The universal library contains a collection of command line tools that help investigate bit-level attributes of the number systems and the values they encode. These command line tools get installed with the make install build target.
The following segments presents short description of their use.
Compare the three IEEE formats on a given real number value:
λ ./compieee.exe
Show the truncated value and (sign/scale/fraction) components of different floating point types.
Usage: compieee floating_point_value
Example: compieee 0.03124999
input value: 0.03124999
float: 0.0312499907 (+,-6,11111111111111111111011)
double: 0.031249989999999998 (+,-6,1111111111111111111101010100001100111000100011101110)
long double: 0.0312499899999999983247 (+,-6,111111111111111111101001011110100011111111111110001111111001111)
Show the sign/scale/fraction components of an IEEE float.
λ ./compf.exe
compf : components of an IEEE single-precision float
Show the sign/scale/fraction components of an IEEE float.
Usage: compf float_value
Example: compf 0.03124999
float: 0.031249990686774254 (+,-6,11111111111111111111011)
Show the sign/scale/fraction components of an IEEE double.
λ ./compd.exe
compd : components of an IEEE double-precision float
Show the sign/scale/fraction components of an IEEE double.
Usage: compf double_value
Example: compd 0.03124999
double: 0.031249989999999998 (+,-6,1111111111111111111101010100001100111000100011101110)
Show the sign/scale/fraction components of an IEEE long double. On Windows using the Microsoft Visual Studio environment, the long double is aliased to double.
λ ./compld.exe
compld: components of an IEEE long-double (compiler dependent, 80-bit extended precision on x86 and ARM, 128-bit on RISC-V
Show the sign/scale/fraction components of an IEEE long double.
Usage: compld long_double_value
Example: compld 0.03124999
long double: 0.0312499899999999983247 (+,-6,000000000000000000000000000000000011111111111110000000000000000)
Show the sign/scale/fraction components of a fixed-point value.
λ ./compfp.exe
compfp : components of a fixed-point value
Show the sign/scale/fraction components of a fixed-point value.
Usage: compfp float_value
Example: compfp 1.0625
class sw::unum::fixpnt<32,16,1,unsigned char>: 1.0625000000000000 b0000000000000001.0001000000000000
Show the arithmetic properties of a posit environment, including its quire.
λ ./propp.exe
Show the arithmetic properties of a posit.
Usage: propp [nbits es capacity]
Example: propp 16 1 8
arithmetic properties of a posit<16, 1> environment
posit< 16, 1> useed scale 2 minpos scale - 28 maxpos scale 28
minpos : 16.1x0001p + 3.72529e-09
maxpos : 16.1x7fffp + 2.68435e+08
Properties of a quire<16, 1, 8>
dynamic range of product : 112
radix point of accumulator : 56
full quire size in bits : 120
lower quire size in bits : 56
upper quire size in bits : 57
capacity bits : 8
Quire segments
+ : 00000000_000000000000000000000000000000000000000000000000000000000.00000000000000000000000000000000000000000000000000000000
Show the sign/scale/fraction components of a signed integer.
λ ./compsi.exe
compsi : components of a signed integer
Show the sign/scale/fraction components of a signed integer.
Usage: compsi integer_value
Example: compsi 1234567890123456789012345
class sw::unum::integer<128,unsigned int> : 1234567890123456789012345 (+,80,00000101011011100000111100110110101001100100010000111101111000101101111101111001)
Show the sign/scale/fraction components of an unsigned integer.
λ ./compui.exe
compui : components of an unsigned integer
Show the sign/scale/fraction components of an unsigned integer.
Usage: compui integer_value
Example: compui 123456789012345670
TBD:
Show the sign/scale/regime/exponent/fraction components of a posit.
λ ./compp.exe
pc : posit components
Show the sign/scale/regime/exponent/fraction components of a posit.
