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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
This commit is contained in:
Jan Philipp Hafer
Andrew Kelley
parent
a15d2d582b
commit
fc59a04061
6 changed files with 289 additions and 1 deletions
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@ -112,6 +112,12 @@ comptime {
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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 __subosi4 = @import("compiler_rt/subo.zig").__subosi4;
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@export(__subosi4, .{ .name = "__subosi4", .linkage = linkage });
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const __subodi4 = @import("compiler_rt/subo.zig").__subodi4;
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@export(__subodi4, .{ .name = "__subodi4", .linkage = linkage });
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const __suboti4 = @import("compiler_rt/subo.zig").__suboti4;
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@export(__suboti4, .{ .name = "__suboti4", .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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@ -15,7 +15,7 @@ inline fn addoXi4_generic(comptime ST: type, a: ST, b: ST, overflow: *c_int) ST
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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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// Overflow 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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38
lib/std/special/compiler_rt/subo.zig
Normal file
38
lib/std/special/compiler_rt/subo.zig
Normal file
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@ -0,0 +1,38 @@
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const builtin = @import("builtin");
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// subo - subtract overflow
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// * return a-%b.
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// * return if a-b overflows => 1 else => 0
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// - suboXi4_generic as default
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inline fn suboXi4_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 subtraction.
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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 opposite of a (or equivalently same as b).
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// Faster routine: res = (a ^ b) & (sum ^ a)
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// Slower routine: res = (sum^a) & ~(sum^b)
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// Overflow occured, iff (res < 0)
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if (((a ^ b) & (sum ^ a)) < 0)
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overflow.* = 1;
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return sum;
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}
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pub fn __subosi4(a: i32, b: i32, overflow: *c_int) callconv(.C) i32 {
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return suboXi4_generic(i32, a, b, overflow);
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}
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pub fn __subodi4(a: i64, b: i64, overflow: *c_int) callconv(.C) i64 {
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return suboXi4_generic(i64, a, b, overflow);
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}
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pub fn __suboti4(a: i128, b: i128, overflow: *c_int) callconv(.C) i128 {
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return suboXi4_generic(i128, a, b, overflow);
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}
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test {
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_ = @import("subosi4_test.zig");
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_ = @import("subodi4_test.zig");
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_ = @import("suboti4_test.zig");
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}
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81
lib/std/special/compiler_rt/subodi4_test.zig
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81
lib/std/special/compiler_rt/subodi4_test.zig
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@ -0,0 +1,81 @@
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const subo = @import("subo.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__subodi4(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 = subo.__subodi4(a, b, &result_ov);
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var expected: i64 = simple_subodi4(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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// 2 cases on evaluating `a-b`:
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// 1. `a-b` may underflow, iff b>0 && a<0 and a-b < min <=> a<min+b
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// 2. `a-b` may overflow, iff b<0 && a>0 and a-b > max <=> a>max+b
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// `-b` evaluation may overflow, iff b==min, but this is handled by the hardware
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pub fn simple_subodi4(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 (((b > 0) and (a < min + b)) or
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((b < 0) and (a > max + b)))
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overflow.* = 1;
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return a -% b;
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}
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test "subodi3" {
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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__subodi4(i, i);
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try test__subodi4(-i, -i);
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try test__subodi4(i, -i);
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try test__subodi4(-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 = 0
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// MAX - MAX = 0
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// 0 - MIN overflow
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// 0 - MAX = MIN+1
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// MIN - 0 = MIN
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// MAX - 0 = MAX
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// MIN - MAX overflow
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// MAX - MIN overflow
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try test__subodi4(0, 0);
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try test__subodi4(min, min);
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try test__subodi4(max, max);
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try test__subodi4(0, min);
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try test__subodi4(0, max);
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try test__subodi4(min, 0);
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try test__subodi4(max, 0);
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try test__subodi4(min, max);
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try test__subodi4(max, min);
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// derived edge cases
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// MIN+1 - MIN = 1
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// MAX-1 - MAX = -1
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// 1 - MIN overflow
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// -1 - MIN = MAX
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// -1 - MAX = MIN
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// +1 - MAX = MIN+2
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// MIN - 1 overflow
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// MIN - -1 = MIN+1
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// MAX - 1 = MAX-1
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// MAX - -1 overflow
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try test__subodi4(min + 1, min);
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try test__subodi4(max - 1, max);
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try test__subodi4(1, min);
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try test__subodi4(-1, min);
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try test__subodi4(-1, max);
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try test__subodi4(1, max);
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try test__subodi4(min, 1);
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try test__subodi4(min, -1);
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try test__subodi4(max, -1);
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try test__subodi4(max, 1);
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}
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82
lib/std/special/compiler_rt/subosi4_test.zig
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82
lib/std/special/compiler_rt/subosi4_test.zig
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@ -0,0 +1,82 @@
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const subo = @import("subo.zig");
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const testing = @import("std").testing;
