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flops.jl
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flops.jl
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import Printf.@printf
function dtime(p)
q = p[2]
p[2] = time()
p[1] = p[2] - q
end
function main()
A0 = 1.0
A1 = -0.1666666666671334
A2 = 0.833333333809067E-2
A3 = 0.198412715551283E-3
A4 = 0.27557589750762E-5
A5 = 0.2507059876207E-7
A6 = 0.164105986683E-9
B0 = 1.0
B1 = -0.4999999999982
B2 = 0.4166666664651E-1
B3 = -0.1388888805755E-2
B4 = 0.24801428034E-4
B5 = -0.2754213324E-6
B6 = 0.20189405E-8
C0 = 1.0
C1 = 0.99999999668
C2 = 0.49999995173
C3 = 0.16666704243
C4 = 0.4166685027E-1
C5 = 0.832672635E-2
C6 = 0.140836136E-2
C7 = 0.17358267E-3
C8 = 0.3931683E-4
D1 = 0.3999999946405E-1
D2 = 0.96E-3
D3 = 0.1233153E-5
E2 = 0.48E-3
E3 = 0.411051E-6
s = 0.0
u = 0.0
v = 0.0
w = 0.0
x = 0.0
println(" FLOPS Julia Program (Double Precision), V2.0 18 Dec 1992")
T = zeros(Float64, 36)
loops = 15625
T[1] = 1.0E+06/loops
TLimit = 15.0
NLimit = 512000000
piref = 3.14159265358979324
one = 1.0
two = 2.0
three = 3.0
four = 4.0
five = 5.0
scale = one
println(" Module Error RunTime MFLOPS")
println(" (usec)")
TimeArray = Array{Float64}(undef,4)
dtime(TimeArray)
dtime(TimeArray)
#/*******************************************************/
#/* Module 1. Calculate integral of df(x)/f(x) defined */
#/* below. Result is ln(f(1)). There are 14 */
#/* double precision operations per loop */
#/* ( 7 +, 0 -, 6 *, 1 / ) that are included */
#/* in the timing. */
#/* 50.0% +, 00.0% -, 42.9% *, and 07.1% / */
#/*******************************************************/
n = loops
sa = 0.0
while sa < TLimit
n = 2 * n
x = one / n # /*********************/
s = 0.0 # /* Loop 1. */
v = 0.0 # /*********************/
w = one
dtime(TimeArray)
for i in 1:n
v = v + w
u = v * x
s = s + (D1+u*(D2+u*D3))/(w+u*(D1+u*(E2+u*E3)))
end
dtime(TimeArray)
sa = TimeArray[1]
if n == NLimit
break
#/* printf(" %10ld %12.5lf\n",n,sa); */
end
end
scale = 1.0E+06 / n
T[1] = scale
#/****************************************/
#/* Estimate nulltime ('for' loop time). */
#/****************************************/
dtime(TimeArray)
for i in 1:n
end
dtime(TimeArray)
nulltime = T[1] * TimeArray[1]
if nulltime < 0.0
nulltime = 0.0
end
T[2] = T[1] * sa - nulltime
sa = (D1+D2+D3)/(one+D1+E2+E3)
sb = D1
T[3] = T[2] / 14.0# /*********************/
sa = x * ( sa + sb + two * s ) / two# /* Module 1 Results. */
sb = one / sa# /*********************/
n = round( ( 40000 * sb ) / scale )
sc = sb - 25.2
T[4] = one / T[3]
# /********************/
# /* DO NOT REMOVE */
# /* THIS PRINTOUT! */
# /********************/
#// printf(" 1 %13.4le %10.4lf %10.4lf\n",sc,T[2],T[4])
@printf( " 1 %13.4e %10.4f %10.4f\n", sc,T[2],T[4])
m = n
#/*******************************************************/
#/* Module 2. Calculate value of PI from Taylor Series */
#/* expansion of atan(1.0). There are 7 */
#/* double precision operations per loop */
#/* ( 3 +, 2 -, 1 *, 1 / ) that are included */
#/* in the timing. */
#/* 42.9% +, 28.6% -, 14.3% *, and 14.3% / */
#/*******************************************************/
