106 /* Lp4 */ 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
107 /* Lp5 */ 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
108 /* Lp6 */ 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
109 /* Lp7 */ 1.479819860511658591e-01, /* 3FC2F112 DF3E5244 */
110 /* zero */ 0.0
111 };
112 #define ln2_hi xxx[0]
113 #define ln2_lo xxx[1]
114 #define two54 xxx[2]
115 #define Lp1 xxx[3]
116 #define Lp2 xxx[4]
117 #define Lp3 xxx[5]
118 #define Lp4 xxx[6]
119 #define Lp5 xxx[7]
120 #define Lp6 xxx[8]
121 #define Lp7 xxx[9]
122 #define zero xxx[10]
123
124 double
125 log1p(double x) {
126 double hfsq, f, c, s, z, R, u;
127 int k, hx, hu, ax;
128
129 hx = ((int *)&x)[HIWORD]; /* high word of x */
130 ax = hx & 0x7fffffff;
131
132 if (ax >= 0x7ff00000) { /* x is inf or nan */
133 if (((hx - 0xfff00000) | ((int *)&x)[LOWORD]) == 0) /* -inf */
134 return (_SVID_libm_err(x, x, 44));
135 return (x * x);
136 }
137
138 k = 1;
139 if (hx < 0x3FDA827A) { /* x < 0.41422 */
140 if (ax >= 0x3ff00000) /* x <= -1.0 */
141 return (_SVID_libm_err(x, x, x == -1.0 ? 43 : 44));
142 if (ax < 0x3e200000) { /* |x| < 2**-29 */
143 if (two54 + x > zero && /* raise inexact */
144 ax < 0x3c900000) /* |x| < 2**-54 */
145 return (x);
146 else
147 return (x - x * x * 0.5);
148 }
149 if (hx > 0 || hx <= (int)0xbfd2bec3) { /* -0.2929<x<0.41422 */
150 k = 0;
151 f = x;
152 hu = 1;
153 }
154 }
155 if (k != 0) {
156 if (hx < 0x43400000) {
157 u = 1.0 + x;
158 hu = ((int *)&u)[HIWORD]; /* high word of u */
159 k = (hu >> 20) - 1023;
160 /*
161 * correction term
162 */
163 c = k > 0 ? 1.0 - (u - x) : x - (u - 1.0);
164 c /= u;
165 } else {
166 u = x;
167 hu = ((int *)&u)[HIWORD]; /* high word of u */
168 k = (hu >> 20) - 1023;
169 c = 0;
170 }
171 hu &= 0x000fffff;
172 if (hu < 0x6a09e) { /* normalize u */
173 ((int *)&u)[HIWORD] = hu | 0x3ff00000;
174 } else { /* normalize u/2 */
175 k += 1;
176 ((int *)&u)[HIWORD] = hu | 0x3fe00000;
177 hu = (0x00100000 - hu) >> 2;
178 }
179 f = u - 1.0;
180 }
181 hfsq = 0.5 * f * f;
182 if (hu == 0) { /* |f| < 2**-20 */
183 if (f == zero) {
184 if (k == 0)
185 return (zero);
186 c += k * ln2_lo;
187 return (k * ln2_hi + c);
188 }
189 R = hfsq * (1.0 - 0.66666666666666666 * f);
190 if (k == 0)
191 return (f - R);
192 return (k * ln2_hi - ((R - (k * ln2_lo + c)) - f));
193 }
194 s = f / (2.0 + f);
195 z = s * s;
196 R = z * (Lp1 + z * (Lp2 + z * (Lp3 + z * (Lp4 + z * (Lp5 +
197 z * (Lp6 + z * Lp7))))));
198 if (k == 0)
199 return (f - (hfsq - s * (hfsq + R)));
200 return (k * ln2_hi - ((hfsq - (s * (hfsq + R) +
201 (k * ln2_lo + c))) - f));
202 }
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106 /* Lp4 */ 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
