LUT-based SSE2 Exp evaluation stub
PiperOrigin-RevId: 332790971
diff --git a/src/math/exp-sse2-lut64-p2.c b/src/math/exp-sse2-lut64-p2.c
new file mode 100644
index 0000000..09e293c
--- /dev/null
+++ b/src/math/exp-sse2-lut64-p2.c
@@ -0,0 +1,121 @@
+// 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 <math.h>
+#include <stddef.h>
+
+#include <emmintrin.h>
+
+#include <xnnpack/common.h>
+#include <xnnpack/math-stubs.h>
+
+
+// Table of exp2(k / 64) values, k = 0..63
+extern XNN_INTERNAL const float xnn_table_exp2_k_over_64[64];
+
+void xnn_math_f32_exp__sse2_lut64_p2(
+ size_t n,
+ const float* input,
+ float* output)
+{
+ assert(n % (4 * sizeof(float)) == 0);
+
+ const __m128 vmagic_bias = _mm_set1_ps(0x1.800000p+23f);
+ // The smallest x for which expf(x) is non-zero.
+ const __m128 vzero_cutoff = _mm_set1_ps(-0x1.9FE368p+6f);
+ // The largest x for which expf(x) is finite.
+ const __m128 vinf_cutoff = _mm_set1_ps(0x1.62E42Ep+6f);
+ const __m128 vlog2e_x64 = _mm_set1_ps(0x1.715476p+6f);
+ // Last 13 bits are zeroes
+ const __m128 vminus_ln2_o64_hi = _mm_set1_ps(-0x1.630000p-7f);
+ const __m128 vminus_ln2_o64_lo = _mm_set1_ps(0x1.BD0106p-19f);
+ const __m128 vplus_inf = _mm_set1_ps(INFINITY);
+
+ const __m128 vc2 = _mm_set1_ps(0x1.FFFF0Ap-2f);
+
+ const __m128i vmin_exponent = _mm_set1_epi32(0xC1000000);
+ const __m128i vmax_exponent = _mm_set1_epi32(0x3F800000);
+ const __m128i vdefault_exponent = vmax_exponent;
+ const __m128i vindex_mask = _mm_set1_epi32(0x3F);
+
+ for (; n != 0; n -= 4 * sizeof(float)) {
+ const __m128 vx = _mm_loadu_ps(input);
+
+ // Compute reduced argument n := round(x * 64 / log(2)).
+ // We do it by adding a large number (magic bias) to the product x * (64/log(2)), which cause rounding of the
+ // result to an integer, then subtracing the large number back. The trick with adding large number is valid only
+ // within certain bounds (|x| <= 2**22), but thats ok, because inputs outside of [-103.97207, 88.72283] underflow
+ // or overflow expf(x) anyway. We fixup the result for such inputs at the very end of the algorithm.
+ __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e_x64), vmagic_bias);
+
+ // Create two floating-point numbers, sn (scale, normal) and so (scale, overflow) such that sn * so == 2**n
+ // for inputs which don't cause overflow, i.e. -103.97207 <= x <= 88.72283, and -150 <= n <= 128 accordingly.
+ // We need to use two numbers rather than one because a normalized single-precision exponent must be in [-127, 126]
+ // range, which is insufficient to cover [-150, 128] range of n.
+ // - When n is within [-127, 126], sn == 2**n and so == 1.0.
+ // - When n < -127, sn == 2**(-127) and so == 2**(n + 127).
+ // - When n > 126, sn == 2**126 and so == 2**(n - 126).
+ // While we explicitly compute sn, the so is fused into the value l fetched from a table by adjusting its exponential.
+ __m128i veo = _mm_slli_epi32(_mm_andnot_si128(vindex_mask, _mm_castps_si128(vn)), 17);
+ __m128i ven = _mm_max_epi16(veo, vmin_exponent);
+ ven = _mm_min_epi16(ven, vmax_exponent);
+ veo = _mm_sub_epi32(veo, ven);
+ const __m128 vsn = _mm_castsi128_ps(_mm_add_epi32(ven, vdefault_exponent));
+
+ // Use the low 6 bits of n (as integer) for table lookup.
