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compiler_rt: add addo (#10824)
- approach by Hacker's Delight with wrapping addition - ca. 1.10x perf over the standard approach on my laptop - tests with all combinations of min,max with -1,0,+1 and combinations of sequences +-1,2,4..,max
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matu3ba
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@ -106,6 +106,12 @@ comptime {
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}
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// Integral arithmetic which returns if overflow
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const __addosi4 = @import("compiler_rt/addo.zig").__addosi4;
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@export(__addosi4, .{ .name = "__addosi4", .linkage = linkage });
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const __addodi4 = @import("compiler_rt/addo.zig").__addodi4;
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@export(__addodi4, .{ .name = "__addodi4", .linkage = linkage });
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const __addoti4 = @import("compiler_rt/addo.zig").__addoti4;
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@export(__addoti4, .{ .name = "__addoti4", .linkage = linkage });
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const __mulosi4 = @import("compiler_rt/mulo.zig").__mulosi4;
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@export(__mulosi4, .{ .name = "__mulosi4", .linkage = linkage });
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const __mulodi4 = @import("compiler_rt/mulo.zig").__mulodi4;
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38
lib/std/special/compiler_rt/addo.zig
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38
lib/std/special/compiler_rt/addo.zig
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@ -0,0 +1,38 @@
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const builtin = @import("builtin");
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// addo - add overflow
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// * return a+%b.
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// * return if a+b overflows => 1 else => 0
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// - addoXi4_generic as default
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inline fn addoXi4_generic(comptime ST: type, a: ST, b: ST, overflow: *c_int) ST {
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@setRuntimeSafety(builtin.is_test);
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overflow.* = 0;
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var sum: ST = a +% b;
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// Hackers Delight: section Overflow Detection, subsection Signed Add/Subtract
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// Let sum = a +% b == a + b + carry == wraparound addition.
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// Overflow in a+b+carry occurs, iff a and b have opposite signs
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// and the sign of a+b+carry is the same as a (or equivalently b).
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// Slower routine: res = ~(a ^ b) & ((sum ^ a)
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// Faster routine: res = (sum ^ a) & (sum ^ b)
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// Oerflow occured, iff (res < 0)
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if (((sum ^ a) & (sum ^ b)) < 0)
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overflow.* = 1;
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return sum;
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}
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pub fn __addosi4(a: i32, b: i32, overflow: *c_int) callconv(.C) i32 {
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return addoXi4_generic(i32, a, b, overflow);
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}
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pub fn __addodi4(a: i64, b: i64, overflow: *c_int) callconv(.C) i64 {
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return addoXi4_generic(i64, a, b, overflow);
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}
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pub fn __addoti4(a: i128, b: i128, overflow: *c_int) callconv(.C) i128 {
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return addoXi4_generic(i128, a, b, overflow);
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}
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test {
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_ = @import("addosi4_test.zig");
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_ = @import("addodi4_test.zig");
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_ = @import("addoti4_test.zig");
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}
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77
lib/std/special/compiler_rt/addodi4_test.zig
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77
lib/std/special/compiler_rt/addodi4_test.zig
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@ -0,0 +1,77 @@
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const addv = @import("addo.zig");
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const std = @import("std");
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const testing = std.testing;
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const math = std.math;
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fn test__addodi4(a: i64, b: i64) !void {
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var result_ov: c_int = undefined;
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var expected_ov: c_int = undefined;
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var result = addv.__addodi4(a, b, &result_ov);
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var expected: i64 = simple_addodi4(a, b, &expected_ov);
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try testing.expectEqual(expected, result);
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try testing.expectEqual(expected_ov, result_ov);
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}
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fn simple_addodi4(a: i64, b: i64, overflow: *c_int) i64 {
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overflow.* = 0;
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const min: i64 = math.minInt(i64);
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const max: i64 = math.maxInt(i64);
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if (((a > 0) and (b > max - a)) or
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((a < 0) and (b < min - a)))
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overflow.* = 1;
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return a +% b;
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}
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test "addodi4" {
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const min: i64 = math.minInt(i64);
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const max: i64 = math.maxInt(i64);
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var i: i64 = 1;
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while (i < max) : (i *|= 2) {
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try test__addodi4(i, i);
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try test__addodi4(-i, -i);
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try test__addodi4(i, -i);
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try test__addodi4(-i, i);
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}
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// edge cases
