This is libc.info, produced by makeinfo version 4.2 from libc.texinfo.

INFO-DIR-SECTION GNU libraries
START-INFO-DIR-ENTRY
* Libc: (libc).                 C library.
END-INFO-DIR-ENTRY

   This file documents the GNU C library.

   This is Edition 0.10, last updated 2001-07-06, of `The GNU C Library
Reference Manual', for Version 2.3.x.

   Copyright (C) 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2001, 2002
Free Software Foundation, Inc.

   Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.1 or
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Invariant Sections being "Free Software Needs Free Documentation" and
"GNU Lesser General Public License", the Front-Cover texts being (a)
(see below), and with the Back-Cover Texts being (b) (see below).  A
copy of the license is included in the section entitled "GNU Free
Documentation License".

   (a) The FSF's Front-Cover Text is:

   A GNU Manual

   (b) The FSF's Back-Cover Text is:

   You have freedom to copy and modify this GNU Manual, like GNU
software.  Copies published by the Free Software Foundation raise
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File: libc.info,  Node: Errors in Math Functions,  Next: Pseudo-Random Numbers,  Prev: Special Functions,  Up: Mathematics

Known Maximum Errors in Math Functions
======================================

   This section lists the known errors of the functions in the math
library.  Errors are measured in "units of the last place".  This is a
measure for the relative error.  For a number z with the representation
d.d...d*2^e (we assume IEEE floating-point numbers with base 2) the ULP
is represented by

     |d.d...d - (z / 2^e)| / 2^(p - 1)

where p is the number of bits in the mantissa of the floating-point
number representation.  Ideally the error for all functions is always
less than 0.5ulps.  Using rounding bits this is also possible and
normally implemented for the basic operations.  To achieve the same for
the complex math functions requires a lot more work and this has not
yet been done.

   Therefore many of the functions in the math library have errors.  The
table lists the maximum error for each function which is exposed by one
of the existing tests in the test suite.  The table tries to cover as
much as possible and list the actual maximum error (or at least a
ballpark figure) but this is often not achieved due to the large search
space.

   The table lists the ULP values for different architectures.
Different architectures have different results since their hardware
support for floating-point operations varies and also the existing
hardware support is different.

