static inline uint32_t _half_to_float( uint16_t h )
{
const uint32_t h_e_mask = _uint32_li( 0x00007c00 );
const uint32_t h_m_mask = _uint32_li( 0x000003ff );
const uint32_t h_s_mask = _uint32_li( 0x00008000 );
const uint32_t h_f_s_pos_offset = _uint32_li( 0x00000010 );
const uint32_t h_f_e_pos_offset = _uint32_li( 0x0000000d );
const uint32_t h_f_bias_offset = _uint32_li( 0x0001c000 );
const uint32_t f_e_mask = _uint32_li( 0x7f800000 );
const uint32_t f_m_mask = _uint32_li( 0x007fffff );
const uint32_t h_f_e_denorm_bias = _uint32_li( 0x0000007e );
const uint32_t h_f_m_denorm_sa_bias = _uint32_li( 0x00000008 );
const uint32_t f_e_pos = _uint32_li( 0x00000017 );
const uint32_t h_e = _uint32_and( h, h_e_mask );
const uint32_t h_m = _uint32_and( h, h_m_mask );
const uint32_t h_s = _uint32_and( h, h_s_mask );
const uint32_t h_e_f_bias = _uint32_add( h_e, h_f_bias_offset );
const uint32_t h_m_nlz = _uint32_cntlz( h_m );
const uint32_t f_s = _uint32_sll( h_s, h_f_s_pos_offset );
const uint32_t f_e = _uint32_sll( h_e_f_bias, h_f_e_pos_offset );
const uint32_t f_m = _uint32_sll( h_m, h_f_e_pos_offset );
const uint32_t h_f_m_sa = _uint32_sub( h_m_nlz, h_f_m_denorm_sa_bias );
const uint32_t f_e_denorm_unpacked = _uint32_sub( h_f_e_denorm_bias, h_f_m_sa );
const uint32_t h_f_m = _uint32_sll( h_m, h_f_m_sa );
const uint32_t f_m_denorm = _uint32_and( h_f_m, f_m_mask );
const uint32_t f_e_denorm = _uint32_sll( f_e_denorm_unpacked, f_e_pos );
const uint32_t f_em_denorm = _uint32_or( f_e_denorm, f_m_denorm );
const uint32_t is_e_eqz_msb = _uint32_dec( h_e );
const uint32_t is_m_nez_msb = _uint32_neg( h_m );
const uint32_t is_e_flagged_msb = _uint32_sub( h_e_mask, is_e_eqz_msb );
const uint32_t is_denorm_msb = _uint32_and( is_e_eqz_msb, is_m_nez_msb );
const uint32_t is_ninf_msb = _uint32_andc( is_m_nez_msb, is_e_flagged_msb );
const uint32_t is_zero_msb = _uint32_andc( is_e_eqz_msb, is_m_nez_msb );
const uint32_t is_ninf = _uint32_ext( is_ninf_msb );
const uint32_t is_zero = _uint32_ext( is_zero_msb );
const uint32_t f_e_flagged_result = _uint32_muxs( is_e_flagged_msb, f_e_mask, f_e );
const uint32_t f_m_inf_result = _uint32_and( f_m, is_ninf );
const uint32_t f_em_result_partial = _uint32_or( f_e_flagged_result, f_m_inf_result );
const uint32_t f_em_denorm_result = _uint32_muxs( is_denorm_msb, f_em_denorm, f_em_result_partial );
const uint32_t f_em_result = _uint32_andc( f_em_denorm_result, is_zero );
const uint32_t f_result = _uint32_or( f_s, f_em_result );
return (f_result);
}
static inline uint32_t _uint32_muxs( uint32_t test, uint32_t a, uint32_t b )
{
const uint32_t mask = _uint32_ext( test );
const uint32_t sel_a = _uint32_and( a, mask );
const uint32_t sel_b = _uint32_andc( b, mask );
const uint32_t result = _uint32_or( sel_a, sel_b );
