1 | /* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2f.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 | * Debugged and optimized by Bruce D. Evans.
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5 | */
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6 | /*
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7 | * ====================================================
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8 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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9 | *
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10 | * Developed at SunPro, a Sun Microsystems, Inc. business.
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11 | * Permission to use, copy, modify, and distribute this
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12 | * software is freely granted, provided that this notice
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13 | * is preserved.
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14 | * ====================================================
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15 | */
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16 | /* __rem_pio2f(x,y)
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17 | *
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18 | * return the remainder of x rem pi/2 in *y
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19 | * use double precision for everything except passing x
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20 | * use __rem_pio2_large() for large x
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21 | */
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22 |
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23 | #include "libm.h"
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24 |
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25 | #if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1
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26 | #define EPS DBL_EPSILON
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27 | #elif FLT_EVAL_METHOD==2
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28 | #define EPS LDBL_EPSILON
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29 | #endif
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30 |
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31 | /*
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32 | * invpio2: 53 bits of 2/pi
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33 | * pio2_1: first 25 bits of pi/2
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34 | * pio2_1t: pi/2 - pio2_1
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35 | */
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36 | static const double
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37 | toint = 1.5/EPS,
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38 | invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
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39 | pio2_1 = 1.57079631090164184570e+00, /* 0x3FF921FB, 0x50000000 */
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40 | pio2_1t = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */
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41 |
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42 | int __rem_pio2f(float x, double *y)
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43 | {
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44 | union {float f; uint32_t i;} u = {x};
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45 | double tx[1],ty[1];
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46 | double_t fn;
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47 | uint32_t ix;
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48 | int n, sign, e0;
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49 |
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50 | ix = u.i & 0x7fffffff;
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51 | /* 25+53 bit pi is good enough for medium size */
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52 | if (ix < 0x4dc90fdb) { /* |x| ~< 2^28*(pi/2), medium size */
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53 | /* Use a specialized rint() to get fn. Assume round-to-nearest. */
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54 | fn = (double_t)x*invpio2 + toint - toint;
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55 | n = (int32_t)fn;
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56 | *y = x - fn*pio2_1 - fn*pio2_1t;
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57 | return n;
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58 | }
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59 | if(ix>=0x7f800000) { /* x is inf or NaN */
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60 | *y = x-x;
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61 | return 0;
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62 | }
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63 | /* scale x into [2^23, 2^24-1] */
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64 | sign = u.i>>31;
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65 | e0 = (ix>>23) - (0x7f+23); /* e0 = ilogb(|x|)-23, positive */
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66 | u.i = ix - (e0<<23);
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67 | tx[0] = u.f;
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68 | n = __rem_pio2_large(tx,ty,e0,1,0);
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69 | if (sign) {
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70 | *y = -ty[0];
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71 | return -n;
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72 | }
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73 | *y = ty[0];
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74 | return n;
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75 | }
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