Class new title: Float
	subclassof: Number
	fields: ''
	declare: 'halfpi sqrt2 twopi fourthpi degreesPerRadian pi radiansPerDegree ln2 ';
	bytesize: true


 t1 
	[self 
 t1 asFloat] primitive: 4

 t1 
	[self  t1 asFloat] primitive: 7

 t1 
	[self  t1 asFloat] primitive: 5

* t1 
	[self * t1 asFloat] primitive: 8

+ t1 
	[self + t1 asFloat]

- t1 
	[self - t1 asFloat] primitive: 1

/ t1 
	[0.0 = t1  [user notify: 'Attempt to divide by 0.0']
	self / t1 asFloat] primitive: 9

< t1 
	[self < t1 asFloat] primitive: 2

= t1 
	[t1 isNumber  [self = t1 asFloat]
	false] primitive: 6

> t1 
	[self > t1 asFloat] primitive: 3

\ t1 
	[self < 0.0  [(self / t1) ipart + 1.0 * t1 + self]
	self - ((self / t1) ipart * t1)]

absprinton: t1 digits: t2 | t3 t4 t5 t6 t7 
	[t5 _ [self < 1.0  [0 - (10.0 / self epart: 10.0)]
			self epart: 10.0].
	t4 _ self / (10.0 ipow: t5).
	t3 _ 10.0 ipow: 1 - t2.
	t4 _ 0.5 * t3 + t4.
	[t4  10.0 
		[t4 _ t4 / 10.0.
		t5 _ t5 + 1]].
	[t5 < 6 and t5 > 4 
		[t6 _ 0.
		t5 < 0  [t1 append: '0.0000'  (1 to: 1 - t5)]]
	t6 _ t5.
	t5 _ 0].
	while t4  t3 do
		[t7 _ t4 asInteger.
		t1 next_ 48 + t7.
		t4 _ t4 - t7 * 10.0.
		t3 _ t3 * 10.0.
		t5 _ t5 - 1.
		t5 = 1  [t1 append: '.']].
	while t5  1 do
		[t1 next_ 48.
		t5 _ t5 - 1.
		t5 = 1  [t1 append: '.']].
	t6  0 
		[t1 append: 'e'.
		t1 print: t6]]

arctan | t1 t2 t3 t4 t5 
	[self = 1.0  [45.0]
	self = 1.0  [45.0]
	[self * self > 1.0 
		[t1 _ halfpi.
		t3 _ 1.0 / (self * self).
		t2 _ 1.0 / self abs]
	t1 _ 0.0.
	t3 _ 0.0 - (self * self).
	t2 _ self abs].
	t5 _ 1.
	t4 _ 1.0e4.
	while t2 abs > t4 do
		[t1 _ t1 + t2.
		t2 _ t2 * t3 * t5 asFloat / (t5 + 2) asFloat.
		t5 _ t5 + 2].
	t1 _ self sign asFloat * t1 * 360.0 / twopi.
	t1]

asDegrees 
	[self / radiansPerDegree]

asDirection 
	[self cos  self sin]

asFloat

asInteger 
	[(self / 10000.0) asInteger * 10000 + (self \ 10000.0) asInteger] primitive: 33

asLarge | t1 t2 t3 t4  
	[self < 0  [(0.0 - self) asLarge negated]
	t2 _ Stream default.
	[self = 0.0  [t2 next_ 0]
	t1 _ self ipart.
	while t1  1 do
		[t2 next_ (t1 \ 256.0) asInteger.
		t1 _ t1 / 256.0]].
	t2 _ t2 contents.
	t3 _ Natural new: t2 length.
	for t4 to: t2 length do
		[t3  t4 _ t2  t4].
	LargeInteger new bytes: t3 neg: false]

asRadians 
	[self * radiansPerDegree]

classInit 
	[pi _ 3.1415927.
	halfpi _ pi / 2.0.
	fourthpi _ pi / 4.0.
	twopi _ pi * 2.0.
	radiansPerDegree _ pi / 180.0.
	degreesPerRadian _ 180.0 / pi.
	ln2 _ 0.69314718.
	sqrt2 _ 1.4142136]

copy

cos 
	[self < 0.0  [(self + halfpi) sin]
	(halfpi - self) sin]

