void LdL21(double x, double *y, double *z) {
  double L[21 + 1];
  double dL[21 + 1];
  L[0] = 1.;
  L[1] = x;
  dL[0] = 0.;
  dL[1] = 1.;
  {
    for (int i = 2; i < 21 + 1; i++) {
      L[i] = 2. * (x)*L[i - 1] - L[i - 2] -
             ((x)*L[i - 1] - L[i - 2]) / ((double)i);
      dL[i] = L[i - 1] * i + dL[i - 1] * (x);
    }
  };
  *y = L[21];
  *z = dL[21];
}


x86 assembly (clang, -O0):
<LdL21>:
push   %rbp
mov    %rsp,%rbp
sub    $0x110,%rsp
movsd  %xmm0,-0x8(%rbp)
mov    %rdi,-0x10(%rbp)
mov    %rsi,-0x18(%rbp)
movsd  0xee0(%rip),%xmm0
movsd  %xmm0,-0xd0(%rbp)
ff
movsd  -0x8(%rbp),%xmm0
movsd  %xmm0,-0xc8(%rbp)
ff
xorps  %xmm0,%xmm0
movsd  %xmm0,-0x180(%rbp)
ff
movsd  0xeb8(%rip),%xmm0
movsd  %xmm0,-0x178(%rbp)
ff
movl   $0x2,-0x184(%rbp)
cmpl   $0x16,-0x184(%rbp)
jge    1288 <LdL21+0x188>
movsd  0xe99(%rip),%xmm0
mulsd  -0x8(%rbp),%xmm0
mov    -0x184(%rbp),%eax
sub    $0x1,%eax
cltq
movsd  -0xd0(%rbp,%rax,8),%xmm2
ff ff
mov    -0x184(%rbp),%eax
sub    $0x2,%eax
cltq
movsd  -0xd0(%rbp,%rax,8),%xmm1
ff ff
movq   %xmm1,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm1
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
movsd  -0x8(%rbp),%xmm1
mov    -0x184(%rbp),%eax
sub    $0x1,%eax
cltq
movsd  -0xd0(%rbp,%rax,8),%xmm3
ff ff
mov    -0x184(%rbp),%eax
sub    $0x2,%eax
cltq
movsd  -0xd0(%rbp,%rax,8),%xmm2
ff ff
movq   %xmm2,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm2
mulsd  %xmm3,%xmm1
addsd  %xmm2,%xmm1
cvtsi2sdl -0x184(%rbp),%xmm2
ff
divsd  %xmm2,%xmm1
subsd  %xmm1,%xmm0
movslq -0x184(%rbp),%rax
movsd  %xmm0,-0xd0(%rbp,%rax,8)
ff ff
mov    -0x184(%rbp),%eax
sub    $0x1,%eax
cltq
movsd  -0xd0(%rbp,%rax,8),%xmm0
ff ff
cvtsi2sdl -0x184(%rbp),%xmm2
ff
mov    -0x184(%rbp),%eax
sub    $0x1,%eax
cltq
movsd  -0x180(%rbp,%rax,8),%xmm1
ff ff
mulsd  -0x8(%rbp),%xmm1
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
movslq -0x184(%rbp),%rax
movsd  %xmm0,-0x180(%rbp,%rax,8)
ff ff
mov    -0x184(%rbp),%eax
add    $0x1,%eax
mov    %eax,-0x184(%rbp)
jmp    115a <LdL21+0x5a>
movsd  -0x28(%rbp),%xmm0
mov    -0x10(%rbp),%rax
movsd  %xmm0,(%rax)
movsd  -0xd8(%rbp),%xmm0
ff
mov    -0x18(%rbp),%rax
movsd  %xmm0,(%rax)
add    $0x110,%rsp
pop    %rbp
ret

x86 assembly (clang, -O2):
<LdL21>:
sub    $0xe8,%rsp
movabs $0x3ff0000000000000,%rax
mov    %rax,-0x80(%rsp)
movsd  %xmm0,-0x78(%rsp)
movsd  0xedc(%rip),%xmm1
xorpd  %xmm2,%xmm2
unpcklpd %xmm1,%xmm2
movapd %xmm2,0x30(%rsp)
movapd %xmm0,%xmm2
addsd  %xmm0,%xmm2
mov    $0x2,%eax
movapd %xmm1,%xmm4
movapd %xmm0,%xmm3
nopw   0x0(%rax,%rax,1)
movapd %xmm2,%xmm5
mulsd  %xmm3,%xmm5
subsd  %xmm4,%xmm5
movapd %xmm0,%xmm6
mulsd  %xmm3,%xmm6
subsd  %xmm4,%xmm6
xorps  %xmm4,%xmm4
cvtsi2sd %eax,%xmm4
divsd  %xmm4,%xmm6
subsd  %xmm6,%xmm5
movsd  %xmm5,-0x80(%rsp,%rax,8)
