[avr32-libc-devel] Summary of functions in newlib's libm and floating point support in AVR32

[usha g. <ush...@gm...>]

Hi All,

I have been investigating newlib's libm and floating point support in AVR32
.Here is the information that i have got so far. I would like to discuss on
implementation of libm for avr32-libc.


**

*AVR32 Floating point support*



Three revisions of the AVR32UC CPU currently exist:

• Revision 1 implementing revision 1 of the AVR32 architecture.

• Revision 2 implementing revision 2 of the AVR32 architecture, and with a
faster divider.

• Revision 3 implementing revision 3 of the AVR32 architecture, and with
optional floating-point hardware.



*Floating-Point Hardware in AVR32UC*



-AVR32UC optionally supports Floating-Point Hardware implemented as
coprocessor instructions.(coprocessor 0)

-The CONFIG0 system register F bit indicates if floating-point hardware is
present on a specific AVR32 device.

-Floating-point compare updates the flags in the AVR32 Status Register, so
that the regular AVR32 branch

instructions can be used directly after a floatingpoint compare.

-The floating-point hardware consists of a fused multiply-accumulate unit.

- Hardware is also provided to convert between integer and floating-point,

- to compare floating-point values

- and to provide initial approximations for reciprocal and reciprocal square
root



-The round-to-nearest, ties to even rounding mode is used for all
instructions except float-to-integer conversions. Float-to-integer
conversions use the round-to-zero mode.

-The hardware supports denormal numbers.

-Signalling NaN are not provided, all NaN are non-signalling (quiet). NaNs
are not propagated, the default quiet NaN is always returned (0x7FC00000).

-No floating-point exceptions are generated



*Floating point Operations*



-no special floating-point data transfer instructions are required



*NOTE:*

Section 4.2 and 4.3 of AVR32UC Technical Reference Manual can be looked into
for instruction set and compare and check operations provided by AVR32UC



*AVR32AP *doest not have an fpu implemented

* *

*Standard Math library routines*

Trigonometric functions:

cos       Compute cosine (function)

sin        Compute sine (function)

tan        Compute tangent (function)

acos     Compute arc cosine (function)

asin      Compute arc sine (function)

atan      Compute arc tangent (function)

atan2    Compute arc tangent with two parameters (function)





Hyperbolic functions:

cosh     Compute hyperbolic cosine (function)

sinh      Compute hyperbolic sine (function)

tanh      Compute hyperbolic tangent (function)





Exponential and logarithmic functions:

exp       Compute exponential function (function)

frexp    Get significand and exponent (function)

ldexp    Generate number from significand and exponent (function)

log        Compute natural logarithm (function)

log10    Compute common logarithm (function)

modf    Break into fractional and integral parts (function)





Power functions

pow     Raise to power (function)

sqrt      Compute square root (function)





Rounding, absolute value and remainder functions:

ceil       Round up value (function)

fabs      Compute absolute value (function)

floor     Round down value (function)

fmod    Compute remainder of division (function)

* *

*Newlib’s libm*

* *

There are four different versions of the math library routines: IEEE, POSIX,
X/Open, or SVID.  The version may be selected at runtime by setting the
global variable {_LIB_VERSION}, defined in {math.h}.  It may be set to one
of the following constants defined in {math.h}: {_IEEE_}, {_POSIX_},
{_XOPEN_}, or {_SVID_}.

The versions of the library differ only in how errors are handled.

Default version is X/Open.



*Standard Math library routines in Newlib*

The list below gives the functions present in different directories. Two
directories namely math/ and mathfp/ has different implementation for the
same functions. The function names are listed along with the directory
names.



*cos()
math/*

*k_cos.c-  _kernel_cos()* – * *The range is [-pi/4,pi/4]; function returning
double

*kf_cos.c-  _kernel_cosf()* – * *The range is [-pi/4,pi/4] ;function
returning float

*s_cos.c-  cos()* – * *The range is [-pi,pi]

*sf_cos.c-  cosf()* – * *The range is [-pi,pi]

*mathfp/*

*s_cos.c-  cos()* –* *It calls sine(x,1) which is  declared in  zmath.h.

