8087 instruction set and examples
About the 8087 • In the old days, you had to buy a -87 chip for numerical co-processing and hand install it. (Back in the 8086, 286, 386 days). • With the 486 processor and later, the -87 coprocessor is integrated.
About the 8087 • The 8087 uses a “stack” or chain of 8 registers to use for internal storage and data manipulation, as well as status and control words to set rounding control and indicate the results of operations. • It has its own instruction set, instructions are recognizable because of the F- in front. (Like FIADD, FCOM, etc)
About the 8087 • FWAIT… checks a control line to see if the 87 is still active. • programmers used to have to use an FWAIT before and after a set of instructions for the -87 to make sure -86 or -87 storage operations had been completed. (Basically, to handle synchronization). • FWAIT should not be necessary.
About the 8087: data transfer • • Data transfer: Instruction result FLD source load a real into st(0) FST dest store real at dest (86 mem) • FSTP dest store/pop st(0) • FXCH {st(i)} exchange two regs (St(0), St(1)) or St(0) and the operand
About the 8087: data transfer • • • FILD source FIST dest FISTP dest FBLD source FBSTP dest int load int store/pop bcd load (tbyte source) bcd store tbyte dest
About the 8087: arithmetic • FADD source add a real (mem) to st(0) • FADD {St(1), ST} • FADD st(i), st … or FADD ST, ST(i) • FADDP St(i), ST add st to st(i) and pop st(0) • FIADD {st, } source int add to st
About the 8087: arithmetic • FSUB for real subtract has same formats as FADD • FISUB {st, } intmem for int sub • ALSO: • FSUBR {st(1), st} • FSUBR {st, } rmem • FSUBRP st(i), st • Etc and … • FISUBR {st, } intmem • Reverse subtract: subtract dest from source
About the 8087: arithmetic • FMUL and FIMUL have same formats available • FDIV and FIDIV have same formats • Also available • FDIVR, FDIVRP and FIDIVR
About the 8087: arithmetic • • • Miscellaneous FSQRT {st} FABS {st} FCHS {ST}… change sign FLDZ {st}… load a zero
Control word • The control word is a 16 bit word that works like a flag register on the 86 processor. It keeps information about zerodivide in bit 2 for example. Bits 3 and 4 are overflow and underflow respectively. • Precision control is set in bits 8 and 9 and rounding is set in bits 10 and 11. • Rounding control bit settings are: • 00 round to nearest/even • O 1 round down • 10 round up • 11 chop/truncate
Status word • Status word is also a 16 bit word value. • condition bits are named c 3, c 2, c 1 and c 0. Their position in the status word, though is: • C 3 is bit 14 • C 2, c 1, c 0 are bits 10, 9, 8 respectively. • If you are curious, the eight possible bit settings in bits (11, 12, 13) indicate which register in the chain is currently st(0)
Temp real (80 bits) • Temp real has an f-p format. Bits 0. . 63 are the significand in hidden bit format. Bits 64 to 78 are the biased exponent, bit 79 is the sign. • You shouldn’t need to worry about these values on the stack.
Packed bcd (80 bits) • • A packed bcd is a tbyte. Bit 79 is the sign. Bits 72 through 78 are not used. Bits 0, 1, 2, 3 store the 0 th (lsd) decimal digit. Bits 4, 5, 6, 7 store the 1 st. The 17 th (msd) digit is in bits 68, 69, 70, 71. You’ll need to pad with zeros if there are fewer than 18 digits.
Int values • 87 processor recognizes word, dword and qword signed int types, in the same manner as the 86 processor.
The stack • Pushing and popping on the stack change the register who is currently the top. • Pushing more than 8 times will push the last piece of data out and put St(0) at the most recently pushed item. • It is the programmer’s responsibility to count stack push/pop operations. • Whoever is on top of the stack, is referenced by St or ST(0). St(1) is next. And so on to St(7).
Int transfer • FILD: load int. Type (word, dword, etc) is whatever the operand type is. St(0) is this new value. St(1) points to the previous value on top. • FIST: copy St(0) value to memory, converting to a signed int (following rounding control settings in the control word) • FISTP: same as above, but pop the stack as well.
BCD • FBLD load a bcd (tbyte) onto the stack • FBSTP store a tbyte bcd value into the memory operand, popping the stack as you go. Example: FBLD myval FBSTP myval
Exchanging/swapping on the stack • FXCHG dest Swap stack top with operand. Example FXCHG St(3) ; swaps St(0) value with St(3) value
Int arithmetic • • • FIADD, FIADD: add FISUB, FISUBR, : sub, or sub reversed. FIMUL FIDIV, FIDIVR Other: FPREM, FRNDINT – partial remainder, round to int • FLDZ push a zero onto the stack. • FLD 1 push a 1
FPREM • Takes implicit operands st, st(1) • Does repeated subtract… leaves st>0, (possibly st==st(1)) or st==0. • May need to repeat it, because it only reduces st by exp(2, 64) • If st>st(1) it needs to be repeated. • FPREM sets bit C 2 of the status word if it needs to be repeated, clears this bit if it completes operation.
operands • Stack operands may be implicitly referenced. • FIADD, FISUB, FIDIVR, FIMUL and FISUBR have only one form (example using add instruction): FIADD {ST, } intmem • St(0) is implied dest for all of these.
comparison • • FCOM ; no operands compares st, st(1) FCOM St(i); one operand compares st with st(i) FCOMP (compare and pop) is the same. FCOMPP - only allows implicit operands St, st(1) (compare then pop twice) • FTST – compares St with 0. • These all use condition codes described above and make the settings in the next slide.
