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simd_utils_helium_float.h
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1234 lines (1062 loc) · 42 KB
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#define SSE_LEN_FLOAT 4
#define SSE_LEN_BYTES 16
typedef float32x4_t v4sf;
typedef float32x4x2_t v4sfx2;
typedef int32x4_t v4si;
static inline void add128f(float *a, float* b, float* c, int len)
{
int stop_len = len / SSE_LEN_FLOAT;
stop_len *= SSE_LEN_FLOAT;
for (int i = 0; i < stop_len; i += SSE_LEN_FLOAT) {
v4sf a_vec = vld1q_f32(a + i);
v4sf b_vec = vld1q_f32(b + i);
vst1q_f32(c + i, vaddq_f32(a_vec, b_vec));
}
for (int i = stop_len; i < len; i++) {
c[i] = a[i] + b[i];
}
}
static inline void cplxtoreal128f(complex32_t *src, float *dstRe, float *dstIm, int len)
{
int stop_len = 2 * len / (4 * SSE_LEN_FLOAT);
stop_len *= 4 * SSE_LEN_FLOAT;
int j = 0;
for (int i = 0; i < stop_len; i += 4 * SSE_LEN_FLOAT) {
/*__builtin_prefetch(&src[i+SSE_LEN_FLOAT], 0, 3);
__builtin_prefetch(&dstRe[i+SSE_LEN_FLOAT], 1, 3);
__builtin_prefetch(&dstIm[i+SSE_LEN_FLOAT], 1, 3);*/
v4sfx2 vec1 = vld2q_f32((float const *) (src) + i);
v4sfx2 vec2 = vld2q_f32((float const *) (src) + i + 2 * SSE_LEN_FLOAT);
vst1q_f32(dstRe + j, vec1.val[0]);
vst1q_f32(dstIm + j, vec1.val[1]);
vst1q_f32(dstRe + j + SSE_LEN_FLOAT, vec2.val[0]);
vst1q_f32(dstIm + j + SSE_LEN_FLOAT, vec2.val[1]);
j += 2 * SSE_LEN_FLOAT;
}
for (int i = j; i < len; i++) {
dstRe[i] = src[i].re;
dstIm[i] = src[i].im;
}
}
static inline void realtocplx128f(float *srcRe, float *srcIm, complex32_t *dst, int len)
{
int stop_len = len / (2 * SSE_LEN_FLOAT);
stop_len *= 2 * SSE_LEN_FLOAT;
int j = 0;
for (int i = 0; i < stop_len; i += 2 * SSE_LEN_FLOAT) {
/*__builtin_prefetch(&srcRe[i+SSE_LEN_FLOAT], 0, 3);
__builtin_prefetch(&srcIm[i+SSE_LEN_FLOAT], 0, 3);
__builtin_prefetch(&dst[i+SSE_LEN_FLOAT], 1, 3);*/
v4sf re = vld1q_f32(srcRe + i);
v4sf im = vld1q_f32(srcIm + i);
v4sf re2 = vld1q_f32(srcRe + i + SSE_LEN_FLOAT);
v4sf im2 = vld1q_f32(srcIm + i + SSE_LEN_FLOAT);
v4sfx2 reim = {{re, im}};
v4sfx2 reim2 = {{re2, im2}};
vst2q_f32((float *) (dst) + j, reim);
vst2q_f32((float *) (dst) + j + 2 * SSE_LEN_FLOAT, reim2);
j += 4 * SSE_LEN_FLOAT;
}
for (int i = stop_len; i < len; i++) {
dst[i].re = srcRe[i];
dst[i].im = srcIm[i];
}
}
void powerspect128f_interleaved(complex32_t *src, float *dst, int len)
{
int stop_len = len / (2 * SSE_LEN_FLOAT);
stop_len *= 2 * SSE_LEN_FLOAT;
int j = 0;
for (int i = 0; i < stop_len; i += 2 * SSE_LEN_FLOAT) {
v4sfx2 src_split = vld2q_f32((float *) (src) + j); // a0a1a2a3, b0b1b2b3
v4sfx2 src_split2 = vld2q_f32((float *) (src) + j + 2 * SSE_LEN_FLOAT);
v4sf split_square0 = vmulq_f32(src_split.val[0], src_split.val[0]);
v4sf split2_square0 = vmulq_f32(src_split2.val[0], src_split2.val[0]);
v4sfx2 dst_split;
dst_split.val[0] = vfmaq_f32(split_square0, src_split.val[1], src_split.val[1]);
dst_split.val[1] = vfmaq_f32(split2_square0, src_split2.val[1], src_split2.val[1]);
vst1q_f32((dst + i), dst_split.val[0]);
vst1q_f32((dst + i + SSE_LEN_FLOAT), dst_split.val[1]);
j += 4 * SSE_LEN_FLOAT;
}
for (int i = stop_len; i < len; i++) {
dst[i] = src[i].re * src[i].re + (src[i].im * src[i].im);
}
}
static inline float32x4_t vrsqrtq_f32(float32x4_t a)
{
// Quake initial approximation via bit trick
uint32x4_t ai = vreinterpretq_u32_f32(a);
ai = vsubq_u32(vdupq_n_u32(0x5f3759dfu), vshrq_n_u32(ai, 1));
float32x4_t y = vreinterpretq_f32_u32(ai);
// Newton-Raphson refinements: y = y*(1.5 - 0.5*a*y*y)
float32x4_t x2 = vmulq_n_f32(a, 0.5f);
// 1st iteration
float32x4_t y2 = vmulq_f32(y, y);
y = vmulq_f32(y, vsubq_f32(*(v4sf *) _ps_1p5, vmulq_f32(x2, y2)));
// 2nd iteration -> almost full float precision
y2 = vmulq_f32(y, y);
y = vmulq_f32(y, vsubq_f32(*(v4sf *) _ps_1p5, vmulq_f32(x2, y2)));
// 3nd iteration -> ~full float precision
y2 = vmulq_f32(y, y);
y = vmulq_f32(y, vsubq_f32(*(v4sf *) _ps_1p5, vmulq_f32(x2, y2)));
