/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
│vi: set et ft=c ts=8 tw=8 fenc=utf-8 :vi│
╚──────────────────────────────────────────────────────────────────────────────╝
│ │
│ FreeBSD lib/msun/src/s_expm1f.c │
│ │
│ Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. │
│ │
│ Developed at SunPro, a Sun Microsystems, Inc. business. │
│ Permission to use, copy, modify, and distribute this │
│ software is freely granted, provided that this notice │
│ is preserved. │
│ │
│ Copyright (c) 1992-2023 The FreeBSD Project. │
│ │
│ Redistribution and use in source and binary forms, with or without │
│ modification, are permitted provided that the following conditions │
│ are met: │
│ 1. Redistributions of source code must retain the above copyright │
│ notice, this list of conditions and the following disclaimer. │
│ 2. Redistributions in binary form must reproduce the above copyright │
│ notice, this list of conditions and the following disclaimer in the │
│ documentation and/or other materials provided with the distribution. │
│ │
│ THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND │
│ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE │
│ IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE │
│ ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE │
│ FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL │
│ DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS │
│ OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) │
│ HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT │
│ LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY │
│ OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF │
│ SUCH DAMAGE. │
│ │
╚─────────────────────────────────────────────────────────────────────────────*/
#include "libc/math.h"
#include "libc/tinymath/freebsd.internal.h"
asm(".ident\t\"\\n\\n\
FreeBSD libm (BSD-2 License)\\n\
Copyright (c) 2005-2011, Bruce D. Evans, Steven G. Kargl, David Schultz.\"");
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
static const float
one = 1.0,
tiny = 1.0e-30,
o_threshold = 8.8721679688e+01,/* 0x42b17180 */
ln2_hi = 6.9313812256e-01,/* 0x3f317180 */
ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */
invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */
/*
* Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
* |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
* Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
*/
Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */
Q2 = 1.5807170421e-3; /* 0xcf3010.0p-33 */
static volatile float huge = 1.0e+30;
/**
* Returns 𝑒ˣ-1.
*/
float
expm1f(float x)
{
float y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
int32_t k,xsb;
uint32_t hx;
GET_FLOAT_WORD(hx,x);
xsb = hx&0x80000000; /* sign bit of x */
hx &= 0x7fffffff; /* high word of |x| */
/* filter out huge and non-finite argument */
if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */
if(hx >= 0x42b17218) { /* if |x|>=88.721... */
if(hx>0x7f800000)
return x+x; /* NaN */
if(hx==0x7f800000)
return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
if(x > o_threshold) return huge*huge; /* overflow */
}
if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
if(x+tiny<(float)0.0) /* raise inexact */
return tiny-one; /* return -1 */
}
}
/* argument reduction */
if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
if(xsb==0)
{hi = x - ln2_hi; lo = ln2_lo; k = 1;}
else
{hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
} else {
k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
t = k;
hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
lo = t*ln2_lo;
}
STRICT_ASSIGN(float, x, hi - lo);
c = (hi-x)-lo;
}
else if(hx < 0x33000000) { /* when |x|<2**-25, return x */
t = huge+x; /* return x with inexact flags when x!=0 */
return x - (t-(huge+x));
}
else k = 0;
/* x is now in primary range */
hfx = (float)0.5*x;
hxs = x*hfx;
r1 = one+hxs*(Q1+hxs*Q2);
t = (float)3.0-r1*hfx;
e = hxs*((r1-t)/((float)6.0 - x*t));
if(k==0) return x - (x*e-hxs); /* c is 0 */
else {
SET_FLOAT_WORD(twopk,((uint32_t)(0x7f+k))<<23); /* 2^k */
e = (x*(e-c)-c);
e -= hxs;
if(k== -1) return (float)0.5*(x-e)-(float)0.5;
if(k==1) {
if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
else return one+(float)2.0*(x-e);
}
if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
y = one-(e-x);
if (k == 128) y = y*2.0F*0x1p127F;
else y = y*twopk;
return y-one;
}
t = one;
if(k<23) {
SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
y = t-(e-x);
y = y*twopk;
} else {
SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */
y = x-(e+t);
y += one;
y = y*twopk;
}
}
return y;
}