Function      Alpha           ARM             Generic         hppa/fpu        ix86
acosf         -               -               -               -               -
acos          -               -               -               -               -
acosl         -               -               -               -               622
acoshf        -               -               -               -               -
acosh         -               -               -               -               -
acoshl        -               -               -               -               -
asinf         -               2               -               -               -
asin          -               1               -               -               -
asinl         -               -               -               -               1
asinhf        -               -               -               -               -
asinh         -               -               -               -               -
asinhl        -               -               -               -               -
atanf         -               -               -               -               -
atan          -               -               -               -               -
atanl         -               -               -               -               -
atanhf        1               -               -               1               -
atanh         -               1               -               -               -
atanhl        -               -               -               -               1
atan2f        3               -               -               3               -
atan2         -               -               -               -               -
atan2l        -               -               -               -               -
cabsf         -               1               -               -               -
cabs          -               1               -               -               -
cabsl         -               -               -               -               -
cacosf        -               1 + i 1         -               -               0 + i 1
cacos         -               1 + i 0         -               -               -
cacosl        -               -               -               -               0 + i 2
cacoshf       7 + i 3         7 + i 3         -               7 + i 3         9 + i 4
cacosh        1 + i 1         1 + i 1         -               1 + i 1         1 + i 1
cacoshl       -               -               -               -               6 + i 1
cargf         -               -               -               -               -
carg          -               -               -               -               -
cargl         -               -               -               -               -
casinf        1 + i 0         2 + i 1         -               1 + i 0         1 + i 1
casin         1 + i 0         3 + i 0         -               1 + i 0         1 + i 0
casinl        -               -               -               -               2 + i 2
casinhf       1 + i 6         1 + i 6         -               1 + i 6         1 + i 6
casinh        5 + i 3         5 + i 3         -               5 + i 3         5 + i 3
casinhl       -               -               -               -               5 + i 5
catanf        4 + i 1         4 + i 1         -               4 + i 1         0 + i 1
catan         0 + i 1         0 + i 1         -               0 + i 1         0 + i 1
catanl        -               -               -               -               -
catanhf       0 + i 6         1 + i 6         -               0 + i 6         1 + i 0
catanh        4 + i 0         4 + i 1         -               4 + i 0         2 + i 0
catanhl       -               -               -               -               1 + i 0
cbrtf         -               -               -               -               -
cbrt          1               1               -               1               -
cbrtl         -               -               -               -               1
ccosf         1 + i 1         0 + i 1         -               1 + i 1         0 + i 1
ccos          1 + i 0         1 + i 1         -               1 + i 0         1 + i 0
ccosl         -               -               -               -               1 + i 1
ccoshf        1 + i 1         1 + i 1         -               1 + i 1         1 + i 1
ccosh         1 + i 0         1 + i 1         -               1 + i 0         1 + i 1
ccoshl        -               -               -               -               0 + i 1
ceilf         -               -               -               -               -
ceil          -               -               -               -               -
ceill         -               -               -               -               -
cexpf         1 + i 1         1 + i 1         -               1 + i 1         -
cexp          -               1 + i 0         -               -               -
cexpl         -               -               -               -               1 + i 1
cimagf        -               -               -               -               -
cimag         -               -               -               -               -
cimagl        -               -               -               -               -
clogf         1 + i 3         0 + i 3         -               1 + i 3         1 + i 0
clog          -               0 + i 1         -               -               -
clogl         -               -               -               -               1 + i 0
clog10f       1 + i 5         1 + i 5         -               1 + i 5         1 + i 1
clog10        0 + i 1         1 + i 1         -               0 + i 1         1 + i 1
clog10l       -               -               -               -               1 + i 1
conjf         -               -               -               -               -
conj          -               -               -               -               -
conjl         -               -               -               -               -
copysignf     -               -               -               -               -
copysign      -               -               -               -               -
copysignl     -               -               -               -               -
cosf          1               1               -               1               1
cos           2               2               -               2               2
cosl          -               -               -               -               1
coshf         -               -               -               -               -
cosh          -               -               -               -               -
coshl         -               -               -               -               -
cpowf         4 + i 2         4 + i 2         -               4 + i 2         4 + i 3
cpow          2 + i 2         1 + i 1.1031    -               2 + i 2         1 + i 2
cpowl         -               -               -               -               763 + i 2
cprojf        -               -               -               -               -
cproj         -               -               -               -               -
cprojl        -               -               -               -               -
crealf        -               -               -               -               -
creal         -               -               -               -               -
creall        -               -               -               -               -
csinf         -               0 + i 1         -               -               1 + i 1
csin          -               -               -               -               -
csinl         -               -               -               -               1 + i 0
csinhf        1 + i 1         1 + i 1         -               1 + i 1         1 + i 1
csinh         0 + i 1         0 + i 1         -               0 + i 1         1 + i 1
csinhl        -               -               -               -               1 + i 2
csqrtf        1 + i 0         1 + i 1         -               1 + i 0         -
csqrt         -               1 + i 0         -               -               -
csqrtl        -               -               -               -               -
ctanf         -               1 + i 1         -               -               0 + i 1
ctan          1 + i 1         1 + i 1         -               1 + i 1         1 + i 1
ctanl         -               -               -               -               439 + i 3
ctanhf        2 + i 1         2 + i 1         -               2 + i 1         1 + i 1
ctanh         1 + i 0         2 + i 2         -               1 + i 0         0 + i 1
ctanhl        -               -               -               -               5 + i 25
erff          -               -               -               -               -
erf           1               -               -               1               1
erfl          -               -               -               -               -
erfcf         -               12              -               -               1
erfc          1               24              -               1               1
erfcl         -               -               -               -               1
expf          -               -               -               -               -
exp           -               -               -               -               -
expl          -               -               -               -               -
exp10f        2               2               -               2               -
exp10         6               6               -               6               -
exp10l        -               -               -               -               8
exp2f         -               -               -               -               -
exp2          -               -               -               -               -
exp2l         -               -               -               -               -
expm1f        1               1               -               1               -
expm1         1               -               -               1               -
expm1l        -               -               -               -               -
fabsf         -               -               -               -               -
fabs          -               -               -               -               -
fabsl         -               -               -               -               -
fdimf         -               -               -               -               -
fdim          -               -               -               -               -
fdiml         -               -               -               -               -
floorf        -               -               -               -               -