mulsd  %xmm0,%xmm1
mulsd  %xmm3,%xmm4
addsd  %xmm4,%xmm1
movsd  %xmm1,0x30(%rsp,%rax,8)
add    $0x1,%rax
movapd %xmm3,%xmm4
movapd %xmm5,%xmm3
cmp    $0x16,%rax
jne    1150 <LdL21+0x50>
movsd  0x28(%rsp),%xmm0
movsd  %xmm0,(%rdi)
movsd  0xd8(%rsp),%xmm0
movsd  %xmm0,(%rsi)
add    $0xe8,%rsp
ret

LLVM IR (-O0):
define void @LdL21(double %0, double* %1, double* %2) {
%4 = alloca double
%5 = alloca double*
%6 = alloca double*
%7 = alloca [22 x double]
%8 = alloca [22 x double]
%9 = alloca i32
store double %0, double* %4
store double* %1, double** %5
store double* %2, double** %6
%10 = getelementptr inbounds [22 x double], [22 x double]* %7, i64 0, i64 0
store double 1.000000e+00, double* %10
%11 = load double, double* %4
%12 = getelementptr inbounds [22 x double], [22 x double]* %7, i64 0, i64 1
store double %11, double* %12
%13 = getelementptr inbounds [22 x double], [22 x double]* %8, i64 0, i64 0
store double 0.000000e+00, double* %13
%14 = getelementptr inbounds [22 x double], [22 x double]* %8, i64 0, i64 1
store double 1.000000e+00, double* %14
store i32 2, i32* %9
br label %15
15: ; preds = %71, %3
%16 = load i32, i32* %9
%17 = icmp slt i32 %16, 22
br i1 %17, label %18, label %74
18: ; preds = %15
%19 = load double, double* %4
%20 = fmul double 2.000000e+00, %19
%21 = load i32, i32* %9
%22 = sub nsw i32 %21, 1
%23 = sext i32 %22 to i64
%24 = getelementptr inbounds [22 x double], [22 x double]* %7, i64 0, i64 %23
%25 = load double, double* %24
%26 = load i32, i32* %9
%27 = sub nsw i32 %26, 2
%28 = sext i32 %27 to i64
%29 = getelementptr inbounds [22 x double], [22 x double]* %7, i64 0, i64 %28
%30 = load double, double* %29
%31 = fneg double %30
%32 = call double @llvm.fmuladd.f64(double %20, double %25, double %31)
%33 = load double, double* %4
%34 = load i32, i32* %9
%35 = sub nsw i32 %34, 1
%36 = sext i32 %35 to i64
%37 = getelementptr inbounds [22 x double], [22 x double]* %7, i64 0, i64 %36
%38 = load double, double* %37
%39 = load i32, i32* %9
%40 = sub nsw i32 %39, 2
%41 = sext i32 %40 to i64
%42 = getelementptr inbounds [22 x double], [22 x double]* %7, i64 0, i64 %41
%43 = load double, double* %42
%44 = fneg double %43
%45 = call double @llvm.fmuladd.f64(double %33, double %38, double %44)
%46 = load i32, i32* %9
%47 = sitofp i32 %46 to double
%48 = fdiv double %45, %47
%49 = fsub double %32, %48
%50 = load i32, i32* %9
%51 = sext i32 %50 to i64
%52 = getelementptr inbounds [22 x double], [22 x double]* %7, i64 0, i64 %51
store double %49, double* %52
%53 = load i32, i32* %9
%54 = sub nsw i32 %53, 1
%55 = sext i32 %54 to i64
%56 = getelementptr inbounds [22 x double], [22 x double]* %7, i64 0, i64 %55
%57 = load double, double* %56
%58 = load i32, i32* %9
%59 = sitofp i32 %58 to double
%60 = load i32, i32* %9
