1. Music Programming Using New Features of Standard C++ Adrian Freed Amar Chaudhary Center for New Music and Audio Technologies University of California, Berkeley

2. Outline Standardization effort for C++ Motivation: to exploit new standard in music applications Work through an example that aggressively uses new features Compiler results Conclusion

3. Standardization effort for C++ NOT a codification of existing practice Introduced many new features (outlined in printed paper) Directly address efficiency issues relevant to reactive music software

4. Motivation Open Sound Library (OSL) Exploit high performance of modern computers –Parallelism –Data and code locality –Multi-level register/primary/secondary/main memory hierarchy Exploit expressivity from new language features

5. Example: Second-order Resonator double damped_sine(double frequency, double amplitude,double rate,Time &t){ return amplitude * exp(-rate*t) * sin(2.0*PI*frequency*t); } Test for(Time t;t<10.0;++t) cout<< damped_sine(440.0, 1.0, 0.1,t)<<endl;

6. Regular 44.1kHz Sampling class Time { double time; const double sampling_interval; public: Time(double srate=44100.0): time(0.0),sampling_interval(1.0/srate) {} operator double() { return time; } friend double operator *(double f, Time &t){ return f * t.time; } Time& operator ++() { time += sampling_interval; return *this; } };

7. Example: Second-order Resonator Simple Easy to Debug Easy to relate to basic mathematical description Too slow

8. Time as Discrete Sequences class Time { int sample_count; const double sampling_interval; public: Time(double srate=44100.0):sample_count(0), sampling_interval(1.0/srate) {} operator double(){ return sample_count*sampling_interval; } friend double operator *(double f, Time &t) { return f * t.sample_count*t.sampling_interval; } Time& operator ++() { ++sample_count; return *this; } };

9. Optimizing Exponentials Operator Strength Reduction using identity:

10. Optimizing Exponentials class expstate { double value, factor; public: double exp(double k, int i) { return (i==0) ? (factor = ::exp(k), value=1.0) : (value *= factor); } };

11. Identity applies to Sinusoids class sinstate { complex value, factor; public: double sin(double k, int i) { return (i==0) ?(factor = ::exp(complex (0.0,k)), value=1.0) : imag(value *= factor); } }; Euler’s identity:

12. Putting it all together class Time { private: const double sampling_interval; mutable double time, *prevs; mutable int index; public: Time (double srate=44100.0, int depth=MAXDEPTH): sampling_interval(1.0/srate), prevs(new double[depth]),index(0), time(0.0) { for (int i = 0; i < depth; ++i) {prevs[i] = 1.0;} }

13. Putting it all together operator double() const { return time; } const Time& operator ++() const { index=0; time += sampling_interval; return *this; } struct defmul{ const Time& t; const double f; defmul(const Time& at, const double af): t(at), f(af) {} operator double() { return f * t; } }; friend defmul operator *(const double f, const Time &t) { return defmul(t, f) ;} friend defmul operator *(const Time &t, const double f) { return defmul(t, f); }

14. Putting it all together double exp(const double f) const { double t = prevs[index]; exp_aux(prevs+(index++),-sampling_interval * f); return t; } friend double exp(const defmul &dm) { return ((const Time &) dm.t).exp(dm.f); } friend void exp_aux ( double * p, const double f) { *p *= ::exp(f); } };

15. Compiler Optimizations Inlining Code hoisting Loop unrolling Constant folding Compile time arithmetic for intrinsics

16. Compiler Results Kuck and Associates Inc. (http://www.kai.com) Microsoft Visual C++ 6.0 (not 4.2) Careful adjustment of optimization options –inline composition closure (i.e., defmul) –exponentiation only computed once

17. Conclusion Did not involve change the original function. Users define their needs in an expressive high-level form. Provide a large family of optimization classes. Code for optimization classes is available at compile time. Optimizations themselves are expressed in a high-level form.