floor         -               -               -               -               -
floorl        -               -               -               -               -
fmaf          -               -               -               -               -
fma           -               -               -               -               -
fmal          -               -               -               -               -
fmaxf         -               -               -               -               -
fmax          -               -               -               -               -
fmaxl         -               -               -               -               -
fminf         -               -               -               -               -
fmin          -               -               -               -               -
fminl         -               -               -               -               -
fmodf         -               1               -               -               -
fmod          -               2               -               -               -
fmodl         -               -               -               -               -
frexpf        -               -               -               -               -
frexp         -               -               -               -               -
frexpl        -               -               -               -               -
gammaf        -               -               -               -               -
gamma         -               -               -               -               1
gammal        -               -               -               -               1
hypotf        1               1               -               1               1
hypot         -               1               -               -               -
hypotl        -               -               -               -               -
ilogbf        -               -               -               -               -
ilogb         -               -               -               -               -
ilogbl        -               -               -               -               -
j0f           2               2               -               2               1
j0            2               2               -               2               1
j0l           -               -               -               -               1
j1f           2               2               -               2               1
j1            1               1               -               1               1
j1l           -               -               -               -               1
jnf           4               4               -               4               2
jn            4               6               -               4               2
jnl           -               -               -               -               2
lgammaf       2               2               -               2               2
lgamma        1               1               -               1               1
lgammal       -               -               -               -               1
lrintf        -               -               -               -               -
lrint         -               -               -               -               -
lrintl        -               -               -               -               -
llrintf       -               -               -               -               -
llrint        -               -               -               -               -
llrintl       -               -               -               -               -
logf          -               1               -               -               1
log           -               1               -               -               -
logl          -               -               -               -               -
log10f        2               1               -               2               1
log10         1               1               -               1               -
log10l        -               -               -               -               1
log1pf        1               1               -               1               -
log1p         -               1               -               -               -
log1pl        -               -               -               -               -
log2f         -               1               -               -               -
log2          -               1               -               -               -
log2l         -               -               -               -               -
logbf         -               -               -               -               -
logb          -               -               -               -               -
logbl         -               -               -               -               -
lroundf       -               -               -               -               -
lround        -               -               -               -               -
lroundl       -               -               -               -               -
llroundf      -               -               -               -               -
llround       -               -               -               -               -
llroundl      -               -               -               -               -
modff         -               -               -               -               -
modf          -               -               -               -               -
modfl         -               -               -               -               -
nearbyintf    -               -               -               -               -
nearbyint     -               -               -               -               -
nearbyintl    -               -               -               -               -
nextafterf    -               -               -               -               -
nextafter     -               -               -               -               -
nextafterl    -               -               -               -               -
nexttowardf   -               -               -               -               -
nexttoward    -               -               -               -               -
nexttowardl   -               -               -               -               -
powf          -               -               -               -               -
pow           -               -               -               -               -
powl          -               -               -               -               -
remainderf    -               -               -               -               -
remainder     -               -               -               -               -
remainderl    -               -               -               -               -
remquof       -               -               -               -               -
remquo        -               -               -               -               -
remquol       -               -               -               -               -
rintf         -               -               -               -               -
rint          -               -               -               -               -
rintl         -               -               -               -               -
roundf        -               -               -               -               -
round         -               -               -               -               -
roundl        -               -               -               -               -
scalbf        -               -               -               -               -
scalb         -               -               -               -               -
scalbl        -               -               -               -               -
scalbnf       -               -               -               -               -
scalbn        -               -               -               -               -
scalbnl       -               -               -               -               -
scalblnf      -               -               -               -               -
scalbln       -               -               -               -               -
scalblnl      -               -               -               -               -
sinf          -               -               -               -               -
sin           -               -               -               -               -
sinl          -               -               -               -               -
sincosf       1               1               -               1               1
sincos        1               1               -               1               1
sincosl       -               -               -               -               1
sinhf         -               1               -               -               -
sinh          -               1               -               -               -
sinhl         -               -               -               -               -
sqrtf         -               -               -               -               -
sqrt          -               -               -               -               -
sqrtl         -               -               -               -               -
tanf          -               -               -               -               -
tan           1               0.5             -               1               1
tanl          -               -               -               -               -
tanhf         -               1               -               -               -
tanh          -               1               -               -               -
tanhl         -               -               -               -               -
tgammaf       1               1               -               1               1
tgamma        1               1               -               1               2
tgammal       -               -               -               -               1
truncf        -               -               -               -               -
trunc         -               -               -               -               -
truncl        -               -               -               -               -
y0f           1               1               -               1               1
y0            2               2               -               2               2
y0l           -               -               -               -               1
y1f           2               2               -               2               2
y1            3               3               -               3               2
y1l           -               -               -               -               1
ynf           2               2               -               2               3
yn            3               3               -               3               2
ynl           -               -               -               -               4

