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Floating-Point Operations

Floating-Point Operations. Chapter 18 S. Dandamudi. Introduction FPU organization Data registers Control and status registers Tag register Floating-point instructions Data movement Addition/Subtraction Multiplication/Division Comparison Miscellaneous Illustrative examples. Outline.

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Floating-Point Operations

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  1. Floating-Point Operations Chapter 18 S. Dandamudi

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

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

  4. 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 S. Dandamudi

  5. FPU Organization (cont’d) FPU Registers S. Dandamudi

  6. FPU Organization (cont’d) FPU Control Register S. Dandamudi

  7. FPU Organization (cont’d) FPU Status Register S. Dandamudi

  8. FPU Organization (cont’d) • FPU Tag Register • Two bits for each register • Gives the following information 00 valid 01 zero 10 special (invalid, infinity, or denormal) 11 empty S. Dandamudi

  9. 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 S. Dandamudi

  10. Floating-Point Instructions (cont’d) • 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 S. Dandamudi

  11. Floating-Point Instructions (cont’d) • 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 S. Dandamudi

  12. Floating-Point Instructions (cont’d) • 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 S. Dandamudi

  13. Floating-Point Instructions (cont’d) • 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 S. Dandamudi

  14. Floating-Point Instructions (cont’d) • 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 S. Dandamudi

  15. Floating-Point Instructions (cont’d) • 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 S. Dandamudi

  16. Floating-Point Instructions (cont’d) • 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 S. Dandamudi

  17. Floating-Point Instructions (cont’d) • 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 > src 0 0 0 ST0 = src 1 0 0 ST0 < 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 S. Dandamudi

  18. Floating-Point Instructions (cont’d) • Comparison (cont’d) • 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 S. Dandamudi

  19. Floating-Point Instructions (cont’d) • 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 S. Dandamudi

  20. Illustrative Examples • Example 1 • Array sum • Example 2 • Quadratic equation solution • Example 3 • Array sum --- Inline version Last slide S. Dandamudi

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