Commit fc59a04061

Jan Philipp Hafer <jan.hafer@rwth-aachen.de>
2022-02-07 00:20:13
compiler_rt: add subo
- approach by Hacker's Delight with wrapping subtraction - performance expected to be similar to addo - tests with all relevant combinations of min,max with -1,0,+1 and all combinations of sequences +-1,2,4..,max
1 parent a15d2d5
lib/std/special/compiler_rt/addo.zig
@@ -15,7 +15,7 @@ inline fn addoXi4_generic(comptime ST: type, a: ST, b: ST, overflow: *c_int) ST
     // and the sign of a+b+carry is the same as a (or equivalently b).
     // Slower routine: res = ~(a ^ b) & ((sum ^ a)
     // Faster routine: res = (sum ^ a) & (sum ^ b)
-    // Oerflow occured, iff (res < 0)
+    // Overflow occured, iff (res < 0)
     if (((sum ^ a) & (sum ^ b)) < 0)
         overflow.* = 1;
     return sum;
lib/std/special/compiler_rt/subo.zig
@@ -0,0 +1,38 @@
+const builtin = @import("builtin");
+
+// subo - subtract overflow
+// * return a-%b.
+// * return if a-b overflows => 1 else => 0
+// - suboXi4_generic as default
+
+inline fn suboXi4_generic(comptime ST: type, a: ST, b: ST, overflow: *c_int) ST {
+    @setRuntimeSafety(builtin.is_test);
+    overflow.* = 0;
+    var sum: ST = a -% b;
+    // Hackers Delight: section Overflow Detection, subsection Signed Add/Subtract
+    // Let sum = a -% b == a - b - carry == wraparound subtraction.
+    // Overflow in a-b-carry occurs, iff a and b have opposite signs
+    // and the sign of a-b-carry is opposite of a (or equivalently same as b).
+    // Faster routine: res = (a ^ b) & (sum ^ a)
+    // Slower routine: res = (sum^a) & ~(sum^b)
+    // Overflow occured, iff (res < 0)
+    if (((a ^ b) & (sum ^ a)) < 0)
+        overflow.* = 1;
+    return sum;
+}
+
+pub fn __subosi4(a: i32, b: i32, overflow: *c_int) callconv(.C) i32 {
+    return suboXi4_generic(i32, a, b, overflow);
+}
+pub fn __subodi4(a: i64, b: i64, overflow: *c_int) callconv(.C) i64 {
+    return suboXi4_generic(i64, a, b, overflow);
+}
+pub fn __suboti4(a: i128, b: i128, overflow: *c_int) callconv(.C) i128 {
+    return suboXi4_generic(i128, a, b, overflow);
+}
+
+test {
+    _ = @import("subosi4_test.zig");
+    _ = @import("subodi4_test.zig");
+    _ = @import("suboti4_test.zig");
+}
lib/std/special/compiler_rt/subodi4_test.zig
@@ -0,0 +1,81 @@
+const subo = @import("subo.zig");
+const std = @import("std");
+const testing = std.testing;
+const math = std.math;
+
+fn test__subodi4(a: i64, b: i64) !void {
+    var result_ov: c_int = undefined;
+    var expected_ov: c_int = undefined;
+    var result = subo.__subodi4(a, b, &result_ov);
+    var expected: i64 = simple_subodi4(a, b, &expected_ov);
+    try testing.expectEqual(expected, result);
+    try testing.expectEqual(expected_ov, result_ov);
+}
+
+// 2 cases on evaluating `a-b`:
+// 1. `a-b` may underflow, iff b>0 && a<0 and a-b < min <=> a<min+b
+// 2. `a-b` may overflow,  iff b<0 && a>0 and a-b > max <=> a>max+b
+// `-b` evaluation may overflow, iff b==min, but this is handled by the hardware
+pub fn simple_subodi4(a: i64, b: i64, overflow: *c_int) i64 {
+    overflow.* = 0;
+    const min: i64 = math.minInt(i64);
+    const max: i64 = math.maxInt(i64);
+    if (((b > 0) and (a < min + b)) or
+        ((b < 0) and (a > max + b)))
+        overflow.* = 1;
+    return a -% b;
+}
+
+test "subodi3" {
+    const min: i64 = math.minInt(i64);
+    const max: i64 = math.maxInt(i64);
+    var i: i64 = 1;
+    while (i < max) : (i *|= 2) {
+        try test__subodi4(i, i);
+        try test__subodi4(-i, -i);
+        try test__subodi4(i, -i);
+        try test__subodi4(-i, i);
+    }
+
+    // edge cases
