Correcting Art of Assembly's flawed acos implementation in Chapter 14

#
# Correcting Art of Assembly's flawed acos implementation in Chapter 14
# http://flint.cs.yale.edu/cs422/doc/art-of-asm/pdf/CH14.PDF
#

import math


# Alias commonly used math functions
sqrt = math.sqrt
atan = math.atan
atan2 = math.atan2


#
# From Art of Assembly, Chapter 14
# States allowable range is -1 <= x <= 1
# Does not work for x < 0
#
def acos_ArtOfASM(x):
	return atan(sqrt((1 - x * x) / (x * x)))


#
# From Mathworld, correctly states range is x >= 0 (with x=0 caveat)
# http://mathworld.wolfram.com/InverseCosine.html
#
def acos_Mathworld(x):
	return atan(sqrt((1 - x * x) / x))


#
# Use atan2 to cater for x <= 0 by taking quadrant shift into account:
#
#    atan2(y, x) = ...
#       atan(y / x)				x > 0
#       atan(y / x) + pi		y >= 0, x < 0
#       atan(y / x) - pi		y < 0, x < 0
#       pi / 2					y > 0, x = 0
#		-pi / 2					y < 0, x = 0
#
def acos_MathworldQuadrant(x):
	return atan2(sqrt(1 - x * x), x)


print acos_ArtOfASM(1)
print acos_ArtOfASM(-1)

print acos_Mathworld(1)
print acos_Mathworld(-1)

print acos_MathworldQuadrant(1)
print acos_MathworldQuadrant(-1)


#
# This results in a more correct implementation with the input range -1 <= x <= 1
# 1 less instruction and fdiv swapped for a fxch instruction
#
__asm
{
	fld st(0)			// [x]
	fld st(0)			// [x] [x]
	fmul				// [x * x] [x]
	fld1				// [1] [x * x] [x]
	fsubr				// [1 - x * x] [x]
	fsqrt				// [sqrt(1 - x * x)] [x]
	fxch st(1)			// [x] [sqrt(1 - x * x)]
	fpatan				// [acos]
	ret
}