mirror of
https://github.com/openhwgroup/cvw
synced 2025-02-11 06:05:49 +00:00
Merge branch 'main' of https://github.com/openhwgroup/cvw
This commit is contained in:
Ross Thompson
commit
d23eda1305
2
Makefile
2
Makefile
@ -4,8 +4,8 @@
|
|||||||
|
|
||||||
all:
|
all:
|
||||||
make install
|
make install
|
||||||
make testfloat
|
|
||||||
make riscof
|
make riscof
|
||||||
|
make testfloat
|
||||||
make verify
|
make verify
|
||||||
make coverage
|
make coverage
|
||||||
make benchmarks
|
make benchmarks
|
||||||
|
|||||||
@ -120,8 +120,8 @@ sudo apt-get install -y perl g++ ccache help2man libgoogle-perftools-dev numactl
|
|||||||
sudo apt-get install -y libfl2 libfl-dev # Ubuntu only (ignore if gives error)
|
sudo apt-get install -y libfl2 libfl-dev # Ubuntu only (ignore if gives error)
|
||||||
cd $RISCV
|
cd $RISCV
|
||||||
git clone https://github.com/verilator/verilator # Only first time
|
git clone https://github.com/verilator/verilator # Only first time
|
||||||
unsetenv VERILATOR_ROOT # For csh; ignore error if on bash
|
# unsetenv VERILATOR_ROOT # For csh; ignore error if on bash
|
||||||
unset VERILATOR_ROOT # For bash
|
unset VERILATOR_ROOT # For bash
|
||||||
cd verilator
|
cd verilator
|
||||||
git pull # Make sure git repository is up-to-date
|
git pull # Make sure git repository is up-to-date
|
||||||
git checkout master # Use development branch (e.g. recent bug fixes)
|
git checkout master # Use development branch (e.g. recent bug fixes)
|
||||||
@ -157,6 +157,8 @@ opam install sail -y
|
|||||||
eval $(opam config env)
|
eval $(opam config env)
|
||||||
git clone https://github.com/riscv/sail-riscv.git
|
git clone https://github.com/riscv/sail-riscv.git
|
||||||
cd sail-riscv
|
cd sail-riscv
|
||||||
|
# For now, use checkout that is stable for Wally
|
||||||
|
git checkout 72b2516d10d472ac77482fd959a9401ce3487f60
|
||||||
make -j ${NUM_THREADS}
|
make -j ${NUM_THREADS}
|
||||||
ARCH=RV32 make -j ${NUM_THREADS}
|
ARCH=RV32 make -j ${NUM_THREADS}
|
||||||
sudo ln -sf $RISCV/sail-riscv/c_emulator/riscv_sim_RV64 /usr/bin/riscv_sim_RV64
|
sudo ln -sf $RISCV/sail-riscv/c_emulator/riscv_sim_RV64 /usr/bin/riscv_sim_RV64
|
||||||
|
|||||||
123
docs/divsqrt_tex/div2.tex
Normal file
123
docs/divsqrt_tex/div2.tex
Normal file
@ -0,0 +1,123 @@
|
|||||||
|
\documentclass[12pt]{article}
|
||||||
|
|
||||||
|
\usepackage{amssymb, amsmath, amsfonts, amsthm, graphicx, tcolorbox}
|
||||||
|
|
||||||
|
\usepackage{arydshln}
|
||||||
|
|
||||||
|
\parindent = 0in
|
||||||
|
|
||||||
|
\pagestyle{empty}
|
||||||
|
|
||||||
|
%==========
|
||||||
|
%==========
|
||||||
|
|
||||||
|
\begin{document}
|
||||||
|
|
||||||
|
\begin{center}
|
||||||
|
\begin{tabular}{cccc}
|
||||||
|
Initialization&$D$&$0001.1010\ 000$&\\
|
||||||
|
&$-D=\overline{D}+1$&$1110.0101\ 111$&(+ 1 ulp)\\
|
||||||
|
&&&\\
|
||||||
|
&$WS_{-1}=X$&$0001.0000\ 010$&\\
|
||||||
|
&$WC_{-1}$&$0000.0000\ 000$&\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 0:&$WS_{-1}$&$0001.0000\ 010$&\\
|
||||||
|
&$WC_{-1}$&$0000.0000\ 00\mathbf{1}$&($W_{msbs}=0001\ \text{so}\ q_0=1$)\\
|
||||||
|
&$-q_0D$&$1110.0101\ 111$&\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum$&$1111.0101\ 100$&$\ll1$\\
|
||||||
|
&$carry$&$0000.0000\ 110$&$\ll1$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 1:&$WS_0$&$1110.1011\ 000$&\\
|
||||||
|
&$WC_0$&$0000.0001\ 10\mathbf{0}$&($W_{msbs}=1110\ \text{so}\ q_1=-1$)\\
|
||||||
|
&$-q_1D$&$0001.1010\ 000$&\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum$&$1111.0000\ 100$&$\ll1$\\
|
||||||
|
&$carry$&$0001.0110\ 000$&$\ll1$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 2:&$WS_1$&$1110.0001\ 000$&\\
|
||||||
|
&$WC_1$&$0010.1100\ 00\mathbf{1}$&($W_{msbs}=0000\ \text{so}\ q_2=1$)\\
|
||||||
|
&$-q_2D$&$1110.0101\ 111$&\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum$&$0010.1000\ 110$&$\ll1$\\
|
||||||
|
&$carry$&$1100.1010\ 010$&$\ll1$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 3:&$WS_2$&$0101.0001\ 100$&\\
|
||||||
|
&$WC_2$&$1001.0100\ 10\mathbf{0}$&($W_{msbs}=1110\ \text{so}\ q_3=-1$)\\
|
||||||
|
&$-q_3D$&$0001.1010\ 000$&\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum$&$1101.1111\ 000$&\\
|
||||||
|
&$carry$&$0010.0001\ 000$&$sum+carry=0$, terminate.\\
|
||||||
|
\hdashline\\
|
||||||
|
Terminate&Quotient&0.101
|
||||||
|
\end{tabular}
|
||||||
|
\end{center}
|
||||||
|
|
||||||
|
\vfill
|
||||||
|
\eject
|
||||||
|
|
||||||
|
X = 1.0110\ 011 (179/128)
|
||||||
|
|
||||||
|
D = 1.0011\ 000 (152/128)
|
||||||
|
|
||||||
|
Q = 1.0010\ 1101\ 0
|
||||||
|
|
||||||
|
D[1.3] = 1.001, so we use the ``"1.001" column of chart 13.X. This means we select a quotient bit of 2 if the partial remainder is greater than or equal to 3.5, a quotient bit of 1 if the partial is greater or equal to than 1.0, a zero if the partial is greater than or equal to -1.5, -1 if the partial is greater than or equal to -3.75, and a -2 otherwise.
|
||||||
|
\begin{center}
|
||||||
|
\begin{tabular}{cccc}
|
||||||
|
Initialization&$D$&$0001.0011\ 000$&\\
|
||||||
|
&$2D$&$0010.0110\ 000$&\\
|
||||||
|
&$-D=\overline{D}+1$&$1110.1100\ 111$&(+ 1 ulp)\\
|
||||||
|
&$-2D=\overline{2D}+1$&$1101.1001\ 111$&(+ 1 ulp)\\
|
||||||
|
&&&\\
|
||||||
|
&$X=WS$&$0001.0110\ 011$&\\
|
||||||
|
&$WC$&$0000.0000\ 000$&\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 4:&$WS$&$0001.0110\ 011$&\\
|
||||||
|
&$WC$&$0000.0000\ 00\mathbf{1}$&($RW_{msbs}=0001.010\ \text{so}\ q_4=1$)\\
|
||||||
|
&$-q_7D$&$1110.1100\ 111$&\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS$&$1111.1010\ 101$&$\ll2$\\
|
||||||
|
&$WC$&$0000.1000\ 110$&$\ll2$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 3:&$WS$&$1110.1010\ 100$&\\
|
||||||
|
&$WC$&$0010.0011\ 000$&($RW_{msbs}=0000.110\ \text{so}\ q_3=1$)\\
|
||||||
|
&$-q_6D$&$0000.0000\ 000$&\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS$&$1100.1001\ 100$&$\ll2$\\
|
||||||
|
&$WC$&$0100.0100\ 000$&$\ll2$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 2:&$WS$&$0010.0110\ 000$&\\
|
||||||
|
&$WC$&$0001.0000\ 00\mathbf{1}$&($RW_{msbs}=0011.010\ \text{so}\ q_2=-1$)\\
|
||||||
|
&$-q_5D$&$1110.0101\ 111$&\\
|
||||||
|
\cline{2-3}
|
||||||
|
\end{tabular}
|
||||||
|
\end{center}
|
||||||
|
|
||||||
|
page 269 306
|
||||||
|
|
||||||
|
\vfill
|
||||||
|
\eject
|
||||||
|
|
||||||
|
\large{\bf{
|
||||||
|
Math for the recurrence relation}}
|
||||||
|
|
||||||
|
**going to have to change notation for sure, change the subscripts for steps and might have to get rid of some exponents**
|
||||||
|
\begin{align*}
|
||||||
|
w[j+1] &= r^{j+1}\big(x-S[j+1]^2\big)\\
|
||||||
|
&= r^{j+1}\big(x-(S[j]+s_{j+1}r^{-(j+1)})^2\big)\\
|
||||||
|
&= r^{j+1}x-r^{j+1}\big(S[j]^2+2S[j]s_{j+1}r^{-(j+1)}+s^2_{j+1}r^{-2(j+1)}\big)\\
|
||||||
|
&= r^{j+1}\big(x-S[j]^2\big)-\big(2S[j]s_{j+1}+s_{j+1}^2r^{-(j+1)}\big)\\
|
||||||
|
&= rw[j]-\big(2S[j]s_{j+1}+s_{j+1}^2r^{-(j+1)}\big)\\
|
||||||
|
&= rw[j]+F[j]
|
||||||
|
\end{align*}
|
||||||
|
where
|
||||||
|
\begin{align*}
|
||||||
|
F[j]=-\big(2S[j]s_{j+1}+s_{j+1}^2r^{-(j+1)}\big)
|
||||||
|
\end{align*}
|
||||||
|
|
||||||
|
Since there is a term of $S$ in the expression of $F$, we must come up with a way to represent $S$ using only zeros and ones, rather than using the bit set $\{-a,\ldots,a\}$. This is done using on-the-fly conversion just as we did to compute the quotient for the divider. We keep a running copy of $S$, but we also keep the value $SM=S-1$. The logic is still the same for computing $S$ and $SM$ on the next step; see figure 13.15.
