diff options
| author | nsz <nsz@port70.net> | 2012-05-05 01:11:56 +0200 |
|---|---|---|
| committer | nsz <nsz@port70.net> | 2012-05-05 01:11:56 +0200 |
| commit | f697d66b81912af59128ac1b96bc0e2a4514b758 (patch) | |
| tree | 32433a4df7d33f692afa2ff6e759fa1c5870b8f0 | |
| parent | db4096c5f2ffb15e52015004ab5a900b820c6683 (diff) | |
| download | musl-f697d66b81912af59128ac1b96bc0e2a4514b758.tar.gz | |
math: change the formula used for acos.s
old: 2*atan2(sqrt(1-x),sqrt(1+x))
new: atan2(fabs(sqrt((1-x)*(1+x))),x)
improvements:
* all edge cases are fixed (sign of zero in downward rounding)
* a bit faster (here a single call is about 131ns vs 162ns)
* a bit more precise (at most 1ulp error on 1M uniform random
samples in [0,1), the old formula gave some 2ulp errors as well)
| -rw-r--r-- | src/math/i386/acos.s | 18 | ||||
| -rw-r--r-- | src/math/x86_64/acosl.s | 18 |
2 files changed, 16 insertions, 20 deletions
diff --git a/src/math/i386/acos.s b/src/math/i386/acos.s index bfff0c5c..47f365ef 100644 --- a/src/math/i386/acos.s +++ b/src/math/i386/acos.s @@ -1,3 +1,5 @@ +# use acos(x) = atan2(fabs(sqrt((1-x)*(1+x))), x) + .global acosf .type acosf,@function acosf: @@ -14,17 +16,13 @@ acosl: .type acos,@function acos: fldl 4(%esp) -1: fld1 - fld %st(1) +1: fld %st(0) fld1 - fsubp - fsqrt - fxch %st(2) - faddp + fsub %st(0),%st(1) + fadd %st(2) + fmulp fsqrt + fabs # fix sign of zero (matters in downward rounding mode) + fxch %st(1) fpatan - fld1 - fld1 - faddp - fmulp ret diff --git a/src/math/x86_64/acosl.s b/src/math/x86_64/acosl.s index db68d2de..88e01b49 100644 --- a/src/math/x86_64/acosl.s +++ b/src/math/x86_64/acosl.s @@ -1,18 +1,16 @@ +# see ../i386/acos.s + .global acosl .type acosl,@function acosl: fldt 8(%rsp) +1: fld %st(0) fld1 - fld %st(1) - fld1 - fsubp - fsqrt - fxch %st(2) - faddp + fsub %st(0),%st(1) + fadd %st(2) + fmulp fsqrt + fabs + fxch %st(1) fpatan - fld1 - fld1 - faddp - fmulp ret |