Xiaobaibai
1 year ago
2 changed files with 591 additions and 0 deletions
@ -0,0 +1,356 @@
@@ -0,0 +1,356 @@
|
||||
/* 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> |
||||
|
||||
typedef float32x4_t v4sf; // vector of 4 float
|
||||
typedef uint32x4_t v4su; // vector of 4 uint32
|
||||
typedef int32x4_t v4si; // vector of 4 uint32
|
||||
|
||||
#define s4f_x(s4f) vgetq_lane_f32(s4f, 0) |
||||
#define s4f_y(s4f) vgetq_lane_f32(s4f, 1) |
||||
#define s4f_z(s4f) vgetq_lane_f32(s4f, 2) |
||||
#define s4f_w(s4f) vgetq_lane_f32(s4f, 3) |
||||
|
||||
#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 |
||||
*/ |
||||
inline v4sf log_ps(v4sf x) { |
||||
v4sf one = vdupq_n_f32(1); |
||||
|
||||
x = vmaxq_f32(x, vdupq_n_f32(0)); /* force flush to zero on denormal values */ |
||||
v4su invalid_mask = vcleq_f32(x, vdupq_n_f32(0)); |
||||
|
||||
v4si ux = vreinterpretq_s32_f32(x); |
||||
|
||||
v4si 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)); |
||||
v4sf 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; } |
||||
*/ |
||||
v4su mask = vcltq_f32(x, vdupq_n_f32(c_cephes_SQRTHF)); |
||||
v4sf 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); |
||||
|
||||
v4sf z = vmulq_f32(x,x); |
||||
|
||||
v4sf 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 */ |
||||
inline v4sf exp_ps(v4sf x) { |
||||
v4sf tmp, fx; |
||||
|
||||
v4sf 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 */ |
||||
v4su 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)); |
||||
v4sf 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 }; |
||||
v4sf y = vld1q_dup_f32(cephes_exp_p+0); |
||||
v4sf c1 = vld1q_dup_f32(cephes_exp_p+1); |
||||
v4sf c2 = vld1q_dup_f32(cephes_exp_p+2); |
||||
v4sf c3 = vld1q_dup_f32(cephes_exp_p+3); |
||||
v4sf c4 = vld1q_dup_f32(cephes_exp_p+4); |
||||
v4sf 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); |
||||
v4sf 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.. |
||||
*/ |
||||
inline void sincos_ps(v4sf x, v4sf *ysin, v4sf *ycos) { // any x
|
||||
v4sf y; |
||||
|
||||
v4su emm2; |
||||
|
||||
v4su 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_n_f32(x, 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. |
||||
*/ |
||||
v4su poly_mask = vtstq_u32(emm2, vdupq_n_u32(2)); |
||||
|
||||
/* The magic pass: "Extended precision modular arithmetic"
|
||||
x = ((x - y * DP1) - y * DP2) - y * DP3; */ |
||||
x = vfmaq_n_f32(x, y, c_minus_cephes_DP1); |
||||
x = vfmaq_n_f32(x, y, c_minus_cephes_DP2); |
||||
x = vfmaq_n_f32(x, y, c_minus_cephes_DP3); |
||||
|
||||
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 */ |
||||
v4sf z = vmulq_f32(x,x); |
||||
v4sf y1, y2; |
||||
|
||||
y1 = vfmaq_n_f32(vdupq_n_f32(c_coscof_p1), z, c_coscof_p0); |
||||
y2 = vfmaq_n_f32(vdupq_n_f32(c_sincof_p1), z, c_sincof_p0); |
