},
|
|
[]su_int{0xFFFFFFFE, 0x00000010, 0x0FFFFFFF},
|
|
[]su_int{0xFFFFFFFE, 0x078644FA, 0x00000022},
|
|
[]su_int{0xFFFFFFFE, 0x0747AE14, 0x00000023},
|
|
[]su_int{0xFFFFFFFE, 0x7FFFFFFF, 0x00000002},
|
|
[]su_int{0xFFFFFFFE, 0x80000000, 0x00000001},
|
|
[]su_int{0xFFFFFFFE, 0xFFFFFFFD, 0x00000001},
|
|
[]su_int{0xFFFFFFFE, 0xFFFFFFFE, 0x00000001},
|
|
[]su_int{0xFFFFFFFE, 0xFFFFFFFF, 0x00000000},
|
|
[]su_int{0xFFFFFFFF, 0x00000001, 0xFFFFFFFF},
|
|
[]su_int{0xFFFFFFFF, 0x00000002, 0x7FFFFFFF},
|
|
[]su_int{0xFFFFFFFF, 0x00000003, 0x55555555},
|
|
[]su_int{0xFFFFFFFF, 0x00000010, 0x0FFFFFFF},
|
|
[]su_int{0xFFFFFFFF, 0x078644FA, 0x00000022},
|
|
[]su_int{0xFFFFFFFF, 0x0747AE14, 0x00000023},
|
|
[]su_int{0xFFFFFFFF, 0x7FFFFFFF, 0x00000002},
|
|
[]su_int{0xFFFFFFFF, 0x80000000, 0x00000001},
|
|
[]su_int{0xFFFFFFFF, 0xFFFFFFFD, 0x00000001},
|
|
[]su_int{0xFFFFFFFF, 0xFFFFFFFE, 0x00000001},
|
|
[]su_int{0xFFFFFFFF, 0xFFFFFFFF, 0x00000001},
|
|
};
|
|
|
|
for (cases) |case| {
|
|
test_one_udivsi3(case[0], case[1], case[2]);
|
|
}
|
|
}
|
|
|
|
fn test_one_udivsi3(a: su_int, b: su_int, expected_q: su_int) {
|
|
const q: su_int = __udivsi3(a, b);
|
|
assert(q == expected_q);
|
|
}
|
|
|
|
|
|
fn assert(ok: bool) {
|
|
if (!ok) unreachable;
|
|
}
|