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cpp2taylor.h2
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259 lines (203 loc) · 5.71 KB
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#ifndef CPP2_CPP2TAYLOR_H
#define CPP2_CPP2TAYLOR_H
cpp2: namespace = {
taylor: <R, dim: int> type = {
public v : std::array<R, dim> = ();
operator=:(out this) = {}
operator=:(out this, d1: R) = {
v = ();
v[0] = d1;
}
operator=:(out this, that) = {}
operator=:(out this, l: std::initializer_list<R>) = {
(copy i := 1)
for l do (cur) {
set(i, cur);
}
}
// C++ interface
operator[]: (this, k: int) -> R = {
assert(1 <= k <= dim);
r: R = v[k - 1];
(copy i := 2)
while i <= k next i += 1 {
r *= i;
}
return r;
}
set: (inout this, k: int, value: R) = {
assert(1 <= k <= dim);
v[k - 1] = value;
(copy i := 2)
while i <= k next i += 1 {
v[k - 1] /= i;
}
}
// C++2 interface / AD interface
get: (this, i: int, v0: R) -> R = {
if i == 0 {
return v0;
}
else if i > dim {
return 0.0;
}
return v[i - 1];
}
// Overload for reverse AD.
operator+=: (inout this, o: taylor) -> forward_ref _ = {
this = this + o;
return this;
}
// Overload for reverse AD.
operator-=: (inout this, o: taylor) -> forward_ref _ = {
this = this - o;
return this;
}
// Overload for simple handling of connected adds.
operator+: (this, o: taylor) -> taylor = {
return add(o, 0.0, 0.0); // Primal values are not required.
}
// Overload for simple handling of connected minuses.
operator-: (this, o: taylor) -> taylor = {
return sub(o, 0.0, 0.0); // Primal values are not required.
}
// Overload for simple handling of prefix +.
operator+: (this) -> taylor = {
return this;
}
// Overload for simple handling of prefix -.
operator-: (this) -> taylor = {
r: taylor = ();
(copy k:= 1)
while k <= dim next k += 1 {
r.v[k - 1] = -v[k - 1];
}
return r;
}
add: (this, o: taylor, v0: R, o0: R) -> taylor = {
r: taylor = ();
(copy k:= 1)
while k <= dim next k += 1 {
r.v[k - 1] = get(k, v0) + o.get(k, o0);
}
return r;
}
sub: (this, o: taylor, v0: R, o0: R) -> taylor = {
r: taylor = ();
(copy k:= 1)
while k <= dim next k += 1 {
r.v[k - 1] = get(k, v0) - o.get(k, o0);
}
return r;
}
mul: <dim_o: int> (this, in_ref o: taylor<R, dim_o>, v0: R, o0: R) -> taylor<R, std::max(dim, dim_o)> = {
dim_r : int == std::max(dim, dim_o);
r: taylor<R, dim_r> = ();
(copy k:= 1)
while k <= dim_r next k += 1 {
(copy j := 0)
while j <= k next j += 1 {
r..v[k - 1] += get(j, v0) * o..get(k - j, o0);
}
}
return r;
}
div: (this, o: taylor, v0: R, o0: R) -> taylor = {
r: taylor = ();
r0: R = v0 / o0;
factor : R = 1.0 / o0;
(copy k:= 1)
while k <= dim next k += 1 {
r..v[k - 1] = get(k, v0);
(copy j := 0)
while j < k next j += 1 {
r..v[k - 1] -= r.get(j, r0) * o..get(k - j, o0);
}
r..v[k - 1] *= factor;
}
return r;
}
sqrt: (this, v0: R) -> taylor = {
r: taylor = ();
r0: R = std::sqrt(v0);
factor : R = 0.5 / r0;
(copy k:= 1)
while k <= dim next k += 1 {
r..v[k - 1] = get(k, v0);
(copy j := 1)
while j < k next j += 1 {
r..v[k - 1] -= r..get(j, r0) * r..get(k - j, r0);
}
r..v[k - 1] *= factor;
}
return r;
}
log: (this, v0: R) -> taylor = {
r: taylor = ();
r0: R = std::log(v0);
factor : R = 1.0 / v0;
(copy k:= 1)
while k <= dim next k += 1 {
r..v[k - 1] =k * get(k, v0);
(copy j := 1)
while j < k next j += 1 {
r..v[k - 1] -= j * get(k - j, v0) * r..get(j, r0);
}
r..v[k - 1] *= factor / k;
}
return r;
}
exp: (this, v0: R) -> taylor = {
r: taylor = ();
r0: R = std::exp(v0);
factor : R = 1.0 / v0;
(copy k:= 1)
while k <= dim next k += 1 {
(copy j := 1)
while j <= k next j += 1 {
r..v[k - 1] += j * r..get(k - j, r0) * get(j, v0);
}
r..v[k - 1] /= k;
}
return r;
}
comp_sin_cos: (inout s: taylor, inout c: taylor, u: taylor, u0: R) = {
s0: R = std::sin(u0);
c0: R = std::cos(u0);
(copy k:= 1)
while k <= dim next k += 1 {
(copy j := 1)
while j <= k next j += 1 {
s..v[k - 1] += j * u..get(j, u0) * c..get(k - j, c0);
c..v[k - 1] -= j * u..get(j, u0) * s..get(k - j, s0);
}
s..v[k - 1] /= k;
c..v[k - 1] /= k;
}
}
sin: (this, v0: R) -> taylor = {
t: taylor = ();
r: taylor = ();
comp_sin_cos(r, t, this, v0);
_ = t;
return r;
}
cos: (this, v0: R) -> taylor = {
t: taylor = ();
r: taylor = ();
comp_sin_cos(t, r, this, v0);
_ = t;
return r;
}
}
to_string: <R, order: int> (o: taylor<R, order>) -> std::string = {
r : std::string = "(";
(copy i := 1)
while i <= order next i += 1 {
r += " (o[i])$";
}
r += " )";
return r;
}
} // cpp2 namespace
#endif // CPP2_CPP2TAYLOR_H