compiler_rt: optimize mulo

- use usize to decide if register size is big enough to store
  multiplication result or if division is necessary
- multiplication routine with check of integer bounds
- wrapping multipliation and division routine from Hacker's Delight

lib/std/special/compiler_rt/mulo.zig

@@ -1,67 +1,68 @@
 const builtin = @import("builtin");
+const std = @import("std");
+const math = std.math;
 
 // mulo - multiplication overflow
-// - muloXi4_generic for unoptimized version
+// * return a*b.
+// * return if a*b overflows => 1 else => 0
+// - muloXi4_genericSmall as default
+// - muloXi4_genericFast for 2*bitsize <= usize
 
-// return a*b.
-// return if a*b overflows => 1 else => 0
-// see https://stackoverflow.com/a/26320664 for possible implementations
-
-inline fn muloXi4_generic(comptime ST: type, a: ST, b: ST, overflow: *c_int) ST {
+inline fn muloXi4_genericSmall(comptime ST: type, a: ST, b: ST, overflow: *c_int) ST {
     @setRuntimeSafety(builtin.is_test);
-    const BSIZE = @bitSizeOf(ST);
-    comptime var UT = switch (ST) {
-        i32 => u32,
-        i64 => u64,
-        i128 => u128,
+    overflow.* = 0;
+    const min = math.minInt(ST);
+    var res: ST = a *% b;
+    // Hacker's Delight section Overflow subsection Multiplication
+    // case a=-2^{31}, b=-1 problem, because
+    // on some machines a*b = -2^{31} with overflow
+    // Then -2^{31}/-1 overflows and any result is possible.
+    // => check with a<0 and b=-2^{31}
+    if ((a < 0 and b == min) or (a != 0 and @divTrunc(res, a) != b))
+        overflow.* = 1;
+    return res;
+}
+
+inline fn muloXi4_genericFast(comptime ST: type, a: ST, b: ST, overflow: *c_int) ST {
+    @setRuntimeSafety(builtin.is_test);
+    overflow.* = 0;
+    const EST = switch (ST) {
+        i32 => i64,
+        i64 => i128,
+        i128 => i256,
         else => unreachable,
     };
-    const min = @bitCast(ST, @as(UT, 1 << (BSIZE - 1)));
-    const max = ~min;
-    overflow.* = 0;
-    const result = a *% b;
-
-    // edge cases
-    if (a == min) {
-        if (b != 0 and b != 1) overflow.* = 1;
-        return result;
-    }
-    if (b == min) {
-        if (a != 0 and a != 1) overflow.* = 1;
-        return result;
-    }
-
-    // take sign of x sx
-    const sa = a >> (BSIZE - 1);
-    const sb = b >> (BSIZE - 1);
-    // take absolute value of a and b via
-    // abs(x) = (x^sx)) - sx
-    const abs_a = (a ^ sa) -% sa;
-    const abs_b = (b ^ sb) -% sb;
-
-    // unitary magnitude, cannot have overflow
-    if (abs_a < 2 or abs_b < 2) return result;
-
-    // compare the signs of operands
-    if ((a ^ b) >> (BSIZE - 1) != 0) {
-        if (abs_a > @divTrunc(max, abs_b)) overflow.* = 1;
-    } else {
-        if (abs_a > @divTrunc(min, -abs_b)) overflow.* = 1;
-    }
-
-    return result;
+    const min = math.minInt(ST);
+    const max = math.maxInt(ST);
+    var res: EST = @as(EST, a) * @as(EST, b);
+    //invariant: -2^{bitwidth(EST)} < res < 2^{bitwidth(EST)-1}
+    if (res < min or max < res)
+        overflow.* = 1;
+    return @truncate(ST, res);
 }
 
 pub fn __mulosi4(a: i32, b: i32, overflow: *c_int) callconv(.C) i32 {
-    return muloXi4_generic(i32, a, b, overflow);
+    if (2 * @bitSizeOf(i32) <= @bitSizeOf(usize)) {
+        return muloXi4_genericFast(i32, a, b, overflow);
+    } else {
+        return muloXi4_genericSmall(i32, a, b, overflow);
+    }
 }
 
 pub fn __mulodi4(a: i64, b: i64, overflow: *c_int) callconv(.C) i64 {
-    return muloXi4_generic(i64, a, b, overflow);
+    if (2 * @bitSizeOf(i64) <= @bitSizeOf(usize)) {
+        return muloXi4_genericFast(i64, a, b, overflow);
+    } else {
+        return muloXi4_genericSmall(i64, a, b, overflow);
+    }
 }
 
 pub fn __muloti4(a: i128, b: i128, overflow: *c_int) callconv(.C) i128 {
-    return muloXi4_generic(i128, a, b, overflow);
+    if (2 * @bitSizeOf(i128) <= @bitSizeOf(usize)) {
+        return muloXi4_genericFast(i128, a, b, overflow);
+    } else {
+        return muloXi4_genericSmall(i128, a, b, overflow);
+    }
 }
 
 test {