+    // 0 - 0       = 0
+    // MIN - MIN   = 0
+    // MAX - MAX   = 0
+    // 0   - MIN     overflow
+    // 0   - MAX   = MIN+1
+    // MIN - 0     = MIN
+    // MAX - 0     = MAX
+    // MIN - MAX     overflow
+    // MAX - MIN     overflow
+    try test__subodi4(0, 0);
+    try test__subodi4(min, min);
+    try test__subodi4(max, max);
+    try test__subodi4(0, min);
+    try test__subodi4(0, max);
+    try test__subodi4(min, 0);
+    try test__subodi4(max, 0);
+    try test__subodi4(min, max);
+    try test__subodi4(max, min);
+
+    // derived edge cases
+    // MIN+1 - MIN = 1
+    // MAX-1 - MAX = -1
+    // 1     - MIN   overflow
+    // -1    - MIN = MAX
+    // -1    - MAX = MIN
+    // +1    - MAX = MIN+2
+    // MIN   - 1     overflow
+    // MIN   - -1  = MIN+1
+    // MAX   - 1   = MAX-1
+    // MAX   - -1    overflow
+    try test__subodi4(min + 1, min);
+    try test__subodi4(max - 1, max);
+    try test__subodi4(1, min);
+    try test__subodi4(-1, min);
+    try test__subodi4(-1, max);
+    try test__subodi4(1, max);
+    try test__subodi4(min, 1);
+    try test__subodi4(min, -1);
+    try test__subodi4(max, -1);
+    try test__subodi4(max, 1);
+}
lib/std/special/compiler_rt/subosi4_test.zig
@@ -0,0 +1,82 @@
+const subo = @import("subo.zig");
+const testing = @import("std").testing;
+
+fn test__subosi4(a: i32, b: i32) !void {
+    var result_ov: c_int = undefined;
+    var expected_ov: c_int = undefined;
+    var result = subo.__subosi4(a, b, &result_ov);
+    var expected: i32 = simple_subosi4(a, b, &expected_ov);
+    try testing.expectEqual(expected, result);
+    try testing.expectEqual(expected_ov, result_ov);
+}
+
+// 2 cases on evaluating `a-b`:
+// 1. `a-b` may underflow, iff b>0 && a<0 and a-b < min <=> a<min+b
+// 2. `a-b` may overflow,  iff b<0 && a>0 and a-b > max <=> a>max+b
+// `-b` evaluation may overflow, iff b==min, but this is handled by the hardware
+pub fn simple_subosi4(a: i32, b: i32, overflow: *c_int) i32 {
+    overflow.* = 0;
+    const min: i32 = -2147483648;
+    const max: i32 = 2147483647;
+    if (((b > 0) and (a < min + b)) or
+        ((b < 0) and (a > max + b)))
+        overflow.* = 1;
+    return a -% b;
+}
+
+test "subosi3" {
+    // -2^31 <= i32 <= 2^31-1
+    // 2^31 = 2147483648
+    // 2^31-1 = 2147483647
+    const min: i32 = -2147483648;
+    const max: i32 = 2147483647;
+    var i: i32 = 1;
+    while (i < max) : (i *|= 2) {
+        try test__subosi4(i, i);
+        try test__subosi4(-i, -i);
+        try test__subosi4(i, -i);
+        try test__subosi4(-i, i);
+    }
+
+    // edge cases
+    // 0 - 0       = 0
+    // MIN - MIN   = 0
+    // MAX - MAX   = 0
+    // 0   - MIN     overflow
+    // 0   - MAX   = MIN+1
+    // MIN - 0     = MIN
+    // MAX - 0     = MAX
+    // MIN - MAX     overflow
+    // MAX - MIN     overflow
+    try test__subosi4(0, 0);
+    try test__subosi4(min, min);
+    try test__subosi4(max, max);
+    try test__subosi4(0, min);
+    try test__subosi4(0, max);
+    try test__subosi4(min, 0);
+    try test__subosi4(max, 0);
+    try test__subosi4(min, max);
+    try test__subosi4(max, min);
+
+    // derived edge cases
+    // MIN+1 - MIN = 1
+    // MAX-1 - MAX = -1
+    // 1     - MIN   overflow
+    // -1    - MIN = MAX
+    // -1    - MAX = MIN
+    // +1    - MAX = MIN+2
+    // MIN   - 1     overflow
+    // MIN   - -1  = MIN+1
+    // MAX   - 1   = MAX-1
+    // MAX   - -1    overflow
+    try test__subosi4(min + 1, min);
+    try test__subosi4(max - 1, max);
+    try test__subosi4(1, min);
+    try test__subosi4(-1, min);
+    try test__subosi4(-1, max);
