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Update f16 to have from_bits 

This CL adds a `from_bits` method to the f16 number to allow converting
a uint16_t representation to a f16.

Bug: tint:1581
Change-Id: I80882e74a88411963f0e30423a72cfca40370af1
Reviewed-on: https://dawn-review.googlesource.com/c/dawn/+/109201
Kokoro: Kokoro <noreply+kokoro@google.com>
Reviewed-by: Ben Clayton <bclayton@google.com>
Commit-Queue: dan sinclair <dsinclair@google.com>
This commit is contained in:
dan sinclair 2022-11-09 20:03:09 +00:00 committed by Dawn LUCI CQ
parent 744d0eb4aa
commit 00d0fd5e84
3 changed files with 232 additions and 106 deletions
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317
src/tint/number.cc
View File

@ -20,8 +20,35 @@
#include <ostream>
#include "src/tint/debug.h"
#include "src/tint/utils/bitcast.h"
namespace tint {
namespace {
constexpr uint16_t kF16Nan = 0x7e00u;
constexpr uint16_t kF16PosInf = 0x7c00u;
constexpr uint16_t kF16NegInf = 0xfc00u;
constexpr uint16_t kF16SignMask = 0x8000u;
constexpr uint16_t kF16ExponentMask = 0x7c00u;
constexpr uint16_t kF16MantissaMask = 0x03ffu;
constexpr uint32_t kF16MantissaBits = 10;
constexpr uint32_t kF16ExponentBias = 15;
constexpr uint32_t kF32SignMask = 0x80000000u;
constexpr uint32_t kF32ExponentMask = 0x7f800000u;
constexpr uint32_t kF32MantissaMask = 0x007fffffu;
constexpr uint32_t kF32MantissaBits = 23;
constexpr uint32_t kF32ExponentBias = 127;
constexpr uint32_t kMaxF32BiasedExpForF16NormalNumber = 142;
constexpr uint32_t kMinF32BiasedExpForF16NormalNumber = 113;
constexpr uint32_t kMaxF32BiasedExpForF16SubnormalNumber = 112;
constexpr uint32_t kMinF32BiasedExpForF16SubnormalNumber = 103;
} // namespace
std::ostream& operator<<(std::ostream& out, ConversionFailure failure) {
switch (failure) {
@ -40,19 +67,16 @@ f16::type f16::Quantize(f16::type value) {
if (value < kLowestValue) {
return -std::numeric_limits<f16::type>::infinity();
}
// Below value must be within the finite range of a f16.
// Assert we use binary32 (i.e. float) as underlying type, which has 4 bytes.
static_assert(std::is_same<f16::type, float>());
const uint32_t sign_mask = 0x80000000u; // Mask for the sign bit
const uint32_t exponent_mask = 0x7f800000u; // Mask for 8 exponent bits
uint32_t u32;
memcpy(&u32, &value, 4);
if ((u32 & ~sign_mask) == 0) {
uint32_t u32 = utils::Bitcast<uint32_t>(value);
if ((u32 & ~kF32SignMask) == 0) {
return value; // +/- zero
}
if ((u32 & exponent_mask) == exponent_mask) { // exponent all 1's
if ((u32 & kF32ExponentMask) == kF32ExponentMask) { // exponent all 1's
return value; // inf or nan
}
@ -62,23 +86,27 @@ f16::type f16::Quantize(f16::type value) {
// bits of the original f32 number.
//
// Note:
// f32 has 1 sign bit, 8 exponent bits for biased exponent (i.e. unbiased exponent + 127), and
// 23 mantissa bits. Binary form: s_eeeeeeee_mmmmmmmmmmmmmmmmmmmmmmm
// f16 has 1 sign bit, 5 exponent bits for biased exponent (i.e. unbiased exponent + 15), and
// 10 mantissa bits. Binary form: s_eeeee_mmmmmmmmmm
// * f32 has 1 sign bit, 8 exponent bits for biased exponent (i.e. unbiased exponent + 127), and
// 23 mantissa bits. Binary form: s_eeeeeeee_mmmmmmmmmmmmmmmmmmmmmmm
//
// * f16 has 1 sign bit, 5 exponent bits for biased exponent (i.e. unbiased exponent + 15), and
// 10 mantissa bits. Binary form: s_eeeee_mmmmmmmmmm
//
// The largest finite f16 number has a biased exponent of 11110 in binary, or 30 decimal, and so
// a unbiased exponent of 30 - 15 = 15.
