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const std = @import("std");
pub const LE = enum(i32) {
Less = -1,
Equal = 0,
Greater = 1,
const Unordered: LE = .Greater;
};
pub const GE = enum(i32) {
Less = -1,
Equal = 0,
Greater = 1,
const Unordered: GE = .Less;
};
pub inline fn cmpf2(comptime T: type, comptime RT: type, a: T, b: T) RT {
const bits = @typeInfo(T).Float.bits;
const srep_t = std.meta.Int(.signed, bits);
const rep_t = std.meta.Int(.unsigned, bits);
const significandBits = std.math.floatMantissaBits(T);
const exponentBits = std.math.floatExponentBits(T);
const signBit = (@as(rep_t, 1) << (significandBits + exponentBits));
const absMask = signBit - 1;
const infT = comptime std.math.inf(T);
const infRep = @as(rep_t, @bitCast(infT));
const aInt = @as(srep_t, @bitCast(a));
const bInt = @as(srep_t, @bitCast(b));
const aAbs = @as(rep_t, @bitCast(aInt)) & absMask;
const bAbs = @as(rep_t, @bitCast(bInt)) & absMask;
// If either a or b is NaN, they are unordered.
if (aAbs > infRep or bAbs > infRep) return RT.Unordered;
// If a and b are both zeros, they are equal.
if ((aAbs | bAbs) == 0) return .Equal;
// If at least one of a and b is positive, we get the same result comparing
// a and b as signed integers as we would with a floating-point compare.
if ((aInt & bInt) >= 0) {
if (aInt < bInt) {
return .Less;
} else if (aInt == bInt) {
return .Equal;
} else return .Greater;
} else {
// Otherwise, both are negative, so we need to flip the sense of the
// comparison to get the correct result. (This assumes a twos- or ones-
// complement integer representation; if integers are represented in a
// sign-magnitude representation, then this flip is incorrect).
if (aInt > bInt) {
return .Less;
} else if (aInt == bInt) {
return .Equal;
} else return .Greater;
}
}
pub inline fn cmp_f80(comptime RT: type, a: f80, b: f80) RT {
const a_rep = std.math.break_f80(a);
const b_rep = std.math.break_f80(b);
const sig_bits = std.math.floatMantissaBits(f80);
const int_bit = 0x8000000000000000;
const sign_bit = 0x8000;
const special_exp = 0x7FFF;
// If either a or b is NaN, they are unordered.
if ((a_rep.exp & special_exp == special_exp and a_rep.fraction ^ int_bit != 0) or
(b_rep.exp & special_exp == special_exp and b_rep.fraction ^ int_bit != 0))
return RT.Unordered;
// If a and b are both zeros, they are equal.
if ((a_rep.fraction | b_rep.fraction) | ((a_rep.exp | b_rep.exp) & special_exp) == 0)
return .Equal;
if (@intFromBool(a_rep.exp == b_rep.exp) & @intFromBool(a_rep.fraction == b_rep.fraction) != 0) {
return .Equal;
} else if (a_rep.exp & sign_bit != b_rep.exp & sign_bit) {
// signs are different
if (@as(i16, @bitCast(a_rep.exp)) < @as(i16, @bitCast(b_rep.exp))) {
return .Less;
} else {
return .Greater;
}
} else {
const a_fraction = a_rep.fraction | (@as(u80, a_rep.exp) << sig_bits);
const b_fraction = b_rep.fraction | (@as(u80, b_rep.exp) << sig_bits);
if ((a_fraction < b_fraction) == (a_rep.exp & sign_bit == 0)) {
return .Less;
} else {
return .Greater;
}
}
}
test "cmp_f80" {
inline for (.{ LE, GE }) |RT| {
try std.testing.expect(cmp_f80(RT, 1.0, 1.0) == RT.Equal);
try std.testing.expect(cmp_f80(RT, 0.0, -0.0) == RT.Equal);
try std.testing.expect(cmp_f80(RT, 2.0, 4.0) == RT.Less);
try std.testing.expect(cmp_f80(RT, 2.0, -4.0) == RT.Greater);
try std.testing.expect(cmp_f80(RT, -2.0, -4.0) == RT.Greater);
try std.testing.expect(cmp_f80(RT, -2.0, 4.0) == RT.Less);
}
}
pub inline fn unordcmp(comptime T: type, a: T, b: T) i32 {
const rep_t = std.meta.Int(.unsigned, @typeInfo(T).Float.bits);
const significandBits = std.math.floatMantissaBits(T);
const exponentBits = std.math.floatExponentBits(T);
const signBit = (@as(rep_t, 1) << (significandBits + exponentBits));
const absMask = signBit - 1;
const infRep = @as(rep_t, @bitCast(std.math.inf(T)));
const aAbs: rep_t = @as(rep_t, @bitCast(a)) & absMask;
const bAbs: rep_t = @as(rep_t, @bitCast(b)) & absMask;
return @intFromBool(aAbs > infRep or bAbs > infRep);
}
test {
_ = @import("comparesf2_test.zig");
_ = @import("comparedf2_test.zig");
}
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