diff mbox

i386: move ULPs to i686 and regenerate new ones for i586

Message ID 1449179075-2420-1-git-send-email-aurelien@aurel32.net
State New, archived
Headers

Commit Message

Aurelien Jarno Dec. 3, 2015, 9:44 p.m. UTC 
  The i386 ULPs are actually the i686 ones. The i586 results are slightly
less precise. Therefore move the current ULPs to the i386/i686 directory
and generate i586 ones for the i386 directory.

---
 ChangeLog                            |    6 +
 sysdeps/i386/fpu/libm-test-ulps      |   40 +-
 sysdeps/i386/i686/fpu/libm-test-ulps | 2176 ++++++++++++++++++++++++++++++++++
 3 files changed, 2214 insertions(+), 8 deletions(-)
 create mode 100644 sysdeps/i386/i686/fpu/libm-test-ulps

Note: In theory we should even put the i486 ULPs in the i386 directory
and put the i586 ones in the i386/i586 directory. Not sure it is worth
it.

Comments

Joseph Myers Dec. 3, 2015, 10:28 p.m. UTC | #1 
On Thu, 3 Dec 2015, Aurelien Jarno wrote:

> The i386 ULPs are actually the i686 ones. The i586 results are slightly
> less precise. Therefore move the current ULPs to the i386/i686 directory
> and generate i586 ones for the i386 directory.

Are you sure they are i686 ones rather than actually i686+SSE2 (does 
--disable-multi-arch make any difference)?

> Note: In theory we should even put the i486 ULPs in the i386 directory
> and put the i586 ones in the i386/i586 directory. Not sure it is worth
> it.

There are no i586-specific libm function implementations, so there should 
be no difference in ulps between glibc built for i486 and i586.

If test inputs can be found that, built for i686, generate the higher ulps 
seen when building for pre-i686, that would reduce the number of variant 
ulps files needing regeneration.
Aurelien Jarno Dec. 4, 2015, 12:18 p.m. UTC | #2 
On 2015-12-03 22:28, Joseph Myers wrote:
> On Thu, 3 Dec 2015, Aurelien Jarno wrote:
> 
> > The i386 ULPs are actually the i686 ones. The i586 results are slightly
> > less precise. Therefore move the current ULPs to the i386/i686 directory
> > and generate i586 ones for the i386 directory.
> 
> Are you sure they are i686 ones rather than actually i686+SSE2 (does 
> --disable-multi-arch make any difference)?

You are actually correct, the current sysdeps/i386/fpu/libm-test-ulps
file corresponds to the i686+SSE2 ULPs.

Also the i586 and i686 ULPs are actually the same.

> > Note: In theory we should even put the i486 ULPs in the i386 directory
> > and put the i586 ones in the i386/i586 directory. Not sure it is worth
> > it.
> 
> There are no i586-specific libm function implementations, so there should 
> be no difference in ulps between glibc built for i486 and i586.
> 
> If test inputs can be found that, built for i686, generate the higher ulps 
> seen when building for pre-i686, that would reduce the number of variant 
> ulps files needing regeneration.

Ok, I'll try that, but between i686 and i686+SSE2.

Aurelien
Aurelien Jarno Dec. 11, 2015, 12:10 p.m. UTC | #3 
On 2015-12-04 13:18, Aurelien Jarno wrote:
> On 2015-12-03 22:28, Joseph Myers wrote:
> > On Thu, 3 Dec 2015, Aurelien Jarno wrote:
> > 
> > > The i386 ULPs are actually the i686 ones. The i586 results are slightly
> > > less precise. Therefore move the current ULPs to the i386/i686 directory
> > > and generate i586 ones for the i386 directory.
> > 
> > Are you sure they are i686 ones rather than actually i686+SSE2 (does 
> > --disable-multi-arch make any difference)?
> 
> You are actually correct, the current sysdeps/i386/fpu/libm-test-ulps
> file corresponds to the i686+SSE2 ULPs.
> 
> Also the i586 and i686 ULPs are actually the same.
> 
> > > Note: In theory we should even put the i486 ULPs in the i386 directory
> > > and put the i586 ones in the i386/i586 directory. Not sure it is worth
> > > it.
> > 
> > There are no i586-specific libm function implementations, so there should 
> > be no difference in ulps between glibc built for i486 and i586.
> > 
> > If test inputs can be found that, built for i686, generate the higher ulps 
> > seen when building for pre-i686, that would reduce the number of variant 
> > ulps files needing regeneration.
> 
> Ok, I'll try that, but between i686 and i686+SSE2.