// an unbiased exponent of 30 - 15 = 15.
//
// The smallest finite f16 number has a biased exponent of 00001 in binary, or 1 decimal, and so
// a unbiased exponent of 1 - 15 = -14.
//
// We may follow the argument below:
// 1. All normal or subnormal f16 values, range from 0x1.p-24 to 0x1.ffcp15, are exactly
// representable by normal f32 number.
// representable by a normal f32 number.
// 1.1. We can denote the set of all f32 number that are exact representation of finite f16
// values by `R`.
// 1.2. We can do the quantization by mapping a normal f32 value v (in the f16 finite range)
// to a certain f32 number v' in the set R, which is the largest (by the meaning of absolute
// value) one among all values in R that are no larger than v.
//
// 2. We can decide whether a given normal f32 number v is in the set R, by looking at its
// mantissa bits and biased exponent `e`. Recall that biased exponent e is unbiased exponent +
// 127, and in the range of 1 to 254 for normal f32 number.
@ -99,100 +127,131 @@ f16::type f16::Quantize(f16::type value) {
// equal to 0.0, thus can not be in set R.
// 2.5. If abs(v) = 0, v is in set R and is just +-0.0.
//
// Proof for 2.2:
// Proof for 2.2
// -------------
// Any normal f16 number, in binary form, s_eeeee_mmmmmmmmmm, has value
// (s==0?1:-1)*(1+uint(mmmmm_mmmmm)*(2^-10))*2^(uint(eeeee)-15)
//
// (s == 0 ? 1 : -1) * (1 + uint(mmmmm_mmmmm) * (2^-10)) * 2^(uint(eeeee) - 15)
//
// in which unit(bbbbb) means interprete binary pattern "bbbbb" as unsigned binary number,
// and we have 1 <= uint(eeeee) <= 30.
//
// This value is equal to a normal f32 number with binary
// s_EEEEEEEE_mmmmmmmmmm0000000000000
// where uint(EEEEEEEE) = uint(eeeee) + 112, so that unbiased exponent keep unchanged
//
// where uint(EEEEEEEE) = uint(eeeee) + 112, so that unbiased exponent is kept unchanged
//
// uint(EEEEEEEE) - 127 = uint(eeeee) - 15
//
// and its value is
// (s==0?1:-1)*(1+uint(mmmmm_mmmmm_00000_00000_000)*(2^-23))*2^(uint(EEEEEEEE)-127)
// == (s==0?1:-1)*(1+uint(mmmmm_mmmmm)*(2^-10))*2^(uint(eeeee)-15)
// (s == 0 ? 1 : -1) *
// (1 + uint(mmmmm_mmmmm_00000_00000_000) * (2^-23)) * 2^(uint(EEEEEEEE) - 127)
// == (s == 0 ? 1 : -1) *
// (1 + uint(mmmmm_mmmmm) * (2^-10)) * 2^(uint(eeeee) - 15)
//
// Notice that uint(EEEEEEEE) is in range [113, 142], showing that it is a normal f32 number.
// So we proof that any normal f16 number can be exactly representd by a normal f32 number
// with biased exponent in range [113,142] and the lowest 13 mantissa bits 0.
// So we proved that any normal f16 number can be exactly representd by a normal f32 number
// with biased exponent in range [113, 142] and the lowest 13 mantissa bits 0.
//
// On the other hand, since mantissa bits mmmmmmmmmm are arbitrary, the value of any f32
// that has a biased exponent in range [113, 142] and lowest 13 mantissa bits zero is equal
// to a normal f16 value. Hence we proof 2.2.
// to a normal f16 value. Hence we prove 2.2.
//
// Proof for 2.3:
// Proof for 2.3
// -------------
// Any subnormal f16 number has a binary form of s_00000_mmmmmmmmmm, and its value is
// (s==0?1:-1)*uint(mmmmmmmmmm)*(2^-10)*(2^-14) = (s==0?1:-1)*uint(mmmmmmmmmm)*(2^-24).
// We discuss on bit pattern of mantissa bits mmmmmmmmmm.
