EXPM1MINUS evaluation stubs
PiperOrigin-RevId: 344736247
diff --git a/src/math/expm1minus-avx-rr2-p6.c b/src/math/expm1minus-avx-rr2-p6.c
new file mode 100644
index 0000000..0956d2d
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+++ b/src/math/expm1minus-avx-rr2-p6.c
@@ -0,0 +1,96 @@
+// Copyright 2020 Google LLC
+//
+// This source code is licensed under the BSD-style license found in the
+// LICENSE file in the root directory of this source tree.
+
+#include <assert.h>
+#include <stddef.h>
+
+#include <immintrin.h>
+
+#include <xnnpack/math-stubs.h>
+
+
+void xnn_math_f32_expm1minus__avx_rr2_p6(
+ size_t n,
+ const float* input,
+ float* output)
+{
+ assert(n % (8 * sizeof(float)) == 0);
+
+ // The largest x for which expm1f(x) is saturated at -1.0f.
+ const __m256 vsat_cutoff = _mm256_set1_ps(-0x1.154246p+4f);
+ // Large number such that ulp(magic bias) == 1 and magic bias === 127 mod 2**22.
+ const __m256 vmagic_bias = _mm256_set1_ps(0x1.8000FEp23f);
+ const __m256 vlog2e = _mm256_set1_ps(0x1.715476p+0f);
+ // Last 5 bits are zeroes
+ const __m256 vminus_ln2_hi = _mm256_set1_ps(-0x1.62E440p-1f);
+ const __m256 vminus_ln2_lo = _mm256_set1_ps(0x1.0105C6p-21f);
+ // 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 __m256 vc6 = _mm256_set1_ps(0x1.6b7338p-10f);
+ const __m256 vc5 = _mm256_set1_ps(0x1.12278Ep-7f);
+ const __m256 vc4 = _mm256_set1_ps(0x1.555716p-5f);
+ const __m256 vc3 = _mm256_set1_ps(0x1.5554B0p-3f);
+ const __m256 vc2 = _mm256_set1_ps(0x1.FFFFFEp-2f);
+ const __m256 vone = _mm256_set1_ps(1.0f);
+
+ for (; n != 0; n -= 8 * sizeof(float)) {
+ __m256 vx = _mm256_loadu_ps(input);
+
+ // The function saturates at -1 for large negative inputs: expm1f(x) == -1.0f for x <= sat_cutoff ~= -17.328680.
+ // To guarantee this behaviour, we clip input at sat_cutoff, and leverage the fact that for our implementation
+ // expm1f(sat_cutoff) == -1.0f. The order of operands in the [V]MAXPS instruction matters: it ensures that NaN
+ // inputs are passed unchanged.
+ vx = _mm256_max_ps(vsat_cutoff, vx);
+
+ // Compute reduced argument n := round(x / log(2)).
+ // We do it by adding a large number (magic bias), which cause rounding of the result to integer, then subtracing
+ // the large number back. The trick with adding large number is valid only within certain bounds
+ // (|x / log(2)| <= 2**22, i.e. |x| <= 0x1.62E43p+21 = 2907270.0), but that is acceptable, because inputs x are
+ // restricted to [-17.328680, 0].
+ // Note that addition-subtraction of the large number doesn't cause overflow for inputs in this range.
+ __m256 vn = _mm256_add_ps(_mm256_mul_ps(vx, vlog2e), vmagic_bias);
+
+ // Create a floating-point number s (scale) such that s == 2**n for valid inputs, i.e.
+ // -17.328680 <= x <= 0.0, and -25 <= n <= 0 accordingly.
+ // For NaN inputs, s would have zero mantissa and can have arbitrary sign and exponent, depending on the input
+ // NaN payload. In these cases, n and t are NaNs with the same payload as input while s is non-NaN, and thus
+ // input payload would be propagated in all computations.
+ const __m128 vs_lo = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(_mm256_castps256_ps128(vn)), 23));
+ const __m128 vs_hi = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(_mm256_extractf128_ps(vn, 1)), 23));
+ const __m256 vs = _mm256_insertf128_ps(_mm256_castps128_ps256(vs_lo), vs_hi, 1);
+
+ // Subtract the large number back to get final n := round(x / log(2)).
+ vn = _mm256_sub_ps(vn, vmagic_bias);
+
+ // Compute reduced argument t := x - n * log(2).
+ // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
+ __m256 vt = _mm256_add_ps(_mm256_mul_ps(vn, vminus_ln2_hi), vx);
+ vt = _mm256_add_ps(_mm256_mul_ps(vn, vminus_ln2_lo), vt);
+
+ // Compute degree-6 polynomial approximation for exp(t) - 1 on [-log(2)/2, log(2)/2].
+ // P(t) = t * (1 + t * (c2 + t * (c3 + t * (c4 + t * (c5 + t * c6)))))
+ // = t + t * (t * (c2 + t * (c3 + t * (c4 + t * (c5 + t * c6))))) = t + t * p
+ __m256 vp = _mm256_add_ps(_mm256_mul_ps(vc6, vt), vc5);
+ vp = _mm256_add_ps(_mm256_mul_ps(vp, vt), vc4);
+ vp = _mm256_add_ps(_mm256_mul_ps(vp, vt), vc3);
+ vp = _mm256_add_ps(_mm256_mul_ps(vp, vt), vc2);
+ vp = _mm256_mul_ps(vp, vt);
+
+ // 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 = _mm256_mul_ps(vt, vs);
+ const __m256 vsm1 = _mm256_sub_ps(vs, vone);
+ vp = _mm256_add_ps(_mm256_mul_ps(vp, vt), vt);
+ const __m256 vf = _mm256_add_ps(vp, vsm1);
+
+ _mm256_storeu_ps(output, vf);
+
+ input += 8;
+ output += 8;
+ }
+}