%61 = sub nsw i32 %60, 1
%62 = sext i32 %61 to i64
%63 = getelementptr inbounds [22 x double], [22 x double]* %8, i64 0, i64 %62
%64 = load double, double* %63
%65 = load double, double* %4
%66 = fmul double %64, %65
%67 = call double @llvm.fmuladd.f64(double %57, double %59, double %66)
%68 = load i32, i32* %9
%69 = sext i32 %68 to i64
%70 = getelementptr inbounds [22 x double], [22 x double]* %8, i64 0, i64 %69
store double %67, double* %70
br label %71
71: ; preds = %18
%72 = load i32, i32* %9
%73 = add nsw i32 %72, 1
store i32 %73, i32* %9
br label %15
74: ; preds = %15
%75 = getelementptr inbounds [22 x double], [22 x double]* %7, i64 0, i64 21
%76 = load double, double* %75
%77 = load double*, double** %5
store double %76, double* %77
%78 = getelementptr inbounds [22 x double], [22 x double]* %8, i64 0, i64 21
%79 = load double, double* %78
%80 = load double*, double** %6
store double %79, double* %80
ret void
}

LLVM IR (-O2):
define void @LdL21(double %0, double* nocapture writeonly %1, double* nocapture writeonly %2) {
%4 = alloca [22 x double]
%5 = alloca [22 x double]
%6 = bitcast [22 x double]* %4 to i8*
%7 = bitcast [22 x double]* %5 to i8*
%8 = getelementptr inbounds [22 x double], [22 x double]* %4, i64 0, i64 0
store double 1.000000e+00, double* %8
%9 = getelementptr inbounds [22 x double], [22 x double]* %4, i64 0, i64 1
store double %0, double* %9
%10 = bitcast [22 x double]* %5 to <2 x double>*
store <2 x double> <double 0.000000e+00, double 1.000000e+00>, <2 x double>* %10
%11 = fmul double %0, 2.000000e+00
br label %17
12: ; preds = %17
%13 = getelementptr inbounds [22 x double], [22 x double]* %4, i64 0, i64 21
%14 = load double, double* %13
store double %14, double* %1
%15 = getelementptr inbounds [22 x double], [22 x double]* %5, i64 0, i64 21
%16 = load double, double* %15
store double %16, double* %2
ret void
17: ; preds = %3, %17
%18 = phi double [ 1.000000e+00, %3 ], [ %31, %17 ]
%19 = phi double [ 1.000000e+00, %3 ], [ %20, %17 ]
%20 = phi double [ %0, %3 ], [ %28, %17 ]
%21 = phi i64 [ 2, %3 ], [ %33, %17 ]
%22 = fneg double %19
%23 = tail call double @llvm.fmuladd.f64(double %11, double %20, double %22)
%24 = tail call double @llvm.fmuladd.f64(double %0, double %20, double %22)
%25 = trunc i64 %21 to i32
%26 = sitofp i32 %25 to double
%27 = fdiv double %24, %26
%28 = fsub double %23, %27
%29 = getelementptr inbounds [22 x double], [22 x double]* %4, i64 0, i64 %21
store double %28, double* %29
%30 = fmul double %18, %0
%31 = tail call double @llvm.fmuladd.f64(double %20, double %26, double %30)
%32 = getelementptr inbounds [22 x double], [22 x double]* %5, i64 0, i64 %21
store double %31, double* %32
%33 = add nuw nsw i64 %21, 1
%34 = icmp eq i64 %33, 22
br i1 %34, label %12, label %17
}