107 /* Lp5 */ 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
108 /* Lp6 */ 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
109 /* Lp7 */ 1.479819860511658591e-01, /* 3FC2F112 DF3E5244 */
110 /* zero */ 0.0
111 };
112 #define ln2_hi xxx[0]
113 #define ln2_lo xxx[1]
114 #define two54 xxx[2]
115 #define Lp1 xxx[3]
116 #define Lp2 xxx[4]
117 #define Lp3 xxx[5]
118 #define Lp4 xxx[6]
119 #define Lp5 xxx[7]
120 #define Lp6 xxx[8]
121 #define Lp7 xxx[9]
122 #define zero xxx[10]
123
124 double
125 log1p(double x) {
126 double hfsq, f, c = 0.0, s, z, R, u;
127 int k, hx, hu, ax;
128
129 hx = ((int *)&x)[HIWORD]; /* high word of x */
130 ax = hx & 0x7fffffff;
131
132 if (ax >= 0x7ff00000) { /* x is inf or nan */
133 if (((hx - 0xfff00000) | ((int *)&x)[LOWORD]) == 0) /* -inf */
134 return (_SVID_libm_err(x, x, 44));
135 return (x * x);
136 }
137
138 k = 1;
139 if (hx < 0x3FDA827A) { /* x < 0.41422 */
140 if (ax >= 0x3ff00000) /* x <= -1.0 */
141 return (_SVID_libm_err(x, x, x == -1.0 ? 43 : 44));
142 if (ax < 0x3e200000) { /* |x| < 2**-29 */
143 if (two54 + x > zero && /* raise inexact */
144 ax < 0x3c900000) /* |x| < 2**-54 */
145 return (x);
146 else
147 return (x - x * x * 0.5);
148 }
149 if (hx > 0 || hx <= (int)0xbfd2bec3) { /* -0.2929<x<0.41422 */
150 k = 0;
151 f = x;
152 hu = 1;
153 }
154 }
155 /* We will initialize 'c' here. */
156 if (k != 0) {
157 if (hx < 0x43400000) {
158 u = 1.0 + x;
159 hu = ((int *)&u)[HIWORD]; /* high word of u */
160 k = (hu >> 20) - 1023;
161 /*
162 * correction term
163 */
164 c = k > 0 ? 1.0 - (u - x) : x - (u - 1.0);
165 c /= u;
166 } else {
167 u = x;
168 hu = ((int *)&u)[HIWORD]; /* high word of u */
169 k = (hu >> 20) - 1023;
170 c = 0;
171 }
172 hu &= 0x000fffff;
173 if (hu < 0x6a09e) { /* normalize u */
174 ((int *)&u)[HIWORD] = hu | 0x3ff00000;
175 } else { /* normalize u/2 */
176 k += 1;
177 ((int *)&u)[HIWORD] = hu | 0x3fe00000;
178 hu = (0x00100000 - hu) >> 2;
179 }
180 f = u - 1.0;
181 }
182 hfsq = 0.5 * f * f;
183 if (hu == 0) { /* |f| < 2**-20 */
184 if (f == zero) {
185 if (k == 0)
186 return (zero);
187 /* We already initialized 'c' before, when (k != 0) */
188 c += k * ln2_lo;
189 return (k * ln2_hi + c);
190 }
191 R = hfsq * (1.0 - 0.66666666666666666 * f);
192 if (k == 0)
193 return (f - R);
194 return (k * ln2_hi - ((R - (k * ln2_lo + c)) - f));
195 }
196 s = f / (2.0 + f);
197 z = s * s;
198 R = z * (Lp1 + z * (Lp2 + z * (Lp3 + z * (Lp4 + z * (Lp5 +
199 z * (Lp6 + z * Lp7))))));
200 if (k == 0)
201 return (f - (hfsq - s * (hfsq + R)));
202 return (k * ln2_hi - ((hfsq - (s * (hfsq + R) +
203 (k * ln2_lo + c))) - f));
204 }
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