Optimize the gelu f16 opt. (#2008)

* Optimize the gelu f16 opt.

* And add a test.

candle-core/src/op.rs

@@ -457,6 +457,13 @@ unary_op!(Recip, "recip", v, v.recip());
 unary_op!(Sqr, "sqr", v, v * v, vs_sqr, vd_sqr);
 unary_op!(Sqrt, "sqrt", v, v.sqrt(), vs_sqrt, vd_sqrt);
 
+// Hardcode the value for sqrt(2/pi)
+// https://github.com/huggingface/candle/issues/1982
+#[allow(clippy::excessive_precision)]
+const SQRT_TWO_OVER_PI_F32: f32 = 0.79788456080286535587989211986876373;
+#[allow(clippy::excessive_precision)]
+const SQRT_TWO_OVER_PI_F64: f64 = 0.79788456080286535587989211986876373;
+
 /// Tanh based approximation of the `gelu` operation
 /// GeluErf is the more precise one.
 /// <https://en.wikipedia.org/wiki/Activation_function#Comparison_of_activation_functions>
@@ -469,7 +476,7 @@ impl UnaryOpT for Gelu {
             * v
             * (bf16::ONE
                 + bf16::tanh(
-                    (bf16::from_f32_const(2.0) / bf16::PI).sqrt()
+                    bf16::from_f32_const(SQRT_TWO_OVER_PI_F32)
                         * v
                         * (bf16::ONE + bf16::from_f32_const(0.044715) * v * v),
                 ))
@@ -480,22 +487,18 @@ impl UnaryOpT for Gelu {
             * v
             * (f16::ONE
                 + f16::tanh(
-                    (f16::from_f32_const(2.0) / f16::PI).sqrt()
+                    f16::from_f32_const(SQRT_TWO_OVER_PI_F32)
                         * v
                         * (f16::ONE + f16::from_f32_const(0.044715) * v * v),
                 ))
     }
     #[inline(always)]
     fn f32(v: f32) -> f32 {
-        0.5 * v
+        0.5 * v * (1.0 + f32::tanh(SQRT_TWO_OVER_PI_F32 * v * (1.0 + 0.044715 * v * v)))
-            * (1.0
-                + f32::tanh((2.0f32 / std::f32::consts::PI).sqrt() * v * (1.0 + 0.044715 * v * v)))
     }
     #[inline(always)]
     fn f64(v: f64) -> f64 {
-        0.5 * v
+        0.5 * v * (1.0 + f64::tanh(SQRT_TWO_OVER_PI_F64 * v * (1.0 + 0.044715 * v * v)))
-            * (1.0
-                + f64::tanh((2.0f64 / std::f64::consts::PI).sqrt() * v * (1.0 + 0.044715 * v * v)))
     }
     #[inline(always)]
     fn u8(_: u8) -> u8 {

candle-core/tests/tensor_tests.rs

@@ -106,6 +106,14 @@ fn unary_op(device: &Device) -> Result<()> {
             [2.6911, -0.0647, -0.1091, 1.7353, 2.7933]
         ]
     );
+    let t_f16 = tensor.to_dtype(DType::F16)?.gelu()?.to_dtype(DType::F32)?;
+    assert_eq!(
+        test_utils::to_vec2_round(&t_f16, 2)?,
+        [
+            [-0.0, 0.84, 4.0, -0.05, 0.35],
+            [2.69, -0.07, -0.11, 1.73, 2.79]
+        ],
+    );
     assert_eq!(
         test_utils::to_vec2_round(&tensor.gelu_erf()?, 4)?,
         [