|
||||||
|
|
||||||
|
Now that $S$ is in a form such that we can use it in a CSA, we need to compute $F$. To do so,
|
||||||
|
|
||||||
|
\end{document}
|
||||||
84
docs/divsqrt_tex/div4.tex
Normal file
84
docs/divsqrt_tex/div4.tex
Normal file
@ -0,0 +1,84 @@
|
|||||||
|
\documentclass[12pt]{article}
|
||||||
|
|
||||||
|
\usepackage{amssymb, amsmath, amsfonts, amsthm, graphicx, tcolorbox}
|
||||||
|
|
||||||
|
\usepackage{arydshln}
|
||||||
|
|
||||||
|
\parskip = .2in
|
||||||
|
\parindent = 0in
|
||||||
|
|
||||||
|
\pagestyle{empty}
|
||||||
|
|
||||||
|
%==========
|
||||||
|
%==========
|
||||||
|
|
||||||
|
\begin{document}
|
||||||
|
|
||||||
|
|
||||||
|
X = 1.0000\ 1101 (269/256)
|
||||||
|
|
||||||
|
D = 1.0011\ 0110 (310/256)
|
||||||
|
|
||||||
|
Q = 0.1101\ 1110 (222/256)
|
||||||
|
|
||||||
|
D[1.3] = 1.001, so we use the ``1.001" column of chart 13.X. This means we select a quotient bit of 2 if the partial remainder is greater than or equal to 3.5, a quotient bit of 1 if the partial is greater or equal to than 1.0, a zero if the partial is greater than or equal to -1.5, -1 if the partial is greater than or equal to -3.75, and a -2 otherwise.
|
||||||
|
|
||||||
|
{\small
|
||||||
|
\begin{center}
|
||||||
|
\begin{tabular}{cccc}
|
||||||
|
Initialization&$D$&$0001.0011\ 0110\ 00$&\\
|
||||||
|
&$2D$&$0010.0110\ 1100\ 00$&\\
|
||||||
|
&$-D=\overline{D}+1$&$1110.1100\ 1001\ 11$&(+ 1 ulp)\\
|
||||||
|
&$-2D=\overline{2D}+1$&$1101.1001\ 0011\ 11$&(+ 1 ulp)\\
|
||||||
|
&&&\\
|
||||||
|
&$WS_{-1}=X$&$0001.0000\ 1101\ 00$&\\
|
||||||
|
&$WC_{-1}$&$0000.0000\ 0000\ 00$&\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 0: &$WS_{-1} $&$0001.0000\ 1101\ 00$&\\
|
||||||
|
&$WC_{-1} $&$0000.0000\ 0000\ 0\mathbf{1}$&($W_{msbs}=0001.000\ \text{so}\ q_0=1$)\\
|
||||||
|
&$-q_0D $&$1110.1100\ 1001\ 11$&\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum $&$1111.1100\ 0100\ 10$&$\ll2$\\
|
||||||
|
&$carry $&$0000.0001\ 0010\ 10$&$\ll2$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 1: &$WS_0 $&$1111.0001\ 0010\ 00$&\\
|
||||||
|
&$WC_0 $&$0000.0100\ 1010\ 0\mathbf{0}$&($W_{msbs}=1111.010\ \text{so}\ q_1=-1$)\\
|
||||||
|
&$-q_1D $&$0001.0011\ 0110\ 00$&\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum $&$1110.0110\ 1110\ 00$&$\ll2$\\
|
||||||
|
&$carry $&$0010.0010\ 0100\ 00$&$\ll2$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 2: &$WS_1 $&$1001.1011\ 1000\ 00$&\\
|
||||||
|
&$WC_1 $&$1000.1001\ 0000\ 0\mathbf{1}$&($W_{msbs}=0010.010\ \text{so}\ q_2=2$)\\
|
||||||
|
&$-q_2D $&$1101.1001\ 0011\ 11$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum $&$1100.1011\ 1011\ 10$&$\ll2$\\
|
||||||
|
&$carry $&$0011.0010\ 0000\ 10$&$\ll2$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 3: &$WS_2 $&$0010.1110\ 1110\ 00$&\\
|
||||||
|
&$WC_2 $&$1100.1000\ 0010\ 0\mathbf{0}$&($W_{msbs}=1111.011\ \text{so}\ q_3=-1$)\\
|
||||||
|
&$-q_3D $&$0001.0011\ 0110\ 00$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum $&$1111.0101\ 1010\ 00$&$\ll2$\\
|
||||||
|
&$carry $&$0001.0100\ 0100\ 00$&$\ll2$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 4: &$WS_3 $&$1101.0110\ 1000\ 00$&\\
|
||||||
|
&$WC_3 $&$0101.0001\ 0000\ 0\mathbf{1}$&($W_{msbs}=0010.011\ \text{so}\ q_4=2$)\\
|
||||||
|
&$-q_4D $&$1101.1001\ 0011\ 11$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum $&$0101.1110\ 1011\ 10$&$\ll2$\\
|
||||||
|
&$carry $&$1010.0010\ 0000\ 10$&$\ll2$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 5: &$WS_4 $&$0111.1010\ 1110\ 00$&\\
|
||||||
|
&$WC_4 $&$1000.1000\ 0010\ 0\mathbf{0}$&($W_{msbs}=0000.001\ \text{so}\ q_5=0$)\\
|
||||||
|
&$-q_5D $&$0000.0000\ 0000\ 00$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum $&$1111.0010\ 1100\ 00$&$\ll2$\\
|
||||||
|
&$carry $&$0001.0000\ 0100\ 00$&$\ll2$\\
|
||||||
|
\hdashline\\
|
||||||
|
Terminate&Quotient&$00.11\ 01\ 11\ 10\ (00\ 1)$
|
||||||
|
\end{tabular}
|
||||||
|
\end{center}
|
||||||
|
}
|
||||||
|
|
||||||
|
\end{document}
|
||||||
385
docs/divsqrt_tex/sqrt2.tex
Normal file
385
docs/divsqrt_tex/sqrt2.tex
Normal file
@ -0,0 +1,385 @@
|
|||||||
|
\documentclass[12pt]{article}
|
||||||
|
\usepackage{amssymb, amsmath, amsfonts, amsthm, graphicx, tcolorbox}
|
||||||
|
\usepackage{arydshln}
|
||||||
|
|
||||||
|
\parskip = .2in
|
||||||
|
\parindent = 0in
|
||||||
|
|
||||||
|
\pagestyle{empty}
|
||||||
|
|
||||||
|
%==========
|
||||||
|
%==========
|
||||||
|
|
||||||
|
\begin{document}
|
||||||
|
|
||||||
|
X = 0.0111 0011 1001 (1849/4096)
|
||||||
|
|
||||||
|
S = 0.1010 1100 0000 (2752/4096)
|
||||||
|
{\small
|
||||||
|
\begin{center}
|
||||||
|
\begin{tabular}{ccccc}
|
||||||
|
&$X $&$ 0000.0111\ 0011\ 1001 $& &$S_0={\color{blue}0001}.0000\ 0000\ 0000$\\
|
||||||
|
&$WS_0=2(X-1) $&$ 1110.1110\ 0111\ 0010 $& &$SM_0={\color{blue}0000}.0000\ 0000\ 0000\phantom{M}$\\
|
||||||
|
&$WC_0 $&$ 0000.0000\ 0000\ 0000 $& &$K_0=0001.0000\ 0000\ 0000\ $\\
|
||||||
|
& & & &$C_0=1111.0000\ 0000\ 0000\,$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 1: &$WS_0 $&$ 1110.1110\ 0111\ 0010 $& &\\
|
||||||
|
&$WC_0 $&$ 0000.0000\ 0000\ 0000 $& &($W_{msbs}=1110\ \text{so}\ s_1=-1$)\\
|
||||||
|
&$F_1=2S_0-K_1 $&${\color{blue}0001.1}000\ 0000\ 0000$& &$S_1={\color{blue}0000.1}000\ 0000\ 0000$\\
|
||||||
|
& & & &$SM_1={\color{blue}0000.0}000\ 0000\ 0000\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum $&$ 1111.0110\ 0111\ 0010 $&$\ll1 $&$K_1=0000.1000\ 0000\ 0000\ $\\
|
||||||
|
&$carry $&$ 0001.0000\ 0000\ 0000 $&$\ll1 $&$C_1=1111.1000\ 0000\ 0000\,$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 2: &$WS_1 $&$ 1110.1100\ 1110\ 0100 $& &\\
|
||||||
|
&$WC_1 $&$ 0010.0000\ 0000\ 0000 $& &($W_{msbs}=0000\ \text{so}\ s_2=1$)\\
|
||||||
|
&$F_2=-2S_1-K_2$&${\color{blue}1110.11}00\ 0000\ 0000$& &$S_2={\color{blue}0000.11}00\ 0000\ 0000$\\
|
||||||
|
& & & &$SM_2={\color{blue}0000.10}00\ 0000\ 0000\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum $&$ 0010.0000\ 1110\ 0100 $&$\ll1 $&$K_2=0000.0100\ 0000\ 0000\ $\\
|
||||||
|
&$carry $&$ 1101.1000\ 0000\ 0000 $&$\ll1 $&$C_2=1111.1100\ 0000\ 0000\,$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 3: &$WS_2 $&$ 0100.0001\ 1100\ 1000 $& &\\
|
||||||
|
&$WC_2 $&$ 1011.0000\ 0000\ 0000 $& &($W_{msbs}=1111\ \text{so}\ s_3=0$)\\
|
||||||
|
&$F_3=0 $&${\color{blue}0000.000}0\ 0000\ 0000$& &$S_3={\color{blue}0000.110}0\ 0000\ 0000$\\
|
||||||
|
& & & &$SM_3={\color{blue}0000.101}0\ 0000\ 0000\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum $&$ 1111.0001\ 1100\ 1000 $&$\ll1 $&$K_3=0000.0010\ 0000\ 0000\ $\\
|
||||||
|
&$carry $&$ 0000.0000\ 0000\ 0000 $&$\ll1 $&$C_3=1111.1110\ 0000\ 0000\,$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 4: &$WS_3 $&$ 1110.0011\ 1001\ 0000 $& &\\
|
||||||
|
&$WC_3 $&$ 0000.0000\ 0000\ 0000 $& &($W_{msbs}=1110\ \text{so}\ s_4=-1$)\\
|
||||||
|
&$F_4=2S_3-K_4 $&${\color{blue}0001.0111}\ 0000\ 0000$& &$S_4={\color{blue}0000.1011}\ 0000\ 0000$\\
|
||||||
|
& & & &$SM_4={\color{blue}0000.1010}\ 0000\ 0000\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum $&$ 1111.0100\ 1001\ 0000 $&$\ll1 $&$K_4=0000.0001\ 0000\ 0000\ $\\
|
||||||
|
&$carry $&$ 0000.0110\ 0000\ 0000 $&$\ll1 $&$C_4=1111.1111\ 0000\ 0000\,$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 5: &$WS_4 $&$ 1110.1001\ 0010\ 0000 $& &\\
