Formal power series: Difference between revisions
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<syntaxhighlight lang="elisa">cos = + 1 / 1 * X ** 0 + -1 / 2 * X ** 2 + 1 / 24 * X ** 4 + -1 / 720 * X ** 6 + 1 / 40320 * X ** 8
sin = + 1 / 1 * X ** 1 + -1 / 6 * X ** 3 + 1 / 120 * X ** 5 + -1 / 5040 * X ** 7 + 1 / 362880 * X ** 9</syntaxhighlight>
=={{header|FreeBASIC}}==
{{trans|C}}
<syntaxhighlight lang="vbnet">Type fps_t
As Integer tipo
As fps_t Ptr s1, s2
As Single a0
End Type
Enum fps_type
FPS_CONST = 0
FPS_ADD
FPS_SUB
FPS_MUL
FPS_DIV
FPS_DERIV
FPS_INT
End Enum
Function fps_new() As fps_t Ptr
Dim As fps_t Ptr x = Callocate(1, Sizeof(fps_t))
x->a0 = 0
x->s1 = 0
x->s2 = 0
x->tipo = 0
Return x
End Function
Sub fps_redefine(x As fps_t Ptr, op As Integer, y As fps_t Ptr, z As fps_t Ptr)
x->tipo = op
x->s1 = y
x->s2 = z
End Sub
Function _binary(x As fps_t Ptr, y As fps_t Ptr, op As Integer) As fps_t Ptr
Dim As fps_t Ptr s = fps_new()
s->s1 = x
s->s2 = y
s->tipo = op
Return s
End Function
Function _unary(x As fps_t Ptr, op As Integer) As fps_t Ptr
Dim As fps_t Ptr s = fps_new()
s->s1 = x
s->tipo = op
Return s
End Function
Function term(x As fps_t Ptr, n As Integer) As Single
Dim As Single ret = 0
Dim As Integer i
Select Case x->tipo
Case FPS_CONST
Return Iif(n > 0, 0, x->a0)
Case FPS_ADD
ret = term(x->s1, n) + term(x->s2, n)
Case FPS_SUB
ret = term(x->s1, n) - term(x->s2, n)
Case FPS_MUL
For i = 0 To n
ret += term(x->s1, i) * term(x->s2, n - i)
Next i
Case FPS_DIV
If term(x->s2, 0) = 0 Then Return 0 / 0 ' NaN
ret = term(x->s1, n)
For i = 1 To n
ret -= term(x->s2, i) * term(x, n - i) / term(x->s2, 0)
Next i
Case FPS_DERIV
ret = n * term(x->s1, n + 1)
Case FPS_INT
If n = 0 Then Return x->a0
ret = term(x->s1, n - 1) / n
Case Else
Print "Unknown operator "; x->tipo
End 1
End Select
Return ret
End Function
Function fps_const(a0 As Single) As fps_t Ptr
Dim As fps_t Ptr x = fps_new()
x->tipo = 0
x->a0 = a0
Return x
End Function
Dim As Integer i
Dim As fps_t Ptr one = fps_const(1)
Dim As fps_t Ptr fcos = fps_new() ' cosine
Dim As fps_t Ptr fsin = _unary(fcos, FPS_INT) ' sine
Dim As fps_t Ptr ftan = _binary(fsin, fcos, FPS_DIV) ' tangent
' redefine cos to complete the mutual recursion
fps_redefine(fcos, FPS_SUB, one, _unary(fsin, FPS_INT))
Dim As fps_t Ptr fexp = fps_const(1) ' exponential
' make exp recurse on self
fps_redefine(fexp, FPS_INT, fexp, 0)
Print "Sin:";
For i = 0 To 9
Print " "; term(fsin, i);
Next i
Print
Print "Cos:";
For i = 0 To 9
Print " "; term(fcos, i);
Next i
Print
Print "Tan:";
For i = 0 To 9
Print " "; term(ftan, i);
Next i
Print
Print "Exp:";
For i = 0 To 9
Print " "; term(fexp, i);
Next i
Print
Sleep</syntaxhighlight>
{{out}}
<pre>Sin: 0 1 0 -0.1666667 0 0.008333334 0 -0.0001984127 0 2.755732e-006
Cos: 1 0 -0.5 0 0.04166667 0 -0.001388889 0 2.480159e-005 0
Tan: 0 1 0 0.3333333 0 0.1333333 0 0.05396825 0 0.02186948
Exp: 1 1 0.5 0.1666667 0.04166667 0.008333334 0.001388889 0.0001984127 2.480159e-005 2.755732e-006</pre>
=={{header|Go}}==
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{{trans|Kotlin}}
{{libheader|Wren-rat}}
<syntaxhighlight lang="
class Gene {
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