s = -five# /********************/
sa = -one# /* Loop 2. */
# /********************/
dtime(TimeArray)
for i in 1:m+1
s = -s
sa = sa + s
end
dtime(TimeArray)
T[5] = T[1] * TimeArray[1]
if T[5] < 0.0
T[5] = 0.0
end
sc = m
u = sa# /*********************/
v = 0.0# /* Loop 3. */
w = 0.0# /*********************/
x = 0.0
dtime(TimeArray)
for i in 1:m+1
s = -s
sa = sa + s
u = u + two
x = x +(s - u)
v = v - s * u
w = w + s / u
end
dtime(TimeArray)
T[6] = T[1] * TimeArray[1]
T[7] = ( T[6] - T[5] ) / 7.0# /*********************/
m = round( sa * x / sc )# /* PI Results */
sa = four * w / five# /*********************/
sb = sa + five / v
sc = 31.25
piprg = sb - sc / (v * v * v)
pierr = piprg - piref
T[8] = one / T[7]
# /*********************/
# /* DO NOT REMOVE */
# /* THIS PRINTOUT! */
# /*********************/
@printf(" 2 %13.4e %10.4f %10.4f\n", pierr,T[6]-T[5],T[8])
#/*******************************************************/
#/* Module 3. Calculate integral of sin(x) from 0.0 to */
#/* PI/3.0 using Trapazoidal Method. Result */
#/* is 0.5. There are 17 double precision */
#/* operations per loop (6 +, 2 -, 9 *, 0 /) */
#/* included in the timing. */
#/* 35.3% +, 11.8% -, 52.9% *, and 00.0% / */
#/*******************************************************/
x = piref / ( three * m )# /*********************/
s = 0.0# /* Loop 4. */
v = 0.0# /*********************/
dtime(TimeArray)
for i in 1:m
v = v + one
u = v * x
w = u * u
s = s + u * ((((((A6*w-A5)*w+A4)*w-A3)*w+A2)*w+A1)*w+one)
end
dtime(TimeArray)
T[9] = T[1] * TimeArray[1] - nulltime
u = piref / three
w = u * u
sa = u * ((((((A6*w-A5)*w+A4)*w-A3)*w+A2)*w+A1)*w+one)
T[10] = T[9] / 17.0# /*********************/
sa = x * ( sa + two * s ) / two# /* sin(x) Results. */
sb = 0.5# /*********************/
sc = sa - sb
T[11] = one / T[10]
# /*********************/
# /* DO NOT REMOVE */
# /* THIS PRINTOUT! */
# /*********************/
@printf(" 3 %13.4e %10.4f %10.4f\n", sc,T[9],T[11])
#/************************************************************/
#/* Module 4. Calculate Integral of cos(x) from 0.0 to PI/3 */
#/* using the Trapazoidal Method. Result is */
#/* sin(PI/3). There are 15 double precision */
#/* operations per loop (7 +, 0 -, 8 *, and 0 / ) */
#/* included in the timing. */
#/* 50.0% +, 00.0% -, 50.0% *, 00.0% / */
#/************************************************************/
A3 = -A3
A5 = -A5
x = piref / ( three * m )# /*********************/
s = 0.0# /* Loop 5. */
v = 0.0# /*********************/
dtime(TimeArray)
for i in 1:m
u = i * x
w = u * u
s = s + w*(w*(w*(w*(w*(B6*w+B5)+B4)+B3)+B2)+B1)+one
end
dtime(TimeArray)
T[12] = T[1] * TimeArray[1] - nulltime
u = piref / three
w = u * u
sa = w*(w*(w*(w*(w*(B6*w+B5)+B4)+B3)+B2)+B1)+one
T[13] = T[12] / 15.0# /*******************/
sa = x * ( sa + one + two * s ) / two# /* Module 4 Result */
u = piref / three# /*******************/
w = u * u
sb = u * ((((((A6*w+A5)*w+A4)*w+A3)*w+A2)*w+A1)*w+A0)
sc = sa - sb
T[14] = one / T[13]
# /*********************/
# /* DO NOT REMOVE */
# /* THIS PRINTOUT! */
# /*********************/
@printf(" 4 %13.4e %10.4f %10.4f\n", sc,T[12],T[14])
#/************************************************************/
