-
The 80x87 is able to multiply, divide, add, subtract, find the sqrt and calculate transcendental functions and logarithms.
-
Data types include 16-, 32- and 64-bit signed integers; 18-digit BCD data; and 32-, 64- and 80-bit (extended precision) floating-point numbers.
-
The directives
dw
,
dd
and
dq
are used for declaring signed integer storage while
dd
,
dq
and
dt
are used for floating-point.
-
Converting from
decimal
to
floating-point
is accomplished:
-
Convert the decimal number into binary.
-
Normalize the binary number.
-
Calculate the biased exponent.
-
Store the number in the floating-point format.
-
Bias is 0x7F, 0x3FF and 0x3FFF for the 3 floating-point number types.
-
Special Rules:
-
The number 0 is stored as all 0s (except for the sign bit).
-
+/- infinity is stored as logic 1s in the exponent, with a significand of all 0s. Sign bit is used to represent +/- infinity.
-
A NAN (not-a-number) is an invalid floating-point result that has all 1s in the exponent with a significand that is NOT all zeros.
-
Converting from
floating-point
to
decimal
is accomplished:
-
Separate the sign-bit, biased exponent, and significand.
-
Convert the biased exponent into a true exponent by subtracting the bias.
-
Write the number as a normalized binary number.
-
Convert it to a de-normalized binary number.
-
Convert the de-normalized binary number to decimal.
-
The 80x87 executes 68 different instructions.
-
Basic structure of the co-processor.
-
The registers in the coprocessor stack always contain 80-bit extended precision data.
-
Memory data, of course, can assume other representations. Therefore, conversions occur during transfers.
-
FSTSW
AX (Floating-point STore Status Word).
-
An instruction that transfers data between the coprocessor and the AX register.
-
Error conditions can be checked in your program by examining bits of this status word.
-
You can use the TEST instruction to test bits or the SAHF instruction to transfer the left-most 8 bits to the EFLAGs register.
-
This register selects precision, rounding control and infinity control.
-
For example, a value of 00 for P and C sets single precision mode.
-
R and C control rounding, e.g. round down, up or truncate toward 0.
-
Data Transfer Instructions:
-
FLD (Load Real)
-
Loads floating-point data to Stack Top (ST). Stack pointer is then decremented by 1.
-
Data can be retrieved from memory, or another stack position.
-
Note that ST is register 0 after initialization.
-
FST (Store Real), FSTP (Store Real and Pop)
-
Stores a copy of the top of the stack (and pop for FSTP) into memory or another coprocessor register.
-
Rounding occurs when the storage operation completes according to the control register.
-
FXCH (Exchange)
-
Exchanges register given as operand with ST.
-
FCMOV (Conditional floating point MOV)
-
Integer Data Transfer Instructions:
-
FILD (load integer)
-
FIST (Store integer)
-
FISTP (Store integer and pop)
-
Similar to FLD, FST and FSTP except they transfer (and convert) integer.
-
Stack addressing mode is restricted to use ST (stack top) and ST1.
-
The source operand is ST while the destination operand is ST1.
-
After the operation, the source is popped, leaving the dest. at ST.
-
Arithmetic Instructions (cont):
-
Note that FSUB subtracts ST from ST1, e.g., ST = ST1 - ST.
-
Use FSUBR to reverse the order.
-
For example, to compute the reciprocal (1/X):
-
Register addressing mode MUST use ST as one of the operands.
-
The other operand can be any register, including ST0 which is ST.
-
Note that the destination can be either ST or STn.
-
Also, unlike stack addressing, non-popping versions can be used.
-
Memory addressing mode always uses ST as the destination.
-
Arithmetic Instructions (cont):
-
The following letters are used to additionally qualify the operation:
-
P: Perform a register pop after the operation, FADD and FADDP.
-
R: Reverse mode for subtraction and division.
-
I: Indicates that the memory operand is an integer. I appears as the second letter in the instruction, e.g., FIADD, FISUB, FIMUL, FIDIV.
-
Arithmetic Related Instructions:
-
FSQRT: Finds the square root of operand at ST. Leave result there. Check IE bit for an invalid result, e.g., the operand was negative using FSTSW AX, and TEST AX, 1.
-
FSCALE: Adds contents of ST1 (interpreted as an integer) to the exponent of ST.
-
FPREM1: Performs modulo division of ST by ST1. The resultant remainder is found at ST.
-
FRNDINT: Rounds ST to an integer.
-
Arithmetic Related Instructions (cont):
-
FXTRACT: Decomposes ST into an unbiased exponent and a significand. Extracted significand is at ST and unbiased exponent at ST1.
-
FABS: Change sign of ST to positive.
-
FCHS: Invert sign of ST.
-
Comparison Instructions:
-
These instructions examine ST in relation to another element and return result of the comparison in the status register bits C3-C0.
-
FCOM: Compares ST with an memory or register operand. FCOM by itself compares ST and ST1.
-
FCOMP/FCOMPP: Compare and pop once or twice.
-
FICOM/FICOMP: Compare ST with integer memory operand and optionally pop the stack.
-
FTST: Compare ST with 0.0.
-
FXAM: Exam ST and modify CC bits to indicate whether contents are positive, negative, normalized, etc. (See text).
-
FCOMI/FUCOMI: Combines FCOM, FNSTSW AX, and SAHF.
-
Transcendental Operations: (See text for semantics).
-
FPTAN
-
FPATAN
-
F2XM1: Compute 2x -1
-
FSIN/FCOS
-
FSINCOS
-
FYL2X: Compute Ylog2X
-
FYL2XP1: Compute Ylog2(X + 1)
-
Constant Returning Operations:
-
FLDZ: Store +0.0 to ST.
-
FLD1: Store +1.0 to ST.
-
FLDPI: Store pi to ST.
-
FLDL2T: Store log210 to ST.
-
FLDL2E: Store log2e to ST.
-
FLDLG2: Store log102 to ST.
-
FLDLN2: Store loge2 to ST.
-
Coprocessor Control Instructions:
-
FINIT/FNINIT: Reset coprocessor with or without waiting afterwards.
-
FWAIT: Stops microprocessor until coprocessor has finished an operation. Should be used before the microprocessor accesses memory data that are affected by the coprocessor.
-
Instruction reference is given in text along with examples.
