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# tfp.math.log_gamma_difference

Returns lgamma(y) - lgamma(x + y), accurately.

This is more accurate than subtracting lgammas directly because lgamma grows as `x log(x) - x + o(x)`, and thus subtracting the value of lgamma for two close, large arguments incurs catastrophic cancellation.

When `y >= 8`, the method is to partition lgamma into the Stirling approximation and the correction `log_gamma_correction`, symbolically cancel the former, and compute and subtract the latter.

`x` Floating-point Tensor. `x` should be non-negative, and elementwise no more than `y`.
`y` Floating-point Tensor. `y` should be positive.
`name` Optional Python `str` naming the operation.

`lgamma_diff` Floating-point Tensor, the difference lgamma(y) - lgamma(x+y), computed elementwise.

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