compiler-rt: implement __udivei4 and __umodei4 (#14023)

Allows dividing and formatting arbitrary-large unsigned integers.

Author: jedisct1

CMakeLists.txt

@@ -472,6 +472,7 @@ set(ZIG_STAGE2_SOURCES
     "${CMAKE_SOURCE_DIR}/lib/compiler_rt/truncxfhf2.zig"
     "${CMAKE_SOURCE_DIR}/lib/compiler_rt/truncxfsf2.zig"
     "${CMAKE_SOURCE_DIR}/lib/compiler_rt/udivmod.zig"
+    "${CMAKE_SOURCE_DIR}/lib/compiler_rt/udivmodei4.zig"
     "${CMAKE_SOURCE_DIR}/lib/compiler_rt/udivmodti4.zig"
     "${CMAKE_SOURCE_DIR}/lib/compiler_rt/udivti3.zig"
     "${CMAKE_SOURCE_DIR}/lib/compiler_rt/umodti3.zig"

lib/compiler_rt.zig

@@ -112,6 +112,7 @@ comptime {
     _ = @import("compiler_rt/modti3.zig");
     _ = @import("compiler_rt/multi3.zig");
     _ = @import("compiler_rt/udivti3.zig");
+    _ = @import("compiler_rt/udivmodei4.zig");
     _ = @import("compiler_rt/udivmodti4.zig");
     _ = @import("compiler_rt/umodti3.zig");
 

