Gobsmacked by ksh93 floating point arithmetic.


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# 15  
Hi C688...
This will probably attach itself to my previous...

Thanks, much like my reply above...

I can see it now.
# 16  
The for-loop comes from C, where it follows the form

Code:
for(statement1;  statement2;  statement3) {
}

which does effectively this:

Code:
statement1;

while(statement2) {
      statement3;
}

It's usually used for(var=0; var<10; var++) but any valid expression will do. Most languages with for() loops allow them to be flexible like that, though few languages can cram as many things into one expression as C Smilie

In the BASH/KSH adaptation, you can put anything inside each statement that you might put inside a (( )) block, including nothing.
# 17  
OK, using Corona688's code for SINE we now have Sin(), Cos(), NthRoot() and Sqrt() functions.
The 'e' and 'PI' constants are to 17 decimal places, NthRoot() and Sqrt() to 16 decimal places and Sin() and Cos() to 8 decimal places.
These precisions are good enough for basic mathematical tasks, after all KSH93 was not designed to send a spacecraft to Neptune. <wink>
Code:
#!/bin/ksh
# ksh_math.sh
# Basic Math extensions.

# CONSTANTS.
PI=3.14159265358979323
e=2.71828182845904523

# Degrees to radians.
TORADIANS=$(( PI/180.0 ))
# Radians to degrees.
TODEGREES=$(( 180.0/PI ))

# NTH ROOT of a positive floating point number.
# Called as:
# NthRoot NUMBER NTHROOT [PRECISION]
# ALL POSITIVE VALUES.
# NUMBER and NTHROOT can be floating point, optional PRECISION is an integer from 1 to 16.
NthRoot()
{
	# Make these local.
	typeset NUMBER var
	typeset NTHROOT var
	typeset PRECISION var

	NUMBER=$1
	NTHROOT=$2
	PRECISION=$3

	if [ "$PRECISION" = "" ] || [ $PRECISION -lt 1 ]
	then
		# My school log table(s) accuracy. ;o)
		PRECISION=4
	fi

	printf "%.${PRECISION}f\n" "$(( NUMBER**(1.0/NTHROOT) ))"
}

# SQUARE ROOT of a positive floating point number.
# Called as:
# Sqrt NUMBER [PRECISION]
# ALL POSITIVE VALUES.
# NUMBER can be floating point, optional PRECISION is an integer from 1 to 16.
Sqrt()
{
	# Make these local.
	typeset NUMBER var
	typeset NTHROOT var
	typeset PRECISION var

	NUMBER=$1
	NTHROOT=2.0
	PRECISION=$2

	NthRoot $NUMBER $NTHROOT $PRECISION
}

# SINE(angle) in degrees.
# Called as:
# Sin some_angle
# Google 'sin X degrees' values for first quadrant.
#
# 0	0.00000000000
# 15	0.25881904510
# 30	0.50000000000
# 45	0.70710678118
# 60	0.86602540378
# 75	0.96592582628
# 90	1.00000000000
#
# Courtesy of Corona688 translated and improved considerably from shell code I wrote.
Sin()
{
	# Make these local.
	typeset ANGLE var
	typeset SIN var

	# ANGLE used instead of RADIANS for consistency in accuracy.
	ANGLE="$1"
	SIN=0.0

	# Compensate for angles less the 0.0 degrees.
	while (( ANGLE<0.0 ))
	do
		(( ANGLE+=360.0 ))
	done

	# Ditto for angles greater than 360.0 degrees.
	while (( ANGLE>=360.0 ))
	do
		(( ANGLE-=360.0 ))
	done

	# Correct for the four quadrants.
	(( ANGLE>270.0 )) && (( ANGLE-=360 ))
	(( ANGLE>180.0 )) && ANGLE=$(( -(ANGLE-180) ))
	(( ANGLE>90.0 )) && ANGLE=$(( 180-ANGLE ))

	# Now convert to RADIANS.
	(( ANGLE*=TORADIANS ))

	# This loop is to calculate this Taylor series:
	# RADIAN-((RADIAN**3)/6.0)+((RADIAN**5)/120.0)-((RADIAN**7)/5040.0)+((RADIAN**9)/362880.0)-((RADIAN**11)/39916800.0)+((RADIAN**13)/6227020800.0) ... etc.
	# Factorial part 'F'.
	F=1
	for (( N=1; N<=13; ))
	do
		(( SIN+=(ANGLE**N)/F ))
		(( F*=++N ))
		(( F*=-(++N) ))
	done