The difference between the two only affects float ULPs for the cos, sin,
ctan and ctanh functions. The difference can be explained by the fact
that the SSE2 version of sinf and cosf basically convert the single
precision input into double precision, do all the computation in double
precision, and convert back the result to single precision.

I am therefore afraid we won't be able to find a case were the i686 and
SSE2 versions produce the same error.


Interestingly it also seems that the i586 ULPs differ between an AMD and
Intel CPU for the cacos_downward, cacos_towardzero and cacosh_downward 
double precision functions. Here is one of the failure on an AMD CPU:

  Failure: Test: Real part of: cacos_downward (1.0 + 0x1.fp-129 i)
  Result:
   is:          5.33563527698223236644e-20   0x1.f7efbeb8d4f100000000p-65
   should be:   5.33563527698223357014e-20   0x1.f7efbeb8d4f120000000p-65
   difference:  1.20370621524202240815e-35   0x1.00000000000000000000p-116
   ulp       :  2.0000
   max.ulp   :  1.0000

However the high precision result (at least the one in libm-test.inc) is
5.335635276982233498398987585285818977930e-20L. The expected result there
seems to me rounded upward and not downward, and thus the actual result
seems to be the correct one. Where am I wrong?

Aurelien
Joseph Myers Dec. 11, 2015, 1:05 p.m. UTC | #4 
On Fri, 11 Dec 2015, Aurelien Jarno wrote:

> The difference between the two only affects float ULPs for the cos, sin,
> ctan and ctanh functions. The difference can be explained by the fact
> that the SSE2 version of sinf and cosf basically convert the single
> precision input into double precision, do all the computation in double
> precision, and convert back the result to single precision.
> 
> I am therefore afraid we won't be able to find a case were the i686 and
> SSE2 versions produce the same error.

In that case maybe we do need a separate file in i686/fpu/multiarch/.

> Interestingly it also seems that the i586 ULPs differ between an AMD and
> Intel CPU for the cacos_downward, cacos_towardzero and cacosh_downward 
> double precision functions. Here is one of the failure on an AMD CPU:
> 
>   Failure: Test: Real part of: cacos_downward (1.0 + 0x1.fp-129 i)
>   Result:
>    is:          5.33563527698223236644e-20   0x1.f7efbeb8d4f100000000p-65
>    should be:   5.33563527698223357014e-20   0x1.f7efbeb8d4f120000000p-65
>    difference:  1.20370621524202240815e-35   0x1.00000000000000000000p-116
>    ulp       :  2.0000
>    max.ulp   :  1.0000
> 
> However the high precision result (at least the one in libm-test.inc) is
> 5.335635276982233498398987585285818977930e-20L. The expected result there
> seems to me rounded upward and not downward, and thus the actual result
> seems to be the correct one. Where am I wrong?

Because MPC is extremely slow for certain cases of complex inverse trig 
and hyperbolic functions, those have not moved to using auto-libm-test-in, 
and so the results given are rounded to a fixed number of decimal places 
and typically are only correct for round-to-nearest (so the computed ulps 
errors may be off by 1 in some cases).

