102 lines
4.4 KiB
C
102 lines
4.4 KiB
C
// 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 <wasm_simd128.h>
|
|
|
|
#include <xnnpack/common.h>
|
|
#include <xnnpack/math-stubs.h>
|
|
|
|
|
|
void xnn_math_f32_sigmoid__wasmsimd_rr2_p5_div(
|
|
size_t n,
|
|
const float* input,
|
|
float* output)
|
|
{
|
|
assert(n % (4 * sizeof(float)) == 0);
|
|
|
|
// Large number such that ulp(magic bias) == 1 and magic bias === 127 mod 2**22.
|
|
const v128_t vmagic_bias = wasm_f32x4_const_splat(0x1.8000FEp23f);
|
|
const v128_t vminus_log2e = wasm_f32x4_const_splat(-0x1.715476p+0f);
|
|
// Last 7 bits are zeroes
|
|
const v128_t vln2_hi = wasm_f32x4_const_splat(0x1.62E400p-1f);
|
|
const v128_t vln2_lo = wasm_f32x4_const_splat(0x1.7F7D1Cp-20f);
|
|
// Coefficient of polynomial approximation of
|
|
// exp(-t) ~ 1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) on [-log(2)/2, log(2)/2]
|
|
const v128_t vc5 = wasm_f32x4_const_splat(-0x1.0F9F9Cp-7f);
|
|
const v128_t vc4 = wasm_f32x4_const_splat( 0x1.573A1Ap-5f);
|
|
const v128_t vc3 = wasm_f32x4_const_splat(-0x1.555A80p-3f);
|
|
const v128_t vc2 = wasm_f32x4_const_splat( 0x1.FFFDC6p-2f);
|
|
const v128_t vc1 = wasm_f32x4_const_splat(-0x1.FFFFF6p-1f);
|
|
const v128_t vone = wasm_f32x4_const_splat(1.0f);
|
|
// The largest z for which sigmoidf(-z) is normalized.
|
|
// This number is also the largest z for which expf(-z) is normalized.
|
|
const v128_t vdenorm_cutoff = wasm_f32x4_const_splat(0x1.5D589Ep+6f);
|
|
|
|
for (; n != 0; n -= 4 * sizeof(float)) {
|
|
const v128_t vx = wasm_v128_load(input);
|
|
input += 4;
|
|
|
|
// General structure of the algorithm:
|
|
//
|
|
// / exp(x) / (1 + exp(x)) if x <= 0
|
|
// f[x] :=
|
|
// \ 1 - f[-x] if x >= 0
|
|
//
|
|
// First we compute f[-z] := exp(-z) / (1 + exp(-z)) where z = abs(x),
|
|
// then replace result with 1 - f[-z] if x >= 0.
|
|
const v128_t vz = wasm_f32x4_abs(vx);
|
|
|
|
// Compute reduced argument n := round(-z / 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
|
|
// (|-z / log(2)| <= 2**22, i.e. |z| <= 0x1.62E43p+21 = 2907270.0), but that is acceptable, because inputs x
|
|
// outside of [-87.336544, 17.328678] (i.e. z outsize [0, 87.336544]) underflow or saturate sigmoidf(x). We fixup
|
|
// the result for such inputs at the very end of the algorithm.
|
|
v128_t vn = wasm_f32x4_add(vmagic_bias, wasm_f32x4_mul(vz, vminus_log2e));
|
|
|
|
// Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
|
|
// -87.336544 <= -z <= 0.0, and -126 <= n <= 0 accordingly.
|
|
const v128_t vs = wasm_i32x4_shl(vn, 23);
|
|
|
|
// Subtract the large number back to get the final n := round(-z / log(2)) as a floating-point number.
|
|
vn = wasm_f32x4_sub(vn, vmagic_bias);
|
|
|
|
// Compute reduced argument t := z + n * log(2). Note that -t = -z - n * log(2).
|
|
// Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
|
|
v128_t vt = wasm_f32x4_add(vz, wasm_f32x4_mul(vn, vln2_hi));
|
|
vt = wasm_f32x4_add(vt, wasm_f32x4_mul(vn, vln2_lo));
|
|
|
|
// Compute degree-5 polynomial approximation for exp(-t) on [-log(2)/2, log(2)/2]:
|
|
// P(t) = 1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) = 1 + t * p
|
|
v128_t vp = wasm_f32x4_add(vc4, wasm_f32x4_mul(vt, vc5));
|
|
vp = wasm_f32x4_add(vc3, wasm_f32x4_mul(vt, vp));
|
|
vp = wasm_f32x4_add(vc2, wasm_f32x4_mul(vt, vp));
|
|
vp = wasm_f32x4_add(vc1, wasm_f32x4_mul(vt, vp));
|
|
|
|
// Reconstruct the exp(-z) value:
|
|
// e = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
|
|
// = s * (1 + t * p)
|
|
// = s + (t * s) * p
|
|
vt = wasm_f32x4_mul(vt, vs);
|
|
const v128_t ve = wasm_f32x4_add(vs, wasm_f32x4_mul(vt, vp));
|
|
|
|
// Reconstruct sigmoid(-z) = exp(-z) / (1.0 + exp(-z))
|
|
v128_t vf = wasm_f32x4_div(ve, wasm_f32x4_add(ve, vone));
|
|
|
|
// For inputs below denormal cutoff, replace output with +0.0f.
|
|
// Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
|
|
vf = wasm_v128_andnot(vf, wasm_f32x4_gt(vz, vdenorm_cutoff));
|
|
|
|
// Reconstruct sigmoid(x) = x < 0 ? sigmoid(-z) : 1.0 - sigmoid(-z)
|
|
vf = wasm_v128_bitselect(vf, wasm_f32x4_sub(vone, vf), wasm_i32x4_shr(vx, 31));
|
|
|
|
wasm_v128_store(output, vf);
|
|
output += 4;
|
|
}
|
|
}
|