return (result);
}
// Select on Sign bit
static inline uint32 _uint32_sels( uint32 test, uint32 a, uint32 b )
{
const uint32 mask = _uint32_ext( test );
const uint32 sel_a = _uint32_and( a, mask );
const uint32 sel_b = _uint32_andc( b, mask );
const uint32 result = _uint32_or( sel_a, sel_b );
return (result);
}
uint32_t
half_to_float( uint16_t h )
{
const uint32_t h_e_mask = _uint32_li( 0x00007c00 );
const uint32_t h_m_mask = _uint32_li( 0x000003ff );
const uint32_t h_s_mask = _uint32_li( 0x00008000 );
const uint32_t h_f_s_pos_offset = _uint32_li( 0x00000010 );
const uint32_t h_f_e_pos_offset = _uint32_li( 0x0000000d );
const uint32_t h_f_bias_offset = _uint32_li( 0x0001c000 );
const uint32_t f_e_mask = _uint32_li( 0x7f800000 );
const uint32_t f_m_mask = _uint32_li( 0x007fffff );
const uint32_t h_f_e_denorm_bias = _uint32_li( 0x0000007e );
const uint32_t h_f_m_denorm_sa_bias = _uint32_li( 0x00000008 );
const uint32_t f_e_pos = _uint32_li( 0x00000017 );
const uint32_t h_e_mask_minus_one = _uint32_li( 0x00007bff );
const uint32_t h_e = _uint32_and( h, h_e_mask );
const uint32_t h_m = _uint32_and( h, h_m_mask );
const uint32_t h_s = _uint32_and( h, h_s_mask );
const uint32_t h_e_f_bias = _uint32_add( h_e, h_f_bias_offset );
const uint32_t h_m_nlz = _uint32_cntlz( h_m );
const uint32_t f_s = _uint32_sll( h_s, h_f_s_pos_offset );
const uint32_t f_e = _uint32_sll( h_e_f_bias, h_f_e_pos_offset );
const uint32_t f_m = _uint32_sll( h_m, h_f_e_pos_offset );
const uint32_t f_em = _uint32_or( f_e, f_m );
const uint32_t h_f_m_sa = _uint32_sub( h_m_nlz, h_f_m_denorm_sa_bias );
const uint32_t f_e_denorm_unpacked = _uint32_sub( h_f_e_denorm_bias, h_f_m_sa );
const uint32_t h_f_m = _uint32_sll( h_m, h_f_m_sa );
const uint32_t f_m_denorm = _uint32_and( h_f_m, f_m_mask );
const uint32_t f_e_denorm = _uint32_sll( f_e_denorm_unpacked, f_e_pos );
const uint32_t f_em_denorm = _uint32_or( f_e_denorm, f_m_denorm );
const uint32_t f_em_nan = _uint32_or( f_e_mask, f_m );
const uint32_t is_e_eqz_msb = _uint32_dec( h_e );
const uint32_t is_m_nez_msb = _uint32_neg( h_m );
const uint32_t is_e_flagged_msb = _uint32_sub( h_e_mask_minus_one, h_e );
const uint32_t is_zero_msb = _uint32_andc( is_e_eqz_msb, is_m_nez_msb );
const uint32_t is_inf_msb = _uint32_andc( is_e_flagged_msb, is_m_nez_msb );
const uint32_t is_denorm_msb = _uint32_and( is_m_nez_msb, is_e_eqz_msb );
const uint32_t is_nan_msb = _uint32_and( is_e_flagged_msb, is_m_nez_msb );
const uint32_t is_zero = _uint32_ext( is_zero_msb );
const uint32_t f_zero_result = _uint32_andc( f_em, is_zero );
const uint32_t f_denorm_result = _uint32_sels( is_denorm_msb, f_em_denorm, f_zero_result );
const uint32_t f_inf_result = _uint32_sels( is_inf_msb, f_e_mask, f_denorm_result );