|
||||||
|
&$WC_4 $&$ 0000.1100\ 0000\ 0000 $& &($W_{msbs}=1110\ \text{so}\ s_5=-1$)\\
|
||||||
|
&$F_5=2S_4-K_5 $&${\color{blue}0001.0101\ 1}000\ 0000$& &$S_5={\color{blue}0000.1010\ 1}000\ 0000$\\
|
||||||
|
& & & &$SM_5={\color{blue}0000.1010\ 0}000\ 0000\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum $&$ 1111.0000\ 1010\ 0000 $&$\ll1 $&$K_5=0000.0000\ 1000\ 0000\ $\\
|
||||||
|
&$carry $&$ 0001.1010\ 0000\ 0000 $&$\ll1 $&$C_5=1111.1111\ 1000\ 0000\,$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 6: &$WS_5 $&$ 1110.0001\ 0100\ 0000 $& &\\
|
||||||
|
&$WC_5 $&$ 0011.0100\ 0000\ 0000 $& &($W_{msbs}=0001\ \text{so}\ s_6=1$)\\
|
||||||
|
&$F_6=-2S_5-K_6$&${\color{blue}1110.1010\ 11}00\ 0000$& &$S_6={\color{blue}0000.1010\ 11}00\ 0000$\\
|
||||||
|
& & & &$SM_6={\color{blue}0000.1010\ 10}00\ 0000\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum $&$ 0011.1111\ 1000\ 0000 $&$\ll1 $&$K_6=0000.0000\ 0100\ 0000\ $\\
|
||||||
|
&$carry $&$ 1100.0000\ 1000\ 0000 $&$\ll1 $&$C_6=1111.1111\ 1100\ 0000\,$\\
|
||||||
|
& & & &$sum+carry=0$, terminate\\
|
||||||
|
\hdashline\\
|
||||||
|
Terminate&Square Root&0.101011
|
||||||
|
\end{tabular}
|
||||||
|
\end{center}
|
||||||
|
}
|
||||||
|
|
||||||
|
{\small
|
||||||
|
\begin{center}
|
||||||
|
\begin{tabular}{cccc}
|
||||||
|
\hdashline\\
|
||||||
|
Step 6: &$WS $&$0111.1111\ 0000\ 00$&\\
|
||||||
|
&$WC $&$1000.0001\ 0000\ 00$&($W_{msbs}=1111\ \text{so}\ s_6=0$)\\
|
||||||
|
&$F $&$0000.0000\ 0000\ 00$&$S_6=\mathbf{1.0101\ 10}00\ 00$\\
|
||||||
|
& & &$SM_6=\mathbf{1.0101\ 01}00\ 00\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS $&$1111.1110\ 0000\ 00$&$\ll1$\\
|
||||||
|
&$WC $&$0000.0010\ 0000\ 00$&$\ll1$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 7: &$WS $&$1111.1100\ 0000\ 00$&\\
|
||||||
|
&$WC $&$0000.0100\ 0000\ 00$&($W_{msbs}=1111\ \text{so}\ s_7=0$)\\
|
||||||
|
&$F $&$0000.0000\ 0000\ 00$&$S_7=\mathbf{1.0101\ 100}0\ 00$\\
|
||||||
|
& & &$SM_7=\mathbf{1.0101\ 011}0\ 00\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS $&$1111.1000\ 0000\ 00$&$\ll1$\\
|
||||||
|
&$WC $&$0000.1000\ 0000\ 00$&$\ll1$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 8: &$WS $&$1111.0000\ 0000\ 00$&\\
|
||||||
|
&$WC $&$0001.0000\ 0000\ 00$&($W_{msbs}=0000\ \text{so}\ s_8=1$)\\
|
||||||
|
&$F $&$1110.1010\ 0111\ 10$&$S_8=\mathbf{1.0101\ 1001}\ 00$\\
|
||||||
|
& & &$SM_8=\mathbf{1.0101\ 1000}\ 00\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS $&$0000.1010\ 0111\ 10$&$\ll1$\\
|
||||||
|
&$WC $&$1110.0000\ 0000\ 00$&$\ll1$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 9: &$WS $&$0001.0100\ 1111\ 00$&\\
|
||||||
|
&$WC $&$1100.0000\ 0000\ 00$&($W_{msbs}=1101\ \text{so}\ s_9=-1$)\\
|
||||||
|
&$F $&$0001.0101\ 1000\ 11$&$S_9=\mathbf{1.0101\ 1000\ 1}0$\\
|
||||||
|
& & &$SM_9=\mathbf{1.0101\ 1000\ 0}0\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS $&$1100.0001\ 0111\ 11$&$\ll1$\\
|
||||||
|
&$WC $&$0010.1001\ 0000\ 00$&$\ll1$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 10:&$WS $&$1000.0010\ 1111\ 10$&\\
|
||||||
|
&$WC $&$0101.0010\ 0000\ 00$&($W_{msbs}=1101\ \text{so}\ s_{10}=-1$)\\
|
||||||
|
&$F $&$0001.0101\ 1000\ 01$&$S_{10}=\mathbf{1.0101\ 1000\ 01}$\\
|
||||||
|
& & &$SM_{10}=\mathbf{1.0101\ 1000\ 00}\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS $&$1100.0001\ 0111\ 11$&$\ll1$\\
|
||||||
|
&$WC $&$0010.0101\ 0000\ 00$&$\ll1$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 11:&$WS $&$1000.0010\ 1111\ 10$&\\
|
||||||
|
&$WC $&$0100.1010\ 0000\ 00$&($W_{msbs}=1101\ \text{so}\ s_{11}=-1$)\\
|
||||||
|
&$F $&$0001.0101\ 1000\ 00$&$S_{11}=\mathbf{1.0101\ 1000\ 00}$\\
|
||||||
|
& & &$SM_{11}=\mathbf{1.0101\ 1000\ 00}\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS $&$1101.1101\ 0111\ 10$&$\ll1$\\
|
||||||
|
&$WC $&$0000.0101\ 0000\ 00$&$\ll1$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 12:&$WS $&$1101.1000\ 0111\ 10$&\\
|
||||||
|
&$WC $&$0000.1010\ 0000\ 00$&($W_{msbs}=1101\ \text{so}\ s_{12}=-1$)\\
|
||||||
|
&$F $&$0001.0101\ 1000\ 00$&$S_{12}=\mathbf{1.0101\ 1000\ 00}$\\
|
||||||
|
& & &$SM_{12}=\mathbf{1.0101\ 1000\ 00}\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS $&$1100.0111\ 1111\ 10$&$\ll1$\\
|
||||||
|
&$WC $&$0011.0000\ 0000\ 00$&$\ll1$\\
|
||||||
|
\end{tabular}
|
||||||
|
\end{center}
|
||||||
|
}
|
||||||
|
|
||||||
|
{\small
|
||||||
|
\begin{center}
|
||||||
|
\begin{tabular}{cccc}
|
||||||
|
Step 13:&$WS $&$1000.1111\ 1111\ 00$&\\
|
||||||
|
&$WC $&$0110.0000\ 0000\ 00$&($W_{msbs}=1110\ \text{so}\ s_{13}=-1$)\\
|
||||||
|
&$F $&$0001.0101\ 1000\ 00$&$S_{13}=\mathbf{1.0101\ 1000\ 00}$\\
|
||||||
|
& & &$SM_{13}=\mathbf{1.0101\ 1000\ 00}\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS $&$1111.1010\ 0111\ 10$&$\ll1$\\
|
||||||
|
&$WC $&$0000.1011\ 0000\ 00$&$\ll1$\\
|
||||||
|
\end{tabular}
|
||||||
|
\end{center}
|
||||||
|
}
|
||||||
|
|
||||||
|
\vfill
|
||||||
|
\eject
|
||||||
|
|
||||||
|
{\small
|
||||||
|
\begin{center}
|
||||||
|
\begin{tabular}{ccccc}
|
||||||
|
&$X $&$ 0000.1100\ 0000 $& &$S_0={\color{blue}0001}.0000\ 0000\ 00$\\
|
||||||
|
&$WS=X-1 $&$ 1111.1100\ 0000 $& &$SM_0={\color{blue}0000}.0000\ 0000\ 00\phantom{M}$\\
|
||||||
|
&$WC $&$ 0000.0000\ 0000 $& &$K_0=0000.0100\ 0000\ 00\ $\\
|
||||||
|
& & & &$C_0=1111.1100\ 0000\ 00\,$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 1: &$WS $&$ 1111.1100\ 0000 $& &\\
|
||||||
|
&$WC $&$ 0000.0000\ 0000 $& &($W_{msbs}=1111\ \text{so}\ s_1=0$)\\
|
||||||
|
&$F_1=0 $&${\color{blue}0000.00}00\ 0000$& &$S_1={\color{blue}0001.0}000\ 0000\ 00$\\
|
||||||
|
& & & &$SM_1={\color{blue}0000.1}000\ 0000\ 00\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS $&$ 1111.1100\ 0000 $&$\ll1 $&$K_1=0000.0010\ 0000\ 00\ $\\
|
||||||
|
&$WC $&$ 0000.0000\ 0000 $&$\ll1 $&$C_1=1111.1110\ 0000\ 00\,$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 2: &$WS $&$ 1111.1000\ 0000 $& &\\
|
||||||
|
&$WC $&$ 0000.0000\ 0000 $& &($W_{msbs}=1111\ \text{so}\ s_2=0$)\\
|
||||||
|
&$F_2=0 $&${\color{blue}0000.000}0\ 0000$& &$S_2={\color{blue}0001.00}00\ 0000\ 00$\\
|
||||||
|
& & & &$SM_2={\color{blue}0000.11}00\ 0000\ 00\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS $&$ 1111.1000\ 0000 $&$\ll1 $&$K_2=0000.0001\ 0000\ 00\ $\\
|
||||||
|
&$WC $&$ 0000.0000\ 0000 $&$\ll1 $&$C_2=1111.1111\ 0000\ 00\,$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 3: &$WS $&$ 1111.0000\ 0000 $& &\\
|
||||||
|
&$WC $&$ 0000.0000\ 0000 $& &($W_{msbs}=1111\ \text{so}\ s_3=0$)\\
|
||||||
|
&$F_3=0 $&${\color{blue}0000.0000}\ 0000$& &$S_3={\color{blue}0001.000}0\ 0000\ 00$\\
|
||||||
|
& & & &$SM_3={\color{blue}0000.111}0\ 0000\ 00\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS $&$1111.0000\ 0000 $&$\ll1 $&$K_3=0000.0000\ 1000\ 00\ $\\
|
||||||
|
&$WC $&$0000.0000\ 0000 $&$\ll1 $&$C_3=1111.1111\ 1000\ 00\,$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 4: &$WS $&$1110.0000\ 0000 $& &\\
|
||||||
|
&$WC $&$0000.0000\ 0000 $& &($W_{msbs}=1110\ \text{so}\ s_4=-1$)\\
|
||||||
|
&$F_4=S_3-K_3 $&${\color{blue}0000.1111\ 1}000$& &$S_4={\color{blue}0000.1111}\ 0000\ 00$\\
|
||||||
|
& & & &$SM_4={\color{blue}0000.1110}\ 0000\ 00\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS $&$1110.1111\ 1000 $&$\ll1 $&$K_4=0000.0000\ 0100\ 00\ $\\
