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1 /* origin: FreeBSD /usr/src/lib/msun/src/e_exp.c */ | 1 /* origin: FreeBSD /usr/src/lib/msun/src/e_exp.c */ |
2 /* | 2 /* |
3 * ==================================================== | 3 * ==================================================== |
4 * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. | 4 * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. |
5 * | 5 * |
6 * Permission to use, copy, modify, and distribute this | 6 * Permission to use, copy, modify, and distribute this |
7 * software is freely granted, provided that this notice | 7 * software is freely granted, provided that this notice |
8 * is preserved. | 8 * is preserved. |
9 * ==================================================== | 9 * ==================================================== |
10 */ | 10 */ |
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60 * 1 ulp (unit in the last place). | 60 * 1 ulp (unit in the last place). |
61 * | 61 * |
62 * Misc. info. | 62 * Misc. info. |
63 * For IEEE double | 63 * For IEEE double |
64 * if x > 709.782712893383973096 then exp(x) overflows | 64 * if x > 709.782712893383973096 then exp(x) overflows |
65 * if x < -745.133219101941108420 then exp(x) underflows | 65 * if x < -745.133219101941108420 then exp(x) underflows |
66 */ | 66 */ |
67 | 67 |
68 #include "libm.h" | 68 #include "libm.h" |
69 | 69 |
70 static const double | 70 static const double half[2] = {0.5, -0.5}, |
71 half[2] = {0.5,-0.5}, | 71 ln2hi = |
72 ln2hi = 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */ | 72 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */ |
73 ln2lo = 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */ | 73 ln2lo = 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */ |
74 invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */ | 74 invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */ |
75 P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ | 75 P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ |
76 P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ | 76 P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ |
77 P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ | 77 P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ |
78 P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ | 78 P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ |
79 P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */ | 79 P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */ |
80 | 80 |
81 double exp(double x) | 81 double exp(double x) { |
82 { | 82 double_t hi, lo, c, xx, y; |
83 » double_t hi, lo, c, xx, y; | 83 int k, sign; |
84 » int k, sign; | 84 uint32_t hx; |
85 » uint32_t hx; | |
86 | 85 |
87 » GET_HIGH_WORD(hx, x); | 86 GET_HIGH_WORD(hx, x); |
88 » sign = hx>>31; | 87 sign = hx >> 31; |
89 » hx &= 0x7fffffff; /* high word of |x| */ | 88 hx &= 0x7fffffff; /* high word of |x| */ |
90 | 89 |
91 » /* special cases */ | 90 /* special cases */ |
92 » if (hx >= 0x4086232b) { /* if |x| >= 708.39... */ | 91 if (hx >= 0x4086232b) { /* if |x| >= 708.39... */ |
93 » » if (isnan(x)) | 92 if (isnan(x)) |
94 » » » return x; | 93 return x; |
95 » » if (x > 709.782712893383973096) { | 94 if (x > 709.782712893383973096) { |
96 » » » /* overflow if x!=inf */ | 95 /* overflow if x!=inf */ |
97 » » » x *= 0x1p1023; | 96 x *= 0x1p1023; |
98 » » » return x; | 97 return x; |
99 » » } | 98 } |
100 » » if (x < -708.39641853226410622) { | 99 if (x < -708.39641853226410622) { |
101 » » » /* underflow if x!=-inf */ | 100 /* underflow if x!=-inf */ |
102 » » » FORCE_EVAL((float)(-0x1p-149/x)); | 101 FORCE_EVAL((float)(-0x1p-149 / x)); |
103 » » » if (x < -745.13321910194110842) | 102 if (x < -745.13321910194110842) |
104 » » » » return 0; | 103 return 0; |
105 » » } | 104 } |
106 » } | 105 } |
107 | 106 |
108 » /* argument reduction */ | 107 /* argument reduction */ |
109 » if (hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ | 108 if (hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ |
110 » » if (hx >= 0x3ff0a2b2) /* if |x| >= 1.5 ln2 */ | 109 if (hx >= 0x3ff0a2b2) /* if |x| >= 1.5 ln2 */ |
111 » » » k = (int)(invln2*x + half[sign]); | 110 k = (int)(invln2 * x + half[sign]); |
112 » » else | 111 else |
113 » » » k = 1 - sign - sign; | 112 k = 1 - sign - sign; |
114 » » hi = x - k*ln2hi; /* k*ln2hi is exact here */ | 113 hi = x - k * ln2hi; /* k*ln2hi is exact here */ |
115 » » lo = k*ln2lo; | 114 lo = k * ln2lo; |
116 » » x = hi - lo; | 115 x = hi - lo; |
117 » } else if (hx > 0x3e300000) { /* if |x| > 2**-28 */ | 116 } else if (hx > 0x3e300000) { /* if |x| > 2**-28 */ |
118 » » k = 0; | 117 k = 0; |
119 » » hi = x; | 118 hi = x; |
120 » » lo = 0; | 119 lo = 0; |
121 » } else { | 120 } else { |
122 » » /* inexact if x!=0 */ | 121 /* inexact if x!=0 */ |
123 » » FORCE_EVAL(0x1p1023 + x); | 122 FORCE_EVAL(0x1p1023 + x); |
124 » » return 1 + x; | 123 return 1 + x; |
125 » } | 124 } |
126 | 125 |
127 » /* x is now in primary range */ | 126 /* x is now in primary range */ |
128 » xx = x*x; | 127 xx = x * x; |
129 » c = x - xx*(P1+xx*(P2+xx*(P3+xx*(P4+xx*P5)))); | 128 c = x - xx * (P1 + xx * (P2 + xx * (P3 + xx * (P4 + xx * P5)))); |
130 » y = 1 + (x*c/(2-c) - lo + hi); | 129 y = 1 + (x * c / (2 - c) - lo + hi); |
131 » if (k == 0) | 130 if (k == 0) |
132 » » return y; | 131 return y; |
133 » return scalbn(y, k); | 132 return scalbn(y, k); |
134 } | 133 } |
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