||||
y1 = vfmaq_f32(vdupq_n_f32(c_coscof_p2), y1, z); |
||||
y2 = vfmaq_f32(vdupq_n_f32(c_sincof_p2), y2, z); |
||||
y1 = vmulq_f32(y1, z); |
||||
y2 = vmulq_f32(y2, z); |
||||
y1 = vmulq_f32(y1, z); |
||||
y1 = vfmsq_n_f32(y1, z, 0.5f); |
||||
y2 = vfmaq_f32(x, y2, x); |
||||
y1 = vaddq_f32(y1, vdupq_n_f32(1)); |
||||
|
||||
/* select the correct result from the two polynoms */ |
||||
v4sf ys = vbslq_f32(poly_mask, y1, y2); |
||||
v4sf 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)); |
||||
} |
||||
|
||||
inline v4sf sin_ps(v4sf x) { |
||||
v4sf ysin, ycos; |
||||
sincos_ps(x, &ysin, &ycos); |
||||
return ysin; |
||||
} |
||||
|
||||
inline v4sf cos_ps(v4sf x) { |
||||
v4sf ysin, ycos; |
||||
sincos_ps(x, &ysin, &ycos); |
||||
return ycos; |
||||
} |
||||
|
||||
static const float asinf_lut[7] = { |
||||
1.5707961728, |
||||
-0.2145852647, |
||||
0.0887556286, |
||||
-0.0488025043, |
||||
0.0268999482, |
||||
-0.0111462294, |
||||
0.0022959648 |
||||
}; |
||||
|
||||
inline void asincos_ps(float32x4_t x, float32x4_t* yasin, float32x4_t* yacos) |
||||
{ |
||||
float32x4_t one = vdupq_n_f32(1); |
||||
float32x4_t negone = vdupq_n_f32(-1); |
||||
float32x4_t lut[7]; |
||||
float32x4_t xv[5]; |
||||
float32x4_t sat = vdupq_n_f32(0.9999999f); |
||||
float32x4_t m_pi_2 = vdupq_n_f32(1.570796326); |
||||
for (int i = 0; i <= 6; i++) |
||||
lut[i] = vdupq_n_f32(asinf_lut[i]); |
||||
|
||||
uint32x4_t sign_mask_asin = vcltq_f32(x, vdupq_n_f32(0)); |
||||
x = vabsq_f32(x); |
||||
uint32x4_t saturate = vcgeq_f32(x, one); |
||||
x = vbslq_f32(saturate, sat, x); |
||||
float32x4_t y = vsubq_f32(one, x); |
||||
y = vsqrtq_f32(y); |
||||
|
||||
xv[0] = vmulq_f32(x, x); |
||||
for (int i = 1; i < 5; i++) |
||||
xv[i] = vmulq_f32(xv[i - 1], x); |
||||
|
||||
float32x4_t a0 = vaddq_f32(lut[0], vmulq_f32(lut[1], x)); |
||||
float32x4_t a1 = vaddq_f32(vmulq_f32(lut[2], xv[0]), vmulq_f32(lut[3], xv[1])); |
||||
float32x4_t a2 = vaddq_f32(vmulq_f32(lut[4], xv[2]), vmulq_f32(lut[5], xv[3])); |
||||
float32x4_t a3 = vmulq_f32(lut[6], xv[4]); |
||||
float32x4_t phx = vaddq_f32(vaddq_f32(a0, vaddq_f32(a1, a2)), a3); |
||||
|
||||
float32x4_t arcsinx = vmulq_f32(y, phx); |
||||
arcsinx = vsubq_f32(m_pi_2, arcsinx); |
||||
float32x4_t arcnsinx = vmulq_f32(negone, arcsinx); |
||||
arcsinx = vbslq_f32(sign_mask_asin, arcnsinx, arcsinx); |
||||
*yasin = arcsinx; |
||||
*yacos = vsubq_f32(m_pi_2, arcsinx); |
||||
} |
||||
|
||||
inline float32x4_t asin_ps(float32x4_t x) |
||||
{ |
||||
float32x4_t yasin, yacos; |
||||
asincos_ps(x, &yasin, &yacos); |
||||
return yasin; |
||||
} |
||||
|
||||
inline float32x4_t acos_ps(float32x4_t x) |
||||
{ |
||||
float32x4_t yasin, yacos; |
||||
asincos_ps(x, &yasin, &yacos); |
||||
return yacos; |
||||
} |
||||
Loading…
Reference in new issue