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fn test__subosi4(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 = subo.__subosi4(a, b, &result_ov);
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var expected: i32 = simple_subosi4(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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// 2 cases on evaluating `a-b`:
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// 1. `a-b` may underflow, iff b>0 && a<0 and a-b < min <=> a<min+b
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// 2. `a-b` may overflow, iff b<0 && a>0 and a-b > max <=> a>max+b
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// `-b` evaluation may overflow, iff b==min, but this is handled by the hardware
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pub fn simple_subosi4(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 (((b > 0) and (a < min + b)) or
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((b < 0) and (a > max + b)))
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overflow.* = 1;
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return a -% b;
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}
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test "subosi3" {
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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__subosi4(i, i);
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try test__subosi4(-i, -i);
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try test__subosi4(i, -i);
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try test__subosi4(-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 = 0
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// MAX - MAX = 0
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// 0 - MIN overflow
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// 0 - MAX = MIN+1
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// MIN - 0 = MIN
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// MAX - 0 = MAX
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// MIN - MAX overflow
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// MAX - MIN overflow
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try test__subosi4(0, 0);
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try test__subosi4(min, min);
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try test__subosi4(max, max);
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try test__subosi4(0, min);
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try test__subosi4(0, max);
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try test__subosi4(min, 0);
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try test__subosi4(max, 0);
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try test__subosi4(min, max);
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try test__subosi4(max, min);
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// derived edge cases
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// MIN+1 - MIN = 1
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// MAX-1 - MAX = -1
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// 1 - MIN overflow
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// -1 - MIN = MAX
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// -1 - MAX = MIN
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// +1 - MAX = MIN+2
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// MIN - 1 overflow
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// MIN - -1 = MIN+1
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// MAX - 1 = MAX-1
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// MAX - -1 overflow
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try test__subosi4(min + 1, min);
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try test__subosi4(max - 1, max);
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try test__subosi4(1, min);
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try test__subosi4(-1, min);
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try test__subosi4(-1, max);
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try test__subosi4(1, max);
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try test__subosi4(min, 1);
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try test__subosi4(min, -1);
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try test__subosi4(max, -1);
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try test__subosi4(max, 1);
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}
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81
lib/std/special/compiler_rt/suboti4_test.zig
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81
lib/std/special/compiler_rt/suboti4_test.zig
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@ -0,0 +1,81 @@
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const subo = @import("subo.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__suboti4(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 = subo.__suboti4(a, b, &result_ov);
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var expected: i128 = simple_suboti4(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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// 2 cases on evaluating `a-b`:
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// 1. `a-b` may underflow, iff b>0 && a<0 and a-b < min <=> a<min+b
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// 2. `a-b` may overflow, iff b<0 && a>0 and a-b > max <=> a>max+b
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// `-b` evaluation may overflow, iff b==min, but this is handled by the hardware
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pub fn simple_suboti4(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 (((b > 0) and (a < min + b)) or
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((b < 0) and (a > max + b)))
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overflow.* = 1;
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return a -% b;
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}
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test "suboti3" {
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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__suboti4(i, i);
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try test__suboti4(-i, -i);
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try test__suboti4(i, -i);
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try test__suboti4(-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 = 0
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// MAX - MAX = 0
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// 0 - MIN overflow
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// 0 - MAX = MIN+1
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// MIN - 0 = MIN
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// MAX - 0 = MAX
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// MIN - MAX overflow
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// MAX - MIN overflow
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try test__suboti4(0, 0);
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try test__suboti4(min, min);
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try test__suboti4(max, max);
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try test__suboti4(0, min);
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try test__suboti4(0, max);
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try test__suboti4(min, 0);
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try test__suboti4(max, 0);
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try test__suboti4(min, max);
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try test__suboti4(max, min);
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// derived edge cases
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// MIN+1 - MIN = 1
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// MAX-1 - MAX = -1
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// 1 - MIN overflow
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// -1 - MIN = MAX
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// -1 - MAX = MIN
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// +1 - MAX = MIN+2
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// MIN - 1 overflow
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// MIN - -1 = MIN+1
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// MAX - 1 = MAX-1
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// MAX - -1 overflow
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try test__suboti4(min + 1, min);
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try test__suboti4(max - 1, max);
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try test__suboti4(1, min);
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try test__suboti4(-1, min);
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try test__suboti4(-1, max);
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try test__suboti4(1, max);
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try test__suboti4(min, 1);
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try test__suboti4(min, -1);
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try test__suboti4(max, -1);
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try test__suboti4(max, 1);
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}
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