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.
Most type-specific inspection tools (quarter, half, single, double, quad, fixpnt,
signedint, unsignedint, posit, float2posit) have been consolidated into
ucalc, the interactive mixed-precision calculator. ucalc provides
the same inspection capabilities via show, compare, precision, and range commands
across all 42+ number types. See the ucalc documentation for details.
The remaining standalone tools are described below.
Compare the three IEEE formats on a given real number value:
$ ieee
Show the truncated value and (sign/scale/fraction) components of different floating point types.
Usage: ieee floating_point_value
Example: ieee 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-754 long double.
On Windows using the Microsoft Visual Studio environment, the long double is aliased to double.
$ longdouble
longdouble: 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: longdouble long_double_value
Example: longdouble 0.03124999
scientific : 0.0312499899999999983247
triple form : (+,-6,111111111111111111110101010000110011100010001110111000000000000)
binary form : 0b0.011'1111'1111'1001.1111'1111'1111'1111'1111'1010'1010'0001'1001'1100'0100'0111'0111'0000'0000'0000
color coded : 0b0.0011'1111'1111'1001.111'1111'1111'1111'1111'1010'1010'0001'1001'1100'0100'0111'0111'0000'0000'0000
Number Traits of IEEE-754 long double
std::numeric_limits< e >
min exponent -16381
max exponent 16384
radix 2
radix digits 64
min 3.3621e-4932
max 1.18973e+4932
lowest -1.18973e+4932
epsilon (1+1ULP-1) 1.0842e-19
round_error 0.5
smallest value 3.6452e-4951
infinity inf
quiet_NAN nan
signaling_NAN nan
smallest normal number
0b0.000000000000001.1000000000000000000000000000000000000000000000000000000000000000
smallest denormalized number
0b0.000000000000000.0000000000000000000000000000000000000000000000000000000000000001
Universal parameterization of IEEE-754 fields
Total number of bits : 80
number of exponent bits : 15
number of fraction bits : 63
exponent bias : 16383
Show the arithmetic properties of a posit environment, including its quire.
$ propp
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 numeric_limits<> of the standard posits.
$ plimits
plimits: numeric_limits<> of standard posits
Numeric limits for posit< 8, 0>
numeric_limits< sw::universal::posit<8, 0> >::min() : 0.015625
numeric_limits< sw::universal::posit<8, 0> >::max() : 64
numeric_limits< sw::universal::posit<8, 0> >::lowest() : -64
numeric_limits< sw::universal::posit<8, 0> >::epsilon() : 0.03125
numeric_limits< sw::universal::posit<8, 0> >::digits : 6
numeric_limits< sw::universal::posit<8, 0> >::digits10 : 1
numeric_limits< sw::universal::posit<8, 0> >::max_digits10 : 2
numeric_limits< sw::universal::posit<8, 0> >::is_signed : 1
numeric_limits< sw::universal::posit<8, 0> >::is_integer : 0
numeric_limits< sw::universal::posit<8, 0> >::is_exact : 0
numeric_limits< sw::universal::posit<8, 0> >::min_exponent : -6
numeric_limits< sw::universal::posit<8, 0> >::min_exponent10 : -1
numeric_limits< sw::universal::posit<8, 0> >::max_exponent : 6
numeric_limits< sw::universal::posit<8, 0> >::max_exponent10 : 1
numeric_limits< sw::universal::posit<8, 0> >::has_infinity : 1
numeric_limits< sw::universal::posit<8, 0> >::has_quiet_NaN : 1
numeric_limits< sw::universal::posit<8, 0> >::has_signaling_NaN : 1
numeric_limits< sw::universal::posit<8, 0> >::has_denorm : 0
numeric_limits< sw::universal::posit<8, 0> >::has_denorm_loss : 0
numeric_limits< sw::universal::posit<8, 0> >::is_iec559 : 0
numeric_limits< sw::universal::posit<8, 0> >::is_bounded : 0
numeric_limits< sw::universal::posit<8, 0> >::is_modulo : 0
numeric_limits< sw::universal::posit<8, 0> >::traps : 0
numeric_limits< sw::universal::posit<8, 0> >::tinyness_before : 0
numeric_limits< sw::universal::posit<8, 0> >::round_style : 1
Numeric limits for posit< 16, 1>
numeric_limits< sw::universal::posit<16, 1> >::min() : 3.72529e-09
numeric_limits< sw::universal::posit<16, 1> >::max() : 2.68435e+08
numeric_limits< sw::universal::posit<16, 1> >::lowest() : -2.68435e+08
numeric_limits< sw::universal::posit<16, 1> >::epsilon() : 0.000244141
numeric_limits< sw::universal::posit<16, 1> >::digits : 13
numeric_limits< sw::universal::posit<16, 1> >::digits10 : 3
numeric_limits< sw::universal::posit<16, 1> >::max_digits10 : 4
...
Show size tables of quires.
$ propq
print quire size tables
Quire size table as a function of <nbits, es, capacity = 10>
Capacity is 2^10 accumulations of max_pos^2
nbits es value
+ 0 1 2 3 4 5 6 7 8 9
4 18 26 42 74 138 266 522 1034 2058 4106
5 22 34 58 106 202 394 778 1546 3082 6154
6 26 42 74 138 266 522 1034 2058 4106 8202
7 30 50 90 170 330 650 1290 2570 5130 10250
8 34 58 106 202 394 778 1546 3082 6154 12298
9 38 66 122 234 458 906 1802 3594 7178 14346
10 42 74 138 266 522 1034 2058 4106 8202 16394
11 46 82 154 298 586 1162 2314 4618 9226 18442
12 50 90 170 330 650 1290 2570 5130 10250 20490