Usage: pc float_value
Example: pc -1.123456789e17
posit< 8, 0> = s1 r1111111 e f qNW v-64
posit< 8, 1> = s1 r1111111 e f qNW v-4096
posit< 8, 2> = s1 r1111111 e f qNW v-16777216
posit< 8, 3> = s1 r1111111 e f qNW v-281474976710656
posit<16, 1> = s1 r111111111111111 e f qNW v-268435456
posit<16, 2> = s1 r111111111111111 e f qNW v-72057594037927936
posit<16, 3> = s1 r111111110 e000 f100 qNW v-1.080863910568919e+17
posit<32, 1> = s1 r111111111111111111111111111110 e1 f qNW v-1.4411518807585587e+17
posit<32, 2> = s1 r1111111111111110 e00 f1000111100100 qNW v-1.1234370007964058e+17
posit<32, 3> = s1 r111111110 e000 f1000111100100001110 qNW v-1.1234562422498918e+17
posit<48, 1> = s1 r111111111111111111111111111110 e0 f1000111100100010 qNW v-1.1234589910289613e+17
posit<48, 2> = s1 r1111111111111110 e00 f10001111001000011100110010111 qNW v-1.1234567885160448e+17
posit<48, 3> = s1 r111111110 e000 f10001111001000011100110010111010111 qNW v-1.1234567889983898e+17
posit<64, 1> = s1 r111111111111111111111111111110 e0 f10001111001000011100110010111011 qNW v-1.1234567890193613e+17
posit<64, 2> = s1 r1111111111111110 e00 f100011110010000111001100101110101110001001111 qNW v-1.1234567890000077e+17
posit<64, 3> = s1 r111111110 e000 f100011110010000111001100101110101110001001110101000 qNW v-1.123456789e+17
posit<64, 4> = s1 r11110 e1000 f100011110010000111001100101110101110001001110101000000 qNW v-1.123456789e+17
Show the conversion of a float to a posit step-by-step.
λ ./float2posit.exe
Show the conversion of a float to a posit step-by-step.
Usage: float2posit floating_point_value posit_size_in_bits[one of 8|16|32|48|64|80|96|128|256]
Example: convert -1.123456789e17 32
$ ./float2posit.exe 1.234567890 32
1.23456789 input value
Test for ZERO
(+, 0, 0011110000001100101001000010100000111101111000011011) input value is NOT zero
Test for NaR
(+, 0, 0011110000001100101001000010100000111101111000011011) input value is NOT NaR
construct the posit
0011'1100'0000'1100'1010'0100'0010'1000'0011'1101'1110'0001'1011 full fraction bits
0000'0000'0000'0000'0000'0000'0000'0111'1111'1111'1111'1111'1111 mask of remainder bits
0'0000'0000'0000'0000'0000'0000'0000'0000'0000 unconstrained posit : length = nbits(32) + es(2) + 3 guard bits : 37
0'0001'0000'0000'0000'0000'0000'0000'0000'0000 runlength = 1
0'0000'0000'0000'0000'0000'0000'0000'0000'0000 exponent value = 0
0'0000'0000'0111'1000'0001'1001'0100'1000'0100 most significant 28 fraction bits(nbits - 1 - run - es)
0'0000'0000'0000'0000'0000'0000'0000'0000'0001 sticky bit representing the truncated fraction bits
0'0001'0000'0111'1000'0001'1001'0100'1000'0101 unconstrained posit bits length = 34
0'0000'0000'0000'0000'0000'0000'0000'0000'0100 last bit mask
0'0000'0000'0000'0000'0000'0000'0000'0000'0010 bit after last bit mask
0'0000'0000'0000'0000'0000'0000'0000'0000'0001 sticky bit mask
rounding decision(blast & bafter) | (bafter & bsticky) : round down
0'1000'0011'1100'0000'1100'1010'0100'0010'1000 shifted posit
0100'0001'1110'0000'0110'0101'0010'0001 truncated posit
0100'0001'1110'0000'0110'0101'0010'0001 rounded posit
0100'0001'1110'0000'0110'0101'0010'0001 final posit
Show the storage properties of the native, standard, and extended posits.
λ ./propenv.exe
Bit sizes for native types
unsigned char 8 bits
unsigned short 16 bits
unsigned int 32 bits
unsigned long long 64 bits
signed char 7 bits
signed short 15 bits
signed int 31 bits
signed long long 63 bits
float 24 bits
double 53 bits
long double 53 bits
Min-Max range for floats and posit<32,2> comparison
float min 1.17549e-38 max 3.40282e+38
class sw::unum::posit<32,2> min 7.52316e-37 max 1.32923e+36
Bit sizes for standard posit configurations
posit<8,0> 8 bits
posit<16,1> 16 bits
posit<32,2> 32 bits
posit<64,3> 64 bits
posit<128,4> 128 bits
posit<256,5> 256 bits
Bit sizes for extended posit configurations
posit<4,0> 8 bits
posit<8,0> 8 bits
posit<16,1> 16 bits
posit<20,1> 32 bits
posit<24,1> 32 bits
posit<28,1> 32 bits
posit<32,2> 32 bits
posit<40,2> 64 bits
posit<48,2> 64 bits
posit<56,2> 64 bits
posit<64,3> 64 bits
posit<80,3> 128 bits
posit<96,3> 128 bits
posit<112,3> 128 bits
posit<128,4> 128 bits
posit<256,5> 256 bits
Long double properties
value 1.2345678901234567
hex 00 00 00 00 00 00 00 04 3f f3 c0 ca 42 8c 59 fb
sign +
scale 1
fraction 1056399862553083
Show the numeric_limits<> of the standard posits.
