Scalar EXPM1MINUS evaluation stubs
PiperOrigin-RevId: 343906379
diff --git a/src/math/expm1minus-sse2-rr2-p6.c b/src/math/expm1minus-sse2-rr2-p6.c
index a3357c7..35787ef 100644
--- a/src/math/expm1minus-sse2-rr2-p6.c
+++ b/src/math/expm1minus-sse2-rr2-p6.c
@@ -20,18 +20,20 @@
// The largest x for which expm1f(x) is saturated at -1.0f.
const __m128 vsat_cutoff = _mm_set1_ps(-0x1.154246p+4f);
+ // Large number such that ulp(magic bias) == 1 and magic bias === 127 mod 2**22.
const __m128 vmagic_bias = _mm_set1_ps(0x1.8000FEp23f);
const __m128 vlog2e = _mm_set1_ps(0x1.715476p+0f);
// Last 7 bits are zeroes
const __m128 vminus_ln2_hi = _mm_set1_ps(-0x1.62E400p-1f);
const __m128 vminus_ln2_lo = _mm_set1_ps(-0x1.7F7D1Cp-20f);
-
+ // Coefficient of polynomial approximation
+ // exp(t) - 1 ~ t * (1 + t * (c2 + t * (c3 + t * (c4 + t * (c5 + t * c6)))))
+ // on [-log(2)/2, log(2)/2]
const __m128 vc6 = _mm_set1_ps(0x1.6b7338p-10f);
const __m128 vc5 = _mm_set1_ps(0x1.12278Ep-7f);
const __m128 vc4 = _mm_set1_ps(0x1.555716p-5f);
const __m128 vc3 = _mm_set1_ps(0x1.5554B0p-3f);
const __m128 vc2 = _mm_set1_ps(0x1.FFFFFEp-2f);
-
const __m128 vone = _mm_set1_ps(1.0f);
for (; n != 0; n -= 4 * sizeof(float)) {
@@ -75,14 +77,14 @@
vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2);
vp = _mm_mul_ps(vp, vt);
- // Reconstruct the final f value:
- // f = s * (1 + t * (1 + t * (c2 + t * (c3 + t * (c4 + t * (c5 + t * c6)))))) - 1
- // = (s - 1) + s * (t + t * p)
- // = (s - 1) + ((t * s) + (t * s) * p)
+ // Reconstruct the exp(x) - 1 value:
+ // exp(x) - 1 = s * (1 + t * (1 + t * (c2 + t * (c3 + t * (c4 + t * (c5 + t * c6)))))) - 1
+ // = (s - 1) + s * (t + t * p)
+ // = ((t * s) + (t * s) * p) + (s - 1)
vt = _mm_mul_ps(vt, vs);
const __m128 vsm1 = _mm_sub_ps(vs, vone);
vp = _mm_add_ps(_mm_mul_ps(vp, vt), vt);
- __m128 vf = _mm_add_ps(vp, vsm1);
+ const __m128 vf = _mm_add_ps(vp, vsm1);
_mm_storeu_ps(output, vf);