AVX512F exp implementation based on PERM2
PiperOrigin-RevId: 277100643
diff --git a/BUILD.bazel b/BUILD.bazel
index 57d4a01..7353044 100644
--- a/BUILD.bazel
+++ b/BUILD.bazel
@@ -430,6 +430,7 @@
"src/math/exp-avx512f-p5-scalef.c",
"src/math/exp-avx512f-p5.c",
"src/math/exp-avx512f-perm-p3.c",
+ "src/math/exp-avx512f-perm2-p2.c",
"src/math/extexp-avx512f-p5.c",
]
diff --git a/CMakeLists.txt b/CMakeLists.txt
index c845750..7c5b58f 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -504,7 +504,8 @@
src/f32-vscaleextexp/avx512f-p5-scalef-unroll128.c
src/math/exp-avx512f-p5-scalef.c
src/math/exp-avx512f-p5.c
- src/math/exp-avx512f-perm-p3.c)
+ src/math/exp-avx512f-perm-p3.c
+ src/math/exp-avx512f-perm2-p2.c)
SET(XNNPACK_AARCH32_ASM_MICROKERNEL_SRCS
src/q8-dwconv/up8x9-aarch32-neon.S)
diff --git a/eval/f32-exp.cc b/eval/f32-exp.cc
index 239df59..5815b0c 100644
--- a/eval/f32-exp.cc
+++ b/eval/f32-exp.cc
@@ -71,6 +71,9 @@
}
#if XNN_ARCH_X86 || XNN_ARCH_X86_64
+ static void f32_exp__avx512f_perm2_p2(benchmark::State& state) {
+ ExpError(state, xnn_math_f32_exp__avx512f_perm2_p2, 16);
+ }
static void f32_exp__avx512f_perm_p3(benchmark::State& state) {
ExpError(state, xnn_math_f32_exp__avx512f_perm_p3, 16);
}
@@ -90,6 +93,7 @@
ExpError(state, xnn_math_f32_exp__avx2_p5, 8);
}
+ BENCHMARK(f32_exp__avx512f_perm2_p2)->Unit(benchmark::kMillisecond)->Iterations(1);
BENCHMARK(f32_exp__avx512f_perm_p3)->Unit(benchmark::kMillisecond)->Iterations(1);
BENCHMARK(f32_exp__avx512f_p5)->Unit(benchmark::kMillisecond)->Iterations(1);
BENCHMARK(f32_exp__avx512f_p5_scalef)->Unit(benchmark::kMillisecond)->Iterations(1);
diff --git a/src/math/exp-avx512f-perm2-p2.c b/src/math/exp-avx512f-perm2-p2.c
new file mode 100644
index 0000000..c7e99b8
--- /dev/null
+++ b/src/math/exp-avx512f-perm2-p2.c
@@ -0,0 +1,106 @@
+// Copyright 2019 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 <immintrin.h>
+
+#include <xnnpack/math-stubs.h>
+
+
+void xnn_math_f32_exp__avx512f_perm2_p2(
+ size_t n,
+ const float* input,
+ float* output)
+{
+ assert(n % (16 * sizeof(float)) == 0);
+
+ const __m512 vmagic_bias = _mm512_set1_ps(0x1.800000p23f);
+ // The smallest x for which expf(x) is non-zero.
+ const __m512 vzero_cutoff = _mm512_set1_ps(-0x1.9FE368p6f);
+ // The largest x for which expf(x) is finite.
+ const __m512 vinf_cutoff = _mm512_set1_ps(0x1.62E42Ep6f);
+ const __m512 vlog2e_x32 = _mm512_set1_ps(0x1.715476p5f);
+ const __m512 vminus_ln2_o32_hi = _mm512_set1_ps(-0x1.62e43p-6f);
+ const __m512 vminus_ln2_o32_lo = _mm512_set1_ps(0x1.05c61p-34f);
+ const __m512 vplus_inf = _mm512_set1_ps(INFINITY);
+
+ const __m512 vc1 = _mm512_set1_ps(0x1.0000F6p-0f);
+ const __m512 vc2 = _mm512_set1_ps(0x1.000000p-1f);
+ const __m512 vtable_hi = _mm512_set_ps(
+ 0x1.F50766p+0f, 0x1.EA4AFAp+0f, 0x1.DFC974p+0f, 0x1.D5818Ep+0f,
+ 0x1.CB720Ep+0f, 0x1.C199BEp+0f, 0x1.B7F770p+0f, 0x1.AE89FAp+0f,
+ 0x1.A5503Cp+0f, 0x1.9C4918p+0f, 0x1.93737Cp+0f, 0x1.8ACE54p+0f,
+ 0x1.82589Ap+0f, 0x1.7A1148p+0f, 0x1.71F75Ep+0f, 0x1.6A09E6p+0f);
+ const __m512 vtable_lo = _mm512_set_ps(
+ 0x1.6247ECp+0f, 0x1.5AB07Ep+0f, 0x1.5342B6p+0f, 0x1.4BFDAEp+0f,
+ 0x1.44E086p+0f, 0x1.3DEA64p+0f, 0x1.371A74p+0f, 0x1.306FE0p+0f,
+ 0x1.29E9E0p+0f, 0x1.2387A6p+0f, 0x1.1D4874p+0f, 0x1.172B84p+0f,
+ 0x1.11301Ep+0f, 0x1.0B5586p+0f, 0x1.059B0Ep+0f, 0x1.000000p+0f);
+
+ const __m512i vmin_exponent = _mm512_set1_epi32(0xC1000000);
+ const __m512i vmax_exponent = _mm512_set1_epi32(0x3F800000);
+ const __m512i vdefault_exponent = vmax_exponent;
+ const __m512i vmantissa_mask = _mm512_set1_epi32(0x007FFFE0);
+
+ for (; n != 0; n -= 16 * sizeof(float)) {
+ const __m512 vx = _mm512_loadu_ps(input);
+
+ // Compute reduced argument n := round(x * 32 / log(2)).