|
||||||
|
&$WC $&$0000.0000\ 0000 $&$\ll1 $&$C_4=1111.1111\ 1100\ 00\,$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 5: &$WS $&$1101.1111\ 0000 $& &\\
|
||||||
|
&$WC $&$0000.0000\ 0000 $& &($W_{msbs}=1101\ \text{so}\ s_5=-1$)\\
|
||||||
|
&$F_5=S_4-K_4 $&${\color{blue}0000.1110\ 11}00$& &$S_5={\color{blue}0000.1110\ 1}000\ 00$\\
|
||||||
|
& & & &$SM_5={\color{blue}0001.1110\ 0}000\ 00\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS $&$1101.0001\ 1100 $&$\ll1 $&$K_5=0000.0000\ 0010\ 00\ $\\
|
||||||
|
&$WC $&$0001.1100\ 0000 $&$\ll1 $&$C_5=1111.1111\ 1110\ 00\,$\\
|
||||||
|
Terminate
|
||||||
|
\end{tabular}
|
||||||
|
\end{center}
|
||||||
|
}
|
||||||
|
|
||||||
|
\vfill
|
||||||
|
\eject
|
||||||
|
|
||||||
|
X = 0.1010101101(685/1024)
|
||||||
|
|
||||||
|
S = 0.1101000110(838/1024)
|
||||||
|
|
||||||
|
once R4 sslc gets here i can fill this in
|
||||||
|
|
||||||
|
\vfill
|
||||||
|
\eject
|
||||||
|
|
||||||
|
X = 1.1001 (25/16)
|
||||||
|
|
||||||
|
S = 1.0100 (20/16)
|
||||||
|
|
||||||
|
{\small
|
||||||
|
\begin{center}
|
||||||
|
\begin{tabular}{cccc}
|
||||||
|
Attempt 1:& $X$ is normalized& to $1/2<X<2$&$W_{msbs}$ looks at Q4.0\\
|
||||||
|
&&&\\
|
||||||
|
&$X $&$0001.1001$&\\
|
||||||
|
&$WS=X-1$&$0000.1001$& $s_0=1$\\
|
||||||
|
&$WC $&$0000.0000$&$S_0=\mathbf{1}.0000,\quad SM_0=\mathbf{0}.0000$ \\
|
||||||
|
\hdashline\\
|
||||||
|
Step 1: &$WS $&$0000.1001$&\\
|
||||||
|
&$WC $&$0000.0000$&($W_{msbs}=0000\ \text{so}\ s_1=1$)\\
|
||||||
|
&$F $&$1110.1100$&$S_1=\mathbf{1.1}000,\quad SM_1=\mathbf{1.0}000$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS $&$1110.0101$&$\ll1$\\
|
||||||
|
&$WC $&$0001.0000$&$\ll1$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 2: &$WS $&$1100.1010$&\\
|
||||||
|
&$WC $&$0010.0000$&($W_{msbs}=1110\ \text{so}\ s_2=-1$)\\
|
||||||
|
&$F $&$0001.0110$&$S_2=\mathbf{1.01}00,\quad SM_2=\mathbf{1.00}00$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS $&$1111.1110$&$\ll1$\\
|
||||||
|
&$WC $&$0000.0010$&$\ll1$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 3: &$WS $&$1111.1100$&\\
|
||||||
|
&$WC $&$0000.0100$&($W_{msbs}=1111\ \text{so}\ s_3=0$)\\
|
||||||
|
&$-q_3D $&$0000.0000$&$S_3=\mathbf{1.010}0,\quad SM_3=\mathbf{1.001}0$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS $&$1111.1000$&$\ll1$\\
|
||||||
|
&$WC $&$0000.1000$&$\ll1$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 4: &$WS $&$1111.0000$&\\
|
||||||
|
&$WC $&$0001.0000$&($W_{msbs}=0000\ \text{so}\ s_4=1$)\\
|
||||||
|
&$F $&$0000.0000$&$S_4=\mathbf{1.0101},\quad SM_4=\mathbf{1.0100}$\\
|
||||||
|
Terminate&&&
|
||||||
|
\end{tabular}
|
||||||
|
\end{center}
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
{\small
|
||||||
|
\begin{center}
|
||||||
|
\begin{tabular}{cccc}
|
||||||
|
Attempt 2:& $X$ is normalized& to $1/2<X<2$&$W_{msbs}$ looks at Q3.1\\
|
||||||
|
&&&\\
|
||||||
|
&$X $&$001.1001$&\\
|
||||||
|
&$WS=X-1$&$000.1001$& $s_0=1$\\
|
||||||
|
&$WC $&$000.0000$&$S_0=\mathbf{1}.0000,\quad SM_0=\mathbf{0}.0000$ \\
|
||||||
|
\hdashline\\
|
||||||
|
Step 1: &$WS $&$000.1001$&\\
|
||||||
|
&$WC $&$000.0000$&($W_{msbs}=000.1\ \text{so}\ s_1=1$)\\
|
||||||
|
&$F $&$110.1000$&$S_1=\mathbf{1.1}000,\quad SM_1=\mathbf{1.0}000$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS $&$110.0001$&$\ll1$\\
|
||||||
|
&$WC $&$001.0000$&$\ll1$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 2: &$WS $&$100.0010$&\\
|
||||||
|
&$WC $&$010.0000$&($W_{msbs}=110.0\ \text{so}\ s_2=-1$)\\
|
||||||
|
&$F $&$001.0100$&$S_2=\mathbf{1.01}00,\quad SM_2=\mathbf{1.00}00$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS $&$111.0110$&$\ll1$\\
|
||||||
|
&$WC $&$000.0000$&$\ll1$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 3: &$WS $&$110.1100$&\\
|
||||||
|
&$WC $&$000.0000$&($W_{msbs}=110.1\ \text{so}\ s_3=-1$)\\
|
||||||
|
&$-q_3D $&$001.0010$&$S_3=\mathbf{1.001}0,\quad SM_3=\mathbf{1.000}0$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS $&$111.1110$&$\ll1$\\
|
||||||
|
&$WC $&$000.0000$&$\ll1$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 4: &$WS $&$111.1110$&\\
|
||||||
|
&$WC $&$000.0000$&($W_{msbs}=111.1\ \text{so}\ s_4=0$)\\
|
||||||
|
&$F $&$000.0000$&$S_4=\mathbf{1.0010},\quad SM_4=\mathbf{1.0001}$\\
|
||||||
|
Terminate&&&
|
||||||
|
\end{tabular}
|
||||||
|
\end{center}
|
||||||
|
}
|
||||||
|
|
||||||
|
{\small
|
||||||
|
\begin{center}
|
||||||
|
\begin{tabular}{cccc}
|
||||||
|
Attempt 3:& $X$ is normalized& to $1<X<4$&$W_{msbs}$ looks at Q4.0\\
|
||||||
|
&&&\\
|
||||||
|
&$X $&$0001.1001$&\\
|
||||||
|
&$WS=X-2$&$1111.1001$& $s_{-1}=10$\\
|
||||||
|
&$WC $&$0000.0000$&$S_{-1}=\mathbf{1}0.0000,\quad SM_{-1}=\mathbf{0}0.0000$ \\
|
||||||
|
\hdashline\\
|
||||||
|
Step 0: &$WS $&$1111.1001$&\\
|
||||||
|
&$WC $&$0000.0000$&($W_{msbs}=1111\ \text{so}\ s_0=0$)\\
|
||||||
|
&$F $&$0000.0000$&$S_0=\mathbf{10}.0000,\quad SM_0=\mathbf{01}.0000$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS $&$1111.1001$&$\ll1$\\
|
||||||
|
&$WC $&$0000.0000$&$\ll1$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 1: &$WS $&$1111.0010$&\\
|
||||||
|
&$WC $&$0000.0000$&($W_{msbs}=1111\ \text{so}\ s_1=0$)\\
|
||||||
|
&$F $&$0000.0000$&$S_1=\mathbf{10.0}000,\quad SM_1=\mathbf{01.1}000$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS $&$1111.0010$&$\ll1$\\
|
||||||
|
&$WC $&$0000.0000$&$\ll1$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 2: &$WS $&$1110.0100$&\\
|
||||||
|
&$WC $&$0000.0000$&($W_{msbs}=1110\ \text{so}\ s_2=-1$)\\
|
||||||
|
&$-q_3D $&$0001.1100$&$S_2=\mathbf{01.01}00,\quad SM_2=\mathbf{01.00}00$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS $&$1111.1000$&$\ll1$\\
|
||||||
|
&$WC $&$0000.1000$&$\ll1$\\
|
||||||
|
Terminate&&&
|
||||||
|
\end{tabular}
|
||||||
|
\end{center}
|
||||||
|
}
|
||||||
|
|
||||||
|
\vfill
|
||||||
|
\eject
|
||||||
|
|
||||||
|
X = 0.011001 (25/64)
|
||||||
|
|
||||||
|
S = 0.101000 (40/64)
|
||||||
|
|
||||||
|
{\small
|
||||||
|
\begin{center}
|
||||||
|
\begin{tabular}{cccc}
|
||||||
|
Attempt 4:& $X$ is normalized& to $1/4<X<1$&$W_{msbs}$ looks at Q3.1\\
|
||||||
|
&&&\\
|
||||||
|
&$X $&$000.0110\ 01$&\\
|
||||||
|
&$WS=X-1$&$111.0110\ 01$& $s_0=1$\\
|
||||||
|
&$WC $&$000.0000\ 00$&$S_0=\mathbf{1}.000000,\quad SM_0=\mathbf{0}.000000$ \\
|
||||||
|
\hdashline\\
|
||||||
|
Step 1: &$WS $&$111.0110\ 01$&\\
|
||||||
|
&$WC $&$000.0000\ 00$&($W_{msbs}=111.0\ \text{so}\ s_1=-1$)\\
|
||||||
|
&$F $&$000.1000\ 00$&$S_1=\mathbf{0.1}00000,\quad SM_1=\mathbf{0.0}00000$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS $&$111.1110\ 01$&$\ll1$\\
|
||||||
|
&$WC $&$000.0000\ 00$&$\ll1$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 2: &$WS $&$111.1100\ 10$&\\
|
||||||
|
&$WC $&$000.0000\ 00$&($W_{msbs}=111.1\ \text{so}\ s_2=0$)\\
|
||||||
|
&$F $&$000.0000\ 00$&$S_2=\mathbf{0.10}0000,\quad SM_2=\mathbf{0.01}0000$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS $&$111.1100\ 10$&$\ll1$\\
|
||||||
|
&$WC $&$000.0000\ 00$&$\ll1$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 3: &$WS $&$111.1001\ 00$&\\
|
||||||
|
&$WC $&$000.0000\ 00$&($W_{msbs}=010.0\ \text{so}\ s_3=1$)\\
|
||||||
|