*sf_cos.c- cosf()* – calls sinef(x,1)



*sin()*

*math/*

*k_sin.c-  _kernel_sin()* – * *The range is [-pi/4,pi/4]; function returning
double

*kf_sin.c-  _kernel_sinf()* – * *The range is [-pi/4,pi/4] ;function
returning float

*s_sin.c-  sin()* – * *The range is [-pi,pi]

*sf_sin.c-  sinf()* – * *The range is [-pi,pi]

*mathfp/*

*s_sin.c-  sin()* –* *It calls sine(x,0) which is  declared in  zmath.h.

*sf_sin.c-  sinf()* – calls sinef(x,0)



*tan()*

*math/*

*k_tan.c- _kernel_tan()* – * *takes 3 arguments. The range is [-pi/4,pi/4];
function returning double

*kf_tan.c-  _kernel_tanf()* – * *The range is [-pi/4,pi/4] ;function
returning float

*s_tan.c-  tan()* – * *The range is [-pi,pi]

*sf_tan.c-  tanf()* – * *The range is [-pi,pi]

*mathfp/*

*s_tan.c- tan()*

*sf_tan.c-  tanf()*



*acos()*

*math/*

*e_acos.c-  __ieee754_acos()*

*ef_acos.c- __ieee754_acosf()*

*w_acos.c-  acos()*

*wf_acos.c-  acosf()*

*mathfp/*

*s_acos.c-  acos()* –* *It calls asine(x,1) which is  declared in  zmath.h.

*sf_acos.c-  acosf()* – calls asinef(x,1)

* *

*asin()*

*math/*

*e_asin.c-  __ieee754_asin()*

*ef_asin.c- __ieee754_asinf()*

*w_asin.c-  asin()*

*wf_asin.c-  asinf()*

*mathfp/*

*s_asin.c-  asin()* –* *It calls asine(x,0) which is  declared in  zmath.h.

*sf_asin.c-  asinf()* – calls asinef(x,0)

* *

*atan()*

*math/*

*s_atan.c-  atan()*

*sf_atan.c-  atanf()*

*mathfp/*

*s_atan.c-  atan()- *calls atangent(x,0,0,0)

*sf_atan.c-  atanf()* - calls atangentf(x,0,0,0)



*atan2()*

*math/*

*e_atan2.c-  __ieee754_atan2()*

*ef_atan2.c- __ieee754_atan2f()*

*w_atan2.c-  atan2()*

*wf_atan2.c-  atan2f()*

*mathfp/*

*s_atan2.c-  atan2()* –* *It calls atangent (0.0, v, u, 1) which is  declared
in  zmath.h.

*sf_atan2.c-  atan2f()* – calls atangentf(0.0, v, u, 1)



*cosh()*

*math/*

*e_cosh.c-  __ieee754_cosh()*

*ef_cosh.c- __ieee754_coshf()*

*w_cosh.c-  cosh()*

*wf_cosh.c-  coshf()*

*mathfp/*

*s_cosh.c-  cosh()* –* *It calls sineh ((float) x, 1) which is  declared in
zmath.h.

*sf_cosh.c-  coshf()* – calls sinehf ((float) x, 1)



*sinh()*

*math/*

*e_sinh.c-  __ieee754_sinh()*

*ef_sinh.c- __ieee754_sinhf()*

*w_sinh.c-  sinh()*

*wf_sinh.c-  sinhf()*

*mathfp/*

*s_sinh.c-  sinh()* –* *It calls sineh ((float) x) which is  declared in
zmath.h.

*sf_sinh.c-  sinhf()* – calls sinehf ((float) x)



*tanh()*

*math/*

*s_tanh.c-  tanh()*

*sf_tanh.c-  tanhf()*

*mathfp/*

*s_tanh.c-  tanh()*

*sf_tanh.c-  tanhf()*



*exp()*

*math/*

*e_exp.c-  __ieee754_exp()*

*ef_exp.c- __ieee754_expf()*

*w_exp.c-  exp()*

*wf_exp.c-  expf()*

*w_exp2.c-  exp2()- *return pow(2,x)

