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-rw-r--r--compute/ncnn/src/layer/arm/neon_mathfun.h315
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diff --git a/compute/ncnn/src/layer/arm/neon_mathfun.h b/compute/ncnn/src/layer/arm/neon_mathfun.h
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-/* NEON implementation of sin, cos, exp and log
- *
- * Inspired by Intel Approximate Math library, and based on the
- * corresponding algorithms of the cephes math library
- */
-
-/* Copyright (C) 2011 Julien Pommier
- *
- * This software is provided 'as-is', without any express or implied
- * warranty. In no event will the authors be held liable for any damages
- * arising from the use of this software.
- *
- * Permission is granted to anyone to use this software for any purpose,
- * including commercial applications, and to alter it and redistribute it
- * freely, subject to the following restrictions:
- *
- * 1. The origin of this software must not be misrepresented; you must not
- * claim that you wrote the original software. If you use this software
- * in a product, an acknowledgment in the product documentation would be
- * appreciated but is not required.
- * 2. Altered source versions must be plainly marked as such, and must not be
- * misrepresented as being the original software.
- * 3. This notice may not be removed or altered from any source distribution.
- *
- * (this is the zlib license)
- */
-
-#include <arm_neon.h>
-
-#define c_inv_mant_mask ~0x7f800000u
-#define c_cephes_SQRTHF 0.707106781186547524
-#define c_cephes_log_p0 7.0376836292E-2
-#define c_cephes_log_p1 -1.1514610310E-1
-#define c_cephes_log_p2 1.1676998740E-1
-#define c_cephes_log_p3 -1.2420140846E-1
-#define c_cephes_log_p4 +1.4249322787E-1
-#define c_cephes_log_p5 -1.6668057665E-1
-#define c_cephes_log_p6 +2.0000714765E-1
-#define c_cephes_log_p7 -2.4999993993E-1
-#define c_cephes_log_p8 +3.3333331174E-1
-#define c_cephes_log_q1 -2.12194440e-4
-#define c_cephes_log_q2 0.693359375
-
-/* natural logarithm computed for 4 simultaneous float
- * return NaN for x <= 0
- */
-static inline float32x4_t log_ps(float32x4_t x)
-{
- float32x4_t one = vdupq_n_f32(1);
-
- x = vmaxq_f32(x, vdupq_n_f32(0)); /* force flush to zero on denormal values */
- uint32x4_t invalid_mask = vcleq_f32(x, vdupq_n_f32(0));
-
- int32x4_t ux = vreinterpretq_s32_f32(x);
-
- int32x4_t emm0 = vshrq_n_s32(ux, 23);
-
- /* keep only the fractional part */
- ux = vandq_s32(ux, vdupq_n_s32(c_inv_mant_mask));
- ux = vorrq_s32(ux, vreinterpretq_s32_f32(vdupq_n_f32(0.5f)));
- x = vreinterpretq_f32_s32(ux);
-
- emm0 = vsubq_s32(emm0, vdupq_n_s32(0x7f));
- float32x4_t e = vcvtq_f32_s32(emm0);
-
- e = vaddq_f32(e, one);
-
- /* part2:
- * if( x < SQRTHF ) {
- * e -= 1;
- * x = x + x - 1.0;
- * } else { x = x - 1.0; }
- */
- uint32x4_t mask = vcltq_f32(x, vdupq_n_f32(c_cephes_SQRTHF));
- float32x4_t tmp = vreinterpretq_f32_u32(vandq_u32(vreinterpretq_u32_f32(x), mask));
- x = vsubq_f32(x, one);
- e = vsubq_f32(e, vreinterpretq_f32_u32(vandq_u32(vreinterpretq_u32_f32(one), mask)));
- x = vaddq_f32(x, tmp);
-
- float32x4_t z = vmulq_f32(x, x);
-
- float32x4_t y = vdupq_n_f32(c_cephes_log_p0);
- y = vmulq_f32(y, x);
- y = vaddq_f32(y, vdupq_n_f32(c_cephes_log_p1));
- y = vmulq_f32(y, x);
- y = vaddq_f32(y, vdupq_n_f32(c_cephes_log_p2));
- y = vmulq_f32(y, x);
- y = vaddq_f32(y, vdupq_n_f32(c_cephes_log_p3));
- y = vmulq_f32(y, x);
- y = vaddq_f32(y, vdupq_n_f32(c_cephes_log_p4));
- y = vmulq_f32(y, x);
- y = vaddq_f32(y, vdupq_n_f32(c_cephes_log_p5));
- y = vmulq_f32(y, x);
- y = vaddq_f32(y, vdupq_n_f32(c_cephes_log_p6));