Function      IA64            M68k            MIPS            PowerPC         powerpc/nofpu
acosf         -               -               -               -               -
acos          -               -               -               -               -
acosl         -               -               -               -               -
acoshf        -               -               -               -               -
acosh         -               -               -               -               -
acoshl        -               1               -               -               -
asinf         -               -               -               -               -
asin          -               -               -               -               -
asinl         -               -               -               -               -
asinhf        -               -               -               -               -
asinh         -               -               -               -               -
asinhl        -               1               -               -               -
atanf         -               -               -               -               -
atan          -               -               -               -               -
atanl         -               -               -               -               -
atanhf        -               -               1               1               1
atanh         -               -               -               -               -
atanhl        -               1               -               -               -
atan2f        -               -               3               3               3
atan2         -               -               -               -               -
atan2l        -               1               -               -               -
cabsf         -               -               -               -               -
cabs          -               -               -               -               -
cabsl         -               -               -               -               -
cacosf        0 + i 1         2 + i 1         -               -               -
cacos         -               -               -               -               -
cacosl        0 + i 2         1 + i 2         -               -               -
cacoshf       7 + i 0         7 + i 1         7 + i 3         7 + i 3         7 + i 3
cacosh        1 + i 1         1 + i 1         1 + i 1         1 + i 1         1 + i 1
cacoshl       7 + i 1         6 + i 2         -               -               -
cargf         -               -               -               -               -
carg          -               -               -               -               -
cargl         -               -               -               -               -
casinf        1 + i 1         5 + i 1         1 + i 0         1 + i 0         1 + i 0
casin         1 + i 0         1 + i 0         1 + i 0         1 + i 0         1 + i 0
casinl        2 + i 2         3 + i 2         -               -               -
casinhf       1 + i 6         19 + i 1        1 + i 6         1 + i 6         1 + i 6
casinh        5 + i 3         6 + i 13        5 + i 3         5 + i 3         5 + i 3
casinhl       5 + i 5         5 + i 6         -               -               -
catanf        0 + i 1         0 + i 1         4 + i 1         4 + i 1         4 + i 1
catan         0 + i 1         0 + i 1         0 + i 1         0 + i 1         0 + i 1
catanl        -               1 + i 0         -               -               -
catanhf       -               -               0 + i 6         0 + i 6         0 + i 6
catanh        4 + i 0         -               4 + i 0         4 + i 0         4 + i 0
catanhl       1 + i 0         1 + i 0         -               -               -
cbrtf         -               -               -               -               -
cbrt          -               -               1               1               1
cbrtl         -               1               -               -               -
ccosf         0 + i 1         1 + i 1         1 + i 1         1 + i 1         1 + i 1
ccos          1 + i 0         -               1 + i 0         1 + i 0         1 + i 0
ccosl         1 + i 1         1 + i 1         -               -               -
ccoshf        1 + i 1         1 + i 1         1 + i 1         1 + i 1         1 + i 1
ccosh         1 + i 1         -               1 + i 0         1 + i 0         1 + i 0
ccoshl        0 + i 1         0 + i 1         -               -               -
ceilf         -               -               -               -               -
ceil          -               -               -               -               -
ceill         -               -               -               -               -
cexpf         1 + i 1         2 + i 1         1 + i 1         1 + i 1         1 + i 1
cexp          -               -               -               -               -
cexpl         0 + i 1         0 + i 1         -               -               -
cimagf        -               -               -               -               -
cimag         -               -               -               -               -
cimagl        -               -               -               -               -
clogf         1 + i 0         1 + i 0         1 + i 3         1 + i 3         1 + i 3
clog          -               -               -               -               -
clogl         1 + i 0         1 + i 1         -               -               -
clog10f       1 + i 1         1 + i 1         1 + i 5         1 + i 5         1 + i 5
clog10        1 + i 1         1 + i 1         0 + i 1         0 + i 1         0 + i 1
clog10l       1 + i 1         1 + i 2         -               -               -
conjf         -               -               -               -               -
conj          -               -               -               -               -
conjl         -               -               -               -               -
copysignf     -               -               -               -               -
copysign      -               -               -               -               -
copysignl     -               -               -               -               -
cosf          1               1               1               1               1
cos           2               2               2               2               2
cosl          1               1               -               -               -
coshf         -               -               -               -               -
cosh          -               -               -               -               -
coshl         -               -               -               -               -
cpowf         5 + i 3         2 + i 6         4 + i 2         4 + i 2         4 + i 2
cpow          2 + i 2         1 + i 2         2 + i 2         2 + i 2         2 + i 2
cpowl         3 + i 4         15 + i 2        -               -               -
cprojf        -               -               -               -               -
cproj         -               -               -               -               -
cprojl        -               -               -               -               -
crealf        -               -               -               -               -
creal         -               -               -               -               -
creall        -               -               -               -               -
csinf         1 + i 1         1 + i 1         -               -               -
csin          -               -               -               -               -
csinl         1 + i 0         1 + i 0         -               -               -
csinhf        1 + i 1         1 + i 1         1 + i 1         1 + i 1         1 + i 1
csinh         1 + i 1         -               0 + i 1         0 + i 1         0 + i 1
csinhl        1 + i 2         1 + i 2         -               -               -
csqrtf        1 + i 0         -               1 + i 0         1 + i 0         1 + i 0
csqrt         -               -               -               -               -
csqrtl        -               -               -               -               -
ctanf         0 + i 1         -               -               -               -
ctan          1 + i 1         -               1 + i 1         1 + i 1         1 + i 1
ctanl         2 + i 1         439 + i 2       -               -               -
ctanhf        0 + i 1         0 + i 1         2 + i 1         2 + i 1         2 + i 1
ctanh         1 + i 1         0 + i 1         1 + i 0         1 + i 0         1 + i 0
ctanhl        1 + i 24        2 + i 25        -               -               -
erff          -               -               -               -               -
erf           1               -               1               1               1
erfl          -               -               -               -               -
erfcf         1               1               -               1               -
erfc          1               -               1               1               1
erfcl         1               1               -               -               -
expf          -               -               -               -               -
exp           -               -               -               -               -
expl          -               -               -               -               -
exp10f        2               -               2               2               2
exp10         6               -               6               6               6
exp10l        3               -               -               -               -
exp2f         -               -               -               -               -
exp2          -               -               -               -               -
exp2l         -               -               -               -               -
expm1f        -               -               1               1               1
expm1         -               -               1               1               1
expm1l        1               1               -               -               -
fabsf         -               -               -               -               -
fabs          -               -               -               -               -
fabsl         -               -               -               -               -
fdimf         -               -               -               -               -
fdim          -               -               -               -               -
fdiml         -               -               -               -               -
floorf        -               -               -               -               -