return y; // ~1/sqrt(a)
}
// Vector sqrt using the inverse-sqrt result (no div; only +/*)
static inline float32x4_t vsqrtq_f32(float32x4_t a)
{
float32x4_t rinv = vrsqrtq_f32(a);
return vmulq_f32(a, rinv); // sqrt(a) = a * (1/sqrt(a))
}
// 1/y
static inline float32x4_t vrecipq_f32(float32x4_t a)
{
// --- Bit-hack initial approximation ---
uint32x4_t ai = vreinterpretq_u32_f32(a);
// magic constant chosen for reciprocal
ai = vsubq_u32(vdupq_n_u32(0x7EEEEEEE), ai);
float32x4_t r = vreinterpretq_f32_u32(ai);
// --- Newton–Raphson refinement: r = r * (2 - a*r) ---
// 1st iteration
float32x4_t ar = vmulq_f32(a, r);
r = vmulq_f32(r, vsubq_f32(*(v4sf *) _ps_2, ar));
// 2nd iteration -> almost full float32 precision (~23 bits)
ar = vmulq_f32(a, r);
r = vmulq_f32(r, vsubq_f32(*(v4sf *) _ps_2, ar));
// 3nd iteration -> full float32 precision
ar = vmulq_f32(a, r);
r = vmulq_f32(r, vsubq_f32(*(v4sf *) _ps_2, ar));
return r;
}
// -1/y
static inline float32x4_t vminrecipq_f32(float32x4_t a)
{
// --- Bit-hack initial approximation ---
uint32x4_t ai = vreinterpretq_u32_f32(a);
// magic constant chosen for reciprocal
ai = vsubq_u32(vdupq_n_u32(0x7EEEEEEE), ai);
float32x4_t r = vreinterpretq_f32_u32(ai);
// --- Newton–Raphson refinement: r = r * (2 - a*r) ---
// 1st iteration
float32x4_t ar = vmulq_f32(a, r);
r = vmulq_f32(r, vsubq_f32(*(v4sf *) _ps_2, ar));
// 2nd iteration -> almost full float32 precision (~23 bits)
ar = vmulq_f32(a, r);
r = vmulq_f32(r, vsubq_f32(*(v4sf *) _ps_2, ar));
// 3nd iteration -> full float32 precision
ar = vmulq_f32(a, r);
r = vmulq_f32(r, vsubq_f32(*(v4sf *) _ps_2, ar));
return vmulq_n_f32(r,-1.0f);
}
static inline float32x4_t vdivq_f32(float32x4_t a, float32x4_t b)
{
float32x4_t oneDivb = vrecipq_f32(b);
return vmulq_f32(a,oneDivb);
}
static inline void print4_4digits(v4sf v)
{
float *p = (float *) &v;
printf("[%3.4g, %3.4g, %3.4g, %3.4g]", p[0], p[1], p[2], p[3]);
}
static inline void print4i(v4si v)
{
int32_t *p = (int32_t *) &v;
printf("[%ld %ld, %ld, %ld]", p[0], p[1], p[2], p[3]);
}
static inline void print4u(v4su v)
{
uint32_t *p = (int32_t *) &v;
printf("[%lu %lu, %lu, %lu]", p[0], p[1], p[2], p[3]);
}
static inline v4sf log10_ps(v4sf x)
{
//printf("x ");print4_4digits(x);printf("\r\n");
v4si emm0;
mve_pred16_t invalid_mask = vcmpleq_f32(x, *(v4sf *) _ps_0);
x = vmaxnmq_f32(x, *(v4sf *) _ps_min_norm_pos); /* cut off denormalized stuff */
emm0 = vshrq_n_s32(vreinterpretq_s32_f32(x), 23);
// printf("emm0 ");print4i_4digits(emm0);printf("\r\n");
/* keep only the fractional part */
x = vandq_f32(x, *(v4sf *) _ps_inv_mant_mask);
x = vorrq_f32(x, *(v4sf *) _ps_0p5);
//printf("x2 ");print4_4digits(x);printf("\r\n");
emm0 = vsubq_n_s32(emm0, 0x7F);
v4sf e = vcvtq_f32_s32(emm0);
e = vaddq_n_f32(e, 1.0f);
//printf("e ");print4_4digits(e);printf("\r\n");
mve_pred16_t mask = vcmpltq_f32(x, *(v4sf *) _ps_cephes_SQRTHF);
x = vsubq_n_f32(x, 1.0f);
e = vsubq_m_n_f32(e, e, 1.0f, mask);
//printf("e2 ");print4_4digits(e);printf("\r\n");
x = vaddq_m_f32(x, x, x, mask);
//printf("x3 ");print4_4digits(x);printf("\r\n");
v4sf z = vmulq_f32(x, x);
// vfmasq_n_f32 : a*b + c (scalar)
v4sf y = vfmasq_n_f32(x, *(v4sf *) _ps_cephes_log_p0, c_cephes_log_p1);
//printf("y ");print4_4digits(y);printf("\r\n");
y = vfmasq_n_f32(y, x, c_cephes_log_p2);
//printf("y2 ");print4_4digits(y);printf("\r\n");
y = vfmasq_n_f32(y, x, c_cephes_log_p3);
y = vfmasq_n_f32(y, x, c_cephes_log_p4);
y = vfmasq_n_f32(y, x, c_cephes_log_p5);
y = vfmasq_n_f32(y, x, c_cephes_log_p6);
y = vfmasq_n_f32(y, x, c_cephes_log_p7);
y = vfmasq_n_f32(y, x, c_cephes_log_p8);
y = vmulq_f32(y, x);
y = vmulq_f32(y, z);
//printf("y3 ");print4_4digits(y);printf("\r\n");
// vfmaq_n_f32 a + b*c (scalar)
y = vfmaq_n_f32(y, z, -0.5f);
//printf("y4 ");print4_4digits(y);printf("\r\n");
// Could it be improved with more parallelism or would it worsen precision?