&$-q_3D $&$111.0010\ 00$&$S_3=\mathbf{0.111}000,\quad SM_3=\mathbf{0.110}000$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$WS $&$1111.1110$&$\ll1$\\
|
||||||
|
&$WC $&$0000.0000$&$\ll1$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 4: &$WS $&$1111.1110$&\\
|
||||||
|
&$WC $&$0000.0000$&($W_{msbs}=111.1\ \text{so}\ s_4=0$)\\
|
||||||
|
&$F $&$0000.0000$&$S_4=\mathbf{1.0010}00,\quad SM_4=\mathbf{1.0001}00$\\
|
||||||
|
Terminate&&&
|
||||||
|
\end{tabular}
|
||||||
|
\end{center}
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
\end{document}
|
||||||
147
docs/divsqrt_tex/sqrt4.tex
Normal file
147
docs/divsqrt_tex/sqrt4.tex
Normal file
@ -0,0 +1,147 @@
|
|||||||
|
\documentclass[12pt]{article}
|
||||||
|
|
||||||
|
\usepackage{amssymb, amsmath, amsfonts, amsthm, graphicx, tcolorbox}
|
||||||
|
|
||||||
|
\usepackage{arydshln}
|
||||||
|
|
||||||
|
\parskip = .2in
|
||||||
|
\parindent = 0in
|
||||||
|
|
||||||
|
\pagestyle{empty}
|
||||||
|
|
||||||
|
%==========
|
||||||
|
%==========
|
||||||
|
|
||||||
|
\begin{document}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
X = 0.1011 0111 10 (734/1024)
|
||||||
|
|
||||||
|
S = 0.1101 1000 11\ 00 (3468/4096), negative sticky bit
|
||||||
|
{\small
|
||||||
|
\begin{center}
|
||||||
|
\begin{tabular}{ccccc}
|
||||||
|
&$X $&$ 0000.1011\ 0111\ 1000 $& &$S_0={\color{blue}0001}.0000\ 0000\ 0000$\\
|
||||||
|
&$WS_0=4(X-1) $&$ 1110.1101\ 1110\ 0000 $& &$SM_0={\color{blue}0000}.0000\ 0000\ 0000\phantom{M}$\\
|
||||||
|
&$WC_0 $&$ 0000.0000\ 0000\ 0000 $& &$K_0=0001.0000\ 0000\ 0000\ $\\
|
||||||
|
& & & &$C_0=1111.0000\ 0000\ 0000\,$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 1: &$WS_0 $&$ 1110.1101\ 1110\ 0000 $& &\\
|
||||||
|
&$WC_0 $&$ 0000.0000\ 0000\ 0000 $& &($W_{msbs}=1110.110\ \text{so}\ s_1=-1$)\\
|
||||||
|
&$F_1=2S_0-K_1$&${\color{blue}0001.11}00\ 0000\ 0000$& &$S_1={\color{blue}0000.11}00\ 0000\ 0000$\\
|
||||||
|
& & & &$SM_1={\color{blue}0000.10}00\ 0000\ 0000\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum $&$ 1111.0001\ 1110\ 0000 $&$\ll2 $&$K_1=0000.0100\ 0000\ 0000\ $\\
|
||||||
|
&$carry $&$ 0001.1000\ 0000\ 0000 $&$\ll2 $&$C_1=1111.1100\ 0000\ 0000\,$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 2: &$WS_1 $&$ 1100.0111\ 1000\ 0000 $& &\\
|
||||||
|
&$WC_1 $&$ 0110.0000\ 0000\ 0000 $& &($W_{msbs}=0010.011\ \text{so}\ s_2=2$)\\
|
||||||
|
&$F_2=-4S_1-4K_2$&${\color{blue}1100.1100}\ 0000\ 0000$& &$S_2={\color{blue}0000.1110}\ 0000\ 0000$\\
|
||||||
|
& & & &$SM_2={\color{blue}0000.1101}\ 0000\ 0000\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum $&$ 0110.1011\ 1000\ 0000 $&$\ll2 $&$K_2=0000.0001\ 0000\ 0000\ $\\
|
||||||
|
&$carry $&$ 1000.1000\ 0000\ 0000 $&$\ll2 $&$C_2=1111.1111\ 0000\ 0000\,$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 3: &$WS_2 $&$ 1010.1110\ 0000\ 0000 $& &\\
|
||||||
|
&$WC_2 $&$ 0010.0000\ 0000\ 0000 $& &($W_{msbs}=1100.111\ \text{so}\ s_3=-2$)\\
|
||||||
|
&$F_3=4S_2-4K_3$&${\color{blue}0011.0111\ 00}00\ 0000$& &$S_3={\color{blue}0000.1101\ 10}00\ 0000$\\
|
||||||
|
& & & &$SM_3={\color{blue}0000.1101\ 01}00\ 0000\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum $&$ 1011.1001\ 0000\ 0000 $&$\ll2 $&$K_3=0000.0000\ 0100\ 0000\ $\\
|
||||||
|
&$carry $&$ 0100.1100\ 0000\ 0000 $&$\ll2 $&$C_3=1111.1111\ 1100\ 0000\,$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 4: &$WS_3 $&$ 1110.0100\ 0000\ 0000 $& &\\
|
||||||
|
&$WC_3 $&$ 0011.0000\ 0000\ 0000 $& &($W_{msbs}=0001.010\ \text{so}\ s_4=1$)\\
|
||||||
|
&$F_4=-2S_3-K_4$&${\color{blue}1110.0100\ 1111}\ 0000$& &$S_4={\color{blue}0000.1101\ 1001}\ 0000$\\
|
||||||
|
& & & &$SM_4={\color{blue}0000.1101\ 1000}\ 0000\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum $&$ 0011.0000\ 1111\ 0000 $&$\ll2 $&$K_4=0000.0000\ 0001\ 0000\ $\\
|
||||||
|
&$carry $&$ 1100.1000\ 0000\ 0000 $&$\ll2 $&$C_4=1111.1111\ 1111\ 0000\,$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 5: &$WS_4 $&$ 1100.0011\ 1100\ 0000 $& &\\
|
||||||
|
&$WC_4 $&$ 0010.0000\ 0000\ 0000 $& &($W_{msbs}=1110.001\ \text{so}\ s_5=-1$)\\
|
||||||
|
&$F_5=2S_4-K_5 $&${\color{blue}0001.1011\ 0001\ 11}00$& &$S_5={\color{blue}0000.1101\ 1000\ 11}00$\\
|
||||||
|
& & & &$SM_5={\color{blue}0000.1101\ 1000\ 10}00\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum $&$ 1111.1000\ 1101\ 1100 $&$\ll2 $&$K_5=0000.0000\ 0000\ 0100\ $\\
|
||||||
|
&$carry $&$ 0000.0110\ 0000\ 0000 $&$\ll2 $&$C_5=1111.1111\ 1111\ 1100\,$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 6: &$WS_5 $&$ 1110.0011\ 0111\ 0000 $& &\\
|
||||||
|
&$WC_5 $&$ 0001.1000\ 0000\ 0000 $& &($W_{msbs}=1111.101\ \text{so}\ s_6=0$)\\
|
||||||
|
&$F_6=0 $&${\color{blue}0000.0000\ 0000\ 0000}$& &$S_6={\color{blue}0000.1101\ 1000\ 1100}$\\
|
||||||
|
& & & &$SM_6={\color{blue}0000.1101\ 1000\ 1011}\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum $&$ 1111.1011\ 0111\ 0111 $&$\ll2 $&$K_6=0000.0000\ 0000\ 0001\ $\\
|
||||||
|
&$carry $&$ 0000.0000\ 0000\ 0000 $&$\ll2 $&$C_6=1111.1111\ 1111\ 1111\,$\\
|
||||||
|
\hdashline\\
|
||||||
|
Terminate&Square Root&0000.11 01\ 10 00\ 10 (11)
|
||||||
|
\end{tabular}
|
||||||
|
\end{center}
|
||||||
|
}
|
||||||
|
|
||||||
|
X = 0.1001\ 0101\ 00 (596/1024)
|
||||||
|
|
||||||
|
S = 0.1100 0011 01\ 01 (3125/4096)
|
||||||
|
{\small
|
||||||
|
\begin{center}
|
||||||
|
\begin{tabular}{ccccc}
|
||||||
|
&$X $&$ 0000.1001\ 0101\ 0000 $& &$S_0={\color{blue}0001}.0000\ 0000\ 0000$\\
|
||||||
|
&$WS_0=4(X-1) $&$ 1110.0101\ 0100\ 0000 $& &$SM_0={\color{blue}0000}.0000\ 0000\ 0000\phantom{M}$\\
|
||||||
|
&$WC_0 $&$ 0000.0000\ 0000\ 0000 $& &$K_0=0001.0000\ 0000\ 0000\ $\\
|
||||||
|
& & & &$C_0=1111.0000\ 0000\ 0000\,$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 1: &$WS_0 $&$ 1110.0101\ 0100\ 0000 $& &\\
|
||||||
|
&$WC_0 $&$ 0000.0000\ 0000\ 0000 $& &($W_{msbs}=1110.010\ \text{so}\ s_1=-1$)\\
|
||||||
|
&$F_1=2S_0-K_1 $&${\color{blue}0001.11}00\ 0000\ 0000$& &$S_1={\color{blue}0000.11}00\ 0000\ 0000$\\
|
||||||
|
& & & &$SM_1={\color{blue}0000.10}00\ 0000\ 0000\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum $&$ 1111.1001\ 0100\ 0000 $&$\ll2 $&$K_1=0000.0100\ 0000\ 0000\ $\\
|
||||||
|
&$carry $&$ 0000.1000\ 0000\ 0000 $&$\ll2 $&$C_1=1111.1100\ 0000\ 0000\,$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 2: &$WS_1 $&$ 1110.0101\ 0000\ 0000 $& &\\
|
||||||
|
&$WC_2 $&$ 0010.0000\ 0000\ 0000 $& &($W_{msbs}=0000.010\ \text{so}\ s_2=0$)\\
|
||||||
|
&$F_2=0 $&${\color{blue}0000.0000}\ 0000\ 0000$& &$S_2={\color{blue}0000.1100}\ 0000\ 0000$\\
|
||||||
|
& & & &$SM_2={\color{blue}0000.1110}\ 0000\ 0000\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum $&$ 1100.0101\ 0000\ 0000 $&$\ll2 $&$K_2=0000.0001\ 0000\ 0000\ $\\
|
||||||
|
&$carry $&$ 0100.0000\ 0000\ 0000 $&$\ll2 $&$C_2=1111.1111\ 0000\ 0000\,$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 3: &$WS_2 $&$ 0001.0100\ 0000\ 0000 $& &\\
|
||||||
|
&$WC_2 $&$ 0000.0000\ 0000\ 0000 $& &($W_{msbs}=0001.010\ \text{so}\ s_3=1$)\\
|
||||||
|
&$F_3=-2S_2-K_3$&${\color{blue}1110.0111\ 11}00\ 0000$& &$S_3={\color{blue}0000.1100\ 01}00\ 0000$\\
|
||||||
|
& & & &$SM_3={\color{blue}0000.1100\ 00}00\ 0000\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum $&$ 1111.0011\ 1100\ 0000 $&$\ll2 $&$K_3=0000.0000\ 0100\ 0000\ $\\