+ // We do it by adding a large number (magic bias), which cause rounding of result to an integer, then subtracing the
+ // large number back. The first addition is combined with multiplication by log2e into a single FMA instruction.
+ // 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.
+ __m512 vn = _mm512_fmadd_ps(vx, vlog2e_x32, 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).
+ __m512i veo = _mm512_slli_epi32(_mm512_and_si512(_mm512_castps_si512(vn), vmantissa_mask), 18);
+ __m512i ven = _mm512_max_epi32(veo, vmin_exponent);
+ ven = _mm512_min_epi32(ven, vmax_exponent);
+ veo = _mm512_sub_epi32(veo, ven);
+ const __m512 vsn = _mm512_castsi512_ps(_mm512_add_epi32(ven, vdefault_exponent));
+ const __m512 vso = _mm512_castsi512_ps(_mm512_add_epi32(veo, vdefault_exponent));
+
+ // Use the low 5 bits of n (as integer) for table lookup.
+ const __m512 vl = _mm512_permutex2var_ps(vtable_lo, _mm512_castps_si512(vn), vtable_hi);
+
+ // Subtract the large number back to get final n := round(x * 32 / log(2)).
+ vn = _mm512_sub_ps(vn, vmagic_bias);
+
+ // Compute reduced argument t := x - n * log(2) / 32.
+ // Use Cody-Waite range reduction method (note two constants to represent log(2) / 32) to improve accuracy.
+ __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_o32_hi, vx);
+ vt = _mm512_fmadd_ps(vn, vminus_ln2_o32_lo, vt);
+
+ // Compute degree-2 polynomial approxiatmion for exp(t) on [-log(2)/64, log(2)/64].
+ __m512 vp = _mm512_fmadd_ps(vt, vc2, vc1);
+
+ // Reconstruct the final f value:
+ // f = so * sn * l * (1 + t * (c1 + t * c2))
+ // = so * sn * (l + l * t * (c1 + t * c2))
+ // = so * sn * (l + (l * t) * p)
+ vt = _mm512_mul_ps(vt, vl);
+ __m512 vf = _mm512_fmadd_ps(vt, vp, vl);
+
+ // 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 = _mm512_maskz_mul_ps(_mm512_cmp_ps_mask(vx, vzero_cutoff, _CMP_NLT_US), vf, vsn);
+ // For inputs above inf cutoff, replace output with +inf.
+ // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
+ vf = _mm512_mask_mul_ps(vplus_inf, _mm512_cmp_ps_mask(vx, vinf_cutoff, _CMP_NGT_US), vso, vf);
+ _mm512_storeu_ps(output, vf);
+
+ input += 16;
+ output += 16;
+ }
+}
diff --git a/src/math/exp.sollya b/src/math/exp.sollya
index 0f8fe11..8b9af58 100644
--- a/src/math/exp.sollya
+++ b/src/math/exp.sollya
@@ -80,6 +80,14 @@
print("Degree-3 P[exp(x)] with 1+x constraint on [-log(2)/32, log(2)/32] =", horner(P));
print("relative error =", round(dirtyinfnorm(P / exp(x) - 1, [lb; ub]), single, RU));
+lb = round(-log(2)/64, single, RN);
+ub = round(log(2)/64, single, RN);
+print("-log(2)/64 =", lb);
+print("+log(2)/64 =", ub);
+P = fpminimax(exp(x), [|1,2|], [|SG...|], [lb; ub], relative, 1);
+print("Degree-2 P[exp(x)] with 1+x constraint on [-log(2)/64, log(2)/64] =", horner(P));
+print("relative error =", round(dirtyinfnorm(P / exp(x) - 1, [lb; ub]), single, RU));
+
lb = round(-log(2)/128, single, RN);
ub = round(log(2)/128, single, RN);
print("-log(2)/128 =", lb);
diff --git a/src/xnnpack/math-stubs.h b/src/xnnpack/math-stubs.h
index 19f9b17..ec755dc 100644
--- a/src/xnnpack/math-stubs.h
+++ b/src/xnnpack/math-stubs.h
@@ -42,6 +42,7 @@
DECLARE_F32_UNARY_MATH_FUNCTION(xnn_math_f32_exp__avx512f_p5)
DECLARE_F32_UNARY_MATH_FUNCTION(xnn_math_f32_exp__avx512f_p5_scalef)
DECLARE_F32_UNARY_MATH_FUNCTION(xnn_math_f32_exp__avx512f_perm_p3)
+DECLARE_F32_UNARY_MATH_FUNCTION(xnn_math_f32_exp__avx512f_perm2_p2)
DECLARE_F32_UNARY_MATH_FUNCTION(xnn_math_f32_expminus__avx2_p5)