1/* origin: FreeBSD /usr/src/lib/msun/src/s_expm1f.c */
  2/*
  3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
  4 */
  5/*
  6 * ====================================================
  7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  8 *
  9 * Developed at SunPro, a Sun Microsystems, Inc. business.
 10 * Permission to use, copy, modify, and distribute this
 11 * software is freely granted, provided that this notice
 12 * is preserved.
 13 * ====================================================
 14 */
 15
 16#include "libm.h"
 17
 18static const float
 19ln2_hi      = 6.9313812256e-01, /* 0x3f317180 */
 20ln2_lo      = 9.0580006145e-06, /* 0x3717f7d1 */
 21invln2      = 1.4426950216e+00, /* 0x3fb8aa3b */
 22/*
 23 * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
 24 * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
 25 * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
 26 */
 27Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */
 28Q2 =  1.5807170421e-3; /*  0xcf3010.0p-33 */
 29
 30float expm1f(float x)
 31{
 32	float_t y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
 33	union {float f; uint32_t i;} u = {x};
 34	uint32_t hx = u.i & 0x7fffffff;
 35	int k, sign = u.i >> 31;
 36
 37	/* filter out huge and non-finite argument */
 38	if (hx >= 0x4195b844) {  /* if |x|>=27*ln2 */
 39		if (hx > 0x7f800000)  /* NaN */
 40			return x;
 41		if (sign)
 42			return -1;
 43		if (hx > 0x42b17217) { /* x > log(FLT_MAX) */
 44			x *= 0x1p127f;
 45			return x;
 46		}
 47	}
 48
 49	/* argument reduction */
 50	if (hx > 0x3eb17218) {           /* if  |x| > 0.5 ln2 */
 51		if (hx < 0x3F851592) {       /* and |x| < 1.5 ln2 */
 52			if (!sign) {
 53				hi = x - ln2_hi;
 54				lo = ln2_lo;
 55				k =  1;
 56			} else {
 57				hi = x + ln2_hi;
 58				lo = -ln2_lo;
 59				k = -1;
 60			}
 61		} else {
 62			k  = invln2*x + (sign ? -0.5f : 0.5f);
 63			t  = k;
 64			hi = x - t*ln2_hi;      /* t*ln2_hi is exact here */
 65			lo = t*ln2_lo;
 66		}
 67		x = hi-lo;
 68		c = (hi-x)-lo;
 69	} else if (hx < 0x33000000) {  /* when |x|<2**-25, return x */
 70		if (hx < 0x00800000)
 71			FORCE_EVAL(x*x);
 72		return x;
 73	} else
 74		k = 0;
 75
 76	/* x is now in primary range */
 77	hfx = 0.5f*x;
 78	hxs = x*hfx;
 79	r1 = 1.0f+hxs*(Q1+hxs*Q2);
 80	t  = 3.0f - r1*hfx;
 81	e  = hxs*((r1-t)/(6.0f - x*t));
 82	if (k == 0)  /* c is 0 */
 83		return x - (x*e-hxs);
 84	e  = x*(e-c) - c;
 85	e -= hxs;
 86	/* exp(x) ~ 2^k (x_reduced - e + 1) */
 87	if (k == -1)
 88		return 0.5f*(x-e) - 0.5f;
 89	if (k == 1) {
 90		if (x < -0.25f)
 91			return -2.0f*(e-(x+0.5f));
 92		return 1.0f + 2.0f*(x-e);
 93	}
 94	u.i = (0x7f+k)<<23;  /* 2^k */
 95	twopk = u.f;
 96	if (k < 0 || k > 56) {   /* suffice to return exp(x)-1 */
 97		y = x - e + 1.0f;
 98		if (k == 128)
 99			y = y*2.0f*0x1p127f;
100		else
101			y = y*twopk;
102		return y - 1.0f;
103	}
104	u.i = (0x7f-k)<<23;  /* 2^-k */
105	if (k < 23)
106		y = (x-e+(1-u.f))*twopk;
107	else
108		y = (x-(e+u.f)+1)*twopk;
109	return y;
110}