float32x4_t tmp = vaddq_f32(x, y);
z = vmulq_n_f32(tmp, c_cephes_L10EB);
//printf("z ");print4_4digits(z);printf("\r\n");
z = vfmaq_n_f32(z, y, c_cephes_L10EA);
//printf("z2 ");print4_4digits(z);printf("\r\n");
z = vfmaq_n_f32(z, x, c_cephes_L10EA);
//printf("z3 ");print4_4digits(z);printf("\r\n");
z = vfmaq_n_f32(z, e, c_cephes_L102B);
//printf("z4 ");print4_4digits(z);printf("\r\n");
x = vfmaq_n_f32(z, e, c_cephes_L102A);
//printf("x5 ");print4_4digits(x);printf("\r\n");
x = vorrq_m_f32(x, x, *(v4sf *) _pi32_0xFFFFFFFF, invalid_mask); // negative arg will be NAN
return x;
}
static inline void log10128f_precise(float *src, float *dst, int len)
{
int stop_len = len / SSE_LEN_FLOAT;
stop_len *= SSE_LEN_FLOAT;
for (int i = 0; i < stop_len; i += SSE_LEN_FLOAT) {
v4sf vec = vld1q_f32(src + i);
vec = log10_ps(vec);
vst1q_f32(dst + i, vec);
}
for (int i = stop_len; i < len; i++) {
dst[i] = log10f(src[i]);
}
}
static inline mve_pred16_t vtstq_u32_m(uint32x4_t a, uint32x4_t b) {
uint32x4_t p = vandq_u32(a, b);
//printf("a");print4u(a);printf("\n\r");
//printf("b");print4u(b);printf("\n\r");
//printf("p");print4u(p);printf("\n\r");
return vcmpneq_u32(p, *(v4su *) _pu32_0);
}
//useful to better match y = a*b + c instead of y = a + b*c
#define vfmasq_f32(b,c,add) vfmaq_f32(add,b,c)
static inline mve_pred16_t xor_pred(mve_pred16_t a, mve_pred16_t b) {
// Materialize predicate bits into uint16_t scalars
uint16_t pa = (uint16_t)a;
uint16_t pb = (uint16_t)b;
uint16_t pc = pa ^ pb;
//printf("%x %x %x\r\n",pa,pb,pc);
return (mve_pred16_t)(pc);
}
static inline mve_pred16_t and_pred(mve_pred16_t a, mve_pred16_t b) {
// Materialize predicate bits into uint16_t scalars
uint16_t pa = (uint16_t)a;
uint16_t pb = (uint16_t)b;
uint16_t pc = pa & pb;
//printf("%x %x %x\r\n",pa,pb,pc);
return (mve_pred16_t)(pc);
}
// FMA version
static inline void sincos_ps(v4sf x, v4sf *ysin, v4sf *ycos)
{ // any x
v4sf y;
v4su emm2;
mve_pred16_t sign_mask_sin, sign_mask_cos;
sign_mask_sin = vcmpltq_f32(x, *(v4sf *) _ps_0);
x = vabsq_f32(x);
//printf("x ");print4_4digits(x);printf("\r\n");
/* 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_n_u32(emm2, 1);
emm2 = vandq_u32(emm2, *(v4su *) _pu32_inv1);
y = vcvtq_f32_u32(emm2);
//printf("y ");print4_4digits(y);printf("\r\n");
/* 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.
*/
mve_pred16_t poly_mask = vtstq_u32_m(emm2, *(v4su *) _pu32_2);
//printf("poly_mask %x\r\n",(uint16_t)poly_mask);
/* 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);
mve_pred16_t sign_mask_sin2 = vcmpeqq_u32(emm2, *(v4su *) _pu32_4);
//printf("sign_mask_sin2 %x\r\n",(uint16_t)sign_mask_sin2);
//printf("sign_mask_sin %x\r\n",(uint16_t)sign_mask_sin);
sign_mask_sin = xor_pred(sign_mask_sin, sign_mask_sin2);
//printf("sign_mask_sin %x\r\n",(uint16_t)sign_mask_sin);
v4su emm2min2 = vsubq_n_u32(emm2, 2);
//printf("emm2 ");print4u(emm2);printf("\r\n");
//printf("emm2min2 ");print4u(emm2min2);printf("\r\n");
sign_mask_cos = vtstq_u32_m(emm2min2, *(v4su *) _pu32_4);
//printf("sign_mask_cos %x\r\n",(uint16_t)sign_mask_sin);
/* 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 = vfmasq_n_f32(y1, z, c_coscof_p2);
y2 = vfmasq_n_f32(y2, z, c_sincof_p2);
y1 = vmulq_f32(y1, z);
y2 = vmulq_f32(y2, z);
y1 = vmulq_f32(y1, z);
y2 = vfmaq_f32(x, y2, x);
y1 = vfmaq_n_f32(y1, z, -0.5f);
y1 = vaddq_n_f32(y1, 1);
/* select the correct result from the two polynoms */
//printf("y1 ");print4_4digits(y1);printf("\r\n");
//printf("y2 ");print4_4digits(y2);printf("\r\n");
v4sf ys = vpselq_f32(y1, y2,poly_mask);
v4sf yc = vpselq_f32(y2, y1, poly_mask);
//printf("ys ");print4_4digits(ys);printf("\r\n");
