Ndtri

Product Support Status

Operator function: computes the inverse standard normal cumulative distribution function (probit / inverse normal CDF). It computes the standard normal quantile element by element for the input probability tensor. The bottom layer uses the piecewise rational approximation algorithm of the Cephes math library.
Computation formula:

yi=ndtri(xi)=Φ−1(xi)=2⋅erf−1(2xi−1),xi∈(0,1)y_i = \mathrm{ndtri}(x_i) = \Phi^{-1}(x_i) = \sqrt{2} \cdot \mathrm{erf}^{-1}(2 x_i - 1), \quad x_i \in (0, 1)

Input $x_i$	Output $y_i$
`0`	`-inf`
`1`	`+inf`
Positive and negative FP32/BF16 subnormal values	`-inf`; the inputs are treated as zero during computation
$x_i < 0$ (excluding the subnormal values above) or $x_i > 1$	`NaN`
`NaN` / `+inf` / `-inf`	`NaN`

FP16 inputs are first promoted to FP32. FP16 subnormal values become normal FP32 values and are processed by the original numerical algorithm.

Parameter Name	Input/Output/Attribute	Description	Data Type	Data Format
x	Input	Probability tensor for the ndtri computation, which is x_i in the formula. The recommended value range is (0, 1).	FLOAT, FLOAT16, BFLOAT16	ND
y	Output	Computation result of the inverse standard normal CDF, which is y_i in the formula. The output has the same shape and data type as the input. A scalar input produces a scalar output, and an empty tensor produces an empty tensor of the same shape.	FLOAT, FLOAT16, BFLOAT16	ND

The input x has at most 8 dimensions.
At runtime, each dimension of input x must be a non-negative integer, and the total number of elements must not exceed the maximum value of INT64.

Invocation Method	Sample Code	Description
GE graph mode	test_geir_ndtri	Invokes the Ndtri operator by building a graph through the operator IR.