floor         -               -               -               -               -
floorl        -               -               -               -               -
fmaf          -               -               -               -               -
fma           -               -               -               -               -
fmal          -               -               -               -               -
fmaxf         -               -               -               -               -
fmax          -               -               -               -               -
fmaxl         -               -               -               -               -
fminf         -               -               -               -               -
fmin          -               -               -               -               -
fminl         -               -               -               -               -
fmodf         -               -               -               -               -
fmod          -               -               -               -               -
fmodl         -               -               -               -               -
frexpf        -               -               -               -               -
frexp         -               -               -               -               -
frexpl        -               -               -               -               -
gammaf        -               -               -               -               -
gamma         -               -               -               -               -
gammal        1               1               -               -               -
hypotf        1               1               1               1               1
hypot         -               -               -               -               -
hypotl        -               -               -               -               -
ilogbf        -               -               -               -               -
ilogb         -               -               -               -               -
ilogbl        -               -               -               -               -
j0f           1               1               2               1               2
j0            2               1               2               2               2
j0l           2               1               -               -               -
j1f           2               2               2               2               2
j1            1               -               1               1               1
j1l           1               1               -               -               -
jnf           3               5               4               3               4
jn            3               1               4               3               4
jnl           2               2               -               -               -
lgammaf       2               2               2               2               2
lgamma        1               1               1               1               1
lgammal       1               1               -               -               -
lrintf        -               -               -               -               -
lrint         -               -               -               -               -
lrintl        -               -               -               -               -
llrintf       -               -               -               -               -
llrint        -               -               -               -               -
llrintl       -               -               -               -               -
logf          1               1               -               -               -
log           -               -               -               -               -
logl          -               1               -               -               -
log10f        1               1               2               2               2
log10         -               -               1               1               1
log10l        1               2               -               -               -
log1pf        -               -               1               1               1
log1p         -               -               -               -               -
log1pl        -               1               -               -               -
log2f         -               -               -               -               -
log2          -               -               -               -               -
log2l         -               1               -               -               -
logbf         -               -               -               -               -
logb          -               -               -               -               -
logbl         -               -               -               -               -
lroundf       -               -               -               -               -
lround        -               -               -               -               -
lroundl       -               -               -               -               -
llroundf      -               -               -               -               -
llround       -               -               -               -               -
llroundl      -               -               -               -               -
modff         -               -               -               -               -
modf          -               -               -               -               -
modfl         -               -               -               -               -
nearbyintf    -               -               -               -               -
nearbyint     -               -               -               -               -
nearbyintl    -               -               -               -               -
nextafterf    -               -               -               -               -
nextafter     -               -               -               -               -
nextafterl    -               -               -               -               -
nexttowardf   -               -               -               -               -
nexttoward    -               -               -               -               -
nexttowardl   -               -               -               -               -
powf          -               -               -               -               -
pow           -               -               -               -               -
powl          -               1               -               -               -
remainderf    -               -               -               -               -
remainder     -               -               -               -               -
remainderl    -               -               -               -               -
remquof       -               -               -               -               -
remquo        -               -               -               -               -
remquol       -               -               -               -               -
rintf         -               -               -               -               -
rint          -               -               -               -               -
rintl         -               -               -               -               -
roundf        -               -               -               -               -
round         -               -               -               -               -
roundl        -               -               -               -               -
scalbf        -               -               -               -               -
scalb         -               -               -               -               -
scalbl        -               -               -               -               -
scalbnf       -               -               -               -               -
scalbn        -               -               -               -               -
scalbnl       -               -               -               -               -
scalblnf      -               -               -               -               -
scalbln       -               -               -               -               -
scalblnl      -               -               -               -               -
sinf          -               -               -               -               -
sin           -               -               -               -               -
sinl          -               -               -               -               -
sincosf       1               1               1               1               1
sincos        1               1               1               1               1
sincosl       1               1               -               -               -
sinhf         -               -               -               -               -
sinh          -               -               -               -               -
sinhl         -               1               -               -               -
sqrtf         -               -               -               -               -
sqrt          -               -               -               -               -
sqrtl         -               -               -               -               -
tanf          -               -               -               -               -
tan           1               1               1               1               1
tanl          -               1               -               -               -
tanhf         -               -               -               -               -
tanh          -               -               -               -               -
tanhl         -               -               -               -               -
tgammaf       1               1               1               1               1
tgamma        1               1               1               1               1
tgammal       1               1               -               -               -
truncf        -               -               -               -               -
trunc         -               -               -               -               -
truncl        -               -               -               -               -
y0f           1               1               1               1               1
y0            2               1               2               2               2
y0l           1               2               -               -               -
y1f           2               2               2               2               2
y1            3               1               3               3               3
y1l           1               1               -               -               -
ynf           2               2               2               2               2
yn            3               1               3               3               3
ynl           2               4               -               -               -

