8.3: Example Program, Pyramid Areas and Volumes
- Page ID
- 19906
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)This example is a simple assembly language program to calculate some geometric information for each square pyramid in a series of square
pyramids. Specifically, the program will find the lateral total
surface area (including the base) and volume of each square
pyramid in a set of square pyramids.
Once the values are computed, the program finds the minimum, maximum, sum, and average for the total surface areas and volumes.
All data are unsigned values (i.e., uses mul and div, not imul or idiv).
This basic approach used in this example is the loop to calculate the surface areas and volumes arrays. A second loop is used to find the sum, minimum, and maximum for each array. To find the minimum and maximum values, the minimum and maximum variables are each initialized to the first value in the list. Then, every element in the list is compared to the current minimum and maximum. If the current value from the list is less than the current minimum, the minimum is set to the current value (over-writing the previous value). When all values have been checked, the minimum will represent the true minimum from the list. If the current value from the list is more than the current maximum, the maximum is set to the current value (over-writing the previous value). When all values have been checked, the maximum will represent the true maximum from the list.
; Example assembly language program to calculate the
; geometric information for each square pyramid in
; a series of square pyramids.
; The program calculates the total surface area
; and volume of each square pyramid.
; Once the values are computed, the program finds
; the minimum, maximum, sum, and average for the
; total surface areas and volumes.
; -----
; Formulas:
; totalSurfaceAreas(n) = aSides(n) *
; (2*aSides(n)*sSides(n))
; volumes(n) = (aSides(n)^2 * heights(n)) / 3
; *************************************************
section .data
; -----
; Define constants
EXIT_SUCCESS equ 0 ; successful operation
SYS_exit equ 60 ; call code for terminate
; -----
; Provided Data
aSides db 10, 14, 13, 37, 54
db 31, 13, 20, 61, 36
db 14, 53, 44, 19, 42
db 27, 41, 53, 62, 10
db 19, 18, 14, 10, 15
db 15, 11, 22, 33, 70
db 15, 23, 15, 63, 26
db 24, 33, 10, 61, 15
db 14, 34, 13, 71, 81
db 38, 13, 29, 17, 93
sSides dw 1233, 1114, 1773, 1131, 1675
dw 1164, 1973, 1974, 1123, 1156
dw 1344, 1752, 1973, 1142, 1456
dw 1165, 1754, 1273, 1175, 1546
dw 1153, 1673, 1453, 1567, 1535
dw 1144, 1579, 1764, 1567, 1334
dw 1456, 1563, 1564, 1753, 1165
dw 1646, 1862, 1457, 1167, 1534
dw 1867, 1864, 1757, 1755, 1453
dw 1863, 1673, 1275, 1756, 1353
heights dd 14145, 11134, 15123, 15123, 14123
dd 18454, 15454, 12156, 12164, 12542
dd 18453, 18453, 11184, 15142, 12354
dd 14564, 14134, 12156, 12344, 13142
dd 11153, 18543, 17156, 12352, 15434
dd 18455, 14134, 12123, 15324, 13453
dd 11134, 14134, 15156, 15234, 17142
dd 19567, 14134, 12134, 17546, 16123
dd 11134, 14134, 14576, 15457, 17142
dd 13153, 11153, 12184, 14142, 17134
length dd 50
taMin dd 0
taMax dd 0
taSum dd 0
taAve dd 0
volMin dd 0
volMax dd 0
volSum dd 0
volAve dd 0
; -----
; Additional Variables
ddTwo dd 2
ddThree dd 3
; -------------------------------------------------
; Uninitialized data
section .bss
totalAreas resd 50
volumes resd 50
; *************************************************
section .text
global _start
_start:
; Calculate volume, lateral and total surface areas
mov ecx, dword [length] ; length counter
mov rsi, 0 ; index
calculationLoop:
; totalAreas(n) = aSides(n) * (2*aSides(n)*sSides(n))
movzx r8d, byte [aSides+rsi] ; aSides[i]
movzx r9d, word [sSides+rsi*2]
mov eax, r8d
mul dword [ddTwo]
mul r9d
mul r8d
mov dword [totalAreas+rsi*4], eax
; volumes(n) = (aSides(n)^2 * heights(n)) / 3
movzx eax, byte [aSides+rsi]
mul eax
mul dword [heights+rsi*4]
div dword [ddThree]
mov dword [volumes+rsi*4], eax
inc rsi
loop calculationLoop
; -----
; Find min, max, sum, and average for the total
; areas and volumes.
mov eax, dword [totalAreas]
mov dword [taMin], eax
mov dword [taMax], eax
mov eax, dword [volumes]
mov dword [volMin], eax
mov dword [volMax], eax
mov dword [taSum], 0
mov dword [volSum], 0
mov ecx, dword [length]
mov rsi, 0
statsLoop:
mov eax, dword [totalAreas+rsi*4]
add dword [taSum], eax
cmp eax, dword [taMin]
jae notNewTaMin
mov dword [taMin], eax
notNewTaMin:
cmp eax, dword [taMax]
jbe notNewTaMax
mov dword [taMax], eax
notNewTaMax:
mov eax, dword [volumes+rsi*4]
add dword [volSum], eax
cmp eax, dword [volMin]
jae notNewVolMin
mov dword [volMin], eax
notNewVolMin:
cmp eax, dword [volMax]
jbe notNewVolMax
mov dword [volMax], eax
notNewVolMax:
inc rsi
loop statsLoop
; -----
; Calculate averages.
mov eax, dword [taSum]
mov edx, 0
div dword [length]
mov dword [taAve], eax
mov eax, dword [volSum]
mov edx, 0
div dword [length]
mov dword [volAve], eax
; -----
; Done, terminate program.
last:
mov rax, SYS_exit ; call code for exit
mov rdi, EXIT_SUCCESS ; exit with success
syscall
This is one example. There are multiple other valid approaches to solving this problem.