tf.math.erf returns NaN for very large finite float64 inputs instead of saturating to +/-1

Issue type

Bug

Have you reproduced the bug with TensorFlow Nightly?

Yes

Source

source

TensorFlow version

tf 2.21.0

Custom code

Yes

OS platform and distribution

Linux Ubuntu 22.04

Mobile device

No response

Python version

Python 3.11

Bazel version

No response

GCC/compiler version

No response

CUDA/cuDNN version

N/A

GPU model and memory

N/A

Current behavior?

tf.math.erf returns NaN for very large finite float64 inputs.

For large positive inputs such as 1e200 and 1e300, erf(x) should saturate to 1.0. For large negative inputs such as -1e200 and -1e300, erf(x) should saturate to -1.0. However, TensorFlow returns NaN for all of these finite inputs.

The same inputs match the expected values in the high-precision mpmath reference, and peer libraries such as jax.scipy.special.erf, scipy.special.erf, torch.erf, and torch.special.erf compute the expected saturated values.

Expected behavior?

tf.math.erf should return values close to 1.0 for very large positive finite float64 inputs and values close to -1.0 for very large negative finite float64 inputs, instead of returning NaN.

Standalone code to reproduce the issue

import os
os.environ.setdefault("TF_CPP_MIN_LOG_LEVEL", "3")
os.environ["CUDA_VISIBLE_DEVICES"] = "-1"

import numpy as np
import tensorflow as tf

x = tf.constant([1e200, 1e300, -1e200, -1e300], dtype=tf.float64)
y = tf.math.erf(x).numpy()

truth = np.array([1.0, 1.0, -1.0, -1.0], dtype=np.float64)

print("input:", x.numpy())
print("tensorflow:", y)
print("truth:", truth)
print("isfinite tensorflow:", np.isfinite(y))
print("isfinite truth:", np.isfinite(truth))

if np.any(np.isnan(y)) and np.all(np.isfinite(truth)):
    print("BUG REPRODUCED: tf.math.erf returns NaN for very large finite float64 inputs")
else:
    print("not reproduced")

Relevant log output

input: [ 1.e+200  1.e+300 -1.e+200 -1.e+300]
tensorflow: [nan nan nan nan]
truth: [ 1.  1. -1. -1.]
isfinite tensorflow: [False False False False]
isfinite truth: [ True  True  True  True]
BUG REPRODUCED: tf.math.erf returns NaN for very large finite float64 inputs