#/* Module 5. Calculate Integral of tan(x) from 0.0 to PI/3 */
#/* using the Trapazoidal Method. Result is */
#/* ln(cos(PI/3)). There are 29 double precision */
#/* operations per loop (13 +, 0 -, 15 *, and 1 /)*/
#/* included in the timing. */
#/* 46.7% +, 00.0% -, 50.0% *, and 03.3% / */
#/************************************************************/
x = piref / ( three * m )# /*********************/
s = 0.0# /* Loop 6. */
v = 0.0# /*********************/
dtime(TimeArray)
for i in 1:m
u = i * x
w = u * u
v = u * ((((((A6*w+A5)*w+A4)*w+A3)*w+A2)*w+A1)*w+one)
s = s + v / (w*(w*(w*(w*(w*(B6*w+B5)+B4)+B3)+B2)+B1)+one)
end
dtime(TimeArray)
T[15] = T[1] * TimeArray[1] - nulltime
u = piref / three
w = u * u
sa = u*((((((A6*w+A5)*w+A4)*w+A3)*w+A2)*w+A1)*w+one)
sb = w*(w*(w*(w*(w*(B6*w+B5)+B4)+B3)+B2)+B1)+one
sa = sa / sb
T[16] = T[15] / 29.0# /*******************/
sa = x * ( sa + two * s ) / two# /* Module 5 Result */
sb = 0.6931471805599453# /*******************/
sc = sa - sb
T[17] = one / T[16]
# /*********************/
# /* DO NOT REMOVE */
# /* THIS PRINTOUT! */
# /*********************/
@printf(" 5 %13.4e %10.4f %10.4f\n", sc,T[15],T[17])
#/************************************************************/
#/* Module 6. Calculate Integral of sin(x)*cos(x) from 0.0 */
#/* to PI/4 using the Trapazoidal Method. Result */
#/* is sin(PI/4)^2. There are 29 double precision */
#/* operations per loop (13 +, 0 -, 16 *, and 0 /)*/
#/* included in the timing. */
#/* 46.7% +, 00.0% -, 53.3% *, and 00.0% / */
#/************************************************************/
x = piref / ( four * m )# /*********************/
s = 0.0# /* Loop 7. */
v = 0.0# /*********************/
dtime(TimeArray)
for i in 1:m
u = i * x
w = u * u
v = u * ((((((A6*w+A5)*w+A4)*w+A3)*w+A2)*w+A1)*w+one)
s = s + v*(w*(w*(w*(w*(w*(B6*w+B5)+B4)+B3)+B2)+B1)+one)
end
dtime(TimeArray)
T[18] = T[1] * TimeArray[1] - nulltime
u = piref / four
w = u * u
sa = u*((((((A6*w+A5)*w+A4)*w+A3)*w+A2)*w+A1)*w+one)
sb = w*(w*(w*(w*(w*(B6*w+B5)+B4)+B3)+B2)+B1)+one
sa = sa * sb
T[19] = T[18] / 29.0# /*******************/
sa = x * ( sa + two * s ) / two# /* Module 6 Result */
sb = 0.25# /*******************/
sc = sa - sb
T[20] = one / T[19]
# /*********************/
# /* DO NOT REMOVE */
# /* THIS PRINTOUT! */
# /*********************/
@printf(" 6 %13.4e %10.4f %10.4f\n",sc,T[18],T[20])
#/*******************************************************/
#/* Module 7. Calculate value of the definite integral */
#/* from 0 to sa of 1/(x+1), x/(x*x+1), and */
#/* x*x/(x*x*x+1) using the Trapizoidal Rule.*/
#/* There are 12 double precision operations */
#/* per loop ( 3 +, 3 -, 3 *, and 3 / ) that */
#/* are included in the timing. */
#/* 25.0% +, 25.0% -, 25.0% *, and 25.0% / */
#/*******************************************************/
# /*********************/
s = 0.0# /* Loop 8. */
w = one# /*********************/
sa = 102.3321513995275
v = sa / m
dtime(TimeArray)
for i in 1:m
x = i * v
u = x * x
s = s - w / ( x + w ) - x / ( u + w ) - u / ( x * u + w )
end
dtime(TimeArray)
T[21] = T[1] * TimeArray[1] - nulltime
