September Morn Update

Task/Numeric-error-propagation/00META.yaml

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+--- {}

Task/Numeric-error-propagation/Phix/numeric-error-propagation.phix

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+enum VALUE, DELTA
+
+type imprecise(object imp)
+    return sequence(imp) and atom(imp[VALUE]) and atom(imp[DELTA])
+end type
+
+function sqr(atom a)
+    return a*a
+end function
+
+function imprecise_add(imprecise a, b)
+    atom delta = sqrt(sqr(a[DELTA]) + sqr(b[DELTA]))
+    imprecise ret = {a[VALUE] + b[VALUE], delta}
+    return ret
+end function
+
+function imprecise_mul(imprecise a, b)
+    atom delta = sqrt(sqr(a[VALUE]*b[DELTA]) + sqr(b[VALUE]*a[DELTA]))
+    imprecise ret = {a[VALUE] * b[VALUE],delta}
+    return ret
+end function
+
+function imprecise_div(imprecise a, b)
+    atom delta = sqrt(sqr(a[VALUE]*b[DELTA]) + sqr(b[VALUE]*a[DELTA]))/sqr(b[VALUE])
+    imprecise ret = {a[VALUE] / b[VALUE], delta}
+    return ret
+end function
+
+function imprecise_pow(imprecise a, atom c)
+    atom v = power(a[VALUE], c),
+         delta = abs(v*c*a[DELTA]/a[VALUE])
+    imprecise ret = {v,delta}
+    return ret
+end function
+
+function printImprecise(imprecise imp)
+    return sprintf("%g+/-%g",imp)
+end function
+
+imprecise x1 = {100, 1.1},
+          y1 = {50, 1.2},
+          x2 = {-200, 2.2},
+          y2 = {-100, 2.3},
+          tmp1, tmp2,
+          d
+
+    tmp1 = imprecise_add(x1, x2)
+    tmp1 = imprecise_pow(tmp1, 2)
+    tmp2 = imprecise_add(y1, y2)
+    tmp2 = imprecise_pow(tmp2, 2)
+    d = imprecise_add(tmp1,tmp2)
+    d = imprecise_pow(d, 0.5)
+    printf(1,"Distance, d, between the following points :")
+    printf(1,"\n( x1, y1) = ( %s, %s)",{printImprecise(x1),printImprecise(y1)})
+    printf(1,"\n( x2, y2) = ( %s, %s)",{printImprecise(x2),printImprecise(y2)})
+    printf(1,"\nis d = %s\n", {printImprecise(d)})