//printf("yc ");print4_4digits(yc);printf("\r\n");
*ysin = vpselq_f32(vnegq_f32(ys), ys, sign_mask_sin);
*ycos = vpselq_f32(yc, vnegq_f32(yc), sign_mask_cos);
//printf("sin ");print4_4digits(*ysin);printf("\r\n");
//printf("cos ");print4_4digits(*ycos);printf("\r\n");
}
static inline void sincos128f(float *src, float *dst_sin, float *dst_cos, int len)
{
int stop_len = len / SSE_LEN_FLOAT;
stop_len *= SSE_LEN_FLOAT;
for (int i = 0; i < stop_len; i += SSE_LEN_FLOAT) {
v4sf src_tmp = vld1q_f32(src + i);
v4sf dst_sin_tmp;
v4sf dst_cos_tmp;
sincos_ps(src_tmp, &dst_sin_tmp, &dst_cos_tmp);
vst1q_f32(dst_sin + i, dst_sin_tmp);
vst1q_f32(dst_cos + i, dst_cos_tmp);
}
for (int i = stop_len; i < len; i++) {
mysincosf(src[i], dst_sin + i, dst_cos + i);
}
}
static inline void sqrt128f(float *src, float *dst, int len)
{
int stop_len = len / SSE_LEN_FLOAT;
stop_len *= SSE_LEN_FLOAT;
for (int i = 0; i < stop_len; i += SSE_LEN_FLOAT) {
v4sf vec = vld1q_f32(src + i);
vec = vsqrtq_f32(vec);
vst1q_f32(dst + i, vec);
}
for (int i = stop_len; i < len; i++) {
dst[i] = sqrtf(src[i]);
}
}
static inline v4sf exp_ps(v4sf x)
{
v4sf fx;
x = vminnmq_f32(x, *(v4sf *) _ps_exp_hi);
x = vmaxnmq_f32(x, *(v4sf *) _ps_exp_lo);
/* express exp(x) as exp(g + n*log(2)) */
fx = vfmaq_n_f32(*(v4sf *) _ps_0p5, x, c_cephes_LOG2EF);
fx = vrndmq_f32(fx); /* perform a floorf */
x = vfmaq_n_f32(x, fx, c_cephes_exp_minC1);
x = vfmaq_n_f32(x, fx, c_cephes_exp_minC2);
v4sf z = vmulq_f32(x, x);
v4sf y = vfmaq_n_f32(*(v4sf *) _ps_cephes_exp_p1, x, c_cephes_exp_p0);
y = vfmasq_n_f32(y, x, c_cephes_exp_p2);
y = vfmasq_n_f32(y, x, c_cephes_exp_p3);
y = vfmasq_n_f32(y, x, c_cephes_exp_p4);
y = vfmasq_n_f32(y, x, c_cephes_exp_p5);
y = vfmaq_f32(x, y, z);
y = vaddq_n_f32(y, 1.0f);
/* build 2^n */
int32x4_t mm;
mm = vcvtq_s32_f32(fx);
mm = vaddq_n_s32(mm, 0x7F);
mm = vshlq_n_s32(mm, 23);
v4sf pow2n = vreinterpretq_f32_s32(mm);
y = vmulq_f32(y, pow2n);
return y;
}
static inline void exp128f(float *src, float *dst, int len)
{
int stop_len = len / SSE_LEN_FLOAT;
stop_len *= SSE_LEN_FLOAT;
for (int i = 0; i < stop_len; i += SSE_LEN_FLOAT) {
vst1q_f32(dst + i, exp_ps(vld1q_f32(src + i)));
}
for (int i = stop_len; i < len; i++) {
dst[i] = expf(src[i]);
}
}
static inline v4sf tanf_ps(v4sf xx)
{
v4sf x, y, z, zz;
v4si j; // long?
v4sf sign;
mve_pred16_t xsupem4;
v4sf tmp;
mve_pred16_t jandone, jandtwo;
x = vandq_f32(*(v4sf *) _ps_pos_sign_mask, xx); // fabs(xx) //OK
sign = vandq_f32(xx, *(v4sf *) _ps_sign_mask);
// printf("x");print4_4digits(x);printf("\r\n");
// printf("xx");print4_4digits(xx);printf("\r\n");
// printf("sign");print4_4digits(sign);printf("\r\n");
/* compute x mod PIO4 */
tmp = vmulq_n_f32(x, c_cephes_FOPI);
// printf("tmp2");print4_4digits(tmp);printf("\r\n");
j = vcvtq_s32_f32(tmp);
//printf("j");print4i(j);printf("\r\n");
y = vcvtq_f32_s32(j);
// printf("y0");print4_4digits(y);printf("\r\n");
jandone = vcmpgtq_s32(vandq_s32(j, *(v4si *) _pi32_1), *(v4si *) _pi32_0);
y = vaddq_m_n_f32(y, y, 1.0f, jandone);
// printf("y1");print4_4digits(y);printf("\r\n");
j = vaddq_m_n_s32(j, j, 1, jandone);
// printf("j1");print4i(j);printf("\r\n");
z = vfmaq_n_f32(x, y, c_minus_cephes_DP1);
z = vfmaq_n_f32(z, y, c_minus_cephes_DP2);
z = vfmaq_n_f32(z, y, c_minus_cephes_DP3);
zz = vmulq_f32(z, z); // z*z
// printf("zz");print4_4digits(z);printf("\r\n");
// TODO : should not be computed if X < 10e-4
/* 1.7e-8 relative error in [-pi/4, +pi/4] */
tmp = vfmasq_n_f32(zz, *(v4sf *) _ps_TAN_P0, TAN_P1);
tmp = vfmasq_n_f32(tmp, zz, TAN_P2);
tmp = vfmasq_n_f32(tmp, zz, TAN_P3);
tmp = vfmasq_n_f32(tmp, zz, TAN_P4);
tmp = vfmasq_n_f32(tmp, zz, TAN_P5);
