Marat Dukhan | a438aca | 2020-11-20 15:45:01 -0800 | [diff] [blame] | 1 | // Copyright 2020 Google LLC |
| 2 | // |
| 3 | // This source code is licensed under the BSD-style license found in the |
| 4 | // LICENSE file in the root directory of this source tree. |
| 5 | |
| 6 | #include <assert.h> |
| 7 | #include <stddef.h> |
| 8 | |
| 9 | #include <emmintrin.h> |
| 10 | |
| 11 | #include <xnnpack/math-stubs.h> |
| 12 | |
| 13 | |
| 14 | void xnn_math_f32_expm1minus__sse2_rr2_p6( |
| 15 | size_t n, |
| 16 | const float* input, |
| 17 | float* output) |
| 18 | { |
| 19 | assert(n % (4 * sizeof(float)) == 0); |
| 20 | |
| 21 | // The largest x for which expm1f(x) is saturated at -1.0f. |
| 22 | const __m128 vsat_cutoff = _mm_set1_ps(-0x1.154246p+4f); |
Marat Dukhan | c60742b | 2020-11-23 12:33:27 -0800 | [diff] [blame] | 23 | // Large number such that ulp(magic bias) == 1 and magic bias === 127 mod 2**22. |
Marat Dukhan | a438aca | 2020-11-20 15:45:01 -0800 | [diff] [blame] | 24 | const __m128 vmagic_bias = _mm_set1_ps(0x1.8000FEp23f); |
| 25 | const __m128 vlog2e = _mm_set1_ps(0x1.715476p+0f); |
Marat Dukhan | de390d4 | 2020-11-29 19:32:18 -0800 | [diff] [blame^] | 26 | // Last 5 bits are zeroes |
| 27 | const __m128 vminus_ln2_hi = _mm_set1_ps(-0x1.62E440p-1f); |
| 28 | const __m128 vminus_ln2_lo = _mm_set1_ps(0x1.0105C6p-21f); |
Marat Dukhan | c60742b | 2020-11-23 12:33:27 -0800 | [diff] [blame] | 29 | // Coefficient of polynomial approximation |
| 30 | // exp(t) - 1 ~ t * (1 + t * (c2 + t * (c3 + t * (c4 + t * (c5 + t * c6))))) |
| 31 | // on [-log(2)/2, log(2)/2] |
Marat Dukhan | a438aca | 2020-11-20 15:45:01 -0800 | [diff] [blame] | 32 | const __m128 vc6 = _mm_set1_ps(0x1.6b7338p-10f); |
| 33 | const __m128 vc5 = _mm_set1_ps(0x1.12278Ep-7f); |
| 34 | const __m128 vc4 = _mm_set1_ps(0x1.555716p-5f); |
| 35 | const __m128 vc3 = _mm_set1_ps(0x1.5554B0p-3f); |
| 36 | const __m128 vc2 = _mm_set1_ps(0x1.FFFFFEp-2f); |
Marat Dukhan | a438aca | 2020-11-20 15:45:01 -0800 | [diff] [blame] | 37 | const __m128 vone = _mm_set1_ps(1.0f); |
| 38 | |
| 39 | for (; n != 0; n -= 4 * sizeof(float)) { |
| 40 | __m128 vx = _mm_loadu_ps(input); |
| 41 | |
| 42 | // The function saturates at -1 for large negative inputs: expm1f(x) == -1.0f for x <= sat_cutoff ~= -17.328680. |
| 43 | // To guarantee this behaviour, we clip input at sat_cutoff, and leverage the fact that for our implementation |
| 44 | // expm1f(sat_cutoff) == -1.0f. The order of operands in the [V]MAXPS instruction matters: it ensures that NaN |
| 45 | // inputs are passed unchanged. |
| 46 | vx = _mm_max_ps(vsat_cutoff, vx); |
| 47 | |
| 48 | // Compute reduced argument n := round(x / log(2)). |
| 49 | // We do it by adding a large number (magic bias), which cause rounding of the result to integer, then subtracing |
| 50 | // the large number back. The trick with adding large number is valid only within certain bounds |
| 51 | // (|x / log(2)| <= 2**22, i.e. |x| <= 0x1.62E43p+21 = 2907270.0), but that is acceptable, because inputs x are |
| 52 | // restricted to [-17.328680, 0]. |
| 53 | // Note that addition-subtraction of the large number doesn't cause overflow for inputs in this range. |
| 54 | __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias); |
| 55 | |
| 56 | // Create a floating-point number s (scale) such that s == 2**n for valid inputs, i.e. |
| 57 | // -17.328680 <= x <= 0.0, and -25 <= n <= 0 accordingly. |
| 58 | // For NaN inputs, s would have zero mantissa and can have arbitrary sign and exponent, depending on the input |
| 59 | // NaN payload. In these cases, n and t are NaNs with the same payload as input while s is non-NaN, and thus |
| 60 | // input payload would be propagated in all computations. |
| 61 | const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23)); |
| 62 | |
| 63 | // Subtract the large number back to get final n := round(x / log(2)). |
| 64 | vn = _mm_sub_ps(vn, vmagic_bias); |
| 65 | |
| 66 | // Compute reduced argument t := x - n * log(2). |
| 67 | // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. |
| 68 | __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx); |
| 69 | vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt); |
| 70 | |
| 71 | // Compute degree-6 polynomial approximation for exp(t) - 1 on [-log(2)/2, log(2)/2]. |
| 72 | // P(t) = t * (1 + t * (c2 + t * (c3 + t * (c4 + t * (c5 + t * c6))))) |
| 73 | // = t + t * (t * (c2 + t * (c3 + t * (c4 + t * (c5 + t * c6))))) = t + t * p |
| 74 | __m128 vp = _mm_add_ps(_mm_mul_ps(vc6, vt), vc5); |
| 75 | vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc4); |
| 76 | vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3); |
| 77 | vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2); |
| 78 | vp = _mm_mul_ps(vp, vt); |
| 79 | |
Marat Dukhan | c60742b | 2020-11-23 12:33:27 -0800 | [diff] [blame] | 80 | // Reconstruct the exp(x) - 1 value: |
| 81 | // exp(x) - 1 = s * (1 + t * (1 + t * (c2 + t * (c3 + t * (c4 + t * (c5 + t * c6)))))) - 1 |
| 82 | // = (s - 1) + s * (t + t * p) |
| 83 | // = ((t * s) + (t * s) * p) + (s - 1) |
Marat Dukhan | a438aca | 2020-11-20 15:45:01 -0800 | [diff] [blame] | 84 | vt = _mm_mul_ps(vt, vs); |
| 85 | const __m128 vsm1 = _mm_sub_ps(vs, vone); |
| 86 | vp = _mm_add_ps(_mm_mul_ps(vp, vt), vt); |
Marat Dukhan | c60742b | 2020-11-23 12:33:27 -0800 | [diff] [blame] | 87 | const __m128 vf = _mm_add_ps(vp, vsm1); |
Marat Dukhan | a438aca | 2020-11-20 15:45:01 -0800 | [diff] [blame] | 88 | |
| 89 | _mm_storeu_ps(output, vf); |
| 90 | |
| 91 | input += 4; |
| 92 | output += 4; |
| 93 | } |
| 94 | } |