gdal - How does gdal_calc numpy operators work?

Gdal_calc manual

Gdal_calc is introduced as :

gdal_calc.py - Command line raster calculator with numpy syntax
gdal_calc.py [-A ] [--A_band] [-B...-Z filename] [other_options]
OPTIONS:
--calc=CALC           calculation in gdalnumeric syntax using +-/* or any
                      numpy array functions (i.e. logical_and())
DESCRIPTION

Command line raster calculator with numpy syntax. Use any basic arithmetic
supported by numpy arrays such as +-*/ along with logical operators such as >.
EXAMPLE
add two files together
   gdal_calc.py -A input1.tif -B input2.tif --outfile=result.tif --calc="A+B"
average of two layers
   gdal_calc.py -A input.tif -B input2.tif --outfile=result.tif --calc="(A+B)/2"`
set values of zero and below to null
   gdal_calc.py -A input.tif --outfile=result.tif --calc="A*(A>0)" --NoDataValue=0

Unexpected results

I made some good uses of gdal_calc in the past, yet, recent results makes no sences to me. I have 3 input files hillshades_A.tmp.tif, hillshades_B.tmp.tif, hillshades_C.tmp.tif and one output composite.tif. I want to make calculations with these inputs. I will follow pixel x=10 y=10 with values are A=222, B=220, C=224 to check the correctness of the output. Let's start.

Example:

 # ASSIGN VALUE. Expect: 300.
 $gdal_calc.py -A ./hillshades_A.tmp.tif --outfile=./composite.tif  \
   --calc="300" --NoDataValue=-1
 $gdallocationinfo ./composite.tif 10 10 -valonly
 >255          # Ergh? Ok, as it's a grey scale [0-255], such auto-correction is ok

Then the fun start !

# SUM: A+B or (A+B), when A=222, B=220. Expect: 442 or 255.
gdal_calc.py -A hillshades_A.tmp.tif -B hillshades_B.tmp.tif --outfile=./composite.tif \
   --calc="(A+B)" --NoDataValue=-1
$gdallocationinfo ./composite.tif 10 10 -valonly
>186          # Ergh? This is A+B-256=442-256=186

# AVERAGE: (A+B)/2, when A=222, B=220. Expect: 221 or 255.
gdal_calc.py -A hillshades_A.tmp.tif -B hillshades_B.tmp.tif --outfile=./composite.tif  \
   --calc="(A+B)/2" --NoDataValue=-1
$gdallocationinfo ./composite.tif 10 10 -valonly

>93           # Ergh? ok, per previous 186/2=93. 
# must use (A/2)+(B/2) => 221        

# MULTIPLY: A*B, when A=222, B=220. Expect: 48840 or 255
gdal_calc.py -A hillshades_A.tmp.tif -B hillshades_B.tmp.tif --outfile=./composite.tif  \
   --calc="A*B" --NoDataValue=-1
$gdallocationinfo ./composite.tif 10 10 -valonly
>200           # Ergh? ok, it's modulo: 222*220 % 256=200  

# MULTIPLY+SCALE BACK: A*B/255, when A=222, B=220. Expect: 191.5 rounded to 191 or 192.

gdal_calc.py -A hillshades_A.tmp.tif -B hillshades_B.tmp.tif --outfile=./composite.tif  \
   --calc="A*B/255" --NoDataValue=-1
$gdallocationinfo ./composite.tif 10 10 -valonly
>0             # Ergh? Maybe A*B/255=200/255 (per previous point) being <0 it get rounded to 0 firt. It confirms: Ergh?

And I may go again and yet again. These are not simple basic arithmetic [...] such as +-*/ .

Question

How does gdal_calc operators works ? and... Is there a comprehensive manual for this gdal_calc / numppy syntaxes equations ? (I didn't find any solid one via google)

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EDIT: may this behavior be the byproduct of [0-255] greyscale hillshade as input.

$gdalinfo ./hillshades_A.tmp.tif -mm
Driver: GTiff/GeoTIFF
Files: ./hillshades_A.tmp.tif
Size is 1920, 1950
Coordinate System is `'
Origin = (66.991666666666674,37.508333333333354)
Pixel Size = (0.016666666666667,-0.016666666666667)
Image Structure Metadata:
  INTERLEAVE=BAND
Corner Coordinates:

Upper Left  (  66.9916667,  37.5083333) 
Lower Left  (  66.9916667,   5.0083333) 
Upper Right (  98.9916667,  37.5083333) 
Lower Right (  98.9916667,   5.0083333) 
Center      (  82.9916667,  21.2583333) 
Band 1 Block=1920x4 Type=Byte, ColorInterp=Gray
    Computed Min/Max=1.000,255.000
  NoData Value=0

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Gdal_calc's numpy seems to have more operators :

+ addition 
- subtraction 
/ division 
* multiplication 
= equals to 
< less than 
> larger than 
! not equal to 
? if clause 

M maximum of two values 
m minimum of two values 
B bit level operator

I haven't found clear and proper examples for how the exotic operators should be used. If you have something, feel free to share.