I suppose maybe I should arrange for auto-libm-test-out to be split by 
function in such a way that outputs for each function are generated 
separately; that way, if it takes hours to regenerate 
auto-libm-test-out-ca{sin,cos,tan}{,h}, it wouldn't affect normal 
regeneration of test results for other functions.
diff mbox

Patch

diff --git a/ChangeLog b/ChangeLog
index 292c495..d30cd47 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,9 @@ 
+2015-12-03  Aurelien Jarno  <aurelien@aurel32.net>
+
+	* sysdeps/i386/fpu/libm-test-ulps: Move to ....
+	* sysdeps/i386/i686/fpu/libm-test-ulps: ...here.
+	* sysdeps/i386/fpu/libm-test-ulps: Regenerate.
+
 2015-12-03  Chris Metcalf  <cmetcalf@ezchip.com>
 
 	* sysdeps/arm/math_private.h (LDBL_CLASSIFY_COMPAT): New symbol.
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index bbb644a..972ccb9 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -960,24 +960,32 @@  ildouble: 1
 ldouble: 1
 
 Function: "cos":
+float: 1
+ifloat: 1
 ildouble: 1
 ldouble: 1
 
 Function: "cos_downward":
 double: 1
+float: 1
 idouble: 1
+ifloat: 1
 ildouble: 3
 ldouble: 3
 
 Function: "cos_towardzero":
 double: 1
+float: 1
 idouble: 1
+ifloat: 1
 ildouble: 2
 ldouble: 2
 
 Function: "cos_upward":
 double: 1
+float: 1
 idouble: 1
+ifloat: 1
 ildouble: 2
 ldouble: 2
 
@@ -1298,17 +1306,17 @@  ldouble: 4
 
 Function: Real part of "ctan_towardzero":
 double: 3
-float: 1
+float: 2
 idouble: 3
-ifloat: 1
+ifloat: 2
 ildouble: 5
 ldouble: 5
 
 Function: Imaginary part of "ctan_towardzero":
 double: 2
-float: 1
+float: 3
 idouble: 2
-ifloat: 1
+ifloat: 3
 ildouble: 4
 ldouble: 4
 
@@ -1362,17 +1370,17 @@  ldouble: 4
 
 Function: Real part of "ctanh_towardzero":
 double: 2
-float: 1
+float: 3
 idouble: 2
-ifloat: 1
+ifloat: 3
 ildouble: 4
 ldouble: 4
 
 Function: Imaginary part of "ctanh_towardzero":
 double: 2
-float: 1
+float: 2
 idouble: 2
-ifloat: 1
+ifloat: 2
 ildouble: 3
 ldouble: 3
 
@@ -1913,46 +1921,62 @@  ildouble: 2
 ldouble: 2
 
 Function: "sin":
+float: 1
+ifloat: 1
 ildouble: 1
 ldouble: 1
 
 Function: "sin_downward":
 double: 1
+float: 1
 idouble: 1
+ifloat: 1
 ildouble: 3
 ldouble: 3
 
 Function: "sin_towardzero":
 double: 1
+float: 1
 idouble: 1
+ifloat: 1
 ildouble: 2
 ldouble: 2
 
 Function: "sin_upward":
 double: 1
+float: 1
 idouble: 1
+ifloat: 1
 ildouble: 3
 ldouble: 3
 
 Function: "sincos":
+float: 1
+ifloat: 1
 ildouble: 1
 ldouble: 1
 
 Function: "sincos_downward":
 double: 1
+float: 1
 idouble: 1
+ifloat: 1
 ildouble: 3
 ldouble: 3
 
 Function: "sincos_towardzero":
 double: 1
+float: 1
 idouble: 1
+ifloat: 1
 ildouble: 2
 ldouble: 2
 
 Function: "sincos_upward":
 double: 1
+float: 1
 idouble: 1
+ifloat: 1
 ildouble: 3
 ldouble: 3
 