const uint32_t f_nan_result = _uint32_sels( is_nan_msb, f_em_nan, f_inf_result );
const uint32_t f_result = _uint32_or( f_s, f_nan_result );
return (f_result);
}
// half_mul
// --------
//
// May have 0 or 1 ulp difference from the following result:
// (Round to nearest)
// NOTE: Rounding mode differs between conversion and multiply
//
// union FLOAT_32
// {
// float f32;
// uint32_t u32;
// };
//
// union FLOAT_32 fx = { .u32 = half_to_float( x ) };
// union FLOAT_32 fy = { .u32 = half_to_float( y ) };
// union FLOAT_32 fz = { .f32 = fx.f32 * fy.f32 };
// uint16_t z = float_to_half( fz );
//
uint16_t
half_mul( uint16_t x, uint16_t y )
{
const uint32_t one = _uint32_li( 0x00000001 );
const uint32_t h_s_mask = _uint32_li( 0x00008000 );
const uint32_t h_e_mask = _uint32_li( 0x00007c00 );
const uint32_t h_m_mask = _uint32_li( 0x000003ff );
const uint32_t h_m_hidden = _uint32_li( 0x00000400 );
const uint32_t h_e_pos = _uint32_li( 0x0000000a );
const uint32_t h_e_bias = _uint32_li( 0x0000000f );
const uint32_t h_m_bit_count = _uint32_li( 0x0000000a );
const uint32_t h_m_bit_half_count = _uint32_li( 0x00000005 );
const uint32_t h_nan_min = _uint32_li( 0x00007c01 );
const uint32_t h_e_mask_minus_one = _uint32_li( 0x00007bff );
const uint32_t h_snan = _uint32_li( 0x0000fe00 );
const uint32_t m_round_overflow_bit = _uint32_li( 0x00000020 );
const uint32_t m_hidden_bit = _uint32_li( 0x00100000 );
const uint32_t a_s = _uint32_and( x, h_s_mask );
const uint32_t b_s = _uint32_and( y, h_s_mask );
const uint32_t c_s = _uint32_xor( a_s, b_s );
const uint32_t x_e = _uint32_and( x, h_e_mask );
const uint32_t x_e_eqz_msb = _uint32_dec( x_e );
const uint32_t a = _uint32_sels( x_e_eqz_msb, y, x );
const uint32_t b = _uint32_sels( x_e_eqz_msb, x, y );
const uint32_t a_e = _uint32_and( a, h_e_mask );
const uint32_t b_e = _uint32_and( b, h_e_mask );
const uint32_t a_m = _uint32_and( a, h_m_mask );
const uint32_t b_m = _uint32_and( b, h_m_mask );
const uint32_t a_e_amount = _uint32_srl( a_e, h_e_pos );
const uint32_t b_e_amount = _uint32_srl( b_e, h_e_pos );
const uint32_t a_m_with_hidden = _uint32_or( a_m, h_m_hidden );
const uint32_t b_m_with_hidden = _uint32_or( b_m, h_m_hidden );
const uint32_t c_m_normal = _uint32_mul( a_m_with_hidden, b_m_with_hidden );
const uint32_t c_m_denorm_biased = _uint32_mul( a_m_with_hidden, b_m );
const uint32_t c_e_denorm_unbias_e = _uint32_sub( h_e_bias, a_e_amount );
const uint32_t c_m_denorm_round_amount = _uint32_and( c_m_denorm_biased, h_m_mask );
const uint32_t c_m_denorm_rounded = _uint32_add( c_m_denorm_biased, c_m_denorm_round_amount );
const uint32_t c_m_denorm_inplace = _uint32_srl( c_m_denorm_rounded, h_m_bit_count );
const uint32_t c_m_denorm_unbiased = _uint32_srl( c_m_denorm_inplace, c_e_denorm_unbias_e );
const uint32_t c_m_denorm = _uint32_and( c_m_denorm_unbiased, h_m_mask );