tmp = vmulq_f32(zz, tmp);
tmp = vmulq_f32(tmp, z);
xsupem4 = vcmpgtq_f32(x, *(v4sf *) _ps_1emin4); // if( x > 1.0e-4 )
y = vaddq_m_f32(z, z, tmp, xsupem4);
jandtwo = vcmpgtq_s32(vandq_s32(j, *(v4si *) _pi32_2), *(v4si *) _pi32_0);
//printf("y");print4_4digits(y);printf("\r\n");
// xor(rcp(y)) gives not good enough result
tmp = vminrecipq_f32(y);
y = vpselq_f32(tmp, y, jandtwo);
//printf("tmp2");print4_4digits(tmp);printf("\r\n");
// printf("y2");print4_4digits(y);printf("\r\n");
y = veorq_f32(y, sign);
// printf("yxor");print4_4digits(y);printf("\r\n"); printf("\r\n");
return (y);
}
static inline void tan128f(float *src, float *dst, int len)
{
int stop_len = len / SSE_LEN_FLOAT;
stop_len *= SSE_LEN_FLOAT;
for (int i = 0; i < stop_len; i += SSE_LEN_FLOAT) {
vst1q_f32(dst + i, tanf_ps(vld1q_f32(src + i)));
}
for (int i = stop_len; i < len; i++) {
dst[i] = tanf(src[i]);
}
}
static inline void threshold128_ltval_gtval_f(float *src, float *dst, int len, float ltlevel, float ltvalue, float gtlevel, float gtvalue)
{
const v4sf ltlevel_v = vdupq_n_f32(ltlevel);
const v4sf ltvalue_v = vdupq_n_f32(ltvalue);
const v4sf gtlevel_v = vdupq_n_f32(gtlevel);
const v4sf gtvalue_v = vdupq_n_f32(gtvalue);
int stop_len = len / (SSE_LEN_FLOAT);
stop_len *= ( SSE_LEN_FLOAT);
for (int i = 0; i < stop_len; i += SSE_LEN_FLOAT) {
v4sf src_tmp = vld1q_f32(src + i); //vldrwq_f32 ?
mve_pred16_t lt_mask = vcmpltq_f32(src_tmp, ltlevel_v);
mve_pred16_t gt_mask = vcmpgtq_f32(src_tmp, gtlevel_v);
v4sf dst_tmp = vpselq_f32(ltvalue_v, src_tmp, lt_mask);
dst_tmp = vpselq_f32(gtvalue_v, dst_tmp, gt_mask);
vst1q_f32(dst + i, dst_tmp);
}
for (int i = stop_len; i < len; i++) {
float tmp = src[i];
float tmp2 = tmp < ltlevel ? ltvalue : tmp;
dst[i] = tmp > gtlevel ? gtvalue : tmp2;
}
}
static inline void threshold128_ltabs_f(float *src, float *dst, int len, float value)
{
const v4sf pval = vdupq_n_f32(value);
int stop_len = len / (SSE_LEN_FLOAT);
stop_len *= (SSE_LEN_FLOAT);
for (int i = 0; i < stop_len; i += SSE_LEN_FLOAT) {
v4sf src_tmp = vld1q_f32(src + i);
v4sf src_sign = vandq_f32(src_tmp, *(v4sf *) _ps_sign_mask); // extract sign
v4sf src_abs = vandq_f32(src_tmp, *(v4sf *) _ps_pos_sign_mask); // take absolute value
v4sf dst_tmp = vmaxnmq_f32(src_abs, pval);
dst_tmp = veorq_f32(dst_tmp, src_sign);
vst1q_f32(dst + i, dst_tmp);
}
for (int i = stop_len; i < len; i++) {
if (src[i] >= 0.0f) {
dst[i] = src[i] < value ? value : src[i];
} else {
dst[i] = src[i] > (-value) ? (-value) : src[i];
}
}
}
static inline void threshold128_lt_f(float *src, float *dst, int len, float value)
{
const v4sf tmp = vdupq_n_f32(value);
int stop_len = len / (2 * SSE_LEN_FLOAT);
stop_len *= (2 * SSE_LEN_FLOAT);
for (int i = 0; i < stop_len; i += 2 * SSE_LEN_FLOAT) {
v4sf src_tmp = vld1q_f32(src + i);
v4sf src_tmp2 = vld1q_f32(src + i + SSE_LEN_FLOAT);
v4sf dst_tmp = vmaxnmq_f32(src_tmp, tmp);
v4sf dst_tmp2 = vmaxnmq_f32(src_tmp2, tmp);
vst1q_f32(dst + i, dst_tmp);
vst1q_f32(dst + i + SSE_LEN_FLOAT, dst_tmp2);
}
for (int i = stop_len; i < len; i++) {
dst[i] = src[i] > value ? src[i] : value;
}
}
static inline void minmax128f(float *src, int len, float *min_value, float *max_value)
{
int stop_len = (len - SSE_LEN_FLOAT) / (2*SSE_LEN_FLOAT);
stop_len *= ( 2*SSE_LEN_FLOAT);
stop_len = (stop_len < 0) ? 0 : stop_len;
v4sf max_v, min_v, max_v2, min_v2;
v4sf src_tmp, src_tmp2;
float min_tmp = src[0];
float max_tmp = src[0];
float min_f[SSE_LEN_FLOAT] __attribute__((aligned(SSE_LEN_BYTES)));
float max_f[SSE_LEN_FLOAT] __attribute__((aligned(SSE_LEN_BYTES)));
if (len >= SSE_LEN_FLOAT) {
src_tmp = vld1q_f32(src + 0);
max_v = src_tmp;
min_v = src_tmp;
