tl;dr
Of the same numpy array, calculating np.cos takes 3.2 seconds, wheras np.sin runs 548 seconds (nine minutes) on Linux Mint.
See this repo for full code.
I've got a pulse signal (see image below) which I need to modulate onto a HF-carrier, simulating a Laser Doppler Vibrometer. Therefore signal and its time basis need to be resampled to match the carrier's higher sampling rate.
In the following demodulation process both the in-phase carrier cos(omega * t) and the phase-shifted carrier sin(omega * t) are needed.
Oddly, the time to evaluate these functions depends highly on the way the time vector has been calculated.
The time vector t1 is being calculated using np.linspace directly, t2 uses the method implemented in scipy.signal.resample.
pulse = np.load('data/pulse.npy') # 768 samples
pulse_samples = len(pulse)
pulse_samplerate = 960 # 960 Hz
pulse_duration = pulse_samples / pulse_samplerate # here: 0.8 s
pulse_time = np.linspace(0, pulse_duration, pulse_samples,
endpoint=False)
carrier_freq = 40e6 # 40 MHz
carrier_samplerate = 100e6 # 100 MHz
carrier_samples = pulse_duration * carrier_samplerate # 80 million
t1 = np.linspace(0, pulse_duration, carrier_samples)
# method used in scipy.signal.resample
# https://github.com/scipy/scipy/blob/v0.17.0/scipy/signal/signaltools.py#L1754
t2 = np.arange(0, carrier_samples) * (pulse_time[1] - pulse_time[0]) \
* pulse_samples / float(carrier_samples) + pulse_time[0]
As can be seen in the picture below, the time vectors are not identical. At 80 million samples the difference t1 - t2 reaches 1e-8.
Calculating the in-phase and shifted carrier of t1 takes 3.2 seconds each on my machine.
With t2, however, calculating the shifted carrier takes 540 seconds. Nine minutes. For nearly the same 80 million values.
omega_t1 = 2 * np.pi * carrier_frequency * t1
np.cos(omega_t1) # 3.2 seconds
np.sin(omega_t1) # 3.3 seconds
omega_t2 = 2 * np.pi * carrier_frequency * t2
np.cos(omega_t2) # 3.2 seconds
np.sin(omega_t2) # 9 minutes
I can reproduce this bug on both my 32-bit laptop and my 64-bit tower, both running Linux Mint 17. On my flat mate's MacBook, however, the "slow sine" takes as little time as the other three calculations.
I run a Linux Mint 17.03 on a 64-bit AMD processor and Linux Mint 17.2 on 32-bit Intel processor.