5 Copyright (c) 2015 Jacques-Henri Jourdan <jourgun@gmail.com>
7 Permission is hereby granted, free of charge, to any person obtaining a copy
8 of this software and associated documentation files (the "Software"), to deal
9 in the Software without restriction, including without limitation the rights
10 to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
11 copies of the Software, and to permit persons to whom the Software is
12 furnished to do so, subject to the following conditions:
14 The above copyright notice and this permission notice shall be included in all
15 copies or substantial portions of the Software.
17 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
18 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
19 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
20 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
21 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
22 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
25 Taken from https://github.com/jhjourdan/SIMD-math-prims/blob/master/simd_math_prims.h
26 Stripped down for BF use
33 /* Workaround a lack of optimization in gcc */
34 float exp_cst1
= 2139095040.f
;
37 /* Relative error bounded by 1e-5 for normalized outputs
38 Returns invalid outputs for nan inputs
40 float exp_approx(float val
) {
41 union { int32_t i
; float f
; } xu
, xu2
;
42 float val2
, val3
, val4
, b
;
44 val2
= 12102203.1615614f
*val
+1065353216.f
;
45 val3
= val2
< exp_cst1
? val2
: exp_cst1
;
46 val4
= val3
> exp_cst2
? val3
: exp_cst2
;
47 val4i
= (int32_t) val4
;
48 xu
.i
= val4i
& 0x7F800000; // mask exponent / round down to neareset 2^n (implicit mantisa bit)
49 xu2
.i
= (val4i
& 0x7FFFFF) | 0x3F800000; // force exponent to 0
52 /* Generated in Sollya with:
53 > f=remez(1-x*exp(-(x-1)*log(2)),
54 [|(x-1)*(x-2), (x-1)*(x-2)*x, (x-1)*(x-2)*x*x|],
55 [1.000001,1.999999], exp(-(x-1)*log(2)));
56 > plot(exp((x-1)*log(2))/(f+x)-1, [1,2]);
60 xu
.f
* (0.509871020343597804469416f
+ b
*
61 (0.312146713032169896138863f
+ b
*
62 (0.166617139319965966118107f
+ b
*
63 (-2.19061993049215080032874e-3f
+ b
*
64 1.3555747234758484073940937e-2f
))));
67 /* Absolute error bounded by 1e-6 for normalized inputs
68 Returns a finite number for +inf input
69 Returns -inf for nan and <= 0 inputs.
71 float log_approx(float val
) {
72 union { float f
; int32_t i
; } valu
;
76 /* 89.970756366f = 127 * log(2) - constant term of polynomial */
77 addcst
= val
> 0 ? -89.970756366f
: -(float)INFINITY
;
78 valu
.i
= (valu
.i
& 0x7FFFFF) | 0x3F800000;
82 /* Generated in Sollya using:
83 > f = remez(log(x)-(x-1)*log(2),
84 [|1,(x-1)*(x-2), (x-1)*(x-2)*x, (x-1)*(x-2)*x*x,
85 (x-1)*(x-2)*x*x*x|], [1,2], 1, 1e-8);
86 > plot(f+(x-1)*log(2)-log(x), [1,2]);
90 x
* (3.529304993f
+ x
* (-2.461222105f
+
91 x
* (1.130626167f
+ x
* (-0.288739945f
+
92 x
* 3.110401639e-2f
))))
93 + (addcst
+ 0.69314718055995f
*exp
);
96 float pow_approx(float a
, float b
)
98 return exp_approx(b
* log_approx(a
));