Function      S/390           SH4             Sparc 32-bit    Sparc 64-bit    x86_64/fpu
acosf         -               -               -               -               -
acos          -               -               -               -               -
acosl         -               -               -               -               -
acoshf        -               -               -               -               -
acosh         -               -               -               -               -
acoshl        -               -               -               -               -
asinf         -               2               -               -               -
asin          -               1               -               -               -
asinl         -               -               -               -               1
asinhf        -               -               -               -               -
asinh         -               -               -               -               -
asinhl        -               -               -               -               -
atanf         -               -               -               -               -
atan          -               -               -               -               -
atanl         -               -               -               -               -
atanhf        1               -               1               1               1
atanh         -               1               -               -               -
atanhl        -               -               -               -               1
atan2f        3               4               3               3               3
atan2         -               -               -               -               -
atan2l        -               -               -               1               -
cabsf         -               1               -               -               -
cabs          -               1               -               -               -
cabsl         -               -               -               -               -
cacosf        -               1 + i 1         -               -               0 + i 1
cacos         -               1 + i 0         -               -               -
cacosl        -               -               -               0 + i 1         0 + i 2
cacoshf       7 + i 3         7 + i 3         7 + i 3         7 + i 3         7 + i 3
cacosh        1 + i 1         1 + i 1         1 + i 1         1 + i 1         1 + i 1
cacoshl       -               -               -               5 + i 1         6 + i 1
cargf         -               -               -               -               -
carg          -               -               -               -               -
cargl         -               -               -               -               -
casinf        1 + i 0         2 + i 1         1 + i 0         1 + i 0         1 + i 1
casin         1 + i 0         3 + i 0         1 + i 0         1 + i 0         1 + i 0
casinl        -               -               -               0 + i 1         2 + i 2
casinhf       1 + i 6         1 + i 6         1 + i 6         1 + i 6         1 + i 6
casinh        5 + i 3         5 + i 3         5 + i 3         5 + i 3         5 + i 3
casinhl       -               -               -               4 + i 2         5 + i 5
catanf        4 + i 1         4 + i 1         4 + i 1         4 + i 1         4 + i 1
catan         0 + i 1         0 + i 1         0 + i 1         0 + i 1         0 + i 1
catanl        -               -               -               0 + i 1         -
catanhf       0 + i 6         1 + i 6         0 + i 6         0 + i 6         0 + i 6
catanh        4 + i 0         4 + i 1         4 + i 0         4 + i 0         4 + i 0
catanhl       -               -               -               1 + i 1         1 + i 0
cbrtf         -               -               -               -               -
cbrt          1               1               1               1               1
cbrtl         -               -               -               1               1
ccosf         1 + i 1         0 + i 1         1 + i 1         1 + i 1         1 + i 1
ccos          1 + i 0         1 + i 1         1 + i 0         1 + i 0         1 + i 0
ccosl         -               -               -               -               1 + i 1
ccoshf        1 + i 1         1 + i 1         1 + i 1         1 + i 1         1 + i 1
ccosh         1 + i 0         1 + i 1         1 + i 0         1 + i 0         1 + i 1
ccoshl        -               -               -               -               0 + i 1
ceilf         -               -               -               -               -
ceil          -               -               -               -               -
ceill         -               -               -               -               -
cexpf         1 + i 1         1 + i 1         1 + i 1         1 + i 1         1 + i 1
cexp          -               1 + i 0         -               -               -
cexpl         -               -               -               1 + i 1         0 + i 1
cimagf        -               -               -               -               -
cimag         -               -               -               -               -
cimagl        -               -               -               -               -
clogf         1 + i 3         0 + i 3         1 + i 3         1 + i 3         1 + i 3
clog          -               0 + i 1         -               -               -
clogl         -               -               -               1 + i 0         1 + i 0
clog10f       1 + i 5         1 + i 5         1 + i 5         1 + i 5         1 + i 5
clog10        0 + i 1         1 + i 1         0 + i 1         0 + i 1         1 + i 1
clog10l       -               -               -               0 + i 1         1 + i 1
conjf         -               -               -               -               -
conj          -               -               -               -               -
conjl         -               -               -               -               -
copysignf     -               -               -               -               -
copysign      -               -               -               -               -
copysignl     -               -               -               -               -
cosf          1               1               1               1               1
cos           2               2               2               2               2
cosl          -               -               -               1               1
coshf         -               -               -               -               -
cosh          -               -               -               -               -
coshl         -               -               -               -               -
cpowf         4 + i 2         4 + i 2         4 + i 2         4 + i 2         5 + i 2
cpow          2 + i 2         1 + i 1.1031    2 + i 2         2 + i 2         2 + i 2
cpowl         -               -               -               1 + i 1         5 + i 2
cprojf        -               -               -               -               -
cproj         -               -               -               -               -
