143 /* Q2 */ 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */
144 /* Q3 */ -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */
145 /* Q4 */ 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */
146 /* Q5 */ -2.01099218183624371326e-07 /* BE8AFDB7 6E09C32D */
147 };
148 #define one xxx[0]
149 #define huge xxx[1]
150 #define tiny xxx[2]
151 #define o_threshold xxx[3]
152 #define ln2_hi xxx[4]
153 #define ln2_lo xxx[5]
154 #define invln2 xxx[6]
155 #define Q1 xxx[7]
156 #define Q2 xxx[8]
157 #define Q3 xxx[9]
158 #define Q4 xxx[10]
159 #define Q5 xxx[11]
160
161 double
162 expm1(double x) {
163 double y, hi, lo, c, t, e, hxs, hfx, r1;
164 int k, xsb;
165 unsigned hx;
166
167 hx = ((unsigned *) &x)[HIWORD]; /* high word of x */
168 xsb = hx & 0x80000000; /* sign bit of x */
169 if (xsb == 0)
170 y = x;
171 else
172 y = -x; /* y = |x| */
173 hx &= 0x7fffffff; /* high word of |x| */
174
175 /* filter out huge and non-finite arugment */
176 if (hx >= 0x4043687A) { /* if |x|>=56*ln2 */
177 if (hx >= 0x40862E42) { /* if |x|>=709.78... */
178 if (hx >= 0x7ff00000) {
179 if (((hx & 0xfffff) | ((int *) &x)[LOWORD])
180 != 0)
181 return x * x; /* + -> * for Cheetah */
182 else
183 return xsb == 0 ? x : -1.0; /* exp(+-inf)={inf,-1} */
184 }
185 if (x > o_threshold)
186 return huge * huge; /* overflow */
187 }
188 if (xsb != 0) { /* x < -56*ln2, return -1.0 w/inexact */
189 if (x + tiny < 0.0) /* raise inexact */
190 return tiny - one; /* return -1 */
191 }
192 }
193
194 /* argument reduction */
195 if (hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
196 if (hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
197 if (xsb == 0) {
198 hi = x - ln2_hi;
199 lo = ln2_lo;
200 k = 1;
201 }
202 else {
203 hi = x + ln2_hi;
204 lo = -ln2_lo;
205 k = -1;
206 }
207 }
208 else {
209 k = (int) (invln2 * x + (xsb == 0 ? 0.5 : -0.5));
210 t = k;
211 hi = x - t * ln2_hi; /* t*ln2_hi is exact here */
212 lo = t * ln2_lo;
213 }
214 x = hi - lo;
215 c = (hi - x) - lo;
216 }
217 else if (hx < 0x3c900000) { /* when |x|<2**-54, return x */
218 t = huge + x; /* return x w/inexact when x != 0 */
219 return x - (t - (huge + x));
220 }
221 else
222 k = 0;
223
224 /* x is now in primary range */
225 hfx = 0.5 * x;
226 hxs = x * hfx;
227 r1 = one + hxs * (Q1 + hxs * (Q2 + hxs * (Q3 + hxs * (Q4 + hxs * Q5))));
228 t = 3.0 - r1 * hfx;
229 e = hxs * ((r1 - t) / (6.0 - x * t));
230 if (k == 0)
231 return x - (x * e - hxs); /* c is 0 */
232 else {
233 e = (x * (e - c) - c);
234 e -= hxs;
235 if (k == -1)
236 return 0.5 * (x - e) - 0.5;
237 if (k == 1)
238 if (x < -0.25)
239 return -2.0 * (e - (x + 0.5));
240 else
241 return one + 2.0 * (x - e);
242 if (k <= -2 || k > 56) { /* suffice to return exp(x)-1 */
243 y = one - (e - x);
244 ((int *) &y)[HIWORD] += k << 20;
245 return y - one;
246 }
247 t = one;
248 if (k < 20) {
249 ((int *) &t)[HIWORD] = 0x3ff00000 - (0x200000 >> k);
250 /* t = 1 - 2^-k */
251 y = t - (e - x);
252 ((int *) &y)[HIWORD] += k << 20;
253 }
254 else {
255 ((int *) &t)[HIWORD] = (0x3ff - k) << 20; /* 2^-k */
256 y = x - (e + t);
257 y += one;
258 ((int *) &y)[HIWORD] += k << 20;
259 }
260 }
261 return y;
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143 /* Q2 */ 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */
144 /* Q3 */ -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */
145 /* Q4 */ 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */
146 /* Q5 */ -2.01099218183624371326e-07 /* BE8AFDB7 6E09C32D */
147 };
148 #define one xxx[0]
149 #define huge xxx[1]
150 #define tiny xxx[2]
151 #define o_threshold xxx[3]
152 #define ln2_hi xxx[4]
153 #define ln2_lo xxx[5]
154 #define invln2 xxx[6]
155 #define Q1 xxx[7]
156 #define Q2 xxx[8]
157 #define Q3 xxx[9]
158 #define Q4 xxx[10]
159 #define Q5 xxx[11]
160
161 double
162 expm1(double x) {
163 double y, hi, lo, c = 0.0L, t, e, hxs, hfx, r1;
164 int k, xsb;
165 unsigned hx;
166
167 hx = ((unsigned *) &x)[HIWORD]; /* high word of x */
168 xsb = hx & 0x80000000; /* sign bit of x */
169 if (xsb == 0)
170 y = x;
171 else
172 y = -x; /* y = |x| */
173 hx &= 0x7fffffff; /* high word of |x| */
174
175 /* filter out huge and non-finite argument */
176 /* for example exp(38)-1 is approximately 3.1855932e+16 */
177 if (hx >= 0x4043687A) { /* if |x|>=56*ln2 (~38.8162...)*/
178 if (hx >= 0x40862E42) { /* if |x|>=709.78... -> inf */
179 if (hx >= 0x7ff00000) {
180 if (((hx & 0xfffff) | ((int *) &x)[LOWORD])
181 != 0)
182 return x * x; /* + -> * for Cheetah */
183 else
184 return xsb == 0 ? x : -1.0; /* exp(+-inf)={inf,-1} */
185 }
186 if (x > o_threshold)
187 return huge * huge; /* overflow */
188 }
189 if (xsb != 0) { /* x < -56*ln2, return -1.0 w/inexact */
190 if (x + tiny < 0.0) /* raise inexact */
191 return tiny - one; /* return -1 */
192 }
193 }
194
195 /* argument reduction */
196 if (hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
197 if (hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
198 if (xsb == 0) { /* positive number */
199 hi = x - ln2_hi;
200 lo = ln2_lo;
201 k = 1;
202 }
203 else { /* negative number */
204 hi = x + ln2_hi;
205 lo = -ln2_lo;
206 k = -1;
207 }
208 }
209 else { /* |x| > 1.5 ln2 */
210 k = (int) (invln2 * x + (xsb == 0 ? 0.5 : -0.5));
211 t = k;
212 hi = x - t * ln2_hi; /* t*ln2_hi is exact here */
213 lo = t * ln2_lo;
214 }
215 x = hi - lo;
216 c = (hi - x) - lo; /* still at |x| > 0.5 ln2 */
217 }
218 else if (hx < 0x3c900000) { /* when |x|<2**-54, return x */
219 t = huge + x; /* return x w/inexact when x != 0 */
220 return x - (t - (huge + x));
221 }
222 else /* |x| <= 0.5 ln2 */
223 k = 0;
224
225 /* x is now in primary range */
226 hfx = 0.5 * x;
227 hxs = x * hfx;
228 r1 = one + hxs * (Q1 + hxs * (Q2 + hxs * (Q3 + hxs * (Q4 + hxs * Q5))));
229 t = 3.0 - r1 * hfx;
230 e = hxs * ((r1 - t) / (6.0 - x * t));
231 if (k == 0) /* |x| <= 0.5 ln2 */
232 return x - (x * e - hxs);
233 else { /* |x| > 0.5 ln2 */
234 e = (x * (e - c) - c);
235 e -= hxs;
236 if (k == -1)
237 return 0.5 * (x - e) - 0.5;
238 if (k == 1) {
239 if (x < -0.25)
240 return -2.0 * (e - (x + 0.5));
241 else
242 return one + 2.0 * (x - e);
243 }
244 if (k <= -2 || k > 56) { /* suffice to return exp(x)-1 */
245 y = one - (e - x);
246 ((int *) &y)[HIWORD] += k << 20;
247 return y - one;
248 }
249 t = one;
250 if (k < 20) {
251 ((int *) &t)[HIWORD] = 0x3ff00000 - (0x200000 >> k);
252 /* t = 1 - 2^-k */
253 y = t - (e - x);
254 ((int *) &y)[HIWORD] += k << 20;
255 }
256 else {
257 ((int *) &t)[HIWORD] = (0x3ff - k) << 20; /* 2^-k */
258 y = x - (e + t);
259 y += one;
260 ((int *) &y)[HIWORD] += k << 20;
261 }
262 }
263 return y;
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