|
||||||
|
&$carry $&$ 1000.1000\ 0000\ 0000 $&$\ll2 $&$C_3=1111.1111\ 1100\ 0000\,$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 4: &$WS_3 $&$ 1100.1111\ 0000\ 0000 $& &\\
|
||||||
|
&$WC_3 $&$ 0010.0000\ 0000\ 0000 $& &($W_{msbs}=1110.111\ \text{so}\ s_4=-1$)\\
|
||||||
|
&$F_4=2S_3-K_3 $&${\color{blue}0001.1000\ 0111}\ 0000$& &$S_4={\color{blue}0000.1100\ 0011}\ 0000$\\
|
||||||
|
& & & &$SM_4={\color{blue}0000.1100\ 0010}\ 0000\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum $&$ 1111.0111\ 0111\ 0000 $&$\ll2 $&$K_4=0000.0000\ 0001\ 0000\ $\\
|
||||||
|
&$carry $&$ 0001.0000\ 0000\ 0000 $&$\ll2 $&$C_4=1111.1111\ 1111\ 0000\,$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 5: &$WS_4 $&$ 1101.1101\ 1100\ 0000 $& &\\
|
||||||
|
&$WC_4 $&$ 0100.0000\ 0000\ 0000 $& &($W_{msbs}=0001.110\ \text{so}\ s_5=1$)\\
|
||||||
|
&$F_5=-2S_4-K_4 $&${\color{blue}1110.0111\ 1001\ 11}00$& &$S_5={\color{blue}0000.1100\ 0011\ 01}00$\\
|
||||||
|
& & & &$SM_5={\color{blue}0000.1100\ 0011\ 00}00\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum $&$ 0111.1010\ 0101\ 1100 $&$\ll1 $&$K_5=0000.0000\ 0000\ 0100\ $\\
|
||||||
|
&$carry $&$ 1000.1011\ 0000\ 0000 $&$\ll1 $&$C_5=1111.1111\ 1111\ 1100\,$\\
|
||||||
|
\hdashline\\
|
||||||
|
Step 6: &$WS_5 $&$ 1110.1001\ 0111\ 0000 $& &\\
|
||||||
|
&$WC_5 $&$ 0010.1100\ 0000\ 0000 $& &($W_{msbs}=0001.010\ \text{so}\ s_6=1$)\\
|
||||||
|
&$F_6= $&$ $& &$S_5={\color{blue}0000.1100\ 0011\ 0101}$\\
|
||||||
|
& & & &$SM_5={\color{blue}0000.1100\ 0011\ 0100}\phantom{M}$\\
|
||||||
|
\cline{2-3}
|
||||||
|
&$sum $&$ 0001.1110\ 1001\ 0111 $&$\ll1 $&$K_5=0000.0000\ 0000\ 0001\ $\\
|
||||||
|
&$carry $&$ 1110.0010\ 1100\ 0000 $&$\ll1 $&$C_5=1111.1111\ 1111\ 1111\,$\\
|
||||||
|
\hdashline\\
|
||||||
|
Terminate
|
||||||
|
\end{tabular}
|
||||||
|
\end{center}
|
||||||
|
}
|
||||||
|
|
||||||
|
\end{document}
|
||||||
@ -2,14 +2,13 @@
|
|||||||
|
|
||||||
CC = gcc
|
CC = gcc
|
||||||
CFLAGS = -O3
|
CFLAGS = -O3
|
||||||
LIBS = -lm
|
|
||||||
LFLAGS = -L.
|
LFLAGS = -L.
|
||||||
# Link against the riscv-isa-sim version of SoftFloat rather than
|
# Link against the riscv-isa-sim version of SoftFloat rather than
|
||||||
# the regular version to get RISC-V NaN behavior
|
# the regular version to get RISC-V NaN behavior
|
||||||
IFLAGS = -I$(RISCV)/riscv-isa-sim/softfloat
|
#IFLAGS = -I$(RISCV)/riscv-isa-sim/softfloat
|
||||||
LIBS = $(RISCV)/riscv-isa-sim/build/libsoftfloat.a
|
#LIBS = $(RISCV)/riscv-isa-sim/build/libsoftfloat.a
|
||||||
#IFLAGS = -I../../../addins/SoftFloat-3e/source/include/
|
IFLAGS = -I../../../addins/SoftFloat-3e/source/include/
|
||||||
#LIBS = ../../../addins/SoftFloat-3e/build/Linux-x86_64-GCC/softfloat.a
|
LIBS = ../../../addins/SoftFloat-3e/build/Linux-x86_64-GCC/softfloat.a -lm -lquadmath
|
||||||
SRCS = $(wildcard *.c)
|
SRCS = $(wildcard *.c)
|
||||||
|
|
||||||
PROGS = $(patsubst %.c,%,$(SRCS))
|
PROGS = $(patsubst %.c,%,$(SRCS))
|
||||||
@ -17,7 +16,7 @@ PROGS = $(patsubst %.c,%,$(SRCS))
|
|||||||
all: $(PROGS)
|
all: $(PROGS)
|
||||||
|
|
||||||
%: %.c
|
%: %.c
|
||||||
$(CC) $(CFLAGS) $(IFLAGS) $(LFLAGS) -o $@ $< $(LIBS)
|
$(CC) $(CFLAGS) -DSOFTFLOAT_FAST_INT64 $(IFLAGS) $(LFLAGS) -o $@ $< $(LIBS)
|
||||||
|
|
||||||
clean:
|
clean:
|
||||||
rm -f $(PROGS)
|
rm -f $(PROGS)
|
||||||
|
|||||||
@ -1,77 +0,0 @@
|
|||||||
//
|
|
||||||
// softfloat_div.c
|
|
||||||
// james.stine@okstate.edu 12 April 2023
|
|
||||||
//
|
|
||||||
// Demonstrate using SoftFloat to compute 754 fp divide, then print results
|
|
||||||
// (adapted from original C built by David Harris)
|
|
||||||
//
|
|
||||||
|
|
||||||
#include <stdio.h>
|
|
||||||
#include <stdint.h>
|
|
||||||
#include "softfloat.h"
|
|
||||||
#include "softfloat_types.h"
|
|
||||||
typedef union sp {
|
|
||||||
uint32_t v;
|
|
||||||
unsigned short x[2];
|
|
||||||
float f;
|
|
||||||
} sp;
|
|
||||||
|
|
||||||
void printF32 (char *msg, float32_t f) {
|
|
||||||
sp conv;
|
|
||||||
int i, j;
|
|
||||||
conv.v = f.v; // use union to convert between hexadecimal and floating-point views
|
|
||||||
printf("%s: ", msg); // print out nicely
|
|
||||||
printf("0x%04x_%04x = %1.15g\n", (conv.v >> 16),(conv.v & 0xFFFF), conv.f);
|
|
||||||
}
|
|
||||||
|
|
||||||
void printFlags(void) {
|
|
||||||
int NX = softfloat_exceptionFlags % 2;
|
|
||||||
int UF = (softfloat_exceptionFlags >> 1) % 2;
|
|
||||||
int OF = (softfloat_exceptionFlags >> 2) % 2;
|
|
||||||
int DZ = (softfloat_exceptionFlags >> 3) % 2;
|
|
||||||
int NV = (softfloat_exceptionFlags >> 4) % 2;
|
|
||||||
printf ("Flags: Inexact %d Underflow %d Overflow %d DivideZero %d Invalid %d\n",
|
|
||||||
NX, UF, OF, DZ, NV);
|
|
||||||
}
|
|
||||||
|
|
||||||
void softfloatInit(void) {
|
|
||||||
// RNE: softfloat_round_near_even
|
|
||||||
// RZ: softfloat_round_minMag
|
|
||||||
// RU: softfloat_round_max
|
|
||||||
// RD: softfloat_round_min
|
|
||||||
// RM: softfloat_round_near_maxMag
|
|
||||||
softfloat_roundingMode = softfloat_round_near_even;
|
|
||||||
softfloat_exceptionFlags = 0; // clear exceptions
|
|
||||||
softfloat_detectTininess = softfloat_tininess_afterRounding; // RISC-V behavior for tininess
|
|
||||||
}
|
|
||||||
|
|
||||||
int main() {
|
|
||||||
|
|
||||||
// float32_t is typedef in SoftFloat
|
|
||||||
float32_t x, y, r1, r2;
|
|
||||||
sp convx, convy;
|
|
||||||
|
|
||||||
// Choose two random values
|
|
||||||
convx.f = 1.30308703073;
|
|
||||||
convy.f = 1.903038030370;
|
|
||||||
// Convert to SoftFloat format
|
|
||||||
x.v = (convx.x[1] << 16) + convx.x[0];
|
|
||||||
y.v = (convy.x[1] << 16) + convy.x[0];
|
|
||||||
|
|
||||||
printf("Example using SoftFloat\n");
|
|
||||||
|
|
||||||
softfloatInit();
|
|
||||||
r1 = f32_div(x, y);
|
|
||||||
printf("-------\n");
|
|
||||||
printF32("X", x);
|
|
||||||
printF32("Y", y);
|
|
||||||
printF32("result = X/Y", r1);
|
|
||||||
printFlags();
|
|
||||||
|
|
||||||
r2 = f32_sqrt(x);
|
|
||||||
printf("-------\n");
|
|
||||||
printF32("X", x);
|
|
||||||
printF32("result = sqrt(X)", r2);
|
|
||||||
printFlags();
|
|
||||||
|
|
||||||
}
|
|
||||||
88
examples/fp/softfloat_demo/softfloat_demoDP.c
Normal file
88
examples/fp/softfloat_demo/softfloat_demoDP.c
Normal file
@ -0,0 +1,88 @@
|
|||||||
|
// softfloat_demo3.c
|
||||||
|
// james.stine@okstate.edu 15 August 2023
|
||||||
|
//
|
||||||
|
// Demonstrate using SoftFloat do compute a floating-point for quad, then print results
|
||||||
|
|
||||||
|
#include <stdio.h>
|
||||||
|
#include <stdint.h>
|
||||||
|
#include <inttypes.h>
|
||||||
|
#include <quadmath.h> // GCC Quad-Math Library
|
||||||
|
#include "softfloat.h"
|
||||||
|
#include "softfloat_types.h"
|
||||||
|
typedef union sp {
|
||||||
|
uint32_t v;
|
||||||
|
float f;
|
||||||
|
} sp;
|
||||||
|
|
||||||
|
typedef union dp {
|
||||||
|
uint64_t v;
|
||||||
|
double d;
|
||||||
|
} dp;
|
||||||
|
|
||||||
|
typedef union qp {
|
||||||
|
uint64_t v[2];
|
||||||
|
__float128 q;
|
||||||
|
} qp;
|
||||||
|
|
||||||
|
|
||||||
|
void printF32 (char *msg, float32_t f) {
|
||||||
|
sp conv;
|
||||||
|
int i, j;
|
||||||
|
conv.v = f.v; // use union to convert between hexadecimal and floating-point views
|
||||||
|
printf("%s: ", msg); // print out nicely
|
||||||
|