+    try test__subosi4(1, max);
+    try test__subosi4(min, 1);
+    try test__subosi4(min, -1);
+    try test__subosi4(max, -1);
+    try test__subosi4(max, 1);
+}
lib/std/special/compiler_rt/suboti4_test.zig
@@ -0,0 +1,81 @@
+const subo = @import("subo.zig");
+const std = @import("std");
+const testing = std.testing;
+const math = std.math;
+
+fn test__suboti4(a: i128, b: i128) !void {
+    var result_ov: c_int = undefined;
+    var expected_ov: c_int = undefined;
+    var result = subo.__suboti4(a, b, &result_ov);
+    var expected: i128 = simple_suboti4(a, b, &expected_ov);
+    try testing.expectEqual(expected, result);
+    try testing.expectEqual(expected_ov, result_ov);
+}
+
+// 2 cases on evaluating `a-b`:
+// 1. `a-b` may underflow, iff b>0 && a<0 and a-b < min <=> a<min+b
+// 2. `a-b` may overflow,  iff b<0 && a>0 and a-b > max <=> a>max+b
+// `-b` evaluation may overflow, iff b==min, but this is handled by the hardware
+pub fn simple_suboti4(a: i128, b: i128, overflow: *c_int) i128 {
+    overflow.* = 0;
+    const min: i128 = math.minInt(i128);
+    const max: i128 = math.maxInt(i128);
+    if (((b > 0) and (a < min + b)) or
+        ((b < 0) and (a > max + b)))
+        overflow.* = 1;
+    return a -% b;
+}
+
+test "suboti3" {
+    const min: i128 = math.minInt(i128);
+    const max: i128 = math.maxInt(i128);
+    var i: i128 = 1;
+    while (i < max) : (i *|= 2) {
+        try test__suboti4(i, i);
+        try test__suboti4(-i, -i);
+        try test__suboti4(i, -i);
+        try test__suboti4(-i, i);
+    }
+
+    // edge cases
+    // 0 - 0       = 0
+    // MIN - MIN   = 0
+    // MAX - MAX   = 0
+    // 0   - MIN     overflow
+    // 0   - MAX   = MIN+1
+    // MIN - 0     = MIN
+    // MAX - 0     = MAX
+    // MIN - MAX     overflow
+    // MAX - MIN     overflow
+    try test__suboti4(0, 0);
+    try test__suboti4(min, min);
+    try test__suboti4(max, max);
+    try test__suboti4(0, min);
+    try test__suboti4(0, max);
+    try test__suboti4(min, 0);
+    try test__suboti4(max, 0);
+    try test__suboti4(min, max);
+    try test__suboti4(max, min);
+
+    // derived edge cases
+    // MIN+1 - MIN = 1
+    // MAX-1 - MAX = -1
+    // 1     - MIN   overflow
+    // -1    - MIN = MAX
+    // -1    - MAX = MIN
+    // +1    - MAX = MIN+2
+    // MIN   - 1     overflow
+    // MIN   - -1  = MIN+1
+    // MAX   - 1   = MAX-1
+    // MAX   - -1    overflow
+    try test__suboti4(min + 1, min);
+    try test__suboti4(max - 1, max);
+    try test__suboti4(1, min);
+    try test__suboti4(-1, min);
+    try test__suboti4(-1, max);
+    try test__suboti4(1, max);
+    try test__suboti4(min, 1);
+    try test__suboti4(min, -1);
+    try test__suboti4(max, -1);
+    try test__suboti4(max, 1);
+}
lib/std/special/compiler_rt.zig
@@ -112,6 +112,12 @@ comptime {
     @export(__addodi4, .{ .name = "__addodi4", .linkage = linkage });
     const __addoti4 = @import("compiler_rt/addo.zig").__addoti4;
     @export(__addoti4, .{ .name = "__addoti4", .linkage = linkage });
+    const __subosi4 = @import("compiler_rt/subo.zig").__subosi4;
+    @export(__subosi4, .{ .name = "__subosi4", .linkage = linkage });
+    const __subodi4 = @import("compiler_rt/subo.zig").__subodi4;
+    @export(__subodi4, .{ .name = "__subodi4", .linkage = linkage });
+    const __suboti4 = @import("compiler_rt/subo.zig").__suboti4;
+    @export(__suboti4, .{ .name = "__suboti4", .linkage = linkage });
     const __mulosi4 = @import("compiler_rt/mulo.zig").__mulosi4;
     @export(__mulosi4, .{ .name = "__mulosi4", .linkage = linkage });
     const __mulodi4 = @import("compiler_rt/mulo.zig").__mulodi4;