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```Date: Sat, 23 Feb 2019 09:21:08 -0500
From: Shane Seelig <stseelig@...l.com>
To: musl@...ts.openwall.com
Subject: x87 asin and acos

Currently 'asin' uses the algorithm:
arcsin(x) == arctan(x/(sqrt((1-x)(1+x))))
If the following algorithm were to be used instead, an 'fadd' could be
removed.
arcsin(x) == arctan(x/(sqrt(1-x**2)))

current:
fldx	X(%esp)		# %st(0) = x

fld 	%st(0)		# %st(1) = x
# %st(0) = x

fld1			# %st(2) = x
# %st(1) = x
# %st(0) = 1
# unixware bug
fsub	%st(0),%st(1)	# %st(2) = x
# %st(1) = 1-x
# %st(0) = 1

fadd	%st(2), %st(0)	# %st(2) = x
# %st(1) = 1-x
# %st(0) = 1+x

fmulp	%st(0), %st(1)	# %st(1) = x
# %st(0) = 1-x**2

fsqrt			# %st(1) = x
# %st(0) = sqrt(1-x**2)

fpatan			# %st(0) = arcsin(x)

ret

new:
fldx	X(%esp)		# %st(0) = x

fld	%st(0)		# %st(1) = x
# %st(0) = x

fmul	%st(0), %st(0)	# %st(1) = x
# %st(0) = x**2

fld1			# %st(2) = x
# %st(1) = x**2
# %st(0) = 1
# unixware bug
fsubp	%st(0), %st(1)	# %st(1) = x
# %st(0) = 1-x**2

fsqrt			# %st(1) = x
# %st(0) = sqrt(1-x**2)

fpatan			# %st(0) = arcsin(x)

ret

affected files:
math/i386/acos.s
math/i386/asin.s
math/x32/acosl.s
math/x32/asinl.s
math/x86_64/acosl.s
math/x86_64/asinl.s