// Case 1: mantissa bits has no leading zero bit, s_00000_1mmmmmmmmm
//
// (s == 0 ? 1 : -1) * uint(mmmmmmmmmm) * (2^-10) * (2^-14)
// == (s == 0 ? 1 : -1) * uint(mmmmmmmmmm) * (2^-24).
//
// We discuss the bit pattern of mantissa bits mmmmmmmmmm.
// Case 1: mantissa bits have no leading zero bit, s_00000_1mmmmmmmmm
// In this case the value is
// (s==0?1:-1)*uint(1mmmm_mmmmm)*(2^-10)*(2^-14)
// == (s==0?1:-1)*(uint(1_mmmmm_mmmm)*(2^-9))*(2^-15)
// == (s==0?1:-1)*(1+uint(mmmmm_mmmm)*(2^-9))*(2^-15)
// == (s==0?1:-1)*(1+uint(mmmmm_mmmm0_00000_00000_000)*(2^-23))*(2^-15)
// which is equal to the value of normal f32 number
// (s == 0 ? 1 : -1) * uint(1mmmm_mmmmm) * (2^-10) * (2^-14)
// == (s == 0 ? 1 : -1) * ( uint(1_mmmmm_mmmm) * (2^-9)) * (2^-15)
// == (s == 0 ? 1 : -1) * (1 + uint(mmmmm_mmmm) * (2^-9)) * (2^-15)
// == (s == 0 ? 1 : -1) * (1 + uint(mmmmm_mmmm0_00000_00000_000) * (2^-23)) * (2^-15)
//
// which is equal to the value of the normal f32 number
//
// s_EEEEEEEE_mmmmm_mmmm0_00000_00000_000
// where uint(EEEEEEEE) = -15 + 127 = 112. Hence we proof that any subnormal f16 number
//
// where uint(EEEEEEEE) == -15 + 127 = 112. Hence we proved that any subnormal f16 number
// with no leading zero mantissa bit can be exactly represented by a f32 number with
// biased exponent 112 and the lowest 14 mantissa bits zero, and the value of any f32
// number with biased exponent 112 and the lowest 14 mantissa bits zero are equal to a
// number with biased exponent 112 and the lowest 14 mantissa bits zero is equal to a
// subnormal f16 number with no leading zero mantissa bit.
//
// Case 2: mantissa bits has 1 leading zero bit, s_00000_01mmmmmmmm
// In this case the value is
// (s==0?1:-1)*uint(01mmm_mmmmm)*(2^-10)*(2^-14)
// == (s==0?1:-1)*(uint(01_mmmmm_mmm)*(2^-8))*(2^-16)
// == (s==0?1:-1)*(1+uint(mmmmm_mmm)*(2^-8))*(2^-16)
// == (s==0?1:-1)*(1+uint(mmmmm_mmm00_00000_00000_000)*(2^-23))*(2^-16)
// (s == 0 ? 1 : -1) * uint(01mmm_mmmmm) * (2^-10) * (2^-14)
// == (s == 0 ? 1 : -1) * ( uint(01_mmmmm_mmm) * (2^-8)) * (2^-16)
// == (s == 0 ? 1 : -1) * (1 + uint(mmmmm_mmm) * (2^-8)) * (2^-16)
// == (s == 0 ? 1 : -1) * (1 + uint(mmmmm_mmm00_00000_00000_000) * (2^-23)) * (2^-16)
//
// which is equal to the value of normal f32 number
//
// s_EEEEEEEE_mmmmm_mmm00_00000_00000_000
// where uint(EEEEEEEE) = -16 + 127 = 111. Hence we proof that any subnormal f16 number
//
// where uint(EEEEEEEE) = -16 + 127 = 111. Hence we proved that any subnormal f16 number
// with 1 leading zero mantissa bit can be exactly represented by a f32 number with
// biased exponent 111 and the lowest 15 mantissa bits zero, and the value of any f32
// number with biased exponent 111 and the lowest 15 mantissa bits zero are equal to a
// number with biased exponent 111 and the lowest 15 mantissa bits zero is equal to a
// subnormal f16 number with 1 leading zero mantissa bit.
//
// Case 3 to case 8: ......