λ ./plimits.exe
C:\Users\tomtz\Documents\dev\clones\universal\build\tools\cmd\Release\plimits.exe: numeric_limits<> of standard posits
Numeric limits for posit< 8, 0>
numeric_limits< sw::unum::posit<8, 0> >::min() : 0.015625
numeric_limits< sw::unum::posit<8, 0> >::max() : 64
numeric_limits< sw::unum::posit<8, 0> >::lowest() : -64
numeric_limits< sw::unum::posit<8, 0> >::epsilon() : 0.03125
numeric_limits< sw::unum::posit<8, 0> >::digits : 6
numeric_limits< sw::unum::posit<8, 0> >::digits10 : 1
numeric_limits< sw::unum::posit<8, 0> >::max_digits10 : 2
numeric_limits< sw::unum::posit<8, 0> >::is_signed : 1
numeric_limits< sw::unum::posit<8, 0> >::is_integer : 0
numeric_limits< sw::unum::posit<8, 0> >::is_exact : 0
numeric_limits< sw::unum::posit<8, 0> >::min_exponent : -6
numeric_limits< sw::unum::posit<8, 0> >::min_exponent10 : -1
numeric_limits< sw::unum::posit<8, 0> >::max_exponent : 6
numeric_limits< sw::unum::posit<8, 0> >::max_exponent10 : 1
numeric_limits< sw::unum::posit<8, 0> >::has_infinity : 1
numeric_limits< sw::unum::posit<8, 0> >::has_quiet_NaN : 1
numeric_limits< sw::unum::posit<8, 0> >::has_signaling_NaN : 1
numeric_limits< sw::unum::posit<8, 0> >::has_denorm : 0
numeric_limits< sw::unum::posit<8, 0> >::has_denorm_loss : 0
numeric_limits< sw::unum::posit<8, 0> >::is_iec559 : 0
numeric_limits< sw::unum::posit<8, 0> >::is_bounded : 0
numeric_limits< sw::unum::posit<8, 0> >::is_modulo : 0
numeric_limits< sw::unum::posit<8, 0> >::traps : 0
numeric_limits< sw::unum::posit<8, 0> >::tinyness_before : 0
numeric_limits< sw::unum::posit<8, 0> >::round_style : 1
Numeric limits for posit< 16, 1>
numeric_limits< sw::unum::posit<16, 1> >::min() : 3.72529e-09
numeric_limits< sw::unum::posit<16, 1> >::max() : 2.68435e+08
numeric_limits< sw::unum::posit<16, 1> >::lowest() : -2.68435e+08
numeric_limits< sw::unum::posit<16, 1> >::epsilon() : 0.000244141
numeric_limits< sw::unum::posit<16, 1> >::digits : 13
numeric_limits< sw::unum::posit<16, 1> >::digits10 : 3
numeric_limits< sw::unum::posit<16, 1> >::max_digits10 : 4
numeric_limits< sw::unum::posit<16, 1> >::is_signed : 1
numeric_limits< sw::unum::posit<16, 1> >::is_integer : 0
numeric_limits< sw::unum::posit<16, 1> >::is_exact : 0
numeric_limits< sw::unum::posit<16, 1> >::min_exponent : -28
numeric_limits< sw::unum::posit<16, 1> >::min_exponent10 : -8
numeric_limits< sw::unum::posit<16, 1> >::max_exponent : 28
numeric_limits< sw::unum::posit<16, 1> >::max_exponent10 : 8
numeric_limits< sw::unum::posit<16, 1> >::has_infinity : 1
numeric_limits< sw::unum::posit<16, 1> >::has_quiet_NaN : 1
numeric_limits< sw::unum::posit<16, 1> >::has_signaling_NaN : 1
numeric_limits< sw::unum::posit<16, 1> >::has_denorm : 0
numeric_limits< sw::unum::posit<16, 1> >::has_denorm_loss : 0
numeric_limits< sw::unum::posit<16, 1> >::is_iec559 : 0
numeric_limits< sw::unum::posit<16, 1> >::is_bounded : 0
numeric_limits< sw::unum::posit<16, 1> >::is_modulo : 0
numeric_limits< sw::unum::posit<16, 1> >::traps : 0
numeric_limits< sw::unum::posit<16, 1> >::tinyness_before : 0
numeric_limits< sw::unum::posit<16, 1> >::round_style : 1
Numeric limits for posit< 32, 2>