cprojl        -               -               -               -               -
crealf        -               -               -               -               -
creal         -               -               -               -               -
creall        -               -               -               -               -
csinf         -               0 + i 1         -               -               0 + i 1
csin          -               -               -               -               -
csinl         -               -               -               1 + i 0         1 + i 0
csinhf        1 + i 1         1 + i 1         1 + i 1         1 + i 1         1 + i 1
csinh         0 + i 1         0 + i 1         0 + i 1         0 + i 1         1 + i 1
csinhl        -               -               -               -               1 + i 2
csqrtf        1 + i 0         1 + i 1         1 + i 0         1 + i 0         1 + i 0
csqrt         -               1 + i 0         -               -               -
csqrtl        -               -               -               1 + i 1         -
ctanf         -               1 + i 1         -               -               0 + i 1
ctan          1 + i 1         1 + i 1         1 + i 1         1 + i 1         1 + i 1
ctanl         -               -               -               0 + i 2         439 + i 3
ctanhf        2 + i 1         2 + i 1         2 + i 1         2 + i 1         2 + i 1
ctanh         1 + i 0         2 + i 2         1 + i 0         1 + i 0         1 + i 1
ctanhl        -               -               -               -               5 + i 25
erff          -               -               -               -               -
erf           1               -               1               1               1
erfl          -               -               -               -               -
erfcf         -               12              -               -               -
erfc          1               24              1               1               1
erfcl         -               -               -               1               1
expf          -               -               -               -               -
exp           -               -               -               -               -
expl          -               -               -               -               -
exp10f        2               2               2               2               2
exp10         6               6               6               6               6
exp10l        -               -               -               1               3
exp2f         -               -               -               -               -
exp2          -               -               -               -               -
exp2l         -               -               -               -               -
expm1f        1               1               1               1               1
expm1         1               -               1               1               1
expm1l        -               -               -               1               -
fabsf         -               -               -               -               -
fabs          -               -               -               -               -
fabsl         -               -               -               -               -
fdimf         -               -               -               -               -
fdim          -               -               -               -               -
fdiml         -               -               -               -               -
floorf        -               -               -               -               -
floor         -               -               -               -               -
floorl        -               -               -               -               -
fmaf          -               -               -               -               -
fma           -               -               -               -               -
fmal          -               -               -               -               -
fmaxf         -               -               -               -               -
fmax          -               -               -               -               -
fmaxl         -               -               -               -               -
fminf         -               -               -               -               -
fmin          -               -               -               -               -
fminl         -               -               -               -               -
fmodf         -               1               -               -               -
fmod          -               2               -               -               -
fmodl         -               -               -               -               -
frexpf        -               -               -               -               -
frexp         -               -               -               -               -
frexpl        -               -               -               -               -
gammaf        -               -               -               -               -
gamma         -               -               -               -               -
gammal        -               -               -               1               1
hypotf        1               1               1               1               1
hypot         -               1               -               -               -
hypotl        -               -               -               -               -
ilogbf        -               -               -               -               -
ilogb         -               -               -               -               -
ilogbl        -               -               -               -               -
j0f           2               2               2               2               2
j0            2               2               2               2               2
j0l           -               -               -               2               1
j1f           2               2               2               2               2
j1            1               1               1               1               1
j1l           -               -               -               4               1
jnf           4               4               4               4               4
jn            4               6               4               4               4
jnl           -               -               -               4               2
lgammaf       2               2               2               2               2
lgamma        1               1               1               1               1
lgammal       -               -               -               1               1
lrintf        -               -               -               -               -
lrint         -               -               -               -               -
lrintl        -               -               -               -               -
llrintf       -               -               -               -               -
llrint        -               -               -               -               -
llrintl       -               -               -               -               -
logf          -               1               -               -               -