- y = vmulq_f32(y, x);
- y = vaddq_f32(y, vdupq_n_f32(c_cephes_log_p7));
- y = vmulq_f32(y, x);
- y = vaddq_f32(y, vdupq_n_f32(c_cephes_log_p8));
- y = vmulq_f32(y, x);
-
- y = vmulq_f32(y, z);
-
- tmp = vmulq_f32(e, vdupq_n_f32(c_cephes_log_q1));
- y = vaddq_f32(y, tmp);
-
- tmp = vmulq_f32(z, vdupq_n_f32(0.5f));
- y = vsubq_f32(y, tmp);
-
- tmp = vmulq_f32(e, vdupq_n_f32(c_cephes_log_q2));
- x = vaddq_f32(x, y);
- x = vaddq_f32(x, tmp);
- x = vreinterpretq_f32_u32(
- vorrq_u32(vreinterpretq_u32_f32(x), invalid_mask)); // negative arg will be NAN
- return x;
-}
-
-#define c_exp_hi 88.3762626647949f
-#define c_exp_lo -88.3762626647949f
-
-#define c_cephes_LOG2EF 1.44269504088896341
-#define c_cephes_exp_C1 0.693359375
-#define c_cephes_exp_C2 -2.12194440e-4
-
-#define c_cephes_exp_p0 1.9875691500E-4
-#define c_cephes_exp_p1 1.3981999507E-3
-#define c_cephes_exp_p2 8.3334519073E-3
-#define c_cephes_exp_p3 4.1665795894E-2
-#define c_cephes_exp_p4 1.6666665459E-1
-#define c_cephes_exp_p5 5.0000001201E-1
-
-/* exp() computed for 4 float at once */
-static inline float32x4_t exp_ps(float32x4_t x)
-{
- float32x4_t tmp, fx;
-
- float32x4_t one = vdupq_n_f32(1);
- x = vminq_f32(x, vdupq_n_f32(c_exp_hi));
- x = vmaxq_f32(x, vdupq_n_f32(c_exp_lo));
-
- /* express exp(x) as exp(g + n*log(2)) */
- fx = vmlaq_f32(vdupq_n_f32(0.5f), x, vdupq_n_f32(c_cephes_LOG2EF));
-
- /* perform a floorf */
- tmp = vcvtq_f32_s32(vcvtq_s32_f32(fx));
-
- /* if greater, substract 1 */
- uint32x4_t mask = vcgtq_f32(tmp, fx);
- mask = vandq_u32(mask, vreinterpretq_u32_f32(one));
-
- fx = vsubq_f32(tmp, vreinterpretq_f32_u32(mask));
-
- tmp = vmulq_f32(fx, vdupq_n_f32(c_cephes_exp_C1));
- float32x4_t z = vmulq_f32(fx, vdupq_n_f32(c_cephes_exp_C2));
- x = vsubq_f32(x, tmp);
- x = vsubq_f32(x, z);
-
- static const float cephes_exp_p[6] = {c_cephes_exp_p0, c_cephes_exp_p1, c_cephes_exp_p2,
- c_cephes_exp_p3, c_cephes_exp_p4, c_cephes_exp_p5};
- float32x4_t y = vld1q_dup_f32(cephes_exp_p + 0);
- float32x4_t c1 = vld1q_dup_f32(cephes_exp_p + 1);
- float32x4_t c2 = vld1q_dup_f32(cephes_exp_p + 2);
- float32x4_t c3 = vld1q_dup_f32(cephes_exp_p + 3);
- float32x4_t c4 = vld1q_dup_f32(cephes_exp_p + 4);
- float32x4_t c5 = vld1q_dup_f32(cephes_exp_p + 5);
-
- y = vmulq_f32(y, x);
- z = vmulq_f32(x, x);
-
- y = vaddq_f32(y, c1);
- y = vmulq_f32(y, x);
- y = vaddq_f32(y, c2);
- y = vmulq_f32(y, x);
- y = vaddq_f32(y, c3);
- y = vmulq_f32(y, x);
- y = vaddq_f32(y, c4);
- y = vmulq_f32(y, x);
- y = vaddq_f32(y, c5);
-
- y = vmulq_f32(y, z);
- y = vaddq_f32(y, x);
- y = vaddq_f32(y, one);
-
- /* build 2^n */
- int32x4_t mm;
- mm = vcvtq_s32_f32(fx);
- mm = vaddq_s32(mm, vdupq_n_s32(0x7f));
- mm = vshlq_n_s32(mm, 23);
- float32x4_t pow2n = vreinterpretq_f32_s32(mm);
-
- y = vmulq_f32(y, pow2n);
- return y;
-}
-
-#define c_minus_cephes_DP1 -0.78515625
-#define c_minus_cephes_DP2 -2.4187564849853515625e-4
-#define c_minus_cephes_DP3 -3.77489497744594108e-8
-#define c_sincof_p0 -1.9515295891E-4
-#define c_sincof_p1 8.3321608736E-3
-#define c_sincof_p2 -1.6666654611E-1
-#define c_coscof_p0 2.443315711809948E-005
-#define c_coscof_p1 -1.388731625493765E-003
-#define c_coscof_p2 4.166664568298827E-002
-#define c_cephes_FOPI 1.27323954473516 // 4 / M_PI
-
-/* evaluation of 4 sines & cosines at once.
- *
- * The code is the exact rewriting of the cephes sinf function.
- * Precision is excellent as long as x < 8192 (I did not bother to
- * take into account the special handling they have for greater values
- * -- it does not return garbage for arguments over 8192, though, but
- * the extra precision is missing).