numeric_limits< sw::unum::posit<32, 2> >::min() : 7.52316e-37
numeric_limits< sw::unum::posit<32, 2> >::max() : 1.32923e+36
numeric_limits< sw::unum::posit<32, 2> >::lowest() : -1.32923e+36
numeric_limits< sw::unum::posit<32, 2> >::epsilon() : 7.45058e-09
numeric_limits< sw::unum::posit<32, 2> >::digits : 28
numeric_limits< sw::unum::posit<32, 2> >::digits10 : 8
numeric_limits< sw::unum::posit<32, 2> >::max_digits10 : 9
numeric_limits< sw::unum::posit<32, 2> >::is_signed : 1
numeric_limits< sw::unum::posit<32, 2> >::is_integer : 0
numeric_limits< sw::unum::posit<32, 2> >::is_exact : 0
numeric_limits< sw::unum::posit<32, 2> >::min_exponent : -120
numeric_limits< sw::unum::posit<32, 2> >::min_exponent10 : -36
numeric_limits< sw::unum::posit<32, 2> >::max_exponent : 120
numeric_limits< sw::unum::posit<32, 2> >::max_exponent10 : 36
numeric_limits< sw::unum::posit<32, 2> >::has_infinity : 1
numeric_limits< sw::unum::posit<32, 2> >::has_quiet_NaN : 1
numeric_limits< sw::unum::posit<32, 2> >::has_signaling_NaN : 1
numeric_limits< sw::unum::posit<32, 2> >::has_denorm : 0
numeric_limits< sw::unum::posit<32, 2> >::has_denorm_loss : 0
numeric_limits< sw::unum::posit<32, 2> >::is_iec559 : 0
numeric_limits< sw::unum::posit<32, 2> >::is_bounded : 0
numeric_limits< sw::unum::posit<32, 2> >::is_modulo : 0
numeric_limits< sw::unum::posit<32, 2> >::traps : 0
numeric_limits< sw::unum::posit<32, 2> >::tinyness_before : 0
numeric_limits< sw::unum::posit<32, 2> >::round_style : 1
Numeric limits for posit< 64, 3>
numeric_limits< sw::unum::posit<64, 3> >::min() : 4.8879e-150
numeric_limits< sw::unum::posit<64, 3> >::max() : 2.04587e+149
numeric_limits< sw::unum::posit<64, 3> >::lowest() : -2.04587e+149
numeric_limits< sw::unum::posit<64, 3> >::epsilon() : 3.46945e-18
numeric_limits< sw::unum::posit<64, 3> >::digits : 59
numeric_limits< sw::unum::posit<64, 3> >::digits10 : 17
numeric_limits< sw::unum::posit<64, 3> >::max_digits10 : 18
numeric_limits< sw::unum::posit<64, 3> >::is_signed : 1
numeric_limits< sw::unum::posit<64, 3> >::is_integer : 0
numeric_limits< sw::unum::posit<64, 3> >::is_exact : 0
numeric_limits< sw::unum::posit<64, 3> >::min_exponent : -496
numeric_limits< sw::unum::posit<64, 3> >::min_exponent10 : -150
numeric_limits< sw::unum::posit<64, 3> >::max_exponent : 496
numeric_limits< sw::unum::posit<64, 3> >::max_exponent10 : 150
numeric_limits< sw::unum::posit<64, 3> >::has_infinity : 1
numeric_limits< sw::unum::posit<64, 3> >::has_quiet_NaN : 1
numeric_limits< sw::unum::posit<64, 3> >::has_signaling_NaN : 1
numeric_limits< sw::unum::posit<64, 3> >::has_denorm : 0
numeric_limits< sw::unum::posit<64, 3> >::has_denorm_loss : 0
numeric_limits< sw::unum::posit<64, 3> >::is_iec559 : 0
numeric_limits< sw::unum::posit<64, 3> >::is_bounded : 0
numeric_limits< sw::unum::posit<64, 3> >::is_modulo : 0
numeric_limits< sw::unum::posit<64, 3> >::traps : 0
numeric_limits< sw::unum::posit<64, 3> >::tinyness_before : 0
numeric_limits< sw::unum::posit<64, 3> >::round_style : 1
>>>>>>>>>>>>>>>>>> posit<128,4> does not render correctly due to limits of native floating point types
Numeric limits for posit< 128, 4>
