1 | /* origin: FreeBSD /usr/src/lib/msun/src/e_expf.c */
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2 | /*
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3 | * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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4 | */
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5 | /*
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6 | * ====================================================
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7 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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8 | *
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9 | * Developed at SunPro, a Sun Microsystems, Inc. business.
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10 | * Permission to use, copy, modify, and distribute this
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11 | * software is freely granted, provided that this notice
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12 | * is preserved.
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13 | * ====================================================
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14 | */
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15 |
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16 | #include "libm.h"
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17 |
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18 | static const float
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19 | half[2] = {0.5,-0.5},
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20 | ln2hi = 6.9314575195e-1f, /* 0x3f317200 */
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21 | ln2lo = 1.4286067653e-6f, /* 0x35bfbe8e */
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22 | invln2 = 1.4426950216e+0f, /* 0x3fb8aa3b */
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23 | /*
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24 | * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
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25 | * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
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26 | */
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27 | P1 = 1.6666625440e-1f, /* 0xaaaa8f.0p-26 */
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28 | P2 = -2.7667332906e-3f; /* -0xb55215.0p-32 */
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29 |
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30 | float expf(float x)
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31 | {
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32 | float_t hi, lo, c, xx, y;
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33 | int k, sign;
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34 | uint32_t hx;
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35 |
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36 | GET_FLOAT_WORD(hx, x);
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37 | sign = hx >> 31; /* sign bit of x */
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38 | hx &= 0x7fffffff; /* high word of |x| */
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39 |
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40 | /* special cases */
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41 | if (hx >= 0x42aeac50) { /* if |x| >= -87.33655f or NaN */
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42 | if (hx > 0x7f800000) /* NaN */
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43 | return x;
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44 | if (hx >= 0x42b17218 && !sign) { /* x >= 88.722839f */
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45 | /* overflow */
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46 | x *= 0x1p127f;
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47 | return x;
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48 | }
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49 | if (sign) {
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50 | /* underflow */
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51 | FORCE_EVAL(-0x1p-149f/x);
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52 | if (hx >= 0x42cff1b5) /* x <= -103.972084f */
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53 | return 0;
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54 | }
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55 | }
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56 |
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57 | /* argument reduction */
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58 | if (hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
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59 | if (hx > 0x3f851592) /* if |x| > 1.5 ln2 */
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60 | k = invln2*x + half[sign];
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61 | else
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62 | k = 1 - sign - sign;
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63 | hi = x - k*ln2hi; /* k*ln2hi is exact here */
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64 | lo = k*ln2lo;
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65 | x = hi - lo;
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66 | } else if (hx > 0x39000000) { /* |x| > 2**-14 */
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67 | k = 0;
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68 | hi = x;
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69 | lo = 0;
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70 | } else {
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71 | /* raise inexact */
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72 | FORCE_EVAL(0x1p127f + x);
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73 | return 1 + x;
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74 | }
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75 |
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76 | /* x is now in primary range */
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77 | xx = x*x;
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78 | c = x - xx*(P1+xx*P2);
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79 | y = 1 + (x*c/(2-c) - lo + hi);
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80 | if (k == 0)
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81 | return y;
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82 | return scalbnf(y, k);
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83 | }
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