Floating-Point Operations

1
Floating-Point Operations

• Chapter 18
• S. Dandamudi

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Outline

• Introduction
• FPU organization
• Data registers
• Control and status registers
• Tag register
• Floating-point instructions
• Data movement
• Addition/Subtraction
• Multiplication/Division
• Comparison
• Miscellaneous
• Illustrative examples

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Introduction

• Three components
• Sign
• Identified the number
• positive or negative
• Mantissa
• Exponent
• Follows IEEE 754 standard
• More details in Appendix A

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FPU Organization

• FPU consists of
• Data registers
• 8 registers ST0, ST1, , ST7
• Organized as a register stack
• Names are not statically assigned
• Control and status registers
• Pointer registers
• Instruction and data pointer registers
• Provides support for programmed exception
  handlers
• Not discussed

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FPU Organization (contd)
FPU Registers
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FPU Organization (contd)
FPU Control Register
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FPU Organization (contd)
FPU Status Register
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FPU Organization (contd)

• FPU Tag Register
• Two bits for each register
• Gives the following information
• 00 valid
• 01 zero
• 10 special (invalid, infinity, or denormal)
• 11 empty

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Floating-Point Instructions

• Several floating-point instructions for
• Data movement
• Addition/Subtraction
• Multiplication/Division
• Comparison
• Miscellaneous
• These instructions, by default, affect the flags
  as follows
• Flag bits C0, C2, and C3 are undefined
• C1 is updated to indicate overflow/underflow
  condition

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Floating-Point Instructions (contd)

• Data movement
• Two types
• Load and store
• Load instructions
• fld src
• Pushes src onto the FPU stack
• src operand can be in a register or in memory
• It can be a single-precision (32 bits),
  double-precision (64 bits) or extended (80-bit)
  floating-point number
• Single- and double-precision numbers are
  converted to extended format

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Floating-Point Instructions (contd)

• FP Instructions to push constants
• Instruction Description
• fldz Push 0.0 onto the stack
• fld1 Push 1.0 onto the stack
• fldpi Push p onto the stack
• fldl2t Push log210 onto the stack
• fldl2e Push log2e onto the stack
• fldlg2 Push log102 onto the stack
• fldln2 Push loge2 onto the stack
• To load an integer fild src

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Floating-Point Instructions (contd)

• Store instructions
• fst dest
• Stores the top-of-stack value at dest
• Does not pop it off the stack
• To the value use
• fstp dest
• Integer version of the store instruction
• fist dest
• Its pop version is
• fistp dest

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Floating-Point Instructions (contd)

• Addition
• fadd src
• adds the number in memory at src to that in ST0
  and stores the result in ST0
• Does not pop the stack
• Two operand version
• fadd dest,src
• Both dest and src must be FPU registers
• Its pop version
• faddp dest,src
• Integer version
• fiadd src

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Floating-Point Instructions (contd)

• Subtraction
• fsub src
• Performs ST0 ST0 - src
• Does not pop the stack
• Two operand version
• fsub dest,src
• Both dest and src must be FPU registers
• Its pop version
• fsubp dest,src
• Reverse subtract version
• fsubr src
• Performs ST0 src ST0

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Floating-Point Instructions (contd)

• Multiplication
• fmul src
• Performs ST0 ST0 src
• Does not pop the stack
• Two operand version
• fmul dest,src
• Both dest and src must be FPU registers
• Its pop version
• fmulp dest,src
• Special pop version with no operands
• fmulp Performs ST0 ST1 ST0
• Multiplication by integer
• fimul src

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Floating-Point Instructions (contd)

• Division
• fdiv src
• Performs ST0 ST0 / src
• Does not pop the stack
• Two operand version
• fdiv dest,src Performs dest dest/src
• Both dest and src must be FPU registers
• Its pop version
• fdivp dest,src
• Reverse division version
• fdivr src Performs ST0 src / ST0
• Multiplication by integer
• fidiv src

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Floating-Point Instructions (contd)

• Comparison
• fcom src
• Compares the value in ST0 with src and sets the
  FPU flags C0, C2, and C3 as follows
• Relationship C3 C2 C0
• ST0 gt src 0 0 0
• ST0 src 1 0 0
• ST0 lt src 0 0 1
• Not comparable 1 1 1
• Double pop version
• fcompp
• Compares ST0 and ST1 and pops these two values
  from the stack

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Floating-Point Instructions (contd)

• Comparison (contd)
• Comparison with an integer
• ficom src
• Comparison with zero
• ftst
• To examine number type
• fxam
• Examines the number in ST0 and returns its sign
  in C1 (0 for positive, 1 for negative)
• C0, C2, and C3 return the following information

Type C3 C2 C0 Unsupported 0 0 0 NaN 0
0 1 Normal 0 1 0 Infinity 0 1
1 Zero 1 0 0 Empty 1 0
1 Denormal 1 1 0
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Floating-Point Instructions (contd)

• Miscellaneous
• Change the sign
• fchs
• Changes the sign of the number in ST0
• Loading the control word
• fldcw src
• Storing the control word
• fstcw dest
• Storing the status word
• fstsw dest

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Illustrative Examples

• Example 1
• Array sum
• Example 2
• Quadratic equation solution
• Example 3
• Array sum --- Inline version

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