epart: t1 | t2 
	[self < t1  [0]
	self < (t1 * t1)  [1]
	t2 _ 2 * (self epart: t1 * t1).
	t2 + (self / (t1 ipow: t2) epart: t1)]

exp | t1 t2 t3 t4 t5 t6   
	[self abs > 9212.0  [user notify: 'exp overflow']
	t3 _ self / ln2.
	t2 _ Float new.
	t2 instfield: 1 _ t3 asInteger * 2.
	t3 _ t3 fpart.
	[t3  0.5 
		[t2 _ t2 * sqrt2.
		t3 _ t3 - 0.5]].
	t4 _ t3 * t3.
	t6 _ 0.0.
	t5 _ t6.
	for t1 from: (28.875564 2525.0429 ) do
		[t5 _ t5 * t4 + t1].
	for t1 from: (1.0 375.02165 7285.7336 ) do
		[t6 _ t6 * t4 + t1].
	t2 * (t6 + (t3 * t5) / (t6 - (t3 * t5)))]

fpart 
	[user croak] primitive: 35

ipart 
	[self - self fpart]

ipow: t1 
	[t1 = 0  [1.0]
	t1 = 1  [self]
	t1 > 1  [(self * self ipow: t1 / 2) * (self ipow: t1 \ 2)]
	1.0 / (self ipow: 0 - t1)]

ln | t1 t2 t3 t4 t5  
	[self 
 0.0  [user notify: 'ln not valid for ' + self asString]
	t2 _ self + 0.0.
	t4 _ ln2 * (((t2 instfield: 1) / 2) asFloat - 0.5).
	t2 instfield: 1 _ 0.
	t2 _ t2 * sqrt2.
	t2 _ t2 - 1.0 / (t2 + 1.0).
	t3 _ t2 * t2.
	t5 _ 0.0.
	for t1 from: (0.23762456 0.28525381 0.40000598 0.66666664 2.0 ) do
		[t5 _ t5 * t3 + t1].
	t4 + (t2 * t5)]

log: t1 
	[self ln / t1 asFloat ln]

near: t1 
	[self near: t1 within: 1.0e4]

near: t1 within: t2 
	[(self - t1) abs 
 t2]

neg 
	[self negated]

negated 
	[0.0 - self]

printon: t1 
	[self printon: t1 digits: 8]

printon: t1 digits: t2 
	[self > 0.0  [self absprinton: t1 digits: t2]
	self = 0.0  [t1 append: '0.0']
	t1 append: ''.
	0.0 - self absprinton: t1 digits: t2]

recopy

round 
	[(self + [self < 0  [0.5]
	0.5]) asInteger]

roundTo: t1 
	[(self / t1 + [self < 0.0  [0.5]
	0.5]) ipart * t1]

sameAs: t1 
	[self = t1]

sin | t1 t2 t3 t4  
	[self < 0.0  [self negated sin negated]
	self > twopi  [(self \ twopi) sin]
	self > pi  [(self - pi) sin negated]
	self > halfpi  [(pi - self) sin]
	t1 _ self.
	t3 _ t1.
	t2 _ t1 * t1.
	for t4 from: (0.16666667 0.0083333315 1.98409e4 2.7526e6 2.39e8 ) do
		[t1 _ t1 * t2.
		t3 _ t4 * t1 + t3].
	t3]

sqrt | t1 t2  
	[[self 
 0.0 
		[self = 0.0  [0.0]
		user notify: 'sqrt invalid for x<0.']].
	t1 _ self + 0.0.
	t1 instfield: 1 _ (t1 instfield: 1) / 4 * 2.
	for t2 to: 5 do
		[t1 _ self - (t1 * t1) / (t1 * 2.0) + t1].
	t1]

tan | t1 t2 t3 t4  
	[self < 0.0  [self negated tan negated]
	self > pi  [(self \ pi) tan]
	self > halfpi  [(self - halfpi) tan negated]
	self > fourthpi  [1.0 / (halfpi - self) tan]
	t1 _ self.
	t3 _ t1.
	t2 _ t1 * t1.
	for t4 from: (0.3333314 0.1333924 0.05337406 0.024565089 0.002900525 0.0095168091 ) do
		[t1 _ t1 * t2.
		t3 _ t4 * t1 + t3].
	t3]

| t1 
	[(self / t1) ipart * t1]