in horovod/common/half.h [79:139]
inline void Float2HalfBits(const float* src, unsigned short* dest) {
// software implementation rounds toward nearest even
unsigned const& s = *reinterpret_cast<unsigned const*>(src);
uint16_t sign = uint16_t((s >> 16) & 0x8000);
int16_t exp = uint16_t(((s >> 23) & 0xff) - 127);
int mantissa = s & 0x7fffff;
uint16_t u = 0;
if ((s & 0x7fffffff) == 0) {
// sign-preserving zero
*dest = sign;
return;
}
if (exp > 15) {
if (exp == 128 && mantissa) {
// not a number
u = 0x7fff;
} else {
// overflow to infinity
u = sign | 0x7c00;
}
*dest = u;
return;
}
int sticky_bit = 0;
if (exp >= -14) {
// normal fp32 to normal fp16
exp = uint16_t(exp + uint16_t(15));
u = uint16_t(((exp & 0x1f) << 10));
u = uint16_t(u | (mantissa >> 13));
} else {
// normal single-precision to subnormal half_t-precision representation
int rshift = (-14 - exp);
if (rshift < 32) {
mantissa |= (1 << 23);
sticky_bit = ((mantissa & ((1 << rshift) - 1)) != 0);
mantissa = (mantissa >> rshift);
u = (uint16_t(mantissa >> 13) & 0x3ff);
} else {
mantissa = 0;
u = 0;
}
}
// round to nearest even
int round_bit = ((mantissa >> 12) & 1);
sticky_bit |= ((mantissa & ((1 << 12) - 1)) != 0);
if ((round_bit && sticky_bit) || (round_bit && (u & 1))) {
u = uint16_t(u + 1);
}
u |= sign;
*dest = u;
}