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// 0 + 0 = 0
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// MIN + MIN overflow
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// MAX + MAX overflow
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// 0 + MIN MIN
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// 0 + MAX MAX
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// MIN + 0 MIN
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// MAX + 0 MAX
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// MIN + MAX -1
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// MAX + MIN -1
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try test__addodi4(0, 0);
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try test__addodi4(min, min);
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try test__addodi4(max, max);
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try test__addodi4(0, min);
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try test__addodi4(0, max);
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try test__addodi4(min, 0);
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try test__addodi4(max, 0);
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try test__addodi4(min, max);
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try test__addodi4(max, min);
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// derived edge cases
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// MIN+1 + MIN overflow
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// MAX-1 + MAX overflow
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// 1 + MIN = MIN+1
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// -1 + MIN overflow
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// -1 + MAX = MAX-1
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// +1 + MAX overflow
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// MIN + 1 = MIN+1
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// MIN + -1 overflow
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// MAX + 1 overflow
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// MAX + -1 = MAX-1
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try test__addodi4(min + 1, min);
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try test__addodi4(max - 1, max);
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try test__addodi4(1, min);
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try test__addodi4(-1, min);
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try test__addodi4(-1, max);
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try test__addodi4(1, max);
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try test__addodi4(min, 1);
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try test__addodi4(min, -1);
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try test__addodi4(max, -1);
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try test__addodi4(max, 1);
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}
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78
lib/std/special/compiler_rt/addosi4_test.zig
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78
lib/std/special/compiler_rt/addosi4_test.zig
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@ -0,0 +1,78 @@
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const addv = @import("addo.zig");
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const testing = @import("std").testing;
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fn test__addosi4(a: i32, b: i32) !void {
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var result_ov: c_int = undefined;
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var expected_ov: c_int = undefined;
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var result = addv.__addosi4(a, b, &result_ov);
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var expected: i32 = simple_addosi4(a, b, &expected_ov);
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try testing.expectEqual(expected, result);
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try testing.expectEqual(expected_ov, result_ov);
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}
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fn simple_addosi4(a: i32, b: i32, overflow: *c_int) i32 {
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overflow.* = 0;
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const min: i32 = -2147483648;
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const max: i32 = 2147483647;
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if (((a > 0) and (b > max - a)) or
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((a < 0) and (b < min - a)))
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overflow.* = 1;
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return a +% b;
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}
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test "addosi4" {
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// -2^31 <= i32 <= 2^31-1
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// 2^31 = 2147483648
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// 2^31-1 = 2147483647
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const min: i32 = -2147483648;
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const max: i32 = 2147483647;
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var i: i32 = 1;
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while (i < max) : (i *|= 2) {
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try test__addosi4(i, i);
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try test__addosi4(-i, -i);
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try test__addosi4(i, -i);
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try test__addosi4(-i, i);
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}
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// edge cases
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// 0 + 0 = 0
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// MIN + MIN overflow
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// MAX + MAX overflow
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// 0 + MIN MIN
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// 0 + MAX MAX
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// MIN + 0 MIN
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// MAX + 0 MAX
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// MIN + MAX -1
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// MAX + MIN -1
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try test__addosi4(0, 0);
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try test__addosi4(min, min);
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try test__addosi4(max, max);
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try test__addosi4(0, min);
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try test__addosi4(0, max);
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try test__addosi4(min, 0);
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try test__addosi4(max, 0);
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try test__addosi4(min, max);
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try test__addosi4(max, min);
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// derived edge cases
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// MIN+1 + MIN overflow
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// MAX-1 + MAX overflow
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// 1 + MIN = MIN+1
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// -1 + MIN overflow
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// -1 + MAX = MAX-1
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// +1 + MAX overflow
