const std = @import("../std.zig");
const builtin = @import("builtin");
const assert = std.debug.assert;
const expect = std.testing.expect;
const expectEqual = std.testing.expectEqual;
inline fn mantissaOne(comptime T: type) comptime_int {
return if (@typeInfo(T).Float.bits == 80) 1 << floatFractionalBits(T) else 0;
}
inline fn reconstructFloat(comptime T: type, comptime exponent: comptime_int, comptime mantissa: comptime_int) T {
const TBits = @Type(.{ .Int = .{ .signedness = .unsigned, .bits = @bitSizeOf(T) } });
const biased_exponent = @as(TBits, exponent + floatExponentMax(T));
return @as(T, @bitCast((biased_exponent << floatMantissaBits(T)) | @as(TBits, mantissa)));
}
pub inline fn floatExponentBits(comptime T: type) comptime_int {
comptime assert(@typeInfo(T) == .Float);
return switch (@typeInfo(T).Float.bits) {
16 => 5,
32 => 8,
64 => 11,
80 => 15,
128 => 15,
else => @compileError("unknown floating point type " ++ @typeName(T)),
};
}
pub inline fn floatMantissaBits(comptime T: type) comptime_int {
comptime assert(@typeInfo(T) == .Float);
return switch (@typeInfo(T).Float.bits) {
16 => 10,
32 => 23,
64 => 52,
80 => 64,
128 => 112,
else => @compileError("unknown floating point type " ++ @typeName(T)),
};
}
pub inline fn floatFractionalBits(comptime T: type) comptime_int {
comptime assert(@typeInfo(T) == .Float);
return switch (@typeInfo(T).Float.bits) {
16 => 10,
32 => 23,
64 => 52,
80 => 63,
128 => 112,
else => @compileError("unknown floating point type " ++ @typeName(T)),
};
}
pub inline fn floatExponentMin(comptime T: type) comptime_int {
return -floatExponentMax(T) + 1;
}
pub inline fn floatExponentMax(comptime T: type) comptime_int {
return (1 << (floatExponentBits(T) - 1)) - 1;
}
pub inline fn floatTrueMin(comptime T: type) T {
return reconstructFloat(T, floatExponentMin(T) - 1, 1);
}
pub inline fn floatMin(comptime T: type) T {
return reconstructFloat(T, floatExponentMin(T), mantissaOne(T));
}
pub inline fn floatMax(comptime T: type) T {
const all1s_mantissa = (1 << floatMantissaBits(T)) - 1;
return reconstructFloat(T, floatExponentMax(T), all1s_mantissa);
}
pub inline fn floatEps(comptime T: type) T {
return reconstructFloat(T, -floatFractionalBits(T), mantissaOne(T));
}
pub inline fn inf(comptime T: type) T {
return reconstructFloat(T, floatExponentMax(T) + 1, mantissaOne(T));
}
pub inline fn nan(comptime T: type) T {
return reconstructFloat(
T,
floatExponentMax(T) + 1,
mantissaOne(T) | 1 << (floatFractionalBits(T) - 1),
);
}
pub inline fn snan(comptime T: type) T {
return reconstructFloat(
T,
floatExponentMax(T) + 1,
mantissaOne(T) | 1 << (floatFractionalBits(T) - 2),
);
}
test "float bits" {
inline for ([_]type{ f16, f32, f64, f80, f128, c_longdouble }) |T| {
const size = 1 + floatExponentBits(T) + floatMantissaBits(T);
try expect(@bitSizeOf(T) == size);
try expect(floatExponentMin(T) <= -floatFractionalBits(T));
try expect(-floatFractionalBits(T) <= floatExponentMax(T));
}
}
test "math.inf" {
const inf_u16: u16 = 0x7C00;
const inf_u32: u32 = 0x7F800000;
const inf_u64: u64 = 0x7FF0000000000000;
const inf_u80: u80 = 0x7FFF8000000000000000;
const inf_u128: u128 = 0x7FFF0000000000000000000000000000;
try expectEqual(inf_u16, @bitCast(inf(f16)));
try expectEqual(inf_u32, @bitCast(inf(f32)));
try expectEqual(inf_u64, @bitCast(inf(f64)));
try expectEqual(inf_u80, @bitCast(inf(f80)));
try expectEqual(inf_u128, @bitCast(inf(f128)));
}
test "math.nan" {
const qnan_u16: u16 = 0x7E00;
const qnan_u32: u32 = 0x7FC00000;
const qnan_u64: u64 = 0x7FF8000000000000;
const qnan_u80: u80 = 0x7FFFC000000000000000;
const qnan_u128: u128 = 0x7FFF8000000000000000000000000000;
try expectEqual(qnan_u16, @bitCast(nan(f16)));
try expectEqual(qnan_u32, @bitCast(nan(f32)));
try expectEqual(qnan_u64, @bitCast(nan(f64)));
try expectEqual(qnan_u80, @bitCast(nan(f80)));
try expectEqual(qnan_u128, @bitCast(nan(f128)));
}
test "math.snan" {
if (builtin.zig_backend == .stage2_llvm and comptime builtin.cpu.arch.isArmOrThumb()) return error.SkipZigTest;
const snan_u16: u16 = 0x7D00;
const snan_u32: u32 = 0x7FA00000;
const snan_u64: u64 = 0x7FF4000000000000;
const snan_u80: u80 = 0x7FFFA000000000000000;
const snan_u128: u128 = 0x7FFF4000000000000000000000000000;
try expectEqual(snan_u16, @bitCast(snan(f16)));
try expectEqual(snan_u32, @bitCast(snan(f32)));
try expectEqual(snan_u64, @bitCast(snan(f64)));
try expectEqual(snan_u80, @bitCast(snan(f80)));
try expectEqual(snan_u128, @bitCast(snan(f128)));
}