max_v2 = src_tmp;
min_v2 = src_tmp;
for (int i = SSE_LEN_FLOAT; i < stop_len; i += 2*SSE_LEN_FLOAT) {
src_tmp = vld1q_f32(src + i);
src_tmp2 = vld1q_f32(src + i + SSE_LEN_FLOAT);
max_v = vmaxnmq_f32(max_v, src_tmp);
min_v = vminnmq_f32(min_v, src_tmp);
max_v2 = vmaxnmq_f32(max_v2, src_tmp2);
min_v2 = vminnmq_f32(min_v2, src_tmp2);
}
max_v = vmaxnmq_f32(max_v, max_v2);
min_v = vminnmq_f32(min_v, min_v2);
vst1q_f32(max_f, max_v);
vst1q_f32(min_f, min_v);
max_f[0] = fmaxf(max_f[0],max_f[1]);
max_f[3] = fmaxf(max_f[2],max_f[3]);
max_f[0] = fmaxf(max_f[0],max_f[3]);
max_tmp = max_f[0];
min_f[0] = fminf(min_f[0],min_f[1]);
min_f[3] = fminf(min_f[2],min_f[3]);
min_f[0] = fminf(min_f[0],min_f[3]);
min_tmp = min_f[0];
}
for (int i = stop_len; i < len; i++) {
max_tmp = fmaxf(max_tmp,src[i]);
min_tmp = fminf(min_tmp,src[i]);
}
*max_value = max_tmp;
*min_value = min_tmp;
}
static inline void flip128f(float *src, float *dst, int len)
{
int stop_len = len / (2 * SSE_LEN_FLOAT);
stop_len *= (2 * SSE_LEN_FLOAT);
int mini = ((len - 1) < (2 * SSE_LEN_FLOAT)) ? (len - 1) : (2 * SSE_LEN_FLOAT);
for (int i = 0; i < mini; i++) {
dst[len - i - 1] = src[i];
}
uint32x4_t idx = {3,2,1,0};
for (int i = 2 * SSE_LEN_FLOAT; i < stop_len; i += 2 * SSE_LEN_FLOAT) {
v4sf src_tmp = vldrwq_gather_shifted_offset_f32(src + i,idx); // load a,b,c,d
v4sf src_tmp2 = vldrwq_gather_shifted_offset_f32(src + i + SSE_LEN_FLOAT,idx);
vst1q_f32(dst + len - i - SSE_LEN_FLOAT, src_tmp); // store the flipped vector
vst1q_f32(dst + len - i - 2 * SSE_LEN_FLOAT, src_tmp2);
}
for (int i = stop_len; i < len; i++) {
dst[len - i - 1] = src[i];
}
}
static inline void fabs128f(float *src, float *dst, int len)
{
int stop_len = len / (2 * SSE_LEN_FLOAT);
stop_len *= (2 * SSE_LEN_FLOAT);
for (int i = 0; i < stop_len; i += 2 * SSE_LEN_FLOAT) {
v4sf src_tmp = vld1q_f32(src + i);
v4sf src_tmp2 = vld1q_f32(src + i + SSE_LEN_FLOAT);
v4sf dst_tmp = vandq_f32(*(v4sf *) _ps_pos_sign_mask, src_tmp);
v4sf dst_tmp2 = vandq_f32(*(v4sf *) _ps_pos_sign_mask, src_tmp2);
vst1q_f32(dst + i, dst_tmp);
vst1q_f32(dst + i + SSE_LEN_FLOAT, dst_tmp2);
}
for (int i = stop_len; i < len; i++) {
dst[i] = fabsf(src[i]);
}
}
static inline void subcrev128f(float *src, float value, float *dst, int len)
{
const v4sf tmp = vdupq_n_f32(value);
int stop_len = len / (2*SSE_LEN_FLOAT);
stop_len *= 2*SSE_LEN_FLOAT;
for (int i = 0; i < stop_len; i += 2*SSE_LEN_FLOAT) {
v4sf src_tmp = vld1q_f32(src + i);
v4sf src_tmp2 = vld1q_f32(src + i + SSE_LEN_FLOAT);
v4sf dst_tmp = vsubq_f32(tmp, src_tmp);
v4sf dst_tmp2 = vsubq_f32(tmp, src_tmp2);
vst1q_f32(dst + i, dst_tmp);
vst1q_f32(dst + i + SSE_LEN_FLOAT, dst_tmp2);
}
for (int i = stop_len; i < len; i++) {
dst[i] = value - src[i];
}
}
static inline void sum128f(float *src, float *dst, int len)
{
int stop_len = len / (2 * SSE_LEN_FLOAT);
stop_len *= (2 * SSE_LEN_FLOAT);
__attribute__((aligned(SSE_LEN_BYTES))) float accumulate[SSE_LEN_FLOAT] = {0.0f, 0.0f, 0.0f, 0.0f};
float tmp_acc = 0.0f;
v4sf vec_acc1 = vdupq_n_f32(0.0f); // initialize the vector accumulator
v4sf vec_acc2 = vdupq_n_f32(0.0f); // initialize the vector accumulator
for (int i = 0; i < stop_len; i += 2 * SSE_LEN_FLOAT) {
v4sf vec_tmp1 = vld1q_f32(src + i);
vec_acc1 = vaddq_f32(vec_acc1, vec_tmp1);
v4sf vec_tmp2 = vld1q_f32(src + i + SSE_LEN_FLOAT);
vec_acc2 = vaddq_f32(vec_acc2, vec_tmp2);
}
vec_acc1 = vaddq_f32(vec_acc1, vec_acc2);
vst1q_f32(accumulate, vec_acc1);
for (int i = stop_len; i < len; i++) {
tmp_acc += src[i];
}
tmp_acc = tmp_acc + accumulate[0] + accumulate[1] + accumulate[2] + accumulate[3];
*dst = tmp_acc;
}
static inline void mean128f(float *src, float *dst, int len)