printf("0x%04x_%04x = %g\n", (conv.v >> 16),(conv.v & 0xFFFF), conv.f);
|
||||||
|
}
|
||||||
|
|
||||||
|
void printF64 (char *msg, float64_t d) {
|
||||||
|
dp conv;
|
||||||
|
int i, j;
|
||||||
|
conv.v = d.v; // use union to convert between hexadecimal and floating-point views
|
||||||
|
printf("%s: ", msg); // print out nicely
|
||||||
|
printf("0x%08x_%08x = %g\n", (conv.v >> 32),(conv.v & 0xFFFFFFFF), conv.d);
|
||||||
|
}
|
||||||
|
|
||||||
|
void printF128 (char *msg, float128_t q) {
|
||||||
|
qp conv;
|
||||||
|
int i, j;
|
||||||
|
conv.v[0] = q.v[0]; // use union to convert between hexadecimal and floating-point views
|
||||||
|
conv.v[1] = q.v[1]; // use union to convert between hexadecimal and floating-point views
|
||||||
|
printf("%s: ", msg); // print out nicely
|
||||||
|
printf("0x%016" PRIx64 "_%016" PRIx64 " = %1.15Qe\n", q.v[1], q.v[0], conv.q);
|
||||||
|
}
|
||||||
|
|
||||||
|
void printFlags(void) {
|
||||||
|
int NX = softfloat_exceptionFlags % 2;
|
||||||
|
int UF = (softfloat_exceptionFlags >> 1) % 2;
|
||||||
|
int OF = (softfloat_exceptionFlags >> 2) % 2;
|
||||||
|
int DZ = (softfloat_exceptionFlags >> 3) % 2;
|
||||||
|
int NV = (softfloat_exceptionFlags >> 4) % 2;
|
||||||
|
printf ("Flags: Inexact %d Underflow %d Overflow %d DivideZero %d Invalid %d\n",
|
||||||
|
NX, UF, OF, DZ, NV);
|
||||||
|
}
|
||||||
|
|
||||||
|
void softfloatInit(void) {
|
||||||
|
// rounding modes: RNE: softfloat_round_near_even
|
||||||
|
// RZ: softfloat_round_minMag
|
||||||
|
// RP: softfloat_round_max
|
||||||
|
// RM: softfloat_round_min
|
||||||
|
softfloat_roundingMode = softfloat_round_near_even;
|
||||||
|
softfloat_exceptionFlags = 0; // clear exceptions
|
||||||
|
softfloat_detectTininess = softfloat_tininess_afterRounding; // RISC-V behavior for tininess
|
||||||
|
}
|
||||||
|
|
||||||
|
int main() {
|
||||||
|
|
||||||
|
float64_t x, y, z;
|
||||||
|
float64_t r;
|
||||||
|
|
||||||
|
x.v = 0xBFFF988ECE97DFEB;
|
||||||
|
y.v = 0x3F8EFFFFFFFFFFFF;
|
||||||
|
z.v = 0x4001000000000000;
|
||||||
|
|
||||||
|
softfloatInit();
|
||||||
|
printF64("X", x); printF64("Y", y); printF64("Z", z);
|
||||||
|
r = f64_mulAdd(x, y, z);
|
||||||
|
printf("\n");
|
||||||
|
printF64("r", r);
|
||||||
|
|
||||||
|
}
|
||||||
91
examples/fp/softfloat_demo/softfloat_demoQP.c
Normal file
91
examples/fp/softfloat_demo/softfloat_demoQP.c
Normal file
@ -0,0 +1,91 @@
|
|||||||
|
// softfloat_demo3.c
|
||||||
|
// james.stine@okstate.edu 15 August 2023
|
||||||
|
//
|
||||||
|
// Demonstrate using SoftFloat do compute a floating-point for quad, then print results
|
||||||
|
|
||||||
|
#include <stdio.h>
|
||||||
|
#include <stdint.h>
|
||||||
|
#include <inttypes.h>
|
||||||
|
#include <quadmath.h> // GCC Quad-Math Library
|
||||||
|
#include "softfloat.h"
|
||||||
|
#include "softfloat_types.h"
|
||||||
|
typedef union sp {
|
||||||
|
uint32_t v;
|
||||||
|
float f;
|
||||||
|
} sp;
|
||||||
|
|
||||||
|
typedef union dp {
|
||||||
|
uint64_t v;
|
||||||
|
double d;
|
||||||
|
} dp;
|
||||||
|
|
||||||
|
typedef union qp {
|
||||||
|
uint64_t v[2];
|
||||||
|
__float128 q;
|
||||||
|
} qp;
|
||||||
|
|
||||||
|
|
||||||
|
void printF32 (char *msg, float32_t f) {
|
||||||
|
sp conv;
|
||||||
|
int i, j;
|
||||||
|
conv.v = f.v; // use union to convert between hexadecimal and floating-point views
|
||||||
|
printf("%s: ", msg); // print out nicely
|
||||||
|
printf("0x%04x_%04x = %g\n", (conv.v >> 16),(conv.v & 0xFFFF), conv.f);
|
||||||
|
}
|
||||||
|
|
||||||
|
void printF64 (char *msg, float64_t d) {
|
||||||
|
dp conv;
|
||||||
|
int i, j;
|
||||||
|
conv.v = d.v; // use union to convert between hexadecimal and floating-point views
|
||||||
|
printf("%s: ", msg); // print out nicely
|
||||||
|
printf("0x%08x_%08x = %g\n", (conv.v >> 32),(conv.v & 0xFFFFFFFF), conv.d);
|
||||||
|
}
|
||||||
|
|
||||||
|
void printF128 (char *msg, float128_t q) {
|
||||||
|
qp conv;
|
||||||
|
int i, j;
|
||||||
|
conv.v[0] = q.v[0]; // use union to convert between hexadecimal and floating-point views
|
||||||
|
conv.v[1] = q.v[1]; // use union to convert between hexadecimal and floating-point views
|
||||||
|
printf("%s: ", msg); // print out nicely
|
||||||
|
printf("0x%016" PRIx64 "_%016" PRIx64 " = %1.15Qe\n", q.v[1], q.v[0], conv.q);
|
||||||
|
}
|
||||||
|
|
||||||
|
void printFlags(void) {
|
||||||
|
int NX = softfloat_exceptionFlags % 2;
|
||||||
|
int UF = (softfloat_exceptionFlags >> 1) % 2;
|
||||||
|
int OF = (softfloat_exceptionFlags >> 2) % 2;
|
||||||
|
int DZ = (softfloat_exceptionFlags >> 3) % 2;
|
||||||
|
int NV = (softfloat_exceptionFlags >> 4) % 2;
|
||||||
|
printf ("Flags: Inexact %d Underflow %d Overflow %d DivideZero %d Invalid %d\n",
|
||||||
|
NX, UF, OF, DZ, NV);
|
||||||
|
}
|
||||||
|
|
||||||
|
void softfloatInit(void) {
|
||||||
|
// rounding modes: RNE: softfloat_round_near_even
|
||||||
|
// RZ: softfloat_round_minMag
|
||||||
|
// RP: softfloat_round_max
|
||||||
|
// RM: softfloat_round_min
|
||||||
|
softfloat_roundingMode = softfloat_round_near_even;
|
||||||
|
softfloat_exceptionFlags = 0; // clear exceptions
|
||||||
|
softfloat_detectTininess = softfloat_tininess_afterRounding; // RISC-V behavior for tininess
|
||||||
|
}
|
||||||
|
|
||||||
|
int main() {
|
||||||
|
|
||||||
|
float128_t x, y, z;
|
||||||
|
float128_t r;
|
||||||
|
|
||||||
|
x.v[1] = 0xBFFF988ECE97DFEB;
|
||||||
|
x.v[0] = 0xC3BBA082445B4836;
|
||||||
|
y.v[1] = 0x3F8EFFFFFFFFFFFF;
|
||||||
|
y.v[0] = 0xFFFFFFFFFFFFFFFF;
|
||||||
|
z.v[1] = 0x4001000000000000;
|
||||||
|
z.v[0] = 0x0000000000000000;
|
||||||
|
|
||||||
|
softfloatInit();
|
||||||
|
printF128("X", x); printF128("Y", y); printF128("Z", z);
|
||||||
|
r = f128_mulAdd(x, y, z);
|
||||||
|
printf("\n");
|
||||||
|
printF128("r", r);
|
||||||
|
|
||||||
|
}
|
||||||
88
examples/fp/softfloat_demo/softfloat_demoSP.c
Normal file
88
examples/fp/softfloat_demo/softfloat_demoSP.c
Normal file
@ -0,0 +1,88 @@
|
|||||||
|
// softfloat_demo3.c
|
||||||
|
// james.stine@okstate.edu 15 August 2023
|
||||||
|
//
|
||||||
|
// Demonstrate using SoftFloat do compute a floating-point for quad, then print results
|
||||||
|
|
||||||
|
#include <stdio.h>
|
||||||
|
#include <stdint.h>
|
||||||
|
#include <inttypes.h>
|
||||||
|
#include <quadmath.h> // GCC Quad-Math Library
|
||||||
|
#include "softfloat.h"
|
||||||
|
#include "softfloat_types.h"
|
||||||
|
typedef union sp {
|
||||||
|
uint32_t v;
|
||||||
|
float f;
|
||||||
|
} sp;
|
||||||
|
|
||||||
|
typedef union dp {
|
||||||
|
uint64_t v;
|
||||||
|
double d;
|
||||||
|
} dp;
|
||||||
|
|
||||||
|
typedef union qp {
|
||||||
|
uint64_t v[2];
|
||||||
|
__float128 q;
|
||||||
|
} qp;
|
||||||
|
|
||||||
|
|
||||||
|
void printF32 (char *msg, float32_t f) {
|
||||||
|
sp conv;
|
||||||
|
int i, j;
|
||||||
|
conv.v = f.v; // use union to convert between hexadecimal and floating-point views
|
||||||
|
printf("%s: ", msg); // print out nicely
|
||||||
|
printf("0x%04x_%04x = %g\n", (conv.v >> 16),(conv.v & 0xFFFF), conv.f);
|
||||||
|
}
|
||||||
|
|
||||||
|
void printF64 (char *msg, float64_t d) {
|
||||||
|
dp conv;
|
||||||
|
int i, j;
|
||||||
|
conv.v = d.v; // use union to convert between hexadecimal and floating-point views
|
||||||
|