diff --git a/sysdeps/i386/i686/fpu/libm-test-ulps b/sysdeps/i386/i686/fpu/libm-test-ulps
new file mode 100644
index 0000000..bbb644a
--- /dev/null
+++ b/sysdeps/i386/i686/fpu/libm-test-ulps
@@ -0,0 +1,2176 @@ 
+# Begin of automatic generation
+
+# Maximal error of functions:
+Function: "acos":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+
+Function: "acos_downward":
+ildouble: 2
+ldouble: 2
+
+Function: "acos_towardzero":
+ildouble: 2
+ldouble: 2
+
+Function: "acos_upward":
+double: 1
+idouble: 1
+ildouble: 2
+ldouble: 2
+
+Function: "acosh":
+double: 1
+idouble: 1
+ildouble: 4
+ldouble: 2
+
+Function: "acosh_downward":
+double: 1
+idouble: 1
+ildouble: 6
+ldouble: 4
+
+Function: "acosh_towardzero":
+double: 1
+idouble: 1
+ildouble: 6
+ldouble: 4
+
+Function: "acosh_upward":
+double: 1
+idouble: 1
+ildouble: 4
+ldouble: 3
+
+Function: "asin":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+
+Function: "asin_downward":
+double: 1
+idouble: 1
+ildouble: 2
+ldouble: 2
+
+Function: "asin_towardzero":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+
+Function: "asin_upward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: "asinh":
+double: 1
+idouble: 1
+ildouble: 3
+ldouble: 3
+
+Function: "asinh_downward":
+double: 1
+float: 1
+idouble: 1
+ildouble: 5
+ldouble: 5
+
+Function: "asinh_towardzero":
+double: 1
+float: 1
+idouble: 1
+ildouble: 4
+ldouble: 4
+
+Function: "asinh_upward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 5
+ldouble: 5
+
+Function: "atan":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+
+Function: "atan2":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+
+Function: "atan2_downward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: "atan2_towardzero":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: "atan2_upward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: "atan_downward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: "atan_towardzero":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: "atan_upward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: "atanh":
+double: 1
+idouble: 1
+ildouble: 3
+ldouble: 3
+
+Function: "atanh_downward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 3
+ldouble: 4
+
+Function: "atanh_towardzero":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 5
+ldouble: 3
+
+Function: "atanh_upward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 5
+ldouble: 5
+
+Function: "cabs":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+
+Function: "cabs_downward":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+
+Function: "cabs_towardzero":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+
+Function: "cabs_upward":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+
+Function: Real part of "cacos":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: Imaginary part of "cacos":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+Function: Real part of "cacos_downward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+Function: Imaginary part of "cacos_downward":
+double: 4
+float: 3
+idouble: 4
+ifloat: 3
+ildouble: 5
+ldouble: 5
+
+Function: Real part of "cacos_towardzero":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+Function: Imaginary part of "cacos_towardzero":
+double: 4
+float: 3
+idouble: 4
+ifloat: 3
+ildouble: 5
+ldouble: 5
+
+Function: Real part of "cacos_upward":
+double: 2
+float: 2
+idouble: 2
+ifloat: 2
+ildouble: 2
+ldouble: 2
+
+Function: Imaginary part of "cacos_upward":
+double: 4
+float: 4
+idouble: 4
+ifloat: 4
+ildouble: 5
+ldouble: 5
+
+Function: Real part of "cacosh":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+Function: Imaginary part of "cacosh":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: Real part of "cacosh_downward":
+double: 4
+float: 3
+idouble: 4
+ifloat: 3
+ildouble: 5
+ldouble: 5
+
+Function: Imaginary part of "cacosh_downward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+Function: Real part of "cacosh_towardzero":
+double: 4
+float: 3
+idouble: 4
+ifloat: 3
+ildouble: 5
+ldouble: 5
+
+Function: Imaginary part of "cacosh_towardzero":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+Function: Real part of "cacosh_upward":
+double: 4
+float: 4
+idouble: 4
+ifloat: 4
+ildouble: 5
