92 lines
4.1 KiB
C
92 lines
4.1 KiB
C
// Copyright 2020 Google LLC
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//
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// This source code is licensed under the BSD-style license found in the
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// LICENSE file in the root directory of this source tree.
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#include <assert.h>
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#include <stddef.h>
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#include <immintrin.h>
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#include <xnnpack/math-stubs.h>
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void xnn_math_f32_expm1minus__avx512f_rr1_p6(
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size_t n,
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const float* input,
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float* output)
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{
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assert(n % (16 * sizeof(float)) == 0);
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// The largest x for which expm1f(x) is saturated at -1.0f.
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const __m512 vsat_cutoff = _mm512_set1_ps(-0x1.154246p+4f);
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// Large number such that ulp(magic bias) == 1 and magic bias === 127 mod 2**22.
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const __m512 vmagic_bias = _mm512_set1_ps(0x1.8000FEp23f);
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const __m512 vlog2e = _mm512_set1_ps(0x1.715476p+0f);
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const __m512 vminus_ln2 = _mm512_set1_ps(-0x1.62E43p-1f);
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// Coefficient of polynomial approximation
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// exp(t) - 1 ~ t * (1 + t * (c2 + t * (c3 + t * (c4 + t * (c5 + t * c6)))))
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// on [-log(2)/2, log(2)/2]
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const __m512 vc6 = _mm512_set1_ps(0x1.6b7338p-10f);
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const __m512 vc5 = _mm512_set1_ps(0x1.12278Ep-7f);
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const __m512 vc4 = _mm512_set1_ps(0x1.555716p-5f);
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const __m512 vc3 = _mm512_set1_ps(0x1.5554B0p-3f);
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const __m512 vc2 = _mm512_set1_ps(0x1.FFFFFEp-2f);
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const __m512 vone = _mm512_set1_ps(1.0f);
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for (; n != 0; n -= 16 * sizeof(float)) {
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__m512 vx = _mm512_loadu_ps(input);
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// The function saturates at -1 for large negative inputs: expm1f(x) == -1.0f for x <= sat_cutoff ~= -17.328680.
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// To guarantee this behaviour, we clip input at sat_cutoff, and leverage the fact that for our implementation
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// expm1f(sat_cutoff) == -1.0f. The order of operands in the [V]MAXPS instruction matters: it ensures that NaN
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// inputs are passed unchanged.
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vx = _mm512_max_ps(vsat_cutoff, vx);
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// Compute reduced argument n := round(x / log(2)).
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// We do it by adding a large number (magic bias), which cause rounding of the result to integer, then subtracing
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// the large number back. The first addition is combined with multiplication by log2e into a single FMA
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// instruction. The trick with adding large number is valid only within certain bounds (|x / log(2)| <= 2**22,
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// i.e. |x| <= 0x1.62E43p+21 = 2907270.0), but that is acceptable, because inputs x are restricted to
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// [-17.328680, 0].
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// Note that addition-subtraction of the large number doesn't cause overflow for inputs in this range.
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__m512 vn = _mm512_fmadd_ps(vx, vlog2e, vmagic_bias);
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// Create a floating-point number s (scale) such that s == 2**n for valid inputs, i.e.
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// -17.328680 <= x <= 0.0, and -25 <= n <= 0 accordingly.
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// For NaN inputs, s would have zero mantissa and can have arbitrary sign and exponent, depending on the input
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// NaN payload. In these cases, n and t are NaNs with the same payload as input while s is non-NaN, and thus
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// input payload would be propagated in all computations.
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const __m512 vs = _mm512_castsi512_ps(_mm512_slli_epi32(_mm512_castps_si512(vn), 23));
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// Subtract the large number back to get final n := round(x / log(2)).
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vn = _mm512_sub_ps(vn, vmagic_bias);
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// Compute reduced argument t := x - n * log(2).
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__m512 vt = _mm512_fmadd_ps(vn, vminus_ln2, vx);
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// Compute degree-6 polynomial approximation for exp(t) - 1 on [-log(2)/2, log(2)/2].
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// P(t) = t * (1 + t * (c2 + t * (c3 + t * (c4 + t * (c5 + t * c6)))))
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// = t + t * (t * (c2 + t * (c3 + t * (c4 + t * (c5 + t * c6))))) = t + t * p
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__m512 vp = _mm512_fmadd_ps(vc6, vt, vc5);
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vp = _mm512_fmadd_ps(vp, vt, vc4);
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vp = _mm512_fmadd_ps(vp, vt, vc3);
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vp = _mm512_fmadd_ps(vp, vt, vc2);
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vp = _mm512_mul_ps(vp, vt);
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// Reconstruct the exp(x) - 1 value:
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// exp(x) - 1 = s * (1 + t * (1 + t * (c2 + t * (c3 + t * (c4 + t * (c5 + t * c6)))))) - 1
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// = (s - 1) + s * (t + t * p)
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// = ((t * s) + (t * s) * p) + (s - 1)
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vt = _mm512_mul_ps(vt, vs);
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const __m512 vsm1 = _mm512_sub_ps(vs, vone);
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vp = _mm512_fmadd_ps(vp, vt, vt);
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const __m512 vf = _mm512_add_ps(vp, vsm1);
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_mm512_storeu_ps(output, vf);
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input += 16;
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output += 16;
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}
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}
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