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Fix std::float16_t rounding of subnormal ties and fast-path overflow #408

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Fix std::float16_t rounding of subnormal ties and fast-path overflow #408

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abb4c86
Fix std::float16_t rounding of subnormal ties and fast-path overflow
jadidbourbaki Sep 15, 2026
20a9b35
Gate the subnormal tie test on a compile-time predicate
jadidbourbaki Sep 15, 2026
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19 changes: 15 additions & 4 deletions include/fast_float/decimal_to_binary.h
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Original file line number Diff line number Diff line change
Expand Up @@ -156,10 +156,21 @@ compute_float(int64_t q, uint64_t w) noexcept {
return answer;
}
// next line is safe because -answer.power2 + 1 < 64
answer.mantissa >>= -answer.power2 + 1;
// Thankfully, we can't have both "round-to-even" and subnormals because
// "round-to-even" only occurs for powers close to 0 in the 32-bit and
// and 64-bit case (with no more than 19 digits).
int const subnormal_shift = -answer.power2 + 1;
answer.mantissa >>= subnormal_shift;
// A subnormal result can also fall exactly between two floats. With at
// most 19 digits this never happens for float and double, but it does for
// std::float16_t (e.g., 2^-25 = 298023223876953125e-25), so we apply the
// same round-to-even test as in the normal case below.
// See script/format_parameters.py.
if (binary::subnormal_ties_possible() && (product.low <= 1) &&
(q >= binary::min_exponent_round_to_even()) &&
(q <= binary::max_exponent_round_to_even()) &&
((answer.mantissa & 3) == 1)) {
if (((answer.mantissa << subnormal_shift) << shift) == product.high) {
answer.mantissa &= ~uint64_t(1); // flip it so that we do not round up
}
}
answer.mantissa += (answer.mantissa & 1); // round up
answer.mantissa >>= 1;
// There is a weird scenario where we don't have a subnormal but just.
Expand Down
42 changes: 34 additions & 8 deletions include/fast_float/float_common.h
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Original file line number Diff line number Diff line change
Expand Up @@ -665,6 +665,8 @@ template <typename T> struct binary_format : binary_format_lookup_tables<T> {
static constexpr uint64_t max_mantissa_fast_path(int64_t power);
static constexpr uint64_t
max_mantissa_fast_path(); // used when fegetround() == FE_TONEAREST
static constexpr bool fast_path_can_overflow();
static constexpr bool subnormal_ties_possible();
static constexpr int largest_power_of_ten();
static constexpr int smallest_power_of_ten();
static constexpr T exact_power_of_ten(int64_t power);
Expand Down Expand Up @@ -696,6 +698,7 @@ template <typename U> struct binary_format_lookup_tables<double, U> {
0x20000000000000 / (constant_55555 * constant_55555 * 5),
0x20000000000000 / (constant_55555 * constant_55555 * 5 * 5),
0x20000000000000 / (constant_55555 * constant_55555 * 5 * 5 * 5),
0x20000000000000 / (constant_55555 * constant_55555 * 5 * 5 * 5 * 5),
0x20000000000000 / (constant_55555 * constant_55555 * constant_55555),
0x20000000000000 / (constant_55555 * constant_55555 * constant_55555 * 5),
0x20000000000000 /
Expand All @@ -711,9 +714,7 @@ template <typename U> struct binary_format_lookup_tables<double, U> {
0x20000000000000 / (constant_55555 * constant_55555 * constant_55555 *
constant_55555 * 5 * 5),
0x20000000000000 / (constant_55555 * constant_55555 * constant_55555 *
constant_55555 * 5 * 5 * 5),
0x20000000000000 / (constant_55555 * constant_55555 * constant_55555 *
constant_55555 * 5 * 5 * 5 * 5)};
constant_55555 * 5 * 5 * 5)};
};

#if FASTFLOAT_DETAIL_MUST_DEFINE_CONSTEXPR_VARIABLE
Expand Down Expand Up @@ -930,7 +931,9 @@ binary_format<std::float16_t>::max_mantissa_fast_path(int64_t power) {

template <>
inline constexpr int binary_format<std::float16_t>::min_exponent_fast_path() {
return 0;
// w / 10^k with w <= 2^11 and k <= 4 rounds correctly even when evaluated
// in float or double first (checked in script/format_parameters.py).
return -4;
}

template <>
Expand All @@ -942,7 +945,9 @@ binary_format<std::float16_t>::max_exponent_round_to_even() {
template <>
inline constexpr int
binary_format<std::float16_t>::min_exponent_round_to_even() {
return -22;
// -22 covers the normal ties; subnormal ties such as
// 2^-25 = 298023223876953125e-25 need q = -25 and q = -26.
return -26;
}

template <>
Expand All @@ -966,7 +971,8 @@ inline constexpr int binary_format<std::float16_t>::largest_power_of_ten() {

template <>
inline constexpr int binary_format<std::float16_t>::smallest_power_of_ten() {
return -27;
// (10^19 - 1) * 10^-27 < 2^-25, so any q < -26 rounds to zero.
return -26;
}

template <>
Expand Down Expand Up @@ -1053,7 +1059,8 @@ binary_format<std::bfloat16_t>::max_mantissa_fast_path(int64_t power) {

template <>
inline constexpr int binary_format<std::bfloat16_t>::min_exponent_fast_path() {
return 0;
// Same argument as for std::float16_t (w <= 2^8, k <= 3).
return -3;
}

template <>
Expand Down Expand Up @@ -1089,7 +1096,8 @@ inline constexpr int binary_format<std::bfloat16_t>::largest_power_of_ten() {

template <>
inline constexpr int binary_format<std::bfloat16_t>::smallest_power_of_ten() {
return -60;
// (10^19 - 1) * 10^-60 < 2^-134, so any q < -59 rounds to zero.
return -59;
}

template <>
Expand All @@ -1098,6 +1106,24 @@ inline constexpr size_t binary_format<std::bfloat16_t>::max_digits() {
}
#endif // __STDCPP_BFLOAT16_T__

// Whether Clinger's fast path can overflow: only for std::float16_t, where
// 2^11 * 10^4 > 65504.
template <typename T>
inline constexpr bool binary_format<T>::fast_path_can_overflow() {
return double(max_mantissa_fast_path()) *
double(exact_power_of_ten(max_exponent_fast_path())) >
double((std::numeric_limits<T>::max)());
}

// A subnormal needs w * 10^q < 2^(minimum_exponent() + 1), so q is at most
// (minimum_exponent() + 1) * log10(2), with 1233/4096 < log10(2). Only
// std::float16_t has such q in its round-to-even range.
template <typename T>
inline constexpr bool binary_format<T>::subnormal_ties_possible() {
return min_exponent_round_to_even() <=
(((minimum_exponent() + 1) * 1233) >> 12);
}

template <>
inline constexpr uint64_t
binary_format<double>::max_mantissa_fast_path(int64_t power) {
Expand Down
6 changes: 6 additions & 0 deletions include/fast_float/parse_number.h
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Expand Up @@ -221,6 +221,12 @@ clinger_fast_path_impl(uint64_t mantissa, int64_t exponent, bool is_negative,
value = value / binary_format<T>::exact_power_of_ten(-exponent);
} else {
value = value * binary_format<T>::exact_power_of_ten(exponent);
// Only std::float16_t can overflow here (e.g., "656e2"); let the
// slow path report result_out_of_range.
if (binary_format<T>::fast_path_can_overflow() &&
value > (std::numeric_limits<T>::max)()) {
return false;
}
}
if (is_negative) {
value = -value;
Expand Down
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