lib/compiler_rt/udivmodei4.zig

@@ -0,0 +1,143 @@
+const std = @import("std");
+const builtin = @import("builtin");
+const common = @import("common.zig");
+const shr = std.math.shr;
+const shl = std.math.shl;
+
+const max_limbs = std.math.divCeil(usize, 65535, 32) catch unreachable; // max supported type is u65535
+
+comptime {
+    @export(__udivei4, .{ .name = "__udivei4", .linkage = common.linkage });
+    @export(__umodei4, .{ .name = "__umodei4", .linkage = common.linkage });
+}
+
+const endian = builtin.cpu.arch.endian();
+
+/// Get the value of a limb.
+inline fn limb(x: []const u32, i: usize) u32 {
+    return if (endian == .Little) x[i] else x[x.len - 1 - i];
+}
+
+/// Change the value of a limb.
+inline fn limb_set(x: []u32, i: usize, v: u32) void {
+    if (endian == .Little) {
+        x[i] = v;
+    } else {
+        x[x.len - 1 - i] = v;
+    }
+}
+
+// Uses Knuth's Algorithm D, 4.3.1, p. 272.
+fn divmod(q: ?[]u32, r: ?[]u32, u: []const u32, v: []const u32) !void {
+    if (q) |q_| std.mem.set(u32, q_[0..], 0);
+    if (r) |r_| std.mem.set(u32, r_[0..], 0);
+
+    if (u.len == 0 or v.len == 0) return error.DivisionByZero;
+
+    var m = u.len - 1;
+    var n = v.len - 1;
+    while (limb(u, m) == 0) : (m -= 1) {
+        if (m == 0) return;
+    }
+    while (limb(v, n) == 0) : (n -= 1) {
+        if (n == 0) return error.DivisionByZero;
+    }
+
+    if (n > m) {
+        if (r) |r_| std.mem.copy(u32, r_[0..], u[0..]);
+        return;
+    }
+
+    const s = @clz(limb(v, n));
+
+    var vn: [max_limbs]u32 = undefined;
+    var i = n;
+    while (i > 0) : (i -= 1) {
+        limb_set(&vn, i, shl(u32, limb(v, i), s) | shr(u32, limb(v, i - 1), 32 - s));
+    }
+    limb_set(&vn, 0, shl(u32, limb(v, 0), s));
+
+    var un: [max_limbs + 1]u32 = undefined;
+    limb_set(&un, m + 1, shr(u32, limb(u, m), 32 - s));
+    i = m;
+    while (i > 0) : (i -= 1) {
+        limb_set(&un, i, shl(u32, limb(u, i), s) | shr(u32, limb(u, i - 1), 32 - s));
+    }
+    limb_set(&un, 0, shl(u32, limb(u, 0), s));
+
+    var j = m - n;
+    while (true) : (j -= 1) {
+        const uu = (@as(u64, limb(&un, j + n + 1)) << 32) + limb(&un, j + n);
+        var qhat = uu / limb(&vn, n);
+        var rhat = uu % limb(&vn, n);
+
+        while (true) {
+            if (qhat >= (1 << 32) or (n > 0 and qhat * limb(&vn, n - 1) > (rhat << 32) + limb(&un, j + n - 1))) {
+                qhat -= 1;
+                rhat += limb(&vn, n);
+                if (rhat < (1 << 32)) continue;
+            }
+            break;
+        }
+        var carry: u64 = 0;
+        i = 0;
+        while (i <= n) : (i += 1) {
+            const p = qhat * limb(&vn, i);
+            const t = limb(&un, i + j) - carry - @truncate(u32, p);
+            limb_set(&un, i + j, @truncate(u32, t));
+            carry = @intCast(u64, p >> 32) - @intCast(u64, t >> 32);
+        }
+        const t = limb(&un, j + n + 1) - carry;
+        limb_set(&un, j + n + 1, @truncate(u32, t));
+        if (q) |q_| limb_set(q_, j, @truncate(u32, qhat));
+        if (t < 0) {
+            if (q) |q_| limb_set(q_, j, limb(q_, j) - 1);
+            var carry2: u64 = 0;
+            i = 0;
+            while (i <= n) : (i += 1) {
+                const t2 = @as(u64, limb(&un, i + j)) + @as(u64, limb(&vn, i)) + carry2;
+                limb_set(&un, i + j, @truncate(u32, t2));
+                carry2 = t2 >> 32;
+            }
+            limb_set(un, j + n + 1, @truncate(u32, limb(&un, j + n + 1) + carry2));
+        }
+        if (j == 0) break;
+    }
+    if (r) |r_| {
+        i = 0;
+        while (i <= n) : (i += 1) {
+            limb_set(r_, i, shr(u32, limb(&un, i), s) | shl(u32, limb(&un, i + 1), 32 - s));
+        }
+        limb_set(r_, n, shr(u32, limb(&un, n), s));
+    }
+}
+
+pub fn __udivei4(r_q: [*c]u32, u_p: [*c]const u32, v_p: [*c]const u32, bits: usize) callconv(.C) void {
+    @setRuntimeSafety(builtin.is_test);
+    const u = u_p[0 .. bits / 32];
+    const v = v_p[0 .. bits / 32];
+    var q = r_q[0 .. bits / 32];
+    @call(.always_inline, divmod, .{ q, null, u, v }) catch unreachable;
+}
+
+pub fn __umodei4(r_p: [*c]u32, u_p: [*c]const u32, v_p: [*c]const u32, bits: usize) callconv(.C) void {
+    @setRuntimeSafety(builtin.is_test);
+    const u = u_p[0 .. bits / 32];
+    const v = v_p[0 .. bits / 32];
+    var r = r_p[0 .. bits / 32];
+    @call(.always_inline, divmod, .{ null, r, u, v }) catch unreachable;
+}
+
+test "__udivei4/__umodei4" {
+    const RndGen = std.rand.DefaultPrng;
+    var rnd = RndGen.init(42);
+    var i: usize = 10000;
+    while (i > 0) : (i -= 1) {
+        const u = rnd.random().int(u1000);
+        const v = 1 + rnd.random().int(u1200);
+        const q = u / v;
+        const r = u % v;
+        const z = q * v + r;
+        try std.testing.expect(z == u);
+    }
+}

tools/gen_stubs.zig

@@ -865,12 +865,14 @@ const blacklisted_symbols = [_][]const u8{
     "__ucmpsi2",
     "__ucmpti2",
     "__udivdi3",
+    "__udivei4",
     "__udivmoddi4",
     "__udivmodsi4",
     "__udivmodti4",
     "__udivsi3",
     "__udivti3",
     "__umoddi3",
+    "__umodei4",
     "__umodsi3",
     "__umodti3",
     "__unorddf2",