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math_powf.c
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math_powf.c
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/*
The MIT License (MIT)
Copyright (c) 2015 Lachlan Tychsen-Smith ([email protected])
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
*/
/*
Based on x ^ n = exp(n * log(x))
Test func : powf(x, n)
Test Range: (1,1) < (x, n) < (10, 10)
Peak Error: ~0.0010%
RMS Error: ~0.0002%
*/
#include "math.h"
#include "math_neon.h"
const float __powf_rng[2] = {
1.442695041f,
0.693147180f
};
const float __powf_lut[16] = {
-2.295614848256274, //p0 log
-2.470711633419806, //p4
-5.686926051100417, //p2
-0.165253547131978, //p6
+5.175912446351073, //p1
+0.844006986174912, //p5
+4.584458825456749, //p3
+0.014127821926000, //p7
0.9999999916728642, //p0 exp
0.04165989275009526, //p4
0.5000006143673624, //p2
0.0014122663401803872, //p6
1.000000059694879, //p1
0.008336936973260111, //p5
0.16666570253074878, //p3
0.00019578093328483123 //p7
};
float powf_c(float x, float n)
{
float a, b, c, d, xx;
int m;
union {
float f;
int i;
} r;
//extract exponent
r.f = x;
m = (r.i >> 23);
m = m - 127;
r.i = r.i - (m << 23);
//Taylor Polynomial (Estrins)
xx = r.f * r.f;
a = (__powf_lut[4] * r.f) + (__powf_lut[0]);
b = (__powf_lut[6] * r.f) + (__powf_lut[2]);
c = (__powf_lut[5] * r.f) + (__powf_lut[1]);
d = (__powf_lut[7] * r.f) + (__powf_lut[3]);
a = a + b * xx;
c = c + d * xx;
xx = xx * xx;
r.f = a + c * xx;
//add exponent
r.f = r.f + ((float) m) * __powf_rng[1];
r.f = r.f * n;
//Range Reduction:
m = (int) (r.f * __powf_rng[0]);
r.f = r.f - ((float) m) * __powf_rng[1];
//Taylor Polynomial (Estrins)
a = (__powf_lut[12] * r.f) + (__powf_lut[8]);
b = (__powf_lut[14] * r.f) + (__powf_lut[10]);
c = (__powf_lut[13] * r.f) + (__powf_lut[9]);
d = (__powf_lut[15] * r.f) + (__powf_lut[11]);
xx = r.f * r.f;
a = a + b * xx;
c = c + d * xx;
xx = xx* xx;
r.f = a + c * xx;
//multiply by 2 ^ m
m = m << 23;
r.i = r.i + m;
return r.f;
}
float powf_neon_hfp(float x, float n)
{
#ifdef __MATH_NEON
asm volatile (
"vdup.f32 d16, d0[1] \n\t" //d16 = {y,y};
"vdup.f32 d0, d0[0] \n\t" //d0 = {x,x};
//extract exponent
"vmov.i32 d2, #127 \n\t" //d2 = 127;
"vshr.u32 d6, d0, #23 \n\t" //d6 = d0 >> 23;
"vsub.i32 d6, d6, d2 \n\t" //d6 = d6 - d2;
"vshl.u32 d1, d6, #23 \n\t" //d1 = d6 << 23;
"vsub.i32 d0, d0, d1 \n\t" //d0 = d0 + d1;
//polynomial:
"vmul.f32 d1, d0, d0 \n\t" //d1 = d0*d0 = {x^2, x^2}
"vld1.32 {d2, d3, d4, d5}, [%1]! \n\t" //q1 = {p0, p4, p2, p6}, q2 = {p1, p5, p3, p7} ;
"vmla.f32 q1, q2, d0[0] \n\t" //q1 = q1 + q2 * d0[0]
"vmla.f32 d2, d3, d1[0] \n\t" //d2 = d2 + d3 * d1[0]
"vmul.f32 d1, d1, d1 \n\t" //d1 = d1 * d1 = {x^4, x^4}
"vmla.f32 d2, d1, d2[1] \n\t" //d2 = d2 + d1 * d2[1]
//add exponent
"vld1.32 d7, [%0] \n\t" //d7 = {invrange, range}
"vcvt.f32.s32 d6, d6 \n\t" //d6 = (float) d6
"vmla.f32 d2, d6, d7[1] \n\t" //d2 = d2 + d6 * d7[1]
"vdup.f32 d0, d2[0] \n\t" //d0 = d2[0]
"vmul.f32 d0, d0, d16 \n\t" //d0 = d0 * d16
//Range Reduction:
"vmul.f32 d6, d0, d7[0] \n\t" //d6 = d0 * d7[0]
"vcvt.u32.f32 d6, d6 \n\t" //d6 = (int) d6
"vcvt.f32.u32 d1, d6 \n\t" //d1 = (float) d6
"vmls.f32 d0, d1, d7[1] \n\t" //d0 = d0 - d1 * d7[1]
//polynomial:
"vmul.f32 d1, d0, d0 \n\t" //d1 = d0*d0 = {x^2, x^2}
"vld1.32 {d2, d3, d4, d5}, [%1] \n\t" //q1 = {p0, p4, p2, p6}, q2 = {p1, p5, p3, p7} ;
"vmla.f32 q1, q2, d0[0] \n\t" //q1 = q1 + q2 * d0[0]
"vmla.f32 d2, d3, d1[0] \n\t" //d2 = d2 + d3 * d1[0]
"vmul.f32 d1, d1, d1 \n\t" //d1 = d1 * d1 = {x^4, x^4}
"vmla.f32 d2, d1, d2[1] \n\t" //d2 = d2 + d1 * d2[1]
//multiply by 2 ^ m
"vshl.i32 d6, d6, #23 \n\t" //d6 = d6 << 23
"vadd.i32 d0, d2, d6 \n\t" //d0 = d2 + d6
:: "r"(__powf_rng), "r"(__powf_lut)
: "d0", "d1", "d2","d3", "d4", "d5", "d6", "d7"
);
#endif
}
float powf_neon_sfp(float x, float n)
{
#ifdef __MATH_NEON
asm volatile ("vmov.f32 s0, r0 \n\t");
asm volatile ("vmov.f32 s1, r1 \n\t");
powf_neon_hfp(x, n);
asm volatile ("vmov.f32 r0, s0 \n\t");
#else
return powf_c(x, n);
#endif
};