log           -               1               -               -               -
logl          -               -               -               -               -
log10f        2               1               2               2               2
log10         1               1               1               1               1
log10l        -               -               -               1               1
log1pf        1               1               1               1               1
log1p         -               1               -               -               -
log1pl        -               -               -               1               -
log2f         -               1               -               -               -
log2          -               1               -               -               -
log2l         -               -               -               1               -
logbf         -               -               -               -               -
logb          -               -               -               -               -
logbl         -               -               -               -               -
lroundf       -               -               -               -               -
lround        -               -               -               -               -
lroundl       -               -               -               -               -
llroundf      -               -               -               -               -
llround       -               -               -               -               -
llroundl      -               -               -               -               -
modff         -               -               -               -               -
modf          -               -               -               -               -
modfl         -               -               -               -               -
nearbyintf    -               -               -               -               -
nearbyint     -               -               -               -               -
nearbyintl    -               -               -               -               -
nextafterf    -               -               -               -               -
nextafter     -               -               -               -               -
nextafterl    -               -               -               -               -
nexttowardf   -               -               -               -               -
nexttoward    -               -               -               -               -
nexttowardl   -               -               -               -               -
powf          -               -               -               -               -
pow           -               -               -               -               -
powl          -               -               -               -               -
remainderf    -               -               -               -               -
remainder     -               -               -               -               -
remainderl    -               -               -               -               -
remquof       -               -               -               -               -
remquo        -               -               -               -               -
remquol       -               -               -               -               -
rintf         -               -               -               -               -
rint          -               -               -               -               -
rintl         -               -               -               -               -
roundf        -               -               -               -               -
round         -               -               -               -               -
roundl        -               -               -               -               -
scalbf        -               -               -               -               -
scalb         -               -               -               -               -
scalbl        -               -               -               -               -
scalbnf       -               -               -               -               -
scalbn        -               -               -               -               -
scalbnl       -               -               -               -               -
scalblnf      -               -               -               -               -
scalbln       -               -               -               -               -
scalblnl      -               -               -               -               -
sinf          -               -               -               -               -
sin           -               -               -               -               -
sinl          -               -               -               -               -
sincosf       1               1               1               1               1
sincos        1               1               1               1               1
sincosl       -               -               -               1               1
sinhf         -               1               -               -               -
sinh          -               1               -               -               -
sinhl         -               -               -               -               -
sqrtf         -               -               -               -               -
sqrt          -               -               -               -               -
sqrtl         -               -               -               1               -
tanf          -               -               -               -               -
tan           1               0.5             1               1               1
tanl          -               -               -               -               -
tanhf         -               1               -               -               -
tanh          -               1               -               -               -
tanhl         -               -               -               1               -
tgammaf       1               1               1               1               1
tgamma        1               1               1               1               1
tgammal       -               -               -               1               1
truncf        -               -               -               -               -
trunc         -               -               -               -               -
truncl        -               -               -               -               -
y0f           1               1               1               1               1
y0            2               2               2               2               2
y0l           -               -               -               3               1
y1f           2               2               2               2               2
y1            3               3               3               3               3
y1l           -               -               -               1               1
ynf           2               2               2               2               2
yn            3               3               3               3               3
ynl           -               -               -               5               4

