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const std = @import("../std.zig");
const math = std.math;
const expect = std.testing.expect;
const expectEqual = std.testing.expectEqual;
const expectApproxEqAbs = std.testing.expectApproxEqAbs;
pub fn Frexp(comptime T: type) type {
return struct {
significand: T,
exponent: i32,
};
}
/// Breaks x into a normalized fraction and an integral power of two.
/// f == frac * 2^exp, with |frac| in the interval [0.5, 1).
///
/// Special Cases:
/// - frexp(+-0) = +-0, 0
/// - frexp(+-inf) = +-inf, 0
/// - frexp(nan) = nan, undefined
pub fn frexp(x: anytype) Frexp(@TypeOf(x)) {
const T: type = @TypeOf(x);
const bits: comptime_int = @typeInfo(T).float.bits;
const Int: type = std.meta.Int(.unsigned, bits);
const exp_bits: comptime_int = math.floatExponentBits(T);
const mant_bits: comptime_int = math.floatMantissaBits(T);
const frac_bits: comptime_int = math.floatFractionalBits(T);
const exp_min: comptime_int = math.floatExponentMin(T);
const ExpInt: type = std.meta.Int(.unsigned, exp_bits);
const MantInt: type = std.meta.Int(.unsigned, mant_bits);
const FracInt: type = std.meta.Int(.unsigned, frac_bits);
const unreal_exponent: comptime_int = (1 << exp_bits) - 1;
const bias: comptime_int = (1 << (exp_bits - 1)) - 2;
const exp_mask: comptime_int = unreal_exponent << mant_bits;
const zero_exponent: comptime_int = bias << mant_bits;
const sign_mask: comptime_int = 1 << (bits - 1);
const not_exp: comptime_int = ~@as(Int, exp_mask);
const ones_place: comptime_int = mant_bits - frac_bits;
const extra_denorm_shift: comptime_int = 1 - ones_place;
var result: Frexp(T) = undefined;
var v: Int = @bitCast(x);
const m: MantInt = @truncate(v);
const e: ExpInt = @truncate(v >> mant_bits);
switch (e) {
0 => {
if (m != 0) {
// subnormal
const offset = @clz(m);
const shift = offset + extra_denorm_shift;
v &= sign_mask;
v |= zero_exponent;
v |= math.shl(MantInt, m, shift);
result.exponent = exp_min - @as(i32, offset) + ones_place;
} else {
// +-0 = (+-0, 0)
result.exponent = 0;
}
},
unreal_exponent => {
// +-nan -> {+-nan, undefined}
result.exponent = undefined;
// +-inf -> {+-inf, 0}
if (@as(FracInt, @truncate(v)) == 0)
result.exponent = 0;
},
else => {
// normal
v &= not_exp;
v |= zero_exponent;
result.exponent = @as(i32, e) - bias;
},
}
result.significand = @bitCast(v);
return result;
}
/// Generate a namespace of tests for frexp on values of the given type
fn FrexpTests(comptime Float: type) type {
return struct {
const T = Float;
test "normal" {
const epsilon = 1e-6;
var r: Frexp(T) = undefined;
r = frexp(@as(T, 1.3));
try expectApproxEqAbs(0.65, r.significand, epsilon);
try expectEqual(1, r.exponent);
r = frexp(@as(T, 78.0234));
try expectApproxEqAbs(0.609558, r.significand, epsilon);
try expectEqual(7, r.exponent);
r = frexp(@as(T, -1234.5678));
try expectEqual(11, r.exponent);
try expectApproxEqAbs(-0.602816, r.significand, epsilon);
}
test "max" {
const exponent = math.floatExponentMax(T) + 1;
const significand = 1.0 - math.floatEps(T) / 2;
const r: Frexp(T) = frexp(math.floatMax(T));
try expectEqual(exponent, r.exponent);
try expectEqual(significand, r.significand);
}
test "min" {
const exponent = math.floatExponentMin(T) + 1;
const r: Frexp(T) = frexp(math.floatMin(T));
try expectEqual(exponent, r.exponent);
try expectEqual(0.5, r.significand);
}
test "subnormal" {
const normal_min_exponent = math.floatExponentMin(T) + 1;
const exponent = normal_min_exponent - math.floatFractionalBits(T);
const r: Frexp(T) = frexp(math.floatTrueMin(T));
try expectEqual(exponent, r.exponent);
try expectEqual(0.5, r.significand);
}
test "zero" {
var r: Frexp(T) = undefined;
r = frexp(@as(T, 0.0));
try expectEqual(0, r.exponent);
try expect(math.isPositiveZero(r.significand));
r = frexp(@as(T, -0.0));
try expectEqual(0, r.exponent);
try expect(math.isNegativeZero(r.significand));
}
test "inf" {
var r: Frexp(T) = undefined;
r = frexp(math.inf(T));
try expectEqual(0, r.exponent);
try expect(math.isPositiveInf(r.significand));
r = frexp(-math.inf(T));
try expectEqual(0, r.exponent);
try expect(math.isNegativeInf(r.significand));
}
test "nan" {
const r: Frexp(T) = frexp(math.nan(T));
try expect(math.isNan(r.significand));
}
};
}
// Generate tests for each floating point type
comptime {
for ([_]type{ f16, f32, f64, f80, f128 }) |T| {
_ = FrexpTests(T);
}
}
test frexp {
inline for ([_]type{ f16, f32, f64, f80, f128 }) |T| {
const max_exponent = math.floatExponentMax(T) + 1;
const min_exponent = math.floatExponentMin(T) + 1;
const truemin_exponent = min_exponent - math.floatFractionalBits(T);
var result: Frexp(T) = undefined;
comptime var x: T = undefined;
// basic usage
// value -> {significand, exponent},
// value == significand * (2 ^ exponent)
x = 1234.5678;
result = frexp(x);
try expectEqual(11, result.exponent);
try expectApproxEqAbs(0.602816, result.significand, 1e-6);
try expectEqual(x, math.ldexp(result.significand, result.exponent));
// float maximum
x = math.floatMax(T);
result = frexp(x);
try expectEqual(max_exponent, result.exponent);
try expectEqual(1.0 - math.floatEps(T) / 2, result.significand);
try expectEqual(x, math.ldexp(result.significand, result.exponent));
// float minimum
x = math.floatMin(T);
result = frexp(x);
try expectEqual(min_exponent, result.exponent);
try expectEqual(0.5, result.significand);
try expectEqual(x, math.ldexp(result.significand, result.exponent));
// float true minimum
// subnormal -> {normal, exponent}
x = math.floatTrueMin(T);
result = frexp(x);
try expectEqual(truemin_exponent, result.exponent);
try expectEqual(0.5, result.significand);
try expectEqual(x, math.ldexp(result.significand, result.exponent));
// infinity -> {infinity, zero} (+)
result = frexp(math.inf(T));
try expectEqual(0, result.exponent);
try expect(math.isPositiveInf(result.significand));
// infinity -> {infinity, zero} (-)
result = frexp(-math.inf(T));
try expectEqual(0, result.exponent);
try expect(math.isNegativeInf(result.significand));
// zero -> {zero, zero} (+)
result = frexp(@as(T, 0.0));
try expectEqual(0, result.exponent);
try expect(math.isPositiveZero(result.significand));
// zero -> {zero, zero} (-)
result = frexp(@as(T, -0.0));
try expectEqual(0, result.exponent);
try expect(math.isNegativeZero(result.significand));
// nan -> {nan, undefined}
result = frexp(math.nan(T));
try expect(math.isNan(result.significand));
}
}
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