| // Auto-generated file. Do not edit! |
| // Template: src/f32-raddstoreexpminusmax/scalar-p5.c.in |
| // Generator: tools/xngen |
| // |
| // 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 <xnnpack/common.h> |
| #include <xnnpack/raddstoreexpminusmax.h> |
| |
| #include <fp16/bitcasts.h> |
| |
| |
| void xnn_f32_raddstoreexpminusmax_ukernel__scalar_p5_x2( |
| size_t elements, |
| const float* input, |
| float* output, |
| float* sum, |
| float vi_max) |
| { |
| assert(elements % sizeof(float) == 0); |
| |
| const float vmagic_bias = 0x1.8000FEp23f; |
| // The smallest x for which expf(x) is normalized. |
| const float vdenorm_cutoff = -0x1.5D589Ep6f; |
| const float vlog2e = 0x1.715476p+0f; |
| // Last 7 bits are zeroes |
| const float vminus_ln2_hi = -0x1.62E400p-1f; |
| const float vminus_ln2_lo = -0x1.7F7D1Cp-20f; |
| |
| const float vc1 = 0x1.FFFFF6p-1f; |
| const float vc2 = 0x1.FFFDC6p-2f; |
| const float vc3 = 0x1.555A80p-3f; |
| const float vc4 = 0x1.573A1Ap-5f; |
| const float vc5 = 0x1.0F9F9Cp-7f; |
| |
| float vacc0 = 0.0f; |
| for (; elements >= 2 * sizeof(float); elements -= 2 * sizeof(float)) { |
| // Load 2 inputs at a time. |
| const float vi0 = input[0]; |
| const float vi1 = input[1]; |
| input += 2; |
| |
| // Subtract maximum input x := i - i_max. This implies x <= 0. |
| const float vx0 = vi0 - vi_max; |
| const float vx1 = vi1 - vi_max; |
| |
| // Compute reduced argument n := round(x / log(2)). |
| // We do it by adding a large number (magic bias) to the product x * (1/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 [-87.336540, 0.0] underflow expf(x) |
| // anyway. We fixup the result for such inputs at the very end of the algorithm. |
| float vn0 = vx0 * vlog2e + vmagic_bias; |
| float vn1 = vx1 * vlog2e + vmagic_bias; |
| |
| // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e. |
| // -87.33642 <= x <= 0.0, and -126 <= n <= 0 accordingly. |
| const float vs0 = fp32_from_bits(fp32_to_bits(vn0) << 23); |
| const float vs1 = fp32_from_bits(fp32_to_bits(vn1) << 23); |
| |
| // Subtract the large number back to get final n := round(x / log(2)). |
| vn0 -= vmagic_bias; |
| vn1 -= 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. |
| float vt0 = vn0 * vminus_ln2_hi + vx0; |
| float vt1 = vn1 * vminus_ln2_hi + vx1; |
| |
| vt0 = vn0 * vminus_ln2_lo + vt0; |
| vt1 = vn1 * vminus_ln2_lo + vt1; |
| |
| // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2]. |
| float vp0 = vc5 * vt0 + vc4; |
| float vp1 = vc5 * vt1 + vc4; |
| |
| vp0 = vp0 * vt0 + vc3; |
| vp1 = vp1 * vt1 + vc3; |
| |
| vp0 = vp0 * vt0 + vc2; |
| vp1 = vp1 * vt1 + vc2; |
| |
| vp0 = vp0 * vt0 + vc1; |
| vp1 = vp1 * vt1 + vc1; |
| |
| // Reconstruct the final f value: |
| // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))) |
| // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) |
| // = s + (t * s) * p |
| vt0 *= vs0; |
| vt1 *= vs1; |
| |
| float vf0 = vt0 * vp0 + vs0; |
| float vf1 = vt1 * vp1 + vs1; |
| |
| // For inputs below denormal cutoff, replace output with +0.0f. |
| // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| if XNN_UNPREDICTABLE(vx0 < vdenorm_cutoff) { |
| vf0 = 0.0f; |
| } |
| if XNN_UNPREDICTABLE(vx1 < vdenorm_cutoff) { |
| vf1 = 0.0f; |
| } |
| |
| // Store 2 outputs at a time. |
| output[0] = vf0; |
| output[1] = vf1; |
| output += 2; |
| |
| // Accumulate computed exponents. |
| vacc0 += vf0; |
| vacc0 += vf1; |
| } |
| |
| float vacc = vacc0; |
| for (; elements >= sizeof(float); elements -= sizeof(float)) { |
| // Load 1 input at a time. |
| const float vi = *input++; |
| |
| // Subtract maximum input x := i - i_max. This implies x <= 0. |
| const float vx = vi - vi_max; |
| |
| // Compute reduced argument n := round(x / log(2)). |
| // We do it by adding a large number (magic bias) to the product x * (1/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 [-87.336540, 0.0] underflow expf(x) |
| // anyway. We fixup the result for such inputs at the very end of the algorithm. |
| float vn = vx * vlog2e + vmagic_bias; |
| |
| // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e. |
| // -87.33642 <= x <= 0.0, and -126 <= n <= 0 accordingly. |
| const float vs = fp32_from_bits(fp32_to_bits(vn) << 23); |
| |
| // Subtract the large number back to get final n := round(x / log(2)). |
| 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. |
| float vt = vn * vminus_ln2_hi + vx; |
| vt = vn * vminus_ln2_lo + vt; |
| |
| // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2]. |
| float vp = vc5 * vt + vc4; |
| vp = vp * vt + vc3; |
| vp = vp * vt + vc2; |
| vp = vp * vt + vc1; |
| |
| // Reconstruct the final f value: |
| // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))) |
| // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) |
| // = s + (t * s) * p |
| vt *= vs; |
| float vf = vt * vp + vs; |
| |
| // For inputs below denormal cutoff, replace output with +0.0f. |
| // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| if XNN_UNPREDICTABLE(vx < vdenorm_cutoff) { |
| vf = 0.0f; |
| } |
| |
| // Store 1 output at a time. |
| *output++ = vf; |
| |
| // Accumulate computed exponents. |
| vacc += vf; |
| } |
| *sum = vacc; |
| } |