Patchwork i386: move ULPs to i686/multiarch and regenerate new ones for i386

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Submitter Aurelien Jarno
Date Dec. 13, 2015, 10:24 p.m.
Message ID <1450045447-21041-1-git-send-email-aurelien@aurel32.net>
Download mbox | patch
Permalink /patch/9996/
State New
Headers show

Comments

Aurelien Jarno - Dec. 13, 2015, 10:24 p.m.
The i386 ULPs are actually the i686/multiarch ones. The i686/multiarch
float ULPs are more precise as the SSE2 version (when available) uses
double for the cosf and sinf functions.

On the other hand the higher precision of the x86 FPU improves the
precision for a few other math functions
---
 ChangeLog                                      |    6 +
 sysdeps/i386/fpu/libm-test-ulps                |  126 +-
 sysdeps/i386/i686/fpu/multiarch/libm-test-ulps | 2176 ++++++++++++++++++++++++
 3 files changed, 2252 insertions(+), 56 deletions(-)
 create mode 100644 sysdeps/i386/i686/fpu/multiarch/libm-test-ulps

I am actually still not sure this is correct the correct way of handling
that. The non-multiarch version is basically the same as the multiarch
version for a machine without SSE2. I believe we might have the same kind
of issues on x86-64 between SSE2 and AVX2 versions as AVX2 gives access to
FMA instructions.
Joseph Myers - Dec. 14, 2015, 10:20 p.m.
On Sun, 13 Dec 2015, Aurelien Jarno wrote:

> I am actually still not sure this is correct the correct way of handling
> that. The non-multiarch version is basically the same as the multiarch
> version for a machine without SSE2. I believe we might have the same kind
> of issues on x86-64 between SSE2 and AVX2 versions as AVX2 gives access to
> FMA instructions.

This is as close as we can get given present sysdeps structures (which 
don't allow distinguishing multiarch ulps depending on what hardware the 
tests were run on).  The patch is OK.

Patch

diff --git a/ChangeLog b/ChangeLog
index 13be8a8..fa09f1f 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,9 @@ 
+2015-12-14  Aurelien Jarno  <aurelien@aurel32.net>
+
+       * sysdeps/i386/fpu/libm-test-ulps: Move to ....
+       * sysdeps/i386/i686/multiarch/fpu/libm-test-ulps: ...here.
+       * sysdeps/i386/fpu/libm-test-ulps: Regenerate.
+
 2015-12-11  Aurelien Jarno  <aurelien@aurel32.net>
 
 	* sysdeps/unix/sysv/linux/arm/ioperm.c: Do not include
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index bbb644a..84da475 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -725,9 +725,9 @@  ldouble: 1
 
 Function: Real part of "ccosh_downward":
 double: 1
-float: 2
+float: 1
 idouble: 1
-ifloat: 2
+ifloat: 1
 ildouble: 3
 ldouble: 3
 
@@ -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
 
@@ -1021,9 +1029,7 @@  ildouble: 3
 ldouble: 3
 
 Function: Imaginary part of "cpow":
-double: 1
 float: 2
-idouble: 1
 ifloat: 2
 ildouble: 4
 ldouble: 4
@@ -1085,9 +1091,7 @@  ildouble: 1
 ldouble: 1
 
 Function: Imaginary part of "csin":
-double: 1
 float: 1
-idouble: 1
 ifloat: 1
 
 Function: Real part of "csin_downward":
@@ -1127,22 +1131,18 @@  double: 3
 float: 2
 idouble: 3
 ifloat: 2
-ildouble: 3
-ldouble: 3
+ildouble: 2
+ldouble: 2
 
 Function: Imaginary part of "csin_upward":
 double: 2
 float: 2
 idouble: 2
 ifloat: 2
-ildouble: 3
-ldouble: 3
+ildouble: 2
+ldouble: 2
 
 Function: Real part of "csinh":
-double: 1
-float: 1
-idouble: 1
-ifloat: 1
 ildouble: 1
 ldouble: 1
 
@@ -1156,9 +1156,9 @@  ldouble: 1
 
 Function: Real part of "csinh_downward":
 double: 1
-float: 2
+float: 1
 idouble: 1
-ifloat: 2
+ifloat: 1
 ildouble: 3
 ldouble: 3
 