// Case 9: mantissa bits has 8 leading zero bit, s_00000_000000001m
//
// Case 9: mantissa bits has 8 leading zero bits, s_00000_000000001m
// In this case the value is
// (s==0?1:-1)*uint(00000_0001m)*(2^-10)*(2^-14)
// == (s==0?1:-1)*(uint(000000001_m)*(2^-1))*(2^-23)
// == (s==0?1:-1)*(1+uint(m)*(2^-1))*(2^-23)
// == (s==0?1:-1)*(1+uint(m0000_00000_00000_00000_000)*(2^-23))*(2^-23)
// (s == 0 ? 1 : -1) * uint(00000_0001m) * (2^-10) * (2^-14)
// == (s == 0 ? 1 : -1) * ( uint(000000001_m) * (2^-1)) * (2^-23)
// == (s == 0 ? 1 : -1) * (1 + uint(m) * (2^-1)) * (2^-23)
// == (s == 0 ? 1 : -1) * (1 + uint(m0000_00000_00000_00000_000) * (2^-23)) * (2^-23)
//
// which is equal to the value of normal f32 number
//
// s_EEEEEEEE_m0000_00000_00000_00000_000
// where uint(EEEEEEEE) = -23 + 127 = 104. Hence we proof that any subnormal f16 number
//
// where uint(EEEEEEEE) = -23 + 127 = 104. Hence we proved that any subnormal f16 number
// with 8 leading zero mantissa bit can be exactly represented by a f32 number with
// biased exponent 104 and the lowest 22 mantissa bits zero, and the value of any f32
// number with biased exponent 104 and the lowest 22 mantissa bits zero are equal to a
// subnormal f16 number with 8 leading zero mantissa bit.
// Case 10: mantissa bits has 9 leading zero bit, s_00000_0000000001
// In this case the value is just +-2^-24 = +-0x1.0p-24,
//
// Case 10: mantissa bits has 9 leading zero bits, s_00000_0000000001
// In this case the value is just +-2^-24 == +-0x1.0p-24,
// the f32 number has biased exponent 103 and all 23 mantissa bits zero.
// Case 11: mantissa bits has 10 leading zero bit, s_00000_0000000000, just 0.0
// Concluding all these case, we proof that any subnormal f16 number with N leading zero
// mantissa bit can be exactly represented by a f32 number with biased exponent 112-N and the
// lowest 14+N mantissa bits zero, and the value of any f32 number with biased exponent 112-N (=
// e) and the lowest 14+N (= 126-e) mantissa bits zero are equal to a subnormal f16 number with
// N leading zero mantissa bit. N is in range [0, 9], so the f32 number's biased exponent e is
// in range [103, 112], or unbiased exponent in [-24, -15].
//
// Case 11: mantissa bits has 10 leading zero bits, s_00000_0000000000, just 0.0
//
// Concluding all these case, we proved that any subnormal f16 number with N leading zero
// mantissa bit can be exactly represented by a f32 number with biased exponent 112 - N and the
// lowest 14 + N mantissa bits zero, and the value of any f32 number with biased exponent
// 112 - N (= e) and the lowest 14 + N (= 126 - e) mantissa bits zero are equal to a subnormal
// f16 number with N leading zero mantissa bits. N is in range [0, 9], so the f32 number's
// biased exponent e is in range [103, 112], or unbiased exponent in [-24, -15].
float abs_value = std::fabs(value);
if (abs_value >= kSmallestValue) {
// Value falls in the normal f16 range, quantize it to a normal f16 value by masking out
// lowest 13 mantissa bits.
u32 = u32 & ~((1u << 13) - 1);
u32 = u32 & ~((1u << (kF32MantissaBits - kF16MantissaBits)) - 1);
} else if (abs_value >= kSmallestSubnormalValue) {
// Value should be quantized to a subnormal f16 value.
// Get the biased exponent `e` of f32 value, e.g. value 127 representing exponent 2^0.
uint32_t biased_exponent_original = (u32 & exponent_mask) >> 23;
uint32_t biased_exponent_original = (u32 & kF32ExponentMask) >> kF32MantissaBits;
// Since we ensure that kSmallestValue = 0x1f-14 > abs(value) >= kSmallestSubnormalValue =
// 0x1f-24, value will have a unbiased exponent in range -24 to -15 (inclusive), and the
// corresponding biased exponent in f32 is in range 103 to 112 (inclusive).