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// MIN + 1 = MIN+1
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// MIN + -1 overflow
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// MAX + 1 overflow
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// MAX + -1 = MAX-1
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try test__addosi4(min + 1, min);
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try test__addosi4(max - 1, max);
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try test__addosi4(1, min);
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try test__addosi4(-1, min);
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try test__addosi4(-1, max);
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try test__addosi4(1, max);
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try test__addosi4(min, 1);
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try test__addosi4(min, -1);
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try test__addosi4(max, -1);
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try test__addosi4(max, 1);
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}
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77
lib/std/special/compiler_rt/addoti4_test.zig
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77
lib/std/special/compiler_rt/addoti4_test.zig
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@ -0,0 +1,77 @@
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const addv = @import("addo.zig");
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const std = @import("std");
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const testing = std.testing;
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const math = std.math;
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fn test__addoti4(a: i128, b: i128) !void {
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var result_ov: c_int = undefined;
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var expected_ov: c_int = undefined;
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var result = addv.__addoti4(a, b, &result_ov);
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var expected: i128 = simple_addoti4(a, b, &expected_ov);
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try testing.expectEqual(expected, result);
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try testing.expectEqual(expected_ov, result_ov);
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}
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fn simple_addoti4(a: i128, b: i128, overflow: *c_int) i128 {
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overflow.* = 0;
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const min: i128 = math.minInt(i128);
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const max: i128 = math.maxInt(i128);
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if (((a > 0) and (b > max - a)) or
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((a < 0) and (b < min - a)))
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overflow.* = 1;
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return a +% b;
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}
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test "addoti4" {
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const min: i128 = math.minInt(i128);
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const max: i128 = math.maxInt(i128);
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var i: i128 = 1;
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while (i < max) : (i *|= 2) {
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try test__addoti4(i, i);
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try test__addoti4(-i, -i);
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try test__addoti4(i, -i);
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try test__addoti4(-i, i);
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}
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// edge cases
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// 0 + 0 = 0
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// MIN + MIN overflow
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// MAX + MAX overflow
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// 0 + MIN MIN
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// 0 + MAX MAX
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// MIN + 0 MIN
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// MAX + 0 MAX
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// MIN + MAX -1
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// MAX + MIN -1
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try test__addoti4(0, 0);
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try test__addoti4(min, min);
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try test__addoti4(max, max);
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try test__addoti4(0, min);
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try test__addoti4(0, max);
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try test__addoti4(min, 0);
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try test__addoti4(max, 0);
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try test__addoti4(min, max);
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try test__addoti4(max, min);
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// derived edge cases
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// MIN+1 + MIN overflow
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// MAX-1 + MAX overflow
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// 1 + MIN = MIN+1
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// -1 + MIN overflow
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// -1 + MAX = MAX-1
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// +1 + MAX overflow
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// MIN + 1 = MIN+1
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// MIN + -1 overflow
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// MAX + 1 overflow
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// MAX + -1 = MAX-1
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try test__addoti4(min + 1, min);
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try test__addoti4(max - 1, max);
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try test__addoti4(1, min);
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try test__addoti4(-1, min);
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try test__addoti4(-1, max);
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try test__addoti4(1, max);
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try test__addoti4(min, 1);
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try test__addoti4(min, -1);
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try test__addoti4(max, -1);
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try test__addoti4(max, 1);
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}
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@ -3,7 +3,7 @@ const std = @import("std");
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const math = std.math;
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// mulo - multiplication overflow
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// * return a*b.
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// * return a*%b.
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// * return if a*b overflows => 1 else => 0
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// - muloXi4_genericSmall as default
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// - muloXi4_genericFast for 2*bitsize <= usize
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