예제 #1
0
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);
}
예제 #2
0
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);
}
예제 #3
0
// 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);
}
예제 #4
0
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);
}
예제 #5
0
// 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);
}