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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
Please CC me.
--
Shane
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