cospi — Compute cos(X*pi) accurately with exact integer and half-integer results.
cospi(X) computes cos(X*pi) without first materializing the approximate floating-point value X*pi. Odd half-integers return exactly zero and integers return exactly +1 or -1.
Syntax
Y = cospi(X)Inputs
| Name | Type | Required | Default | Description |
|---|---|---|---|---|
X | Any | Yes | — | Input scalar, array, logical array, complex value, or gpuArray. |
Returns
| Name | Type | Description |
|---|---|---|
Y | Any | Element-wise cos(X*pi) result with exact integer and half-integer handling. |
Errors
| Identifier | When | Message |
|---|---|---|
RunMat:cospi:InvalidInput | Input cannot be interpreted as supported numeric/logical/complex data. | cospi: invalid input |
RunMat:cospi:Internal | Internal gather/conversion/allocation flow failed. | cospi: internal error |
How cospi works
- Operates element-wise on scalars, vectors, matrices, and N-D tensors.
- Integer and logical inputs are promoted to double precision before evaluation.
- Returns exactly 0 for odd half-integer inputs and exactly ±1 for integer inputs.
- Complex inputs use the analytic extension of
cos(pi*z)while preserving exact real-axis sine/cosine factors when possible. - Output shape matches the input shape; non-finite real inputs produce
NaN. - String inputs are unsupported and raise a builtin-scoped error.
Examples
Cosine of multiples of pi
Y = cospi([0 1/2 1 3/2 2])Expected output:
Y = [1 0 -1 0 1]Avoid floating-point drift at half-integer multiples
y = cospi(1/2)Expected output:
y = 0Using cospi with coding agents
Open a RunMat example with live inputs, then ask the agent to explain how cospi changes the result.
Run a small cospi example, explain the result, then change one input and compare the output.
FAQ
Why use cospi(X) instead of cos(X*pi)?⌄
pi is not exactly representable in binary floating point. cospi short-circuits integer and half-integer multiples so common exact results do not contain small rounding noise.
Does cospi support gpuArray inputs?⌄
Yes. RunMat currently gathers gpuArray inputs and evaluates the exact host implementation; no GPU kernel is launched yet.
Related Math functions
Trigonometry
acos · acosh · asin · asinh · atan · atan2 · atanh · cos · cosd · cosh · deg2rad · pol2cart · rad2deg · sin · sind · sinh · sinpi · tan · tand · tanh
Elementwise
abs · angle · bsxfun · complex · conj · double · erf · erfcinv · exp · expm1 · factorial · flintmax · gamma · gammaln · heaviside · hypot · idivide · imag · intmax · intmin · ldivide · log · log10 · log1p · log2 · minus · nextpow2 · plus · pow2 · power · rdivide · real · realmax · realmin · realsqrt · rescale · sign · single · sqrt · swapbytes · times · uint32
Reduction
all · any · bounds · cummax · cummin · cumprod · cumsum · cumtrapz · diff · gradient · max · maxk · mean · median · min · mink · movmax · movmean · movmedian · movmin · movprod · movstd · movsum · movvar · nnz · prod · rms · std · sum · trapz · var
Structure
bandwidth · isdiag · ishermitian · issymmetric · istril · istriu · symrcm
Signal
blackman · butter · buttord · cheb2ord · conv · conv2 · deconv · downsample · envelope · filter · filtfilt · fir1 · freqz · gauspuls · hamming · hann · hilbert · periodogram · pulstran · pwelch · rectpuls · resample · sawtooth · sinc · spectrogram · square · tripuls · unwrap · upsample · zplane
Optim
coneprog · fminbnd · fminunc · fsolve · fzero · integral · linprog · lsqcurvefit · lsqnonlin · optimset · quad · secondordercone
Ops
cross · ctranspose · dot · mldivide · mpower · mrdivide · mtimes · pagemtimes · pagetranspose · trace · transpose
Open-source implementation
Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how cospi is executed, line by line, in Rust.
- View the source for cospi in Rust on GitHub
- Learn how the RunMat runtime works
- Found a bug? Open an issue with a minimal reproduction.
About RunMat
RunMat is an open-source runtime that executes MATLAB-syntax code blazing on any GPU. It is licensed under the Apache 2.0 license.
- RunMat automatically optimizes your math for GPU execution on Apple, Nvidia, and AMD hardware. No code changes needed. Simulations that took hours now take minutes.
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