{
float coeff = 1.0f / ((float) len);
sum128f(src, dst, len);
*dst *= coeff;
}
static inline v4sf log_ps(v4sf x)
{
x = vmaxnmq_f32(x, *(v4sf *) _ps_0); /* force flush to zero on denormal values */
mve_pred16_t invalid_mask = vcmpleq_f32(x, *(v4sf *) _ps_0);
v4si ux = vreinterpretq_s32_f32(x);
v4si emm0 = vshrq_n_s32(ux, 23);
/* keep only the fractional part */
ux = vandq_s32(ux, *(v4si *) _ps_inv_mant_mask);
ux = vorrq_s32(ux, vreinterpretq_s32_f32(*(v4sf *) _ps_0p5));
x = vreinterpretq_f32_s32(ux);
emm0 = vsubq_n_s32(emm0, 0x7F);
v4sf e = vcvtq_f32_s32(emm0);
e = vaddq_n_f32(e, 1.0f);
/* part2:
if( x < SQRTHF ) {
e -= 1;
x = x + x - 1.0;
} else { x = x - 1.0; }
*/
mve_pred16_t mask = vcmpltq_f32(x, *(v4sf *) _ps_cephes_SQRTHF);
x = vsubq_n_f32(x, 1.0f);
e = vsubq_m_n_f32(e, e, 1.0f, mask);
x = vaddq_m_f32(x, x, x, mask);
v4sf z = vmulq_f32(x, x);
v4sf y = vfmasq_n_f32(x, *(v4sf *) _ps_cephes_log_p0, c_cephes_log_p1);
//printf("y ");print4_4digits(y);printf("\r\n");
y = vfmasq_n_f32(y, x, c_cephes_log_p2);
//printf("y2 ");print4_4digits(y);printf("\r\n");
y = vfmasq_n_f32(y, x, c_cephes_log_p3);
y = vfmasq_n_f32(y, x, c_cephes_log_p4);
y = vfmasq_n_f32(y, x, c_cephes_log_p5);
y = vfmasq_n_f32(y, x, c_cephes_log_p6);
y = vfmasq_n_f32(y, x, c_cephes_log_p7);
y = vfmasq_n_f32(y, x, c_cephes_log_p8);
y = vmulq_f32(y, x);
y = vmulq_f32(y, z);
y = vfmaq_n_f32(y, e, c_cephes_log_q1);
y = vfmaq_n_f32(y, z, -0.5f);
y = vfmaq_n_f32(y, e, c_cephes_log_q2);
x = vaddq_f32(x, y);
x = vorrq_m_f32(x, x, *(v4sf *) _pi32_0xFFFFFFFF, invalid_mask); // negative arg will be NAN
return x;
}
static inline void ln128f(float *src, float *dst, int len)
{
int stop_len = len / SSE_LEN_FLOAT;
stop_len *= SSE_LEN_FLOAT;
for (int i = 0; i < stop_len; i += SSE_LEN_FLOAT) {
vst1q_f32(dst + i, log_ps(vld1q_f32(src + i)));
}
for (int i = stop_len; i < len; i++) {
dst[i] = logf(src[i]);
}
}
static inline v4sf atanhf_ps(v4sf x)
{
v4sf z, tmp, tmp2, z_first_branch, z_second_branch;
mve_pred16_t xsup1, xinfmin1, zinf1emin4, zinf0p5;
z = vandq_f32(*(v4sf *) _ps_pos_sign_mask, x);
xsup1 = vcmpgeq_f32(x, *(v4sf *) _ps_1);
xinfmin1 = vcmpleq_f32(x, *(v4sf *) _ps_min1);
zinf1emin4 = vcmpltq_f32(z, *(v4sf *) _ps_1emin4);
zinf0p5 = vcmpltq_f32(z, *(v4sf *) _ps_0p5);
// First branch
tmp = vmulq_f32(x, x);
z_first_branch = vfmasq_n_f32(tmp, *(v4sf *) _ps_ATANH_P0, ATANH_P1);
z_first_branch = vfmasq_n_f32(z_first_branch, tmp, ATANH_P2);
z_first_branch = vfmasq_n_f32(z_first_branch, tmp, ATANH_P3);
z_first_branch = vfmasq_n_f32(z_first_branch, tmp, ATANH_P4);
z_first_branch = vmulq_f32(z_first_branch, tmp);
z_first_branch = vfmaq_f32(x, z_first_branch, x);
// Second branch
tmp = vsubq_f32(*(v4sf *) _ps_1, x);
tmp2 = vrecipq_f32(tmp);
tmp = vfmaq_f32(tmp2, x, tmp2);
z_second_branch = log_ps(tmp);
z_second_branch = vmulq_n_f32(z_second_branch, 0.5f);
z = vpselq_f32(z_first_branch, z_second_branch, zinf0p5);
z = vpselq_f32(x, z, zinf1emin4);
z = vpselq_f32(*(v4sf *) _ps_MAXNUMF, z, xsup1);
z = vpselq_f32(*(v4sf *) _ps_minMAXNUMF, z, xinfmin1);
return (z);
}
static inline void atanh128f(float *src, float *dst, int len)
{
int stop_len = len / SSE_LEN_FLOAT;
stop_len *= SSE_LEN_FLOAT;
for (int i = 0; i < stop_len; i += SSE_LEN_FLOAT) {
v4sf src_tmp = vld1q_f32(src + i);
vst1q_f32(dst + i, atanhf_ps(src_tmp));
}
for (int i = stop_len; i < len; i++) {
dst[i] = atanhf(src[i]);
}
}
static inline v4sf atanf_ps(v4sf xx)
{
v4sf x, y, z;
v4sf sign;
mve_pred16_t suptan3pi8, inftan3pi8suppi8;
v4sf tmp, tmp2;
x = vandq_f32(*(v4sf *) _ps_pos_sign_mask, xx);
sign = vandq_f32(xx, *(v4sf *) _ps_sign_mask);
/* range reduction */