*wf_exp2.c-  exp2f()*

*mathfp/*

*s_exp.c-  exp()*

*sf_exp.c-  expf()*

*s_exp2.c-  exp2()*

*sf_exp2.c-  exp2f()*



*frexp()*

*math/*

*s_frexp.c- frexp()*

*sf_frexp.c-  frexpf()*

*mathfp/*

*s_frexp.c-  frexp()*

*sf_frexp.c-  frexpf()*



*ldexp()*

*math/*

*s_ldexp.c- ldexp()*

*sf_ldexp.c-  ldexpf()*

*mathfp/*

*s_ldexp.c-  ldexp()*

*sf_ldexp.c-  ldexpf()*



*log()*

*math/*

*e_log.c-  __ieee754_log()*

*ef_log.c- __ieee754_logf()*

*w_log.c-  log()*

*wf_log.c-  logf()*

*mathfp/*

*s_log.c-  log()*

*sf_log.c-  logf()*

* *

*log10()*

*math/*

*e_log10.c-  __ieee754_log10()*

*ef_log10.c- __ieee754_log10f()*

*w_log10.c-  log10()*

*wf_log10.c-  log10f()*

*mathfp/*

*s_log10.c-  log10()*

*sf_log10.c-  log10f()*



*modf()*

*commom/*

*s_modf.c*

*sf_modf.c*

* *

*pow()*

*math/*

*e_pow.c-  __ieee754_pow()*

*ef_pow.c- __ieee754_powf()*

*w_pow.c-  pow()*

*wf_pow.c-  powf()*

*mathfp/*

*s_pow.c-  pow()*

*sf_pow.c-  powf()*

* *

*sqrt()*

*math/*

*e_sqrt.c-  __ieee754_sqrt()*

*ef_sqrt.c- __ieee754_sqrtf()*

*w_sqrt.c-  sqrt()*

*wf_sqrt.c-  sqrtf()*

*mathfp/*

*s_sqrt.c-  sqrt()*

*sf_sqrt.c-  sqrtf()*

* *

*ceil()*

*math/*

*s_ceil.c-  ceil()*

*sf_ceil.c-  ceilf()*

* *

*mathfp/*

*s_ceil.c-  ceil()*

*sf_ceil.c-  ceilf()*

* *

*floor()*

*math/*

*s_floor.c-  floor()*

*sf_floor.c-  floorf()*

*mathfp/*

*s_floor.c-  floor()*

*sf_floor.c-  floorf()*

* *

*fabs()*

*math/*

*s_fabs.c-  fabs()*

*sf_fabs.c-  fabsf()*

*mathfp/*

*s_fabs.c-  fabs()*

*sf_fabs.c-  fabsf()*



*fmod()*

*math/*

*e_fmod.c-  __ieee754_fmod()*

*ef_fmod.c- __ieee754_fmodf()*

*w_fmod.c-  fmod()*

*wf_fmod.c-  fmodf()*

*mathfp/*

*s_fmod.c-  fmod()*

*sf_fmod.c-  fmodf()*



*List of non-standard functions in newlib*



Other functions include

1) Bessel functions – jN, jNf, yN, yNf

2) cbrt, cbrtf

3) copysign, copysignf

4)erf, erff, erfc, erfcf – error functions

5)expm1, expm1f – exponential minus 1

6)gamma, gammaf, lgamma, lgammaf, gamma_r

7)hypot, hypotf

8)ilogb, ilogbf – get exponent of floating point number

9)infinity, infinityf- representation of infinity.

10) isnan, isnanf, isinf, isinff, finite,finitef

11)log1p, log1pf- log of 1+x

12)matherr – modifiable math error handler

13) nan, nanf

14)nextafter, naxtafterf  - get next number

15)remainder, remainderf

16)scalbn, scalbnf –scale by power of 2



*Avr-libc*

*List of non-standard functions in avr-libc*

1)isnan

2)isinf

3)square

4)copysign

5)fdim – returns max of (x-y,0)

6)fma – floating point multiply-add ((x*y)+z) operation

7)fmax

8)fmin

9)signbit

10)trunc

11)isfinite

12)hypot

13)round

14)lround

15)lrint
-- 
Thanks and Regards
 Usha Gupta