+ldouble: 5
+
+Function: Imaginary part of "cacosh_upward":
+double: 2
+float: 2
+idouble: 2
+ifloat: 2
+ildouble: 2
+ldouble: 2
+
+Function: "carg":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+
+Function: "carg_downward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: "carg_towardzero":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: "carg_upward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: Real part of "casin":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: Imaginary part of "casin":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+Function: Real part of "casin_downward":
+double: 2
+float: 2
+idouble: 2
+ifloat: 2
+ildouble: 2
+ldouble: 2
+
+Function: Imaginary part of "casin_downward":
+double: 4
+float: 3
+idouble: 4
+ifloat: 3
+ildouble: 5
+ldouble: 5
+
+Function: Real part of "casin_towardzero":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+Function: Imaginary part of "casin_towardzero":
+double: 4
+float: 3
+idouble: 4
+ifloat: 3
+ildouble: 5
+ldouble: 5
+
+Function: Real part of "casin_upward":
+double: 2
+float: 2
+idouble: 2
+ifloat: 2
+ildouble: 2
+ldouble: 2
+
+Function: Imaginary part of "casin_upward":
+double: 4
+float: 4
+idouble: 4
+ifloat: 4
+ildouble: 5
+ldouble: 5
+
+Function: Real part of "casinh":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+Function: Imaginary part of "casinh":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: Real part of "casinh_downward":
+double: 4
+float: 3
+idouble: 4
+ifloat: 3
+ildouble: 5
+ldouble: 5
+
+Function: Imaginary part of "casinh_downward":
+double: 2
+float: 2
+idouble: 2
+ifloat: 2
+ildouble: 2
+ldouble: 2
+
+Function: Real part of "casinh_towardzero":
+double: 4
+float: 3
+idouble: 4
+ifloat: 3
+ildouble: 5
+ldouble: 5
+
+Function: Imaginary part of "casinh_towardzero":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+Function: Real part of "casinh_upward":
+double: 4
+float: 4
+idouble: 4
+ifloat: 4
+ildouble: 5
+ldouble: 5
+
+Function: Imaginary part of "casinh_upward":
+double: 2
+float: 2
+idouble: 2
+ifloat: 2
+ildouble: 2
+ldouble: 2
+
+Function: Imaginary part of "catan":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: Real part of "catan_downward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: Imaginary part of "catan_downward":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 4
+ldouble: 4
+
+Function: Real part of "catan_towardzero":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: Imaginary part of "catan_towardzero":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 4
+ldouble: 4
+
+Function: Real part of "catan_upward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: Imaginary part of "catan_upward":
+double: 2
+float: 2
+idouble: 2
+ifloat: 2
+ildouble: 3
+ldouble: 3
+
+Function: Real part of "catanh":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: Real part of "catanh_downward":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 4
+ldouble: 4
+
+Function: Imaginary part of "catanh_downward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: Real part of "catanh_towardzero":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 4
+ldouble: 4
+
+Function: Imaginary part of "catanh_towardzero":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: Real part of "catanh_upward":
+double: 2
+float: 2
+idouble: 2
+ifloat: 2
+ildouble: 4
+ldouble: 4
+
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+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+
+Function: "log10":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+
+Function: "log10_downward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+Function: "log10_towardzero":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+Function: "log10_upward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: "log1p":
+double: 1
+idouble: 1
+ildouble: 2
+ldouble: 2
+
+Function: "log1p_downward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 4
+ldouble: 4
+
+Function: "log1p_towardzero":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 4
+ldouble: 4
+
+Function: "log1p_upward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 3
+ldouble: 3
+
+Function: "log2":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+
