openpower/isafunctions/double2single.mdwn

   1 # A.1 Floating-Point Round to Single-Precision Model
   2
   3 The following describes algorithmically the operation of the Floating
   4 Round to Single-Precision instruction.
   5
   6 <!-- Power ISA Book I Version 3.0B Section A.1 page 775-778 -->
   7
   8     def Round_Single( sign, exp, frac, G, R, X, round_mode ):
   9         inc <- 0
  10         lsb  <- frac[23]
  11         gbit <- frac[24]
  12         rbit <- frac[25]
  13         xbit <- (frac[26:52] || G || R || X) != 0
  14
  15         if round_mode  = 0b00  then           # Round to Nearest
  16             if (lsb = 1) & (gbit = 1)              then inc <- 1
  17             if (lsb = 0) & (gbit = 1) & (rbit = 1) then inc <- 1
  18             if (lsb = 0) & (gbit = 1) & (xbit = 1) then inc <- 1
  19         if round_mode  = 0b10  then           # Round toward + Infinity
  20             if (sign = 0) & (gbit = 1) then inc <-1
  21             if (sign = 0) & (rbit = 1) then inc <-1
  22             if (sign = 0) & (xbit = 1) then inc <-1
  23         if round_mode  = 0b11  then           # Round toward - Infinity
  24             if (sign = 1) & (gbit = 1) then inc <-1
  25             if (sign = 1) & (rbit = 1) then inc <-1
  26             if (sign = 1) & (xbit = 1) then inc <-1
  27
  28         # add with carry-out
  29         tmp        <- [0]*25
  30         tmp[1:24]  <- frac[0:23]
  31         tmp[0:24]  <- tmp[0:24] + inc
  32         carry_out  <- tmp[0]
  33         frac[0:23] <- tmp[1:24]
  34         if carry_out = 1 then
  35             exp[0:10] <- exp + 1
  36             frac[0:23] <- 0b1 || frac[0:22]
  37         frac[24:52] <- [0]*29
  38         # TODO, later
  39         # FPSCR[FR] <- inc
  40         # FPSCR[FI] <- gbit || rbit || xbit
  41
  42     def DOUBLE2SINGLE(FR):
  43         if (FR[1:11] <u 897) & (FR[1:63] >u 0) then
  44             # exponent underflow
  45             mode = 'disabled_exp_underflow'
  46             # TODO if FPSCR_UE = 0 then mode = 'disabled_exp_underflow'
  47             # TODO if FPSCR_UE = 1 then mode = 'enabled_exp_underflow'
  48         else if (FR[1:11] >u 1150) & (FR[1:11] <u 2047) then
  49             # exponent overflow
  50             mode = 'disabled_exp_overflow'
  51             # TODO if FPSCR_OE = 0 then mode = 'disabled_exp_overflow'
  52             # TODO if FPSCR_OE = 1 then mode = 'enabled_exp_overflow'
  53         else if (FR[1:11] >u 896) & (FR[1:11] <u 1151) then
  54             # normal operand
  55             mode <- 'normal_operand'
  56         else if (FR[1:63] = 0) then
  57             # zero operand
  58             mode <- 'zero_operand'
  59         else if (FR[1:11] = 2047) then
  60             # inf / nan
  61             if (FR[12:63] = 0) then
  62                 mode <- 'inf_operand'
  63             else if (FR[12] = 1) then
  64                 mode <- 'qnan_operand'
  65             else if (FR[12] = 0) & (FR[13:63] >u 0) then
  66                 mode <- 'snan_operand'
  67
  68         frac <- [0]*53
  69         exp <- [0]*11
  70         result <- [0] * 64
  71
  72         if mode = 'normal_operand' then
  73             sign       <- FR[0]
  74             exp <- FR[1:11] - 1023
  75             frac[0:52] <- 0b1 || FR[12:63]
  76             RN <- 0b00 # TODO
  77             Round_Single(sign, exp, frac, 0b0, 0b0, 0b0, RN)
  78             # TODO FPSCR[XX] <- FPSCR[XX] || FPSCR[FI]
  79             if exp > 127 then
  80                 mode = 'disabled_exp_overflow'
  81                 #   if FPSCR_OE = 0 then mode = 'disabled_exp_overflow'
  82                 #   if FPSCR_OE = 1 then mode = 'enabled_overflow'
  83             else
  84                 result[0] <- sign
  85                 result[1:11] <- exp + 1023
  86                 result[12:63] <- frac[1:52]
  87                 # if sign = 0 then
  88                 #    FPSCR[FPRF] <- '+ normal number'
  89                 # else
  90                 #    FPSCR[FPRF] <- '- normal number'
  91
  92         if mode = 'enabled_exp_underflow':
  93             sign       <- FR[0]
  94             if FR[1:11] = 0 then
  95                 exp <- 1022
  96                 frac[0:52] <- 0b0 || FRB[12:63]
  97             if FR[1:11] >u 0 then
  98                 exp <- FRB[1:11] - 1023
  99                 frac[0:52] <- 0b1 || FRB[12:63]
 100             # denormalise operand
 101             G = 0b0
 102             R = 0b0
 103             X = 0b0
 104             do while exp < -126
 105                 exp <- exp + 1
 106                 X <- R | X
 107                 R <- G
 108                 G <- frac[52]
 109                 frac[0:52] <- frac[1:52] || 0b0
 110             # TODO
 111             # FPCSR_UX <- (frac[0:52] || G || R || X) >u 0)
 112             RN <- 0b00 # TODO
 113             Round_Single(sign, exp, frac, G, R, X, RN)
 114
 115         if mode = 'zero_operand':
 116             # Zero Operand
 117             result[0]  <- FR[0] # copy sign, the rest is zero
 118             # TODO, FPSCR
 119             #FPSCR[FR] <- 0b00
 120             #FPSCR[FI] <- 0b00
 121             #FPSCR[FPRF] <- '+ zero'
 122
 123         if mode = 'disabled_exp_underflow':
 124             if sign = 1 then frac[0:63] <- ¬frac[0:63] + 1
 125             # do the loop 0 times if FR = max negative 64-bit integer or
 126             #                     if FR = max unsigned 64-bit integer
 127             do while frac[0] = 0
 128                 frac[0:63] <- frac[1:63] || 0b0
 129                 exp <- exp - 1
 130             # round to nearest
 131             RN <- 0b00 # TODO, FPSCR[RN]
 132             Round_Float( tgt_precision, sign, exp, frac, RN )
 133             # TODO, FPSCR
 134             #if sign = 0 then FPSCR[FPRF] <- '+normal number'
 135             #if sign = 1 then FPSCR[FPRF] <- '-normal number'
 136             result[0]    <- sign
 137             result[1:11] <- exp + 1023     # exp + bias
 138             result[12:63] <- frac[1:52]
 139
 140         return result
 141