const uint32_t c_e_amount_biased = _uint32_add( a_e_amount, b_e_amount );
const uint32_t c_e_amount_unbiased = _uint32_sub( c_e_amount_biased, h_e_bias );
const uint32_t is_c_e_unbiased_underflow = _uint32_ext( c_e_amount_unbiased );
const uint32_t c_e_underflow_half_sa = _uint32_neg( c_e_amount_unbiased );
const uint32_t c_e_underflow_sa = _uint32_sll( c_e_underflow_half_sa, one );
const uint32_t c_m_underflow = _uint32_srl( c_m_normal, c_e_underflow_sa );
const uint32_t c_e_underflow_added = _uint32_andc( c_e_amount_unbiased, is_c_e_unbiased_underflow );
const uint32_t c_m_underflow_added = _uint32_selb( is_c_e_unbiased_underflow, c_m_underflow, c_m_normal );
const uint32_t is_mul_overflow_test = _uint32_and( c_e_underflow_added, m_round_overflow_bit );
const uint32_t is_mul_overflow_msb = _uint32_neg( is_mul_overflow_test );
const uint32_t c_e_norm_radix_corrected = _uint32_inc( c_e_underflow_added );
const uint32_t c_m_norm_radix_corrected = _uint32_srl( c_m_underflow_added, one );
const uint32_t c_m_norm_hidden_bit = _uint32_and( c_m_norm_radix_corrected, m_hidden_bit );
const uint32_t is_c_m_norm_no_hidden_msb = _uint32_dec( c_m_norm_hidden_bit );
const uint32_t c_m_norm_lo = _uint32_srl( c_m_norm_radix_corrected, h_m_bit_half_count );
const uint32_t c_m_norm_lo_nlz = _uint16_cntlz( c_m_norm_lo );
const uint32_t is_c_m_hidden_nunderflow_msb = _uint32_sub( c_m_norm_lo_nlz, c_e_norm_radix_corrected );
const uint32_t is_c_m_hidden_underflow_msb = _uint32_not( is_c_m_hidden_nunderflow_msb );
const uint32_t is_c_m_hidden_underflow = _uint32_ext( is_c_m_hidden_underflow_msb );
const uint32_t c_m_hidden_underflow_normalized_sa = _uint32_srl( c_m_norm_lo_nlz, one );
const uint32_t c_m_hidden_underflow_normalized = _uint32_sll( c_m_norm_radix_corrected, c_m_hidden_underflow_normalized_sa );
const uint32_t c_m_hidden_normalized = _uint32_sll( c_m_norm_radix_corrected, c_m_norm_lo_nlz );
const uint32_t c_e_hidden_normalized = _uint32_sub( c_e_norm_radix_corrected, c_m_norm_lo_nlz );
const uint32_t c_e_hidden = _uint32_andc( c_e_hidden_normalized, is_c_m_hidden_underflow );
const uint32_t c_m_hidden = _uint32_sels( is_c_m_hidden_underflow_msb, c_m_hidden_underflow_normalized, c_m_hidden_normalized );
const uint32_t c_m_normalized = _uint32_sels( is_c_m_norm_no_hidden_msb, c_m_hidden, c_m_norm_radix_corrected );
const uint32_t c_e_normalized = _uint32_sels( is_c_m_norm_no_hidden_msb, c_e_hidden, c_e_norm_radix_corrected );
const uint32_t c_m_norm_round_amount = _uint32_and( c_m_normalized, h_m_mask );
const uint32_t c_m_norm_rounded = _uint32_add( c_m_normalized, c_m_norm_round_amount );
const uint32_t is_round_overflow_test = _uint32_and( c_e_normalized, m_round_overflow_bit );