@@ -1172,9 +1172,9 @@  ldouble: 3
 
 Function: Real part of "csinh_towardzero":
 double: 1
-float: 2
+float: 1
 idouble: 1
-ifloat: 2
+ifloat: 1
 ildouble: 3
 ldouble: 3
 
@@ -1191,16 +1191,16 @@  double: 2
 float: 2
 idouble: 2
 ifloat: 2
-ildouble: 3
-ldouble: 3
+ildouble: 2
+ldouble: 2
 
 Function: Imaginary part of "csinh_upward":
 double: 3
 float: 2
 idouble: 3
 ifloat: 2
-ildouble: 3
-ldouble: 3
+ildouble: 2
+ldouble: 2
 
 Function: Real part of "csqrt":
 double: 1
@@ -1282,33 +1282,33 @@  ldouble: 1
 
 Function: Real part of "ctan_downward":
 double: 1
-float: 2
+float: 1
 idouble: 1
-ifloat: 2
+ifloat: 1
 ildouble: 5
 ldouble: 5
 
 Function: Imaginary part of "ctan_downward":
 double: 2
-float: 2
+float: 1
 idouble: 2
-ifloat: 2
+ifloat: 1
 ildouble: 4
 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 +1362,17 @@  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
 
@@ -1526,9 +1526,7 @@  ldouble: 2
 
 Function: "exp_upward":
 double: 1
-float: 1
 idouble: 1
-ifloat: 1
 ildouble: 1
 ldouble: 1
 
@@ -1564,9 +1562,9 @@  ldouble: 4
 
 Function: "gamma":
 double: 3
-float: 3
+float: 2
 idouble: 3
-ifloat: 3
+ifloat: 2
 ildouble: 4
 ldouble: 4
 
@@ -1580,9 +1578,9 @@  ldouble: 7
 
 Function: "gamma_towardzero":
 double: 4
-float: 4
+float: 2
 idouble: 4
-ifloat: 4
+ifloat: 2
 ildouble: 7
 ldouble: 7
 
@@ -1716,9 +1714,9 @@  ldouble: 5
 
 Function: "lgamma":
 double: 3
-float: 3
+float: 2
 idouble: 3
-ifloat: 3
+ifloat: 2
 ildouble: 4
 ldouble: 4
 
@@ -1732,9 +1730,9 @@  ldouble: 7
 
 Function: "lgamma_towardzero":
 double: 4
-float: 4
+float: 2
 idouble: 4
-ifloat: 4
+ifloat: 2
 ildouble: 7
 ldouble: 7
 
@@ -1913,46 +1911,62 @@  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
 
@@ -2055,25 +2069,25 @@  ldouble: 5
 
 Function: "tgamma_downward":
 double: 3
-float: 4
+float: 3
 idouble: 3
-ifloat: 4
+ifloat: 3
 ildouble: 5
 ldouble: 5
 
 Function: "tgamma_towardzero":
-double: 4
-float: 4
-idouble: 4
-ifloat: 4
+double: 3
+float: 3
+idouble: 3
+ifloat: 3
 ildouble: 5
 ldouble: 5
 
 Function: "tgamma_upward":
-double: 4
-float: 4
-idouble: 4
-ifloat: 4
+double: 3
+float: 3
+idouble: 3
+ifloat: 3
 ildouble: 5
 ldouble: 5
 
@@ -2135,9 +2149,9 @@  ldouble: 5
 
 Function: "y1_upward":
 double: 1
-float: 3
+float: 2
 idouble: 1
-ifloat: 3
+ifloat: 2
 ildouble: 7
 ldouble: 7
 
diff --git a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
new file mode 100644
index 0000000..bbb644a
--- /dev/null
+++ b/sysdeps/i386/i686/fpu/multiarch/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
+
+Function: Imaginary part of "catanh_upward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: "cbrt":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 3
+ldouble: 3
+
+Function: "cbrt_downward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 4
+ldouble: 4
+
+Function: "cbrt_towardzero":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 3
+ldouble: 3
+
+Function: "cbrt_upward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 4
+ldouble: 4
+
+Function: Real part of "ccos":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: Imaginary part of "ccos":
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+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