numeric_limits< sw::unum::posit<128, 4> >::min() : 0
numeric_limits< sw::unum::posit<128, 4> >::max() : inf
numeric_limits< sw::unum::posit<128, 4> >::lowest() : -inf
numeric_limits< sw::unum::posit<128, 4> >::epsilon() : 3.76158e-37
numeric_limits< sw::unum::posit<128, 4> >::digits : 122
numeric_limits< sw::unum::posit<128, 4> >::digits10 : 36
numeric_limits< sw::unum::posit<128, 4> >::max_digits10 : 37
numeric_limits< sw::unum::posit<128, 4> >::is_signed : 1
numeric_limits< sw::unum::posit<128, 4> >::is_integer : 0
numeric_limits< sw::unum::posit<128, 4> >::is_exact : 0
numeric_limits< sw::unum::posit<128, 4> >::min_exponent : -2016
numeric_limits< sw::unum::posit<128, 4> >::min_exponent10 : -610
numeric_limits< sw::unum::posit<128, 4> >::max_exponent : 2016
numeric_limits< sw::unum::posit<128, 4> >::max_exponent10 : 610
numeric_limits< sw::unum::posit<128, 4> >::has_infinity : 1
numeric_limits< sw::unum::posit<128, 4> >::has_quiet_NaN : 1
numeric_limits< sw::unum::posit<128, 4> >::has_signaling_NaN : 1
numeric_limits< sw::unum::posit<128, 4> >::has_denorm : 0
numeric_limits< sw::unum::posit<128, 4> >::has_denorm_loss : 0
numeric_limits< sw::unum::posit<128, 4> >::is_iec559 : 0
numeric_limits< sw::unum::posit<128, 4> >::is_bounded : 0
numeric_limits< sw::unum::posit<128, 4> >::is_modulo : 0
numeric_limits< sw::unum::posit<128, 4> >::traps : 0
numeric_limits< sw::unum::posit<128, 4> >::tinyness_before : 0
numeric_limits< sw::unum::posit<128, 4> >::round_style : 1
>>>>>>>>>>>>>>>>>> posit<256,5> does not render correctly due to limits of native floating point types
Numeric limits for posit< 256, 5>
numeric_limits< sw::unum::posit<256, 5> >::min() : 0
numeric_limits< sw::unum::posit<256, 5> >::max() : inf
numeric_limits< sw::unum::posit<256, 5> >::lowest() : -inf
numeric_limits< sw::unum::posit<256, 5> >::epsilon() : 2.21086e-75
numeric_limits< sw::unum::posit<256, 5> >::digits : 249
numeric_limits< sw::unum::posit<256, 5> >::digits10 : 75
numeric_limits< sw::unum::posit<256, 5> >::max_digits10 : 76
numeric_limits< sw::unum::posit<256, 5> >::is_signed : 1
numeric_limits< sw::unum::posit<256, 5> >::is_integer : 0
numeric_limits< sw::unum::posit<256, 5> >::is_exact : 0
numeric_limits< sw::unum::posit<256, 5> >::min_exponent : -8128
numeric_limits< sw::unum::posit<256, 5> >::min_exponent10 : -2463
numeric_limits< sw::unum::posit<256, 5> >::max_exponent : 8128
numeric_limits< sw::unum::posit<256, 5> >::max_exponent10 : 2463
numeric_limits< sw::unum::posit<256, 5> >::has_infinity : 1
numeric_limits< sw::unum::posit<256, 5> >::has_quiet_NaN : 1
numeric_limits< sw::unum::posit<256, 5> >::has_signaling_NaN : 1
numeric_limits< sw::unum::posit<256, 5> >::has_denorm : 0
numeric_limits< sw::unum::posit<256, 5> >::has_denorm_loss : 0
numeric_limits< sw::unum::posit<256, 5> >::is_iec559 : 0
numeric_limits< sw::unum::posit<256, 5> >::is_bounded : 0
numeric_limits< sw::unum::posit<256, 5> >::is_modulo : 0
numeric_limits< sw::unum::posit<256, 5> >::traps : 0
numeric_limits< sw::unum::posit<256, 5> >::tinyness_before : 0
numeric_limits< sw::unum::posit<256, 5> >::round_style : 1
Show size tables of quires.