User's Manual

FPTAN
FPATAN
F2XM1
FYL2X
FYL2XP1
PROGRAMMING NUMERIC APPLICATIONS
Table 2-9. Transcendental Instructions
Partial tangent
Partial arctangent
2X-1
Y ·log.X
Y .log.(X + 1)
The ratio result of FPTAN and the ratio argument of FPATAN are designed to optimize the calcula-
tiori of the other trigonometric functions, including SIN, COS, ARCSIN, and ARCCOS. These can
be derived from
TAN and ARCTAN via standard trigonometric identities.
FPATAN
0.:5 ST(1) < ST(O) < 00
FPATAN (partial arctangent) computes the function 8 = ARCTAN (Y IX). X is taken from the top
stack element and
Y from ST(l). Y and X must observe the inequality 0 .:5 Y < X < 00. The
instruction pops the stack and returns
8 to the (new) stack top, overwriting the Yoperand.
F2XM1
o .:5 ST(O) .:5 0.5
F2XMl (2 to the X minus 1) calculates the function Y = 2
X
-1. X is taken from the stack top and
must be in the range
0 .:5 X .:5 0.5. The result Y replaces X at the stack top.
This instruction
is designed to produce a very accurate result even when X is close to O. To obtain
Y=2
x
, add 1 to the result delivered by F2XM1.
The following formulas show
how values other than 2 may be raised to a power of X:
lOx = 2xoLOG210
eX = 2
x
•
LOG2
•
yX = 2xoLOG2Y
As shown in the next section, the 80287 has built-in instructions for loading the constants LOG
2
1O and
LOG
2
e, and the FYL2X instruction may be used to calculate X·LOG
2
Y.
FYL2X
0< ST(O) < 00-00 < ST(1) < 00
,
FYL2X (Y log base 2 of X) calculates the function Z = Y.LOG
2
X. X is taken from the stack top and
Y from ST(l). The operands must be in the ranges 0 < X < 00 and - 00 < Y < + 00. The
instruction pops the stack and returns Z at the (new) stack top, replacing the Yoperand.
This function optimizes the calculations of log to any base other than two, because a multiplication is
always required: ,
2-13