TINT_ASSERT(Semantic,
(103 <= biased_exponent_original) && (biased_exponent_original <= 112));
(kMinF32BiasedExpForF16SubnormalNumber <= biased_exponent_original) &&
(biased_exponent_original <= kMaxF32BiasedExpForF16SubnormalNumber));
// As we have proved, masking out the lowest 126-e mantissa bits of input value will result
// in a valid subnormal f16 value, which is exactly the required quantization result.
uint32_t discard_bits = 126 - biased_exponent_original; // In range 14 to 23 (inclusive)
TINT_ASSERT(Semantic, (14 <= discard_bits) && (discard_bits <= 23));
TINT_ASSERT(Semantic, (14 <= discard_bits) && (discard_bits <= kF32MantissaBits));
uint32_t discard_mask = (1u << discard_bits) - 1;
u32 = u32 & ~discard_mask;
} else {
@ -200,15 +259,11 @@ f16::type f16::Quantize(f16::type value) {
// to zero.
return value > 0 ? 0.0 : -0.0;
}
memcpy(&value, &u32, 4);
return value;
return utils::Bitcast<f16::type>(u32);
}
uint16_t f16::BitsRepresentation() const {
constexpr uint16_t f16_nan = 0x7e00u;
constexpr uint16_t f16_pos_inf = 0x7c00u;
constexpr uint16_t f16_neg_inf = 0xfc00u;
// Assert we use binary32 (i.e. float) as underlying type, which has 4 bytes.
static_assert(std::is_same<f16::type, float>());
@ -216,11 +271,11 @@ uint16_t f16::BitsRepresentation() const {
// Inf, or exactly representable by normal or subnormal f16.
if (std::isnan(value)) {
return f16_nan;
return kF16Nan;
}
if (std::isinf(value)) {
return value > 0 ? f16_pos_inf : f16_neg_inf;
return value > 0 ? kF16PosInf : kF16NegInf;
}
// Now quantized_value must be a finite f16 exactly-representable value.
@ -230,56 +285,37 @@ uint16_t f16::BitsRepresentation() const {
// |------------------|----------------|------------------|------------------|
// | +/- zero | \ | 0 | 0 |
// | Subnormal f16 | [-24, -15] | 0 | [103, 112] |
// | Normal f16 | [-14, 15] | [1, 30] | [113, 142] |
// | Normal f16 | [-14, 15] | [1, 30] | [113, 142] |
// ---------------------------------------------------------------------------
constexpr uint32_t max_f32_biased_exp_for_f16_normal_number = 142;
constexpr uint32_t min_f32_biased_exp_for_f16_normal_number = 113;
constexpr uint32_t max_f32_biased_exp_for_f16_subnormal_number = 112;
constexpr uint32_t min_f32_biased_exp_for_f16_subnormal_number = 103;
uint32_t f32_bit_pattern = utils::Bitcast<uint32_t>(value);
uint32_t f32_biased_exponent = (f32_bit_pattern & kF32ExponentMask) >> kF32MantissaBits;
uint32_t f32_mantissa = f32_bit_pattern & kF32MantissaMask;
constexpr uint32_t f32_sign_mask = 0x80000000u;
constexpr uint32_t f32_exp_mask = 0x7f800000u;
constexpr uint32_t f32_mantissa_mask = 0x007fffffu;
constexpr uint32_t f32_mantissa_bis_number = 23;
constexpr uint32_t f32_exp_bias = 127;
uint16_t f16_sign_part = static_cast<uint16_t>((f32_bit_pattern & kF32SignMask) >> 16);
TINT_ASSERT(Semantic, (f16_sign_part & ~kF16SignMask) == 0);
constexpr uint16_t f16_sign_mask = 0x8000u;
constexpr uint16_t f16_exp_mask = 0x7c00u;
constexpr uint16_t f16_mantissa_mask = 0x03ffu;
constexpr uint32_t f16_mantissa_bis_number = 10;
constexpr uint32_t f16_exp_bias = 15;
uint32_t f32_bit_pattern;
memcpy(&f32_bit_pattern, &value, 4);
uint32_t f32_biased_exponent = (f32_bit_pattern & f32_exp_mask) >> f32_mantissa_bis_number;
uint32_t f32_mantissa = f32_bit_pattern & f32_mantissa_mask;