# /*********************/
# /* Module 7 Results */
# /*********************/
T[22] = T[21] / 12.0
x = sa
u = x * x
sa = -w - w / ( x + w ) - x / ( u + w ) - u / ( x * u + w )
sa = 18.0 * v * (sa + two * s )
m = -2000 * round(sa)
m = round( m / scale )
sc = sa + 500.2
T[23] = one / T[22]
# /********************/
# /* DO NOT REMOVE */
# /* THIS PRINTOUT! */
# /********************/
@printf(" 7 %13.4e %10.4f %10.4f\n", sc,T[21],T[23])
#/************************************************************/
#/* Module 8. Calculate Integral of sin(x)*cos(x)*cos(x) */
#/* from 0 to PI/3 using the Trapazoidal Method. */
#/* Result is (1-cos(PI/3)^3)/3. There are 30 */
#/* double precision operations per loop included */
#/* in the timing: */
#/* 13 +, 0 -, 17 * 0 / */
#/* 46.7% +, 00.0% -, 53.3% *, and 00.0% / */
#/************************************************************/
x = piref / ( three * m )# /*********************/
s = 0.0# /* Loop 9. */
v = 0.0# /*********************/
dtime(TimeArray)
for i in 1:m
u = i * x
w = u * u
v = w*(w*(w*(w*(w*(B6*w+B5)+B4)+B3)+B2)+B1)+one
s = s + v*v*u*((((((A6*w+A5)*w+A4)*w+A3)*w+A2)*w+A1)*w+one)
end
dtime(TimeArray)
T[24] = T[1] * TimeArray[1] - nulltime
u = piref / three
w = u * u
sa = u*((((((A6*w+A5)*w+A4)*w+A3)*w+A2)*w+A1)*w+one)
sb = w*(w*(w*(w*(w*(B6*w+B5)+B4)+B3)+B2)+B1)+one
sa = sa * sb * sb
T[25] = T[24] / 30.0# /*******************/
sa = x * ( sa + two * s ) / two# /* Module 8 Result */
sb = 0.29166666666666667# /*******************/
sc = sa - sb
T[26] = one / T[25]
# /*********************/
# /* DO NOT REMOVE */
# /* THIS PRINTOUT! */
# /*********************/
@printf(" 8 %13.4e %10.4f %10.4f\n", sc,T[24],T[26])
#/**************************************************/
#/* MFLOPS(1) output. This is the same weighting */
#/* used for all previous versions of the flops.c */
#/* program. Includes Modules 2 and 3 only. */
#/**************************************************/
T[27] = ( five * (T[6] - T[5]) + T[9] ) / 52.0
T[28] = one / T[27]
#/**************************************************/
#/* MFLOPS(2) output. This output does not include */
#/* Module 2, but it still does 9.2% FDIV's. */
#/**************************************************/
T[29] = T[2] + T[9] + T[12] + T[15] + T[18]
T[29] = (T[29] + four * T[21]) / 152.0
T[30] = one / T[29]
#/**************************************************/
#/* MFLOPS(3) output. This output does not include */
#/* Module 2, but it still does 3.4% FDIV's. */
#/**************************************************/
T[31] = T[2] + T[9] + T[12] + T[15] + T[18]
T[31] = (T[31] + T[21] + T[24]) / 146.0
T[32] = one / T[31]
#/**************************************************/
#/* MFLOPS(4) output. This output does not include */
#/* Module 2, and it does NO FDIV's. */
#/**************************************************/
T[33] = (T[9] + T[12] + T[18] + T[24]) / 91.0
T[34] = one / T[33]
@printf("\n")
@printf(" Iterations = %10d\n", m)
@printf(" NullTime (usec) = %10.4f\n", nulltime)
@printf(" MFLOPS(1) = %10.4f\n", T[28])
@printf(" MFLOPS(2) = %10.4f\n", T[30])
@printf(" MFLOPS(3) = %10.4f\n", T[32])
@printf(" MFLOPS(4) = %10.4f\n\n", T[34])
end
main()