[libc] Update COEFF.

Author: harrisonGPU

libc/src/math/generic/atanhf16.cpp

@@ -22,17 +22,11 @@
 
 namespace LIBC_NAMESPACE_DECL {
 
-static constexpr size_t N_EXCEPTS = 4;
+static constexpr size_t N_EXCEPTS = 1;
 static constexpr fputil::ExceptValues<float16, N_EXCEPTS> ATANHF16_EXCEPTS{{
     // (input, RZ output, RU offset, RD offset, RN offset)
     // x = 0x1.a5cp-4, atanhf16(x) = 0x1.a74p-4 (RZ)
     {0x2E97, 0x2E9D, 1, 0, 0},
-    // x = -0x1.a5cp-4, atanhf16(x) = -0x1.a74p-4 (RZ)
-    {0xAE97, 0xAE9D, 0, 1, 0},
-    // x = -0x1.99cp-4, atanhf16(x) = -0x1.9bp-4 (RZ)
-    {0xAE67, 0xAE6C, 0, 1, 1},
-    // x = -0x1.b8cp-3, atanhf16(x) = -0x1.bfcp-3 (RZ)
-    {0xB2E3, 0xB2FF, 0, 1, 0},
 }};
 
 LLVM_LIBC_FUNCTION(float16, atanhf16, (float16 x)) {
@@ -76,9 +70,9 @@ LLVM_LIBC_FUNCTION(float16, atanhf16, (float16 x)) {
     // The Taylor expansion of atanh(x) is:
     //    atanh(x) = x + x^3/3 + x^5/5 + x^7/7 + x^9/9 + x^11/11
     //             = x * [1 + x^2/3 + x^4/5 + x^6/7 + x^8/9 + x^10/11]
-    // When |x| < 2^-16, this can be approximated by:
+    // When |x| < 2^-6 (0x2400U), this can be approximated by:
     //    atanh(x) ≈ x + (1/3)*x^3
-    if (LIBC_UNLIKELY(x_abs < 0x0100U)) {
+    if (LIBC_UNLIKELY(x_abs < 0x2400U)) {
       float xf = x;
       return fputil::cast<float16>(xf + 0x1.555556p-2f * xf * xf * xf);
     }

libc/src/math/generic/explogxf.h

@@ -314,10 +314,13 @@ LIBC_INLINE static float log_eval_f(float x) {
   // dx = (mx - p1*2^(-7)) / (1 + p1*2^(-7)).
   float dx = (xbits.get_val() - 1.0f) * ONE_OVER_F_FLOAT[p1];
 
-  // Minimax polynomial of log(1 + dx) generated by Sollya with:
-  // > P = fpminimax(log(1 + x)/x, 6, [|D...|], [0, 2^-7]);
-  const float COEFFS[6] = {-0x1.fffffep-2f, 0x1.555556p-2f,  -0x1.fffefep-3f,
-                           0x1.99999ap-3f,  -0x1.554318p-3f, 0x1.1dc5c4p-3f};
+  // Minimax polynomial for log(1 + dx), generated using Sollya:
+  //   > P = fpminimax(log(1 + x)/x, 6, [|SG...|], [0, 2^-7]);
+  //   > Q = (P - 1) / x;
+  //   > for i from 0 to degree(Q) do print(coeff(Q, i));
+  static constexpr float COEFFS[6] = {-0x1p-1f,        0x1.555556p-2f,
+                                      -0x1.00022ep-2f, 0x1.9ea056p-3f,
+                                      -0x1.e50324p-2f, 0x1.c018fp3f};
 
   float dx2 = dx * dx;
 
@@ -330,7 +333,7 @@ LIBC_INLINE static float log_eval_f(float x) {
   // Generated by Sollya with the following commands:
   //   > display = hexadecimal;
   //   > round(log(2), SG, RN);
-  static constexpr float LOGF_2 = 0x1.62e43p-1f;
+  constexpr float LOGF_2 = 0x1.62e43p-1f;
 
   float result = fputil::multiply_add(ex, LOGF_2, LOG_F_FLOAT[p1] + p);
   return result;