uint16_t f16_sign_part = static_cast<uint16_t>((f32_bit_pattern & f32_sign_mask) >> 16);
TINT_ASSERT(Semantic, (f16_sign_part & ~f16_sign_mask) == 0);
if ((f32_bit_pattern & ~f32_sign_mask) == 0) {
if ((f32_bit_pattern & ~kF32SignMask) == 0) {
// +/- zero
return f16_sign_part;
}
if ((min_f32_biased_exp_for_f16_normal_number <= f32_biased_exponent) &&
(f32_biased_exponent <= max_f32_biased_exp_for_f16_normal_number)) {
if ((kMinF32BiasedExpForF16NormalNumber <= f32_biased_exponent) &&
(f32_biased_exponent <= kMaxF32BiasedExpForF16NormalNumber)) {
// Normal f16
uint32_t f16_biased_exponent = f32_biased_exponent - f32_exp_bias + f16_exp_bias;
uint16_t f16_exp_part =
static_cast<uint16_t>(f16_biased_exponent << f16_mantissa_bis_number);
uint16_t f16_mantissa_part = static_cast<uint16_t>(
f32_mantissa >> (f32_mantissa_bis_number - f16_mantissa_bis_number));
uint32_t f16_biased_exponent = f32_biased_exponent - kF32ExponentBias + kF16ExponentBias;
uint16_t f16_exp_part = static_cast<uint16_t>(f16_biased_exponent << kF16MantissaBits);
uint16_t f16_mantissa_part =
static_cast<uint16_t>(f32_mantissa >> (kF32MantissaBits - kF16MantissaBits));
TINT_ASSERT(Semantic, (f16_exp_part & ~f16_exp_mask) == 0);
TINT_ASSERT(Semantic, (f16_mantissa_part & ~f16_mantissa_mask) == 0);
TINT_ASSERT(Semantic, (f16_exp_part & ~kF16ExponentMask) == 0);
TINT_ASSERT(Semantic, (f16_mantissa_part & ~kF16MantissaMask) == 0);
return f16_sign_part | f16_exp_part | f16_mantissa_part;
}
if ((min_f32_biased_exp_for_f16_subnormal_number <= f32_biased_exponent) &&
(f32_biased_exponent <= max_f32_biased_exp_for_f16_subnormal_number)) {
if ((kMinF32BiasedExpForF16SubnormalNumber <= f32_biased_exponent) &&
(f32_biased_exponent <= kMaxF32BiasedExpForF16SubnormalNumber)) {
// Subnormal f16
// The resulting exp bits are always 0, and the mantissa bits should be handled specially.
uint16_t f16_exp_part = 0;
@ -287,15 +323,15 @@ uint16_t f16::BitsRepresentation() const {
// of value is of the minimum, i.e. -24; and have all 10 mantissa bits valid if the unbiased
// exponent of value is of the maximum, i.e. -15.
uint32_t f16_valid_mantissa_bits =
f32_biased_exponent - min_f32_biased_exp_for_f16_subnormal_number + 1;
f32_biased_exponent - kMinF32BiasedExpForF16SubnormalNumber + 1;
// The resulting f16 mantissa part comes from right-shifting the f32 mantissa bits with
// leading 1 added.
uint16_t f16_mantissa_part =
static_cast<uint16_t>((f32_mantissa | (f32_mantissa_mask + 1)) >>
(f32_mantissa_bis_number + 1 - f16_valid_mantissa_bits));
static_cast<uint16_t>((f32_mantissa | (kF32MantissaMask + 1)) >>
(kF32MantissaBits + 1 - f16_valid_mantissa_bits));
TINT_ASSERT(Semantic, (1 <= f16_valid_mantissa_bits) &&
(f16_valid_mantissa_bits <= f16_mantissa_bis_number));
(f16_valid_mantissa_bits <= kF16MantissaBits));
TINT_ASSERT(Semantic, (f16_mantissa_part & ~((1u << f16_valid_mantissa_bits) - 1)) == 0);
TINT_ASSERT(Semantic, (f16_mantissa_part != 0));
@ -305,7 +341,76 @@ uint16_t f16::BitsRepresentation() const {
// Neither zero, subnormal f16 or normal f16, shall never hit.
tint::diag::List diag;
TINT_UNREACHABLE(Semantic, diag);
return f16_nan;
return kF16Nan;
}
// static
Number<detail::NumberKindF16> f16::FromBits(uint16_t bits) {
// Assert we use binary32 (i.e. float) as underlying type, which has 4 bytes.