suptan3pi8 = vcmpgtq_f32(x, *(v4sf *) _ps_TAN3PI8F); // if( x > tan 3pi/8 )
tmp = vminrecipq_f32(x);
x = vpselq_f32(tmp, x, suptan3pi8);
y = vpselq_f32(*(v4sf *) _ps_PIO2F, *(v4sf *) _ps_0, suptan3pi8);
mve_pred16_t letan3pi8 = vcmpleq_f32(x, *(v4sf *) _ps_TAN3PI8F);
mve_pred16_t gttanpi8 = vcmpgtq_f32(x, *(v4sf *) _ps_TANPI8F);
inftan3pi8suppi8 = and_pred(letan3pi8, gttanpi8); // if( x > tan 3pi/8 )
tmp = vsubq_n_f32(x, 1.0f);
tmp2 = vaddq_n_f32(x, 1.0f);
tmp = vdivq_f32(tmp, tmp2);
x = vpselq_f32(tmp, x, inftan3pi8suppi8);
y = vpselq_f32(*(v4sf *) _ps_PIO4F, y, inftan3pi8suppi8);
z = vmulq_f32(x, x);
tmp = vfmasq_n_f32(z, *(v4sf *) _ps_ATAN_P0, ATAN_P1);
tmp = vfmasq_n_f32(tmp, z, ATAN_P2);
tmp = vfmasq_n_f32(tmp, z, ATAN_P3);
tmp = vmulq_f32(z, tmp);
tmp = vfmasq_f32(tmp, x, x);
y = vaddq_f32(y, tmp);
y = veorq_f32(y, sign);
return (y);
}
static inline void atan128f(float *src, float *dst, int len)
{
int stop_len = len / SSE_LEN_FLOAT;
stop_len *= SSE_LEN_FLOAT;
for (int i = 0; i < stop_len; i += SSE_LEN_FLOAT) {
v4sf src_tmp = vld1q_f32(src + i);
vst1q_f32(dst + i, atanf_ps(src_tmp));
}
for (int i = stop_len; i < len; i++) {
dst[i] = atanf(src[i]);
}
}
//rounds away from zero like IPP, whereas SSE/AVx/AVX512 rounds to nearest even (IEEE-754)
static inline void rint128f(float *src, float *dst, int len)
{
int stop_len = len / (2 * SSE_LEN_FLOAT);
stop_len *= (2 * SSE_LEN_FLOAT);
for (int i = 0; i < stop_len; i += 2 * SSE_LEN_FLOAT) {
v4sf src_tmp = vld1q_f32(src + i);
v4sf src_tmp2 = vld1q_f32(src + i + SSE_LEN_FLOAT);
v4sf dst_tmp = vrndnq_f32(src_tmp);
v4sf dst_tmp2 = vrndnq_f32(src_tmp2);
vst1q_f32(dst + i, dst_tmp);
vst1q_f32(dst + i + SSE_LEN_FLOAT, dst_tmp2);
}
for (int i = stop_len; i < len; i++) {
dst[i] = rintf(src[i]);
}
}
//rounds away from zero like IPP, whereas SSE/AVx/AVX512 rounds to nearest even (IEEE-754)
static inline void round128f(float *src, float *dst, int len)
{
int stop_len = len / (2 * SSE_LEN_FLOAT);
stop_len *= (2 * SSE_LEN_FLOAT);
for (int i = 0; i < stop_len; i += 2 * SSE_LEN_FLOAT) {
v4sf src_tmp = vld1q_f32(src + i);
v4sf src_tmp2 = vld1q_f32(src + i + SSE_LEN_FLOAT);
#if 1
v4sf dst_tmp = vrndaq(src_tmp);
v4sf dst_tmp2 = vrndaq(src_tmp2);
#else
v4sf spe1 = vandq_f32(src_tmp, *(v4sf*)_ps_sign_mask);
spe1 = vorrq_f32(spe1,*(v4sf*)_ps_mid_mask);
spe1 = vaddq_f32(src_tmp, spe1);
v4sf spe2 = vandq_f32(src_tmp2, *(v4sf*)_ps_sign_mask);
spe2 = vorrq_f32(spe2,*(v4sf*)_ps_mid_mask);
spe2 = vaddq_f32(src_tmp2, spe2);
v4sf dst_tmp = vrndq_f32(spe1);
v4sf dst_tmp2 = vrndq_f32(spe2);
#endif
vst1q_f32(dst + i, dst_tmp);
vst1q_f32(dst + i + SSE_LEN_FLOAT, dst_tmp2);
}
for (int i = stop_len; i < len; i++) {
dst[i] = roundf(src[i]);
}
}
static inline void ceil128f(float *src, float *dst, int len)
{
int stop_len = len / (2 * SSE_LEN_FLOAT);
stop_len *= (2 * SSE_LEN_FLOAT);
for (int i = 0; i < stop_len; i += 2 * SSE_LEN_FLOAT) {
v4sf src_tmp = vld1q_f32(src + i);
v4sf src_tmp2 = vld1q_f32(src + i + SSE_LEN_FLOAT);
v4sf dst_tmp = vrndpq_f32(src_tmp);
v4sf dst_tmp2 = vrndpq_f32(src_tmp2);
vst1q_f32(dst + i, dst_tmp);
vst1q_f32(dst + i + SSE_LEN_FLOAT, dst_tmp2);
}
for (int i = stop_len; i < len; i++) {
dst[i] = ceilf(src[i]);
}
}
static inline void floor128f(float *src, float *dst, int len)
{
int stop_len = len / (2 * SSE_LEN_FLOAT);
stop_len *= (2 * SSE_LEN_FLOAT);
for (int i = 0; i < stop_len; i += 2 * SSE_LEN_FLOAT) {
v4sf src_tmp = vld1q_f32(src + i);
v4sf src_tmp2 = vld1q_f32(src + i + SSE_LEN_FLOAT);
v4sf dst_tmp = vrndmq_f32(src_tmp);
v4sf dst_tmp2 = vrndmq_f32(src_tmp2);
vst1q_f32(dst + i, dst_tmp);
vst1q_f32(dst + i + SSE_LEN_FLOAT, dst_tmp2);
}