Condition codes • • • C 3 0 0 1 1 c 0 0 1 st>source st<source st==source not comparable
Getting status and control words • FSTSW intmem ; copy status word to 16 bit mem location for examination. • FLDCW intmem; load control word (to set rounding, for example, from 16 bit int mem) • FSTCW intmem; copy control word to int mem
Some -87 examples
16 -bit vs 32 -bit? • Almost all the examples here were done in 32 bit. • But the coprocessor works in 16 bit as well.
excerpt from a 16 -bit program & ouptut value word 1234. code main PROC mov ax, @data mov ds, ax mov ax, value call writedec fild value fiadd value fistp value mov ax, value call crlf call writedec C: MASM 615>coprocessor 1234 2468 C: MASM 615>
adding up an array (example from notes) include irvine 16. inc. data array dword 12, 33, 44, 55, 77, 88, 99, 101, 202, 9999, 111 sum dword ? . code main proc mov ax, @data mov ds, ax xor bx, bx fldz fist sum mov eax, sum; ; ; call writeint; print zero call crlf mov cx, 10 top: mov eax, array[bx]; ; get value call writeint; ; ; print it call crlf fiadd array[bx]; ; add to st(0) add bx, 4 loop top fistp sum; ; when done pop to dword int mov eax, sum call write. Int; ; print it mov ax, 4 c 00 h int 21 h main endp end main
adding up an array (example from notes)
Getting sqrt call readint fstcw control; ; ; store current control word or control, 0800 h; set bit 11 clear bit 10 to round up fldcw control; ; load new control word mov num, eax fild num fsqrt fistp sqr fwait mov edx, offset prompt 2 call writestring mov eax, sqr call writeint
Rounding set to round up • c: Masm 615>primes • enter an integer 125 • sqrt of integer+12
Add code to check for prime and print divisors for composites mov eax, num call crlf mov ebx, 2; ; ; first divisor top: xor edx, edx push eax div ebx; ; divide mov divi, ebx cmp edx, 0 je notprime inc ebx cmp ebx, sqr jg prime pop eax jmp top notprime: call writedec call crlf mov eax, divi call writedec call crlf mov edx, offset f call writestring prime: mov edx, offset t call writestring
Output from primes enter an integer 1337711 18841 71 not a prime c: Masm 615>primes enter an integer 17171731 746597 23 not a prime c: Masm 615>primes enter an integer 313713 104571 3 not a prime c: Masm 615>primes enter an integer 313717 prime c: Masm 615>
factorials call readint mov num, eax call crlf fld 1 ; ; load a 1 for subtacting and comparing. . this will be st(2) fld 1 ; ; prod value initialized in st(1) fild num; ; ; multiplier. . . need to count down and multiply st by st(1) theloop: ftst ; ; is st==0? fstsw status and status, 4100 h; check bits c 3 and c 0. . . c 3=0 c 0=1 means st<source cmp status, 4000 h; ; st==source jz done fmul st(1), st ; ; leave prod in st(1) fsub st, st(2) jmp theloop done: fistp dummy fistp answer mov edx, offset p 2 call writestring call crlf fwait mov eax, answer call writedec
factorials c: Masm 615>factorials enter an integer 6 factorial is 720 c: Masm 615>factorials enter an integer 7 factorial is 5040 c: Masm 615>
Fibonacci values mov edx, offset prompt call crlf call writestring call readint call crlf fld 1 ; ; load a 1 for subtacting and comparing. . this will be st(2) fld 1 ; ; prod value initialized in st(1) top: cmp eax, 0 je done fadd st(1), st fsubr st, st(1) ; ; ; cute huhn? st=st(1)-st dec eax jmp top done: fistp dummy fistp answer mov edx, offset p 2 call writestring call crlf fwait mov eax, answer call writedec
Fibonacci c: Masm 615>fibs enter an integer 4 fib is 8 c: Masm 615>fibs enter an integer 6 fib is 21 c: Masm 615>fibs enter an integer 7 fib is 34 c: Masm 615>
Mimicking real io • You can output reals by outputting first the integer part, subtracting this from the original value, then repeatedly multiplying the fraction by ten, (subtracting this off from the remainder) and outputting this sequence of fractional digits. • This is NOT an IEEE f-p conversion routine!
Rounding control & the int part fstcw control or control, 0 C 00 h ; ; ; chop or truncate fldcw control fild ten ; ; ten is in st(1) fild num ; ; num is in st(0) fsqrt ; ; sqrt in st fist intsqr ; ; ; store chopped result, don’t pop call crlf mov edx, offset message call writestring fwait mov ax, intsqr ; ; write the int part call writedec
realio mov edx, offset dot; ; decimal point call writestring fisub intsqr ; ; subtract from sqrt the int part leaving fractional part ; now loop & store 5 decimal places mov edi, offset decimals mov ecx, 5 up: fmul st, st(1) ; ; multiply by 10 to shift dec point fist digit ; store truncated int fisub digit ; ; subtract it off of the total fwait mov ax, digit add al, 48 mov byte ptr [edi], al ; ; store this digit inc edi loop up
Run of realio c: Masm 615>realio enter an integer: 121 sqrt of integer 11. 00000 c: Masm 615>realio enter an integer: 123 sqrt of integer 11. 09053 c: Masm 615>realio enter an integer: 143 sqrt of integer 11. 95826 c: Masm 615>
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