static_assert(std::is_same<f16::type, float>());
if (bits == kF16PosInf) {
return f16(std::numeric_limits<f16::type>::infinity());
}
if (bits == kF16NegInf) {
return f16(-std::numeric_limits<f16::type>::infinity());
}
auto f16_sign_bit = uint32_t(bits & kF16SignMask);
// If none of the other bits are set we have a 0. If only the sign bit is set we have a -0.
if ((bits & ~kF16SignMask) == 0) {
return f16(f16_sign_bit > 0 ? -0.f : 0.f);
}
auto f16_mantissa = uint32_t(bits & kF16MantissaMask);
auto f16_biased_exponent = uint32_t(bits & kF16ExponentMask);
// F16 NaN has all expoennt bits set and at least one mantissa bit set
if (((f16_biased_exponent & kF16ExponentMask) == kF16ExponentMask) && f16_mantissa != 0) {
return f16(std::numeric_limits<f16::type>::quiet_NaN());
}
// Shift the exponent over to be a regular number.
f16_biased_exponent >>= kF16MantissaBits;
// Add the F32 bias and remove the F16 bias.
uint32_t f32_biased_exponent = f16_biased_exponent + kF32ExponentBias - kF16ExponentBias;
if (f16_biased_exponent == 0) {
// Subnormal number
//
// All subnormal F16 values can be represented as normal F32 values. Shift the mantissa and
// set the exponent as if this was a normal f16 value.
// While the first F16 exponent bit is not set
constexpr uint32_t kF16FirstExponentBit = 0x0400;
while ((f16_mantissa & kF16FirstExponentBit) == 0) {
// Shift the mantissa to the left
f16_mantissa <<= 1;
// Decrease the biased exponent to counter the shift
f32_biased_exponent -= 1;
}
// Remove the first exponent bit from the mantissa value
f16_mantissa &= ~kF16FirstExponentBit;
// Increase the exponent to deal with the masked off value.
f32_biased_exponent += 1;
}
// The mantissa bits are shifted over the difference in mantissa size to be in the F32 location.
uint32_t f32_mantissa = f16_mantissa << (kF32MantissaBits - kF16MantissaBits);
// Shift the exponent to the F32 exponent position before the mantissa.
f32_biased_exponent <<= kF32MantissaBits;
// Shift the sign bit over to the f32 sign bit position
uint32_t f32_sign_bit = f16_sign_bit << 16;
// Combine values together into the F32 value as a uint32_t.
uint32_t val = f32_sign_bit | f32_biased_exponent | f32_mantissa;
// Bitcast to a F32 and then store into the F16 Number
return f16(utils::Bitcast<f16::type>(val));
}
} // namespace tint

5
src/tint/number.h
View File

@ -237,6 +237,11 @@ struct Number<detail::NumberKindF16> : NumberBase<Number<detail::NumberKindF16>>
/// will be 0xfc00u.
uint16_t BitsRepresentation() const;
/// Creates an f16 value from the uint16_t bit representation.
/// @param bits the bits to convert from
/// @returns the binary16 value based off the provided bit pattern.
static Number<detail::NumberKindF16> FromBits(uint16_t bits);
/// @param value the input float32 value
/// @returns the float32 value quantized to the smaller float16 value, through truncation of the
/// mantissa bits (no rounding). If the float32 value is too large (positive or negative) to be

16
src/tint/number_test.cc
View File

@ -268,6 +268,22 @@ TEST_P(NumberF16Test, BitsRepresentation) {
EXPECT_EQ(f16(input_value).BitsRepresentation(), representation);
}
TEST_P(NumberF16Test, FromBits) {
float input_value = GetParam().quantized_value;
uint16_t representation = GetParam().f16_bit_pattern;
std::stringstream ss;
ss << "binary16 bits representation = " << std::hex << std::showbase << representation
<< " expected value = " << input_value;
SCOPED_TRACE(ss.str());
if (std::isnan(input_value)) {
EXPECT_TRUE(std::isnan(f16::FromBits(representation)));
} else {
EXPECT_EQ(f16::FromBits(representation), f16(input_value));
}
}
INSTANTIATE_TEST_SUITE_P(
NumberF16Test,
NumberF16Test,