	# Precision returned to 8 Decimal places.
	printf "%.8f\n" "$SIN"
}

# COSINE(angle) in degrees.
# Called as:
# Cos some_angle
Cos()
{
	# Make this local.
	typeset COS var

	COS=$(( $1 + 90.0 ))
	# Call the 'Sin()' function.
	Sin $COS
}

# ****************************************************
#
# All of below will be removed when finished.
# Test degrees.
echo ""
echo "SINE and COSINE of an ANGLE:"
echo ""
for x in $( seq 0.0 15.0 360.0 )
do
	MYSIN=$( Sin x )
	printf "%s" "SIN $x -> $MYSIN"
	MYCOS=$( Cos x )
	printf "%s\n" "		COS $x -> $MYCOS"
done

# Tests nth roots...
SQRT=$( Sqrt 813.7173 10 )
echo ""
echo "Floating Point Square Root:"
echo "KSH93 FP maths routines = $SQRT."
echo "From Google calculator = 28.5257304902."
echo ""
echo "Floating Point Number And Nth Root:"
NTHROOT=$( NthRoot 10.5 12.3 11 )
echo "KSH93 FP maths routines = $NTHROOT."
echo "From Google calculator = 1.21066369814."
echo ""
#
# ****************************************************

Results on OSX 10.13.6, default bash terminal calling ksh.
Note the code is sourced into current ksh shell...
Code:
Last login: Sat Oct 27 12:49:46 on ttys000
AMIGA:amiga~> cd Desktop/Code/Shell
AMIGA:amiga~/Desktop/Code/Shell> ksh
AMIGA:uw> . ./ksh_math.sh

SINE and COSINE of an ANGLE:

SIN 0 -> 0.00000000		COS 0 -> 1.00000000
SIN 15 -> 0.25881905		COS 15 -> 0.96592583
SIN 30 -> 0.50000000		COS 30 -> 0.86602540
SIN 45 -> 0.70710678		COS 45 -> 0.70710678
SIN 60 -> 0.86602540		COS 60 -> 0.50000000
SIN 75 -> 0.96592583		COS 75 -> 0.25881905
SIN 90 -> 1.00000000		COS 90 -> 0.00000000
SIN 105 -> 0.96592583		COS 105 -> -0.25881905
SIN 120 -> 0.86602540		COS 120 -> -0.50000000
SIN 135 -> 0.70710678		COS 135 -> -0.70710678
SIN 150 -> 0.50000000		COS 150 -> -0.86602540
SIN 165 -> 0.25881905		COS 165 -> -0.96592583
SIN 180 -> 0.00000000		COS 180 -> -1.00000000
SIN 195 -> -0.25881905		COS 195 -> -0.96592583
SIN 210 -> -0.50000000		COS 210 -> -0.86602540
SIN 225 -> -0.70710678		COS 225 -> -0.70710678
SIN 240 -> -0.86602540		COS 240 -> -0.50000000
SIN 255 -> -0.96592583		COS 255 -> -0.25881905
SIN 270 -> -1.00000000		COS 270 -> 0.00000000
SIN 285 -> -0.96592583		COS 285 -> 0.25881905
SIN 300 -> -0.86602540		COS 300 -> 0.50000000
SIN 315 -> -0.70710678		COS 315 -> 0.70710678
SIN 330 -> -0.50000000		COS 330 -> 0.86602540
SIN 345 -> -0.25881905		COS 345 -> 0.96592583
SIN 360 -> 0.00000000		COS 360 -> 1.00000000

Floating Point Square Root:
KSH93 FP maths routines = 28.5257304902.
From Google calculator = 28.5257304902.

Floating Point Number And Nth Root:
KSH93 FP maths routines = 1.21066369814.
From Google calculator = 1.21066369814.

AMIGA:uw> Sin 45.1
0.70833984
AMIGA:uw> Sin 45.0
0.70710678
AMIGA:uw> Sin 44.9
0.70587157
AMIGA:uw> Cos 45.1
0.70587157
AMIGA:uw> Cos 45.0
0.70710678
AMIGA:uw> Cos 44.9
0.70833984
AMIGA:uw> Sqrt 10
3.1623
AMIGA:uw> Sqrt 10 10
3.1622776602
AMIGA:uw> NthRoot 9113.762 3.12   
18.5838
AMIGA:uw> NthRoot 9113.762 3.12 11
18.58377218033
AMIGA:uw> echo $(( $(Sqrt 10 16)*$(Sqrt 10 16) ))
10.0000000000000011
AMIGA:uw> x=$( NthRoot 9138052765.123 6.711 16 )
AMIGA:uw> echo $x
30.4970432230686335
AMIGA:uw> echo $(( x**6.711 ))
9138052765.12300491
AMIGA:uw> _

Hope you are all enjoying this exercise in futility... ;oD
This User Gave Thanks to wisecracker For This Post:
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