+Function: "log2_downward":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+
+Function: "log2_towardzero":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: "log2_upward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: "log_downward":
+double: 1
+idouble: 1
+ildouble: 2
+ldouble: 2
+
+Function: "log_towardzero":
+double: 1
+idouble: 1
+ildouble: 2
+ldouble: 2
+
+Function: "log_upward":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+
+Function: "pow":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+
+Function: "pow10":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+
+Function: "pow10_downward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+Function: "pow10_towardzero":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+Function: "pow10_upward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+Function: "pow_downward":
+double: 1
+idouble: 1
+ildouble: 4
+ldouble: 4
+
+Function: "pow_towardzero":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+
+Function: "pow_upward":
+double: 1
+idouble: 1
+ildouble: 2
+ldouble: 2
+
+Function: "sin":
+ildouble: 1
+ldouble: 1
+
+Function: "sin_downward":
+double: 1
+idouble: 1
+ildouble: 3
+ldouble: 3
+
+Function: "sin_towardzero":
+double: 1
+idouble: 1
+ildouble: 2
+ldouble: 2
+
+Function: "sin_upward":
+double: 1
+idouble: 1
+ildouble: 3
+ldouble: 3
+
+Function: "sincos":
+ildouble: 1
+ldouble: 1
+
+Function: "sincos_downward":
+double: 1
+idouble: 1
+ildouble: 3
+ldouble: 3
+
+Function: "sincos_towardzero":
+double: 1
+idouble: 1
+ildouble: 2
+ldouble: 2
+
+Function: "sincos_upward":
+double: 1
+idouble: 1
+ildouble: 3
+ldouble: 3
+
+Function: "sinh":
+double: 1
+ildouble: 2
+ldouble: 2
+
+Function: "sinh_downward":
+double: 2
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 4
+ldouble: 5
+
+Function: "sinh_towardzero":
+double: 2
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 3
+ldouble: 4
+
+Function: "sinh_upward":
+double: 4
+float: 2
+idouble: 1
+ifloat: 1
+ildouble: 4
+ldouble: 5
+
+Function: "tan":
+float: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+Function: "tan_downward":
+double: 1
+float: 2
+idouble: 1
+ifloat: 2
+ildouble: 3
+ldouble: 3
+
+Function: "tan_towardzero":
+double: 1
+float: 2
+idouble: 1
+ifloat: 2
+ildouble: 3
+ldouble: 3
+
+Function: "tan_upward":
+double: 1
+float: 2
+idouble: 1
+ifloat: 2
+ildouble: 2
+ldouble: 2
+
+Function: "tanh":
+double: 1
+idouble: 1
+ildouble: 3
+ldouble: 3
+
+Function: "tanh_downward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 7
+ldouble: 4
+
+Function: "tanh_towardzero":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 3
+ldouble: 3
+
+Function: "tanh_upward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 5
+ldouble: 4
+
+Function: "tgamma":
+double: 3
+float: 3
+idouble: 3
+ifloat: 3
+ildouble: 5
+ldouble: 5
+
+Function: "tgamma_downward":
+double: 3
+float: 4
+idouble: 3
+ifloat: 4
+ildouble: 5
+ldouble: 5
+
+Function: "tgamma_towardzero":
+double: 4
+float: 4
+idouble: 4
+ifloat: 4
+ildouble: 5
+ldouble: 5
+
+Function: "tgamma_upward":
+double: 4
+float: 4
+idouble: 4
+ifloat: 4
+ildouble: 5
+ldouble: 5
+
+Function: "y0":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: "y0_downward":
+double: 2
+float: 2
+idouble: 2
+ifloat: 2
+ildouble: 5
+ldouble: 5
+
+Function: "y0_towardzero":
+double: 2
+float: 2
+idouble: 2
+ifloat: 2
+ildouble: 5
+ldouble: 5
+
+Function: "y0_upward":
+double: 1
+float: 2
+idouble: 1
+ifloat: 2
+ildouble: 3
+ldouble: 3
+
+Function: "y1":
+double: 2
+float: 2
+idouble: 2
+ifloat: 2
+ildouble: 2
+ldouble: 2
+
+Function: "y1_downward":
+double: 2
+float: 2
+idouble: 2
+ifloat: 2
+ildouble: 7
+ldouble: 7
+
+Function: "y1_towardzero":
+double: 2
+float: 2
+idouble: 2
+ifloat: 2
+ildouble: 5
+ldouble: 5
+
+Function: "y1_upward":
+double: 1
+float: 3
+idouble: 1
+ifloat: 3
+ildouble: 7
+ldouble: 7
+
+Function: "yn":
+double: 2
+float: 3
+idouble: 2
+ifloat: 3
+ildouble: 4
+ldouble: 4
+
+Function: "yn_downward":
+double: 2
+float: 2
+idouble: 2
+ifloat: 2
+ildouble: 5
+ldouble: 5
+
+Function: "yn_towardzero":
+double: 3
+float: 3
+idouble: 3
+ifloat: 3
+ildouble: 5
+ldouble: 5
+
+Function: "yn_upward":
+double: 3
+float: 3
+idouble: 3
+ifloat: 3
+ildouble: 4
+ldouble: 4
+
+# end of automatic generation