MATHEMATICAL OPERATIONS
DEFINITIONS
Only integer mathematics in the Forth ROM are shown,
see below for a summary of integer extensions, floating point and other
methods.
| * |
(
n1 n2 - n1*n2 ) |
|
| */ |
(
n1 n2 n3 - n4 ) |
Scale n1 by ratio
n2/n3. |
| */MOD |
(
n1 n2 n3 - n4 n5 ) |
Leave quotient
n5 and remainder n4 of operation n1*n2/n3. |
| + |
(
n1 n2 - n1+n2 ) |
|
| +! |
(
n addr - ) |
Add n to value
at address. |
| - |
(
n1 n2 - n1-n2 ) |
|
| / |
(
n1 n2 - n1/n2 ) |
|
| /MOD |
(
n1 n2 - rem quot ) |
Leave remainder
and signed quotient n1/n2. |
| 0< |
(
n - f ) |
True if number
less than zero. |
| 0<> |
(
n - f ) |
f = -1 if n not
zero, f = 0 if n is zero. |
| 0= |
(
n - f ) |
True if number
equal to zero. |
| 0> |
(
n - f ) |
True if number
greater than zero. |
| 1+ |
(
n - n+1 ) |
|
| 1- |
(
n - n-1 ) |
|
| 2* |
(
n - n*2 ) |
|
| 2+ |
(
n - n+2 ) |
|
| 2- |
(
n - n-2 ) |
|
| 2/ |
(
n - n/2 ) |
|
| < |
(
n1 n2 - f ) |
True if n1 less
than n2. |
| <> |
(
n1 n2 - f ) |
True if n1 not
equal to n2. |
| = |
(
n1 n2 - f ) |
True if n1 equal
to n2. |
| > |
(
n1 n2 - f ) |
True if n1 greater
than n2. |
| ABS |
(
n - u ) |
Leave absolute
value u of number n. |
| D*S |
(
d1 n - d2 ) |
d2=d1*n |
| D+ |
(
d1 d2 - d1+d2 ) |
|
| D- |
(
d1 d2 - d1-d2 ) |
|
| D/ |
(
d1 d2 - n ) |
n=d1/d2 |
| D/S |
(
d1 n - d2 ) |
d2=d1/n |
| D0< |
(
d - f ) |
True if double
number less than 0. |
| D0= |
(
d - f ) |
True if double
number equal to zero. |
| D2* |
(
d - d*2 ) |
|
| D2/ |
(
d - d/2 ) |
|
| D< |
(
d1 d2 - f ) |
True if d1 less
than d2. |
| D= |
(
d1 d2 - f ) |
True if d1 equal
to d2. |
| D>S |
(
d - n ) |
Convert double
number to single. |
| DABS |
(
d - ud ) |
Leave absolute
value ud of double number d. |
| DMAX |
(
d1 d2 - d3) |
d3 is the greater
of d1 and d2 |
| DMIN |
(
d1 d2 -- d3) |
d3 is the lesser of
d1 and d2 |
| DNEGATE |
(
d1 - d2 ) |
d2=-d1 |
| DU< |
(
ud1 ud2 - f ) |
True if ud1 less
than ud2. |
| M* |
(
n1 n2 - d ) |
d=n1*n2 |
| M*/ |
(
d1 n1 n2 - d2 ) |
Scale double number
d1 by ratio n1/n2. |
| M+ |
(
d1 n - d2 ) |
d2=d1+n |
| MAX |
(
n1 n2 - n3 ) |
n3 is the greater
of n1 and n2. |
| MIN |
(
n1 n2 - n3 ) |
n3 is the lesser
of n1 and n2. |
| MOD |
(
n1 n2 - n3 ) |
n3 is the remainder
of n1/n2. |
| NEGATE |
(
n1 - n2 ) |
n2= -n1 |
| S>D |
(
n - d ) |
Sign extend single
number n to form double number d. |
| T* |
(
ud u - ut ) |
ud * u giving
48-bit product. |
| T/ |
(
ut u - ud ) |
ut / u 48-bit
integer divided by single to give double integer. |
| U< |
(
u1 u2 - f ) |
True if u1 less
than u2. |
| U> |
(
u1 u2 - f ) |
True if u1 greater
than u2. |
| UM* |
(
u1 u2 - ud ) |
ud=u1*u2 |
| UM/MOD |
(
ud u1 - u2 u3 ) |
Leave remainder
u2 and quotient u3 of ud/u1. |
INTEGER TYPES (Forth
ROM, #MATH.TDS & #MATH1.TDS)
Use integer (16-bit) or double-integer (32-bit) where
possible because you get the best speed. Both are built into the Forth
kernel of the TDS2020F. Scaling the input and output to fit
in the range �2,000,000,000 generally allows this.
