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https://github.com/libretro/RetroArch
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136 lines
3.5 KiB
C
136 lines
3.5 KiB
C
/*
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The MIT License (MIT)
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Copyright (c) 2015 Lachlan Tychsen-Smith (lachlan.ts@gmail.com)
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in
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all copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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THE SOFTWARE.
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*/
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/*
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Based on:
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e ^ x = (1+m) * (2^n)
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x = log(1+m) + n * log(2)
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n = (int) (x * 1.0 / log(2))
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(1+m) = e ^ (x - n * log(2))
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(1+m) = Poly(x - n * log(2))
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where Poly(x) is the Minimax approximation of e ^ x over the
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range [-Log(2), Log(2)]
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Test func : expf(x)
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Test Range: 0 < x < 50
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Peak Error: ~0.00024%
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RMS Error: ~0.00007%
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*/
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#include "math.h"
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#include "math_neon.h"
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const float __expf_rng[2] = {
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1.442695041f,
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0.693147180f
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};
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const float __expf_lut[8] = {
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0.9999999916728642, //p0
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0.04165989275009526, //p4
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0.5000006143673624, //p2
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0.0014122663401803872, //p6
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1.000000059694879, //p1
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0.008336936973260111, //p5
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0.16666570253074878, //p3
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0.00019578093328483123 //p7
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};
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float expf_c(float x)
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{
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float a, b, c, d, xx;
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int m;
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union {
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float f;
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int i;
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} r;
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//Range Reduction:
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m = (int) (x * __expf_rng[0]);
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x = x - ((float) m) * __expf_rng[1];
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//Taylor Polynomial (Estrins)
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a = (__expf_lut[4] * x) + (__expf_lut[0]);
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b = (__expf_lut[6] * x) + (__expf_lut[2]);
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c = (__expf_lut[5] * x) + (__expf_lut[1]);
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d = (__expf_lut[7] * x) + (__expf_lut[3]);
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xx = x * x;
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a = a + b * xx;
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c = c + d * xx;
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xx = xx* xx;
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r.f = a + c * xx;
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//multiply by 2 ^ m
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m = m << 23;
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r.i = r.i + m;
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return r.f;
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}
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float expf_neon_hfp(float x)
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{
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#ifdef __MATH_NEON
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asm volatile (
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"vdup.f32 d0, d0[0] \n\t" //d0 = {x, x}
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//Range Reduction:
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"vld1.32 d2, [%0] \n\t" //d2 = {invrange, range}
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"vmul.f32 d6, d0, d2[0] \n\t" //d6 = d0 * d2[0]
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"vcvt.s32.f32 d6, d6 \n\t" //d6 = (int) d6
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"vcvt.f32.s32 d1, d6 \n\t" //d1 = (float) d6
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"vmls.f32 d0, d1, d2[1] \n\t" //d0 = d0 - d1 * d2[1]
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//polynomial:
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"vmul.f32 d1, d0, d0 \n\t" //d1 = d0*d0 = {x^2, x^2}
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"vld1.32 {d2, d3, d4, d5}, [%1] \n\t" //q1 = {p0, p4, p2, p6}, q2 = {p1, p5, p3, p7} ;
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"vmla.f32 q1, q2, d0[0] \n\t" //q1 = q1 + q2 * d0[0]
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"vmla.f32 d2, d3, d1[0] \n\t" //d2 = d2 + d3 * d1[0]
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"vmul.f32 d1, d1, d1 \n\t" //d1 = d1 * d1 = {x^4, x^4}
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"vmla.f32 d2, d1, d2[1] \n\t" //d2 = d2 + d1 * d2[1]
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//multiply by 2 ^ m
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"vshl.i32 d6, d6, #23 \n\t" //d6 = d6 << 23
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"vadd.i32 d0, d2, d6 \n\t" //d0 = d2 + d6
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:: "r"(__expf_rng), "r"(__expf_lut)
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: "d0", "d1", "q1", "q2", "d6"
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);
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#endif
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}
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float expf_neon_sfp(float x)
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{
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#ifdef __MATH_NEON
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asm volatile ("vmov.f32 s0, r0 \n\t");
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expf_neon_hfp(x);
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asm volatile ("vmov.f32 r0, s0 \n\t");
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#else
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return expf_c(x);
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#endif
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};
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