+ const __m128i vidx = _mm_and_si128(_mm_castps_si128(vn), vindex_mask);
+#if XNN_ARCH_X86_64
+ const uint64_t vidx01 = (uint64_t) _mm_cvtsi128_si64(vidx);
+ const uint64_t vidx23 = (uint64_t) _mm_cvtsi128_si64(_mm_unpackhi_epi64(vidx, vidx));
+ const __m128i vl0 = _mm_cvtsi32_si128(*((const int*) &xnn_table_exp2_k_over_64[(uint32_t) vidx01]));
+ const __m128i vl2 = _mm_cvtsi32_si128(*((const int*) &xnn_table_exp2_k_over_64[(uint32_t) vidx23]));
+ const __m128i vl1 = _mm_cvtsi32_si128(*((const int*) &xnn_table_exp2_k_over_64[(uint32_t) (vidx01 >> 32)]));
+ const __m128i vl3 = _mm_cvtsi32_si128(*((const int*) &xnn_table_exp2_k_over_64[(uint32_t) (vidx23 >> 32)]));
+#else
+ const uint32_t vidx0 = (uint32_t) _mm_cvtsi128_si32(vidx);
+ const uint32_t vidx1 = (uint32_t) _mm_extract_epi16(vidx, 2);
+ const uint32_t vidx2 = (uint32_t) _mm_extract_epi16(vidx, 4);
+ const uint32_t vidx3 = (uint32_t) _mm_extract_epi16(vidx, 6);
+ const __m128i vl0 = _mm_cvtsi32_si128(*((const int*) &xnn_table_exp2_k_over_64[vidx0]));
+ const __m128i vl2 = _mm_cvtsi32_si128(*((const int*) &xnn_table_exp2_k_over_64[vidx2]));
+ const __m128i vl1 = _mm_cvtsi32_si128(*((const int*) &xnn_table_exp2_k_over_64[vidx1]));
+ const __m128i vl3 = _mm_cvtsi32_si128(*((const int*) &xnn_table_exp2_k_over_64[vidx3]));
+#endif
+ // Fuse so into the value l fetched from a table by adjusting its exponential.
+ const __m128 vl = _mm_castsi128_ps(_mm_add_epi32(_mm_unpacklo_epi64(_mm_unpacklo_epi32(vl0, vl1), _mm_unpacklo_epi32(vl2, vl3)), veo));
+
+ // Subtract the large number back to get final n := round(x * 64 / log(2)).
+ vn = _mm_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.
+ __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_o64_hi), vx);
+ vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_o64_lo), vt);
+
+ // Compute degree-2 polynomial approxiatmion for exp(t) on [-log(2)/128, log(2)/128].
+ __m128 vp = _mm_mul_ps(vt, vc2);
+ vp = _mm_add_ps(vt, _mm_mul_ps(vt, vp));
+
+ // Reconstruct the final f value:
+ // f = sn * (so * l) * (1 + t * (1 + t * c2))
+ // = sn * (so * l) * (1 + t + t * (t * c2))
+ // = sn * ((so * l) + (so * l) * (t + t * (t * c2)))
+ __m128 vf = _mm_add_ps(vl, _mm_mul_ps(vl, vp));
+ vf = _mm_mul_ps(vf, vsn);
+
+ // For inputs below zero cutoff, replace output with +0.0f.
+ // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
+ vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vzero_cutoff), vf);
+ // For inputs above inf cutoff, replace output with +inf.
+ // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
+ const __m128 vm = _mm_cmpgt_ps(vx, vinf_cutoff);
+ vf = _mm_or_ps(_mm_and_ps(vplus_inf, vm), _mm_andnot_ps(vm, vf));
+ _mm_storeu_ps(output, vf);
+
+ input += 4;
+ output += 4;
+ }
+}