printf("%s: ", msg); // print out nicely
|
||||||
|
printf("0x%08x_%08x = %g\n", (conv.v >> 32),(conv.v & 0xFFFFFFFF), conv.d);
|
||||||
|
}
|
||||||
|
|
||||||
|
void printF128 (char *msg, float128_t q) {
|
||||||
|
qp conv;
|
||||||
|
int i, j;
|
||||||
|
conv.v[0] = q.v[0]; // use union to convert between hexadecimal and floating-point views
|
||||||
|
conv.v[1] = q.v[1]; // use union to convert between hexadecimal and floating-point views
|
||||||
|
printf("%s: ", msg); // print out nicely
|
||||||
|
printf("0x%016" PRIx64 "_%016" PRIx64 " = %1.15Qe\n", q.v[1], q.v[0], conv.q);
|
||||||
|
}
|
||||||
|
|
||||||
|
void printFlags(void) {
|
||||||
|
int NX = softfloat_exceptionFlags % 2;
|
||||||
|
int UF = (softfloat_exceptionFlags >> 1) % 2;
|
||||||
|
int OF = (softfloat_exceptionFlags >> 2) % 2;
|
||||||
|
int DZ = (softfloat_exceptionFlags >> 3) % 2;
|
||||||
|
int NV = (softfloat_exceptionFlags >> 4) % 2;
|
||||||
|
printf ("Flags: Inexact %d Underflow %d Overflow %d DivideZero %d Invalid %d\n",
|
||||||
|
NX, UF, OF, DZ, NV);
|
||||||
|
}
|
||||||
|
|
||||||
|
void softfloatInit(void) {
|
||||||
|
// rounding modes: RNE: softfloat_round_near_even
|
||||||
|
// RZ: softfloat_round_minMag
|
||||||
|
// RP: softfloat_round_max
|
||||||
|
// RM: softfloat_round_min
|
||||||
|
softfloat_roundingMode = softfloat_round_near_even;
|
||||||
|
softfloat_exceptionFlags = 0; // clear exceptions
|
||||||
|
softfloat_detectTininess = softfloat_tininess_afterRounding; // RISC-V behavior for tininess
|
||||||
|
}
|
||||||
|
|
||||||
|
int main() {
|
||||||
|
|
||||||
|
float32_t x, y, z;
|
||||||
|
float32_t r;
|
||||||
|
|
||||||
|
x.v = 0xBFFF988E;
|
||||||
|
y.v = 0x3F8EFFFF;
|
||||||
|
z.v = 0x40010000;
|
||||||
|
|
||||||
|
softfloatInit();
|
||||||
|
printF32("X", x); printF32("Y", y); printF32("Z", z);
|
||||||
|
r = f32_mulAdd(x, y, z);
|
||||||
|
printf("\n");
|
||||||
|
printF32("r", r);
|
||||||
|
|
||||||
|
}
|
||||||
@ -15,7 +15,7 @@ WALLYBOARD := $(BUILDROOT)/board/wally
|
|||||||
PACKAGE_SOURCE := ${WALLYLINUX}/buildroot-packages/package-source
|
PACKAGE_SOURCE := ${WALLYLINUX}/buildroot-packages/package-source
|
||||||
FPGA_AXI_SDC := ${WALLYLINUX}/buildroot-packages/fpga-axi-sdc
|
FPGA_AXI_SDC := ${WALLYLINUX}/buildroot-packages/fpga-axi-sdc
|
||||||
DRIVER := ${PACKAGE_SOURCE}/fpga-axi-sdc.c
|
DRIVER := ${PACKAGE_SOURCE}/fpga-axi-sdc.c
|
||||||
PATCHFILE := $(BRPACKAGES)/package.patch
|
PATCHFILE := $(BRPACKAGES)/package-2023.05.1.patch
|
||||||
|
|
||||||
# Device tree files
|
# Device tree files
|
||||||
DTS ?= $(shell find -type f -regex ".*\.dts" | sort)
|
DTS ?= $(shell find -type f -regex ".*\.dts" | sort)
|
||||||
@ -32,8 +32,17 @@ OBJDUMPS := $(foreach name, $(OBJDUMPS), $(DIS)/$(name).objdump)
|
|||||||
# BUSYBOXDIR := $(shell ls $(BUILDROOT)/output/build | grep -e '^linux-[0-9]\+\.[0-9]\+\.[0-9]\+$$' )
|
# BUSYBOXDIR := $(shell ls $(BUILDROOT)/output/build | grep -e '^linux-[0-9]\+\.[0-9]\+\.[0-9]\+$$' )
|
||||||
# BUSYBOXDIR := $(BUILDROOT)/output/build/$(BUSYBOXDIR)
|
# BUSYBOXDIR := $(BUILDROOT)/output/build/$(BUSYBOXDIR)
|
||||||
|
|
||||||
LINUXDIR := $(shell find $(BUILDROOT)/output/build -maxdepth 2 -type d -regex ".*/linux-[0-9]+\.[0-9]+\.[0-9]+$$")
|
# Gets Linux and Busybox output folders for objedect dumps
|
||||||
BUSYBOXDIR := $(shell find $(BUILDROOT)/output/build -maxdepth 2 -type d -regex ".*/busybox-[0-9]+\.[0-9]+\.[0-9]+$$")
|
# LINUXDIR ?= $(shell find $(BUILDROOT)/output/build -maxdepth 2 -type d -regex ".*/linux-[0-9]+\.[0-9]+\.[0-9]+$$")
|
||||||
|
# BUSYBOXDIR ?= $(shell find $(BUILDROOT)/output/build -maxdepth 2 -type d -regex ".*/busybox-[0-9]+\.[0-9]+\.[0-9]+$$")
|
||||||
|
|
||||||
|
define linuxDir =
|
||||||
|
$(shell find $(BUILDROOT)/output/build -maxdepth 2 -type d -regex ".*/linux-[0-9]+\.[0-9]+\.[0-9]+$$")
|
||||||
|
endef
|
||||||
|
|
||||||
|
define busyboxDir =
|
||||||
|
$(shell find $(BUILDROOT)/output/build -maxdepth 2 -type d -regex ".*/busybox-[0-9]+\.[0-9]+\.[0-9]+$$")
|
||||||
|
endef
|
||||||
|
|
||||||
.PHONY: all generate disassemble install clean cleanDTB cleanDriver test
|
.PHONY: all generate disassemble install clean cleanDTB cleanDriver test
|
||||||
|
|
||||||
@ -50,8 +59,8 @@ all:
|
|||||||
|
|
||||||
# Temp rule for debugging
|
# Temp rule for debugging
|
||||||
test:
|
test:
|
||||||
@echo $(LINUXDIR)
|
@echo $(linuxDir)
|
||||||
@echo $(BUSYBOXDIR)
|
@echo $(busyboxDir)
|
||||||
|
|
||||||
generate: $(DTB) $(IMAGES)
|
generate: $(DTB) $(IMAGES)
|
||||||
|
|
||||||
@ -78,16 +87,16 @@ $(DIS)/%.objdump: $(IMAGES)/%.elf
|
|||||||
$(DIS)/%.objdump: $(IMAGES)/%
|
$(DIS)/%.objdump: $(IMAGES)/%
|
||||||
riscv64-unknown-elf-objdump -S $< >> $@
|
riscv64-unknown-elf-objdump -S $< >> $@
|
||||||
|
|
||||||
$(IMAGES)/vmlinux: $(LINUXDIR)/vmlinux
|
$(IMAGES)/vmlinux: $(call linuxDir)/vmlinux
|
||||||
cp $< $@
|
cp $< $@
|
||||||
|
|
||||||
$(IMAGES)/busybox: $(BUSYBOXDIR)/busybox
|
$(IMAGES)/busybox: $(call busyboxDir)/busybox
|
||||||
cp $< $@
|
cp $< $@
|
||||||
|
|
||||||
# Generating new Buildroot directories --------------------------------
|
# Generating new Buildroot directories --------------------------------
|
||||||
|
|
||||||
# This directive should be run as: make install BUILDROOT=path/to/buildroot
|
# This directive should be run as: make install BUILDROOT=path/to/buildroot
|
||||||
install: $(BUILDROOT)/package/fpga-axi-sdc $(WALLYBOARD) $(DRIVER)
|
install: $(BUILDROOT)/package/fpga-axi-sdc $(WALLYBOARD)
|
||||||
cp $(WALLYBOARD)/main.config $(BUILDROOT)/.config
|
cp $(WALLYBOARD)/main.config $(BUILDROOT)/.config
|
||||||
|
|
||||||
# CONFIG DEPENDENCIES 2021.05 -----------------------------------------
|
# CONFIG DEPENDENCIES 2021.05 -----------------------------------------
|
||||||
@ -122,9 +131,9 @@ $(BUILDROOT):
|
|||||||
cd $@; git checkout 2023.05.x
|
cd $@; git checkout 2023.05.x
|
||||||
#cd $@; git checkout 2021.05
|
#cd $@; git checkout 2021.05
|
||||||
|
|
||||||
$(DRIVER):
|
#$(DRIVER):
|
||||||
@ if [ -d "$(WALLY)/addins/vivado-risc-v" ] ; then git submodule update --init $(WALLY)/addins/vivado-risc-v; fi
|
# @ if [ -d "$(WALLY)/addins/vivado-risc-v" ] ; then git submodule update --init $(WALLY)/addins/vivado-risc-v; fi
|
||||||
cp ../addins/vivado-risc-v/patches/fpga-axi-sdc.c $@
|
# cp ../addins/vivado-risc-v/patches/fpga-axi-sdc.c $@
|
||||||
# For 2021.05
|
# For 2021.05
|
||||||
#sed -i "s|card_hw_reset|hw_reset|1" $@
|
#sed -i "s|card_hw_reset|hw_reset|1" $@
|
||||||
|
|
||||||
|
|||||||
@ -1000,7 +1000,7 @@ module testbenchfp;
|
|||||||
endmodule
|
endmodule
|
||||||
|
|
||||||
|
|
||||||
module readvectors (
|
module readvectors import cvw::*; #(parameter cvw_t P) (
|
||||||
input logic clk,
|
input logic clk,
|
||||||
input logic [P.FLEN*4+7:0] TestVector,
|
input logic [P.FLEN*4+7:0] TestVector,
|
||||||
input logic [P.FMTBITS-1:0] ModFmt,
|
input logic [P.FMTBITS-1:0] ModFmt,
|
||||||
@ -1026,7 +1026,7 @@ module readvectors (
|
|||||||
);
|
);
|
||||||
|
|
||||||
localparam Q_LEN = 32'd128;
|
localparam Q_LEN = 32'd128;
|
||||||
`include "parameter-defs.vh"
|
//`include "parameter-defs.vh"
|
||||||
|
|
||||||
logic XEn;
|
logic XEn;
|
||||||
logic YEn;
|
logic YEn;
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user