Integer functions in the Forth ROM are shown above
but in the files #MATH.TDS & #MATH1.TDS there are many others including
48-bit and 64-bit arithmetic, logarithms, exponentials and trigonometry.
FIXED POINT (#FIXED.TDS-comes with Update Service)
Uses 32-bit integer arithmetic for speed and accuracy
but has fixed decimal point for input and output. You can choose between
0 and 4 decimal places.
FRACTIONAL ARITHMETIC (#TRIG.TDS-comes with
Update Service)
This uses 16-bit integer arithmetic for speed. You
scale input and output to the range �2.000 before using the mathematical
operations. Apart from the main four functions and conversion words,
sine, cosine, logarithms, exponentials, inverse sine & cosine and
square roots are provided.
FLOATING POINT (TDS-FLOAT-ANS-optional
extra)
Click here for full details
of the ANS Floating Point software, the following is only a summary.
DESCRIPTION
The package TDS-FLOAT-ANS is a fully featured floating-point
package for the TDS2020F available
as an option. Use the parts of it you need in your application code.
Be sure you really need floating point. Floating point
arithmetic enables very small numbers (like 0.0000000001) to very large
numbers (like 3000000000000) to be handled at the same time. This is
very rarely needed and the extensive 32-bit double number arithmetic
routines in the TDS2020F cater
for most needs. These can handle from 0 to �2000000000, or 0.00000 to �20000.00000
for example.
Occasions do arise where floating point would be useful-please
request a copy of the 16-page TDS-FLOAT-ANS Technical Manual. The software
is supplied as source code on disk. Apart from normal calculator functions,
a full range of trigonometrical and log/exponential functions is included
with accuracy 8 to 10 decimal digits.
TYPICAL PERFORMANCE
These are measured using TDS2020F. Adding the TDS2020DV development board will make times longer.
| Floating
point multiply F* |
0.6ms |
| Floating
point divide F/ |
5.4ms |
| Floating
point add F+ |
0.49ms |
| Floating
point subtract F- |
0.45ms |
| Floating
point sine FSIN |
13.7ms |
| Floating
point logarithm FLOG |
12.3ms |
STACK & ADDRESS MANIPULATION
F! F@ FALIGN FALIGNED FCONSTANT FDEPTH
FDROP FDUP FINT FLITERAL FLOAT+ FLOATS
FOVER FROT FSWAP FVARIABLE
ARITHMETIC
F* F+ F- F/ F0< F0= F2*
F2/ F FLOOR FMAX FMIN FNEGATE
FROUND
FSQRT F~
TRIGONOMETRY
DEG>RAD FACOS FASIN FATAN FATAN2 FCOS FSIN
FSINCOS FTAN PI PI/2 PI/4 RAD>DEG
HYPERBOLIC FUNCTIONS
FACOSH FASINH FATANH FCOSH FSINH FTANH
EXPONENTIALS & POWERS
FALOG FEXP FEXPM1
F**
LOGARITHM
SFLN FLNP1 FLOG
INPUT FUNCTIONS
>FLOAT D>F FINPUT" FLOAT-OFF FLOAT-ON S>F
OUTPUT FUNCTIONS
F>S F. F>D FE. FS. PRECISION REPRESENT
SET-PRECISION
IEEE FLOATING POINT REPRESENTATION
DF! DF@ DFALIGN DFALIGNED DFLOAT+ DFLOATS
SF! SF@ SFALIGN SFALIGNED SFLOAT+ SFLOATS
FOURIER TRANSFORMS (TDS2020FFT-optional
extra)
A demonstration Fast Fourier Transform program is
provided with the Starter Pack. A separate data sheet gives details of
the full version.
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