- *
- * Note that it is such that sinf((float)M_PI) = 8.74e-8, which is the
- * surprising but correct result.
- *
- * Note also that when you compute sin(x), cos(x) is available at
- * almost no extra price so both sin_ps and cos_ps make use of
- * sincos_ps..
- */
-static inline void sincos_ps(float32x4_t x, float32x4_t *ysin, float32x4_t *ycos)
-{
- // any x
- float32x4_t xmm1, xmm2, xmm3, y;
-
- uint32x4_t emm2;
-
- uint32x4_t sign_mask_sin, sign_mask_cos;
- sign_mask_sin = vcltq_f32(x, vdupq_n_f32(0));
- x = vabsq_f32(x);
-
- /* scale by 4/Pi */
- y = vmulq_f32(x, vdupq_n_f32(c_cephes_FOPI));
-
- /* store the integer part of y in mm0 */
- emm2 = vcvtq_u32_f32(y);
- /* j=(j+1) & (~1) (see the cephes sources) */
- emm2 = vaddq_u32(emm2, vdupq_n_u32(1));
- emm2 = vandq_u32(emm2, vdupq_n_u32(~1));
- y = vcvtq_f32_u32(emm2);
-
- /* get the polynom selection mask
- * there is one polynom for 0 <= x <= Pi/4
- * and another one for Pi/4<x<=Pi/2
- *
- * Both branches will be computed.
- */
- uint32x4_t poly_mask = vtstq_u32(emm2, vdupq_n_u32(2));
-
- /* The magic pass: "Extended precision modular arithmetic"
- * x = ((x - y * DP1) - y * DP2) - y * DP3; */
- xmm1 = vmulq_n_f32(y, c_minus_cephes_DP1);
- xmm2 = vmulq_n_f32(y, c_minus_cephes_DP2);
- xmm3 = vmulq_n_f32(y, c_minus_cephes_DP3);
- x = vaddq_f32(x, xmm1);
- x = vaddq_f32(x, xmm2);
- x = vaddq_f32(x, xmm3);
-
- sign_mask_sin = veorq_u32(sign_mask_sin, vtstq_u32(emm2, vdupq_n_u32(4)));
- sign_mask_cos = vtstq_u32(vsubq_u32(emm2, vdupq_n_u32(2)), vdupq_n_u32(4));
-
- /* Evaluate the first polynom (0 <= x <= Pi/4) in y1,
- * and the second polynom (Pi/4 <= x <= 0) in y2 */
- float32x4_t z = vmulq_f32(x, x);
- float32x4_t y1, y2;
-
- y1 = vmulq_n_f32(z, c_coscof_p0);
- y2 = vmulq_n_f32(z, c_sincof_p0);
- y1 = vaddq_f32(y1, vdupq_n_f32(c_coscof_p1));
- y2 = vaddq_f32(y2, vdupq_n_f32(c_sincof_p1));
- y1 = vmulq_f32(y1, z);
- y2 = vmulq_f32(y2, z);
- y1 = vaddq_f32(y1, vdupq_n_f32(c_coscof_p2));
- y2 = vaddq_f32(y2, vdupq_n_f32(c_sincof_p2));
- y1 = vmulq_f32(y1, z);
- y2 = vmulq_f32(y2, z);
- y1 = vmulq_f32(y1, z);
- y2 = vmulq_f32(y2, x);
- y1 = vsubq_f32(y1, vmulq_f32(z, vdupq_n_f32(0.5f)));
- y2 = vaddq_f32(y2, x);
- y1 = vaddq_f32(y1, vdupq_n_f32(1));
-
- /* select the correct result from the two polynoms */
- float32x4_t ys = vbslq_f32(poly_mask, y1, y2);
- float32x4_t yc = vbslq_f32(poly_mask, y2, y1);
- *ysin = vbslq_f32(sign_mask_sin, vnegq_f32(ys), ys);
- *ycos = vbslq_f32(sign_mask_cos, yc, vnegq_f32(yc));
-}
-
-static inline float32x4_t sin_ps(float32x4_t x)
-{
- float32x4_t ysin, ycos;
- sincos_ps(x, &ysin, &ycos);
- return ysin;
-}
-
-static inline float32x4_t cos_ps(float32x4_t x)
-{
- float32x4_t ysin, ycos;
- sincos_ps(x, &ysin, &ycos);
- return ycos;
-}
-
-static inline float32x4_t div_ps(float32x4_t a, float32x4_t b)
-{
- float32x4_t reciprocal = vrecpeq_f32(b);
- reciprocal = vmulq_f32(vrecpsq_f32(b, reciprocal), reciprocal);
- // reciprocal = vmulq_f32(vrecpsq_f32(b, reciprocal), reciprocal);
- return vmulq_f32(a, reciprocal);
-}
-
-static inline float32x4_t pow_ps(float32x4_t a, float32x4_t b)
-{
- // pow(x, m) = exp(m * log(x))
- return exp_ps(vmulq_f32(b, log_ps(a)));
-}
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