const uint32_t is_round_overflow_msb = _uint32_neg( is_round_overflow_test );
const uint32_t c_m_norm_inplace = _uint32_srl( c_m_norm_rounded, h_m_bit_count );
const uint32_t c_m = _uint32_and( c_m_norm_inplace, h_m_mask );
const uint32_t c_e_norm_inplace = _uint32_sll( c_e_normalized, h_e_pos );
const uint32_t c_e = _uint32_and( c_e_norm_inplace, h_e_mask );
const uint32_t c_em_nan = _uint32_or( h_e_mask, a_m );
const uint32_t c_nan = _uint32_or( a_s, c_em_nan );
const uint32_t c_denorm = _uint32_or( c_s, c_m_denorm );
const uint32_t c_inf = _uint32_or( c_s, h_e_mask );
const uint32_t c_em_norm = _uint32_or( c_e, c_m );
const uint32_t is_a_e_flagged_msb = _uint32_sub( h_e_mask_minus_one, a_e );
const uint32_t is_b_e_flagged_msb = _uint32_sub( h_e_mask_minus_one, b_e );
const uint32_t is_a_e_eqz_msb = _uint32_dec( a_e );
const uint32_t is_a_m_eqz_msb = _uint32_dec( a_m );
const uint32_t is_b_e_eqz_msb = _uint32_dec( b_e );
const uint32_t is_b_m_eqz_msb = _uint32_dec( b_m );
const uint32_t is_b_eqz_msb = _uint32_and( is_b_e_eqz_msb, is_b_m_eqz_msb );
const uint32_t is_a_eqz_msb = _uint32_and( is_a_e_eqz_msb, is_a_m_eqz_msb );
const uint32_t is_c_nan_via_a_msb = _uint32_andc( is_a_e_flagged_msb, is_b_e_flagged_msb );
const uint32_t is_c_nan_via_b_msb = _uint32_andc( is_b_e_flagged_msb, is_b_m_eqz_msb );
const uint32_t is_c_nan_msb = _uint32_or( is_c_nan_via_a_msb, is_c_nan_via_b_msb );
const uint32_t is_c_denorm_msb = _uint32_andc( is_b_e_eqz_msb, is_a_e_flagged_msb );
const uint32_t is_a_inf_msb = _uint32_and( is_a_e_flagged_msb, is_a_m_eqz_msb );
const uint32_t is_c_snan_msb = _uint32_and( is_a_inf_msb, is_b_eqz_msb );
const uint32_t is_c_nan_min_via_a_msb = _uint32_and( is_a_e_flagged_msb, is_b_eqz_msb );
const uint32_t is_c_nan_min_via_b_msb = _uint32_and( is_b_e_flagged_msb, is_a_eqz_msb );
const uint32_t is_c_nan_min_msb = _uint32_or( is_c_nan_min_via_a_msb, is_c_nan_min_via_b_msb );
const uint32_t is_c_inf_msb = _uint32_or( is_a_e_flagged_msb, is_b_e_flagged_msb );
const uint32_t is_overflow_msb = _uint32_or( is_round_overflow_msb, is_mul_overflow_msb );
const uint32_t c_em_overflow_result = _uint32_sels( is_overflow_msb, h_e_mask, c_em_norm );
const uint32_t c_common_result = _uint32_or( c_s, c_em_overflow_result );
const uint32_t c_zero_result = _uint32_sels( is_b_eqz_msb, c_s, c_common_result );
const uint32_t c_nan_result = _uint32_sels( is_c_nan_msb, c_nan, c_zero_result );
const uint32_t c_nan_min_result = _uint32_sels( is_c_nan_min_msb, h_nan_min, c_nan_result );
const uint32_t c_inf_result = _uint32_sels( is_c_inf_msb, c_inf, c_nan_min_result );
const uint32_t c_denorm_result = _uint32_sels( is_c_denorm_msb, c_denorm, c_inf_result);
const uint32_t c_result = _uint32_sels( is_c_snan_msb, h_snan, c_denorm_result );
return (uint16_t)(c_result);
}