1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
|
#!/bin/zsh
function usage() {
cat <<EOF
Usage: $0 [options] <input number>
This tool splits an arbitrary number into IEEE 768 floats.
Options:
--help|-h this message
-m <bits> mantissa bits, 23 for sp and 52 for dp (default 23)
-n <count> number of constants to split the input into (default 2)
-z <bits> number of trailing zero bits in the first count-1 constants (default 12)
-p only output positive numbers (or rather numbers with the same sign as the input number)
-o <offset> add this offset to the mantissa of the first value
-f <function> use the argument as output function name for easier cut and paste (default depends on -m)
Available functions:
fak(x) : factorial of x
floor(x)
round(x)
log2(x)
abs(x)
sign(x)
exponent(x)
l(x)
s(x)
c(x)
EOF
}
bits=23
count=2
zerobits=12
mantissaReduction=round
offset=0
const_fun=
while (( $# > 0 )); do
case "$1" in
--help|-h) usage; exit ;;
-m) bits=$2; shift ;;
-m*) bits=${1#-m} ;;
-n) count=$2; shift ;;
-n*) count=${1#-n} ;;
-z) zerobits=$2; shift ;;
-z*) zerobits=${1#-z} ;;
-o) offset=$2; shift ;;
-o*) offset=${1#-o} ;;
-f) const_fun=$2; shift ;;
-f*) const_fun=${1#-o} ;;
-p) mantissaReduction=floor ;;
*) input="$input $1" ;;
esac
shift
done
if (($bits == 23)) && [[ -z "$const_fun" ]]; then
const_fun="const auto c## = Vc::Detail::floatConstant"
elif [[ -z "$const_fun" ]]; then
const_fun="const auto c## = Vc::Detail::doubleConstant"
fi
BC_LINE_LENGTH=0 bc -l <<EOF
scale=400
pi=3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936073
oneoverlog2=1/l(2)
scale=100
define fak(x) { r=x; while(x>1) { r *= --x; }; return r; }
define floor(x) { tmp=scale; scale=0; n = x/1; scale=tmp; return n; }
define round(x) { return floor(x + 0.5); }
define log2(x) { return l(x)*oneoverlog2; }
define abs(x) { if(x < 0) return -x; return x; }
define sign(x) { tmp=scale; scale=0; n = x/abs(x); scale=tmp; return n; }
define exponent(x) { x = abs(x); e = floor(log2(x)); while(x*2^-e < 1) e -= 1; while(x*2^-e >= 2) e += 1; return e; }
define setprecision(x, p) { return round(x * 2^(p-exponent(x))) * 2^(exponent(x)-p); }
define float(x) { return setprecision(x,${bits}); }
define void printfloat(s,m,e) {
print "${const_fun}<", s, ", 0x"
obase=16
print m
obase=10
print ", ", e, ">(); // ", s*(m*2^(e-${bits})+2^e), "\n"
}
/* unused, but can be used to print full binary representation of floats */
define void printfloat_int(x) {
h=0
if (x < 0) {
h = 2^31
x = -x;
}
e=exponent(x)
h+=${mantissaReduction}(x*2^(${bits}-e)-2^${bits})
h+=(e+127)*2^23
obase=16
print "0x", h
obase=10
}
in=${input}
print "// ", in, "\n"
x=in
shift1=${bits}-${zerobits}
shift2=${bits}-shift1
for(i = 1; i < ${count}; ++i) {
s=sign(x)
x=abs(x)
e=exponent(x)
m=(${mantissaReduction}(x*2^(shift1-e)-2^shift1) + ${offset})*(2^shift2)
printfloat(s,m,e)
x=s*(x-(m*(2^-${bits})+1)*(2^e))
if(x == 0) {
break
}
}
if(x == 0) {
print "no remainder.\n"
} else {
s=sign(x)
x=abs(x)
e=exponent(x)
m=${mantissaReduction}(x*2^(${bits}-e)-2^${bits})
printfloat(s,m,e)
x=s*(x-(m*(2^-${bits})+1)*(2^e))
if(x == 0) {
print "no remainder.\n"
} else {
err=abs(x/in)
e=floor(l(err)/l(10))-1
ulp=x * 2^(23 - exponent(in))
scale=1
print "relative error: ", (err*10^-e)/1, "e", e, "\n"
print (ulp*1000+0.5)/1*0.001, " ulp\n"
}
}
EOF
# vim: sw=2 et
|
