IEEE754 Rounding Modes

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IEEE754 Rounding Modes

• Four Rounding modes
• Plus infinity
• Minus inifinity
• Truncate
• Nearest even

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Examples
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Convert_float
my_float convert_my_float(float num) struct
my_float my_num new(my_float) if (my_num)
union converter c c.f num
my_num-gtsign c.i gtgt 31 my_num-gtexponent
((c.i gtgt 23) 0xff) my_num-gtmantissa
(((c.i 0x7FFFFF) 0x800000) ltlt 3)
return my_num
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Print Binary function
void print_binary(int num) unsigned mask
0x80000000 int anded for (int i 0 i lt
32 i ) if ((i gt 0) (i 4) 0) cout
ltlt " " anded num mask if (anded)
cout ltlt "1" else cout
ltlt "0" mask mask gtgt 1
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Add function
define DBG(a) a
struct my_float my_float_add(struct my_float
first, struct my_float second,\ int
rnd_mode) int first_mantissa
first-gtmantissa int second_mantissa
second-gtmantissa int exp_diff
first-gtexponent - second-gtexponent my_float
my_result new(my_float) DBG(cout ltlt
"Starting to add" ltlt endl) if (exp_diff gt 0)
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Hazard notation

• IN our previous example the twop pairs of hazrard
  condditions are
• 1a. EX/Mem.RegisterRd ID/EX.RegisterRs
• 1b. EX/Mem.RegisterRd ID/EX.RegisterRt
• 2a. Mem/WB.RegisterRd ID/EX.RegisterRs
• 2b. Mem/WB.RegisterRd ID/EX.RegisterRs
• Hazard on 2 between the sub and and instructions
  is
• EX/Mem.RegisterRd ID/EX.RegisterRs 2

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Hazards

• Above notation will do forwarding unecessarily as
  some instruction do not write registers
• Soln can check WB control to check if register
  writes back
• What about 0
• Do not foraward as shpuld always be zero

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No Forwarding
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Forwarding
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EX Hazard

• If (EX/Mem.RegWrite) and (EX/Mem.RegRd ! 0)
  and (EM/Mem.RegRd ID/EX.RegRs) then
  ForwardA 10
• If (EX/Mem.RegWrite) and (EX/Mem.RegRd ! 0)
  and (EM/Mem.RegRd ID/EX.RegRt) then
  ForwardB 10

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Mem Hazard

• If (Mem/WB.RegWrite) and (Mem/WB.RegRd ! 0)
  and (Mem/WB.RegRd ID/EX.RegRs) then
  ForwardA 01If (Mem/WB.RegWrite) and
  (Mem/WB.RegRd ! 0) and (Mem/WB.RegRd
  ID/EX.RegRt) then ForwardB 01

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What about
Add 1, 1, 2 Add 1, 1, 3 Add 1, 1, 4

• If (Mem/WB.RegWrite) and (Mem/WB.RegRd ! 0)
  and (EX/Mem.RegRd ! ID/EX.RegRs) and
  (Mem/WB.RegRd ID/EX.RegRs) then ForwardA
  01If (Mem/WB.RegWrite) and (Mem/WB.RegRd !
  0) and (EX/Mem.RegRd ! ID/EX.RegRt) and
  (Mem/WB.RegRd ID/EX.RegRt) then ForwardB
  01

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Updated datapath to resolve data hazards
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Data Hazards and Stalls

• Forwarding will not work where an instruction
  tries to read a register following a load
  instruction that writes the same register

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Stalls

• Hazard detection unit required at the ID stage
• If (ID/EX.MemRead) and (ID/EX.RegRt
  IF/ID.RegRs) or (ID/EX.RegRt IF/ID.RegRt
  then stall the pipeline

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