compiler/stdc/math/ld128/e_rem_pio2l.h

   1 /* From: @(#)e_rem_pio2.c 1.4 95/01/18 */
   2 /*
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
   6  *
   7  * Developed at SunSoft, a Sun Microsystems, Inc. business.
   8  * Permission to use, copy, modify, and distribute this
   9  * software is freely granted, provided that this notice
  10  * is preserved.
  11  * ====================================================
  12  *
  13  * Optimized by Bruce D. Evans.
  14  */
  15
  16 //__FBSDID("$FreeBSD: src/lib/msun/ld128/e_rem_pio2l.h,v 1.2 2011/05/30 19:41:28 kargl Exp $");
  17
  18 /* ld128 version of __ieee754_rem_pio2l(x,y)
  19  *
  20  * return the remainder of x rem pi/2 in y[0]+y[1]
  21  * use __kernel_rem_pio2()
  22  */
  23
  24 #include <float.h>
  25 #include "math.h"
  26
  27 #include "math_private.h"
  28 #include "fpmath.h"
  29
  30 #define BIAS    (LDBL_MAX_EXP - 1)
  31
  32 /*
  33  * XXX need to verify that nonzero integer multiples of pi/2 within the
  34  * range get no closer to a long double than 2**-140, or that
  35  * ilogb(x) + ilogb(min_delta) < 45 - -140.
  36  */
  37 /*
  38  * invpio2:  113 bits of 2/pi
  39  * pio2_1:   first  68 bits of pi/2
  40  * pio2_1t:  pi/2 - pio2_1
  41  * pio2_2:   second 68 bits of pi/2
  42  * pio2_2t:  pi/2 - (pio2_1+pio2_2)
  43  * pio2_3:   third  68 bits of pi/2
  44  * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
  45  */
  46
  47 static const double
  48 zero =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
  49 two24 =  1.67772160000000000000e+07; /* 0x41700000, 0x00000000 */
  50
  51 static const long double
  52 invpio2 =  6.3661977236758134307553505349005747e-01L,   /*  0x145f306dc9c882a53f84eafa3ea6a.0p-113 */
  53 pio2_1  =  1.5707963267948966192292994253909555e+00L,   /*  0x1921fb54442d18469800000000000.0p-112 */
  54 pio2_1t =  2.0222662487959507323996846200947577e-21L,   /*  0x13198a2e03707344a4093822299f3.0p-181 */
  55 pio2_2  =  2.0222662487959507323994779168837751e-21L,   /*  0x13198a2e03707344a400000000000.0p-181 */
  56 pio2_2t =  2.0670321098263988236496903051604844e-43L,   /*  0x127044533e63a0105df531d89cd91.0p-254 */
  57 pio2_3  =  2.0670321098263988236499468110329591e-43L,   /*  0x127044533e63a0105e00000000000.0p-254 */
  58 pio2_3t = -2.5650587247459238361625433492959285e-65L;   /* -0x159c4ec64ddaeb5f78671cbfb2210.0p-327 */
  59
  60 //VBS
  61 //static inline __always_inline int
  62 //__ieee754_rem_pio2l(long double x, long double *y)
  63
  64 static inline int
  65 __ieee754_rem_pio2l(long double x, long double *y)
  66 {
  67         union IEEEl2bits u,u1;
  68         long double z,w,t,r,fn;
  69         double tx[5],ty[3];
  70         int64_t n;
  71         int e0,ex,i,j,nx;
  72         int16_t expsign;
  73
  74         u.e = x;
  75         expsign = u.xbits.expsign;
  76         ex = expsign & 0x7fff;
  77         if (ex < BIAS + 45 || ex == BIAS + 45 &&
  78             u.bits.manh < 0x921fb54442d1LL) {
  79             /* |x| ~< 2^45*(pi/2), medium size */
  80             /* Use a specialized rint() to get fn.  Assume round-to-nearest. */
  81             fn = x*invpio2+0x1.8p112;
  82             fn = fn-0x1.8p112;
  83 #ifdef HAVE_EFFICIENT_I64RINT
  84             n  = i64rint(fn);
  85 #else
  86             n  = fn;
  87 #endif
  88             r  = x-fn*pio2_1;
  89             w  = fn*pio2_1t;    /* 1st round good to 180 bit */
  90             {
  91                 union IEEEl2bits u2;
  92                 int ex1;
  93                 j  = ex;
  94                 y[0] = r-w;
  95                 u2.e = y[0];
  96                 ex1 = u2.xbits.expsign & 0x7fff;
  97                 i = j-ex1;
  98                 if(i>51) {  /* 2nd iteration needed, good to 248 */
  99                     t  = r;
 100                     w  = fn*pio2_2;
 101                     r  = t-w;
 102                     w  = fn*pio2_2t-((t-r)-w);
 103                     y[0] = r-w;
 104                     u2.e = y[0];
 105                     ex1 = u2.xbits.expsign & 0x7fff;
 106                     i = j-ex1;
 107                     if(i>119) { /* 3rd iteration need, 316 bits acc */
 108                         t  = r; /* will cover all possible cases */
 109                         w  = fn*pio2_3;
 110                         r  = t-w;
 111                         w  = fn*pio2_3t-((t-r)-w);
 112                         y[0] = r-w;
 113                     }
 114                 }
 115             }
 116             y[1] = (r-y[0])-w;
 117             return n;
 118         }
 119     /*
 120      * all other (large) arguments
 121      */
 122         if(ex==0x7fff) {                /* x is inf or NaN */
 123             y[0]=y[1]=x-x; return 0;
 124         }
 125     /* set z = scalbn(|x|,ilogb(x)-23) */
 126         u1.e = x;
 127         e0 = ex - BIAS - 23;            /* e0 = ilogb(|x|)-23; */
 128         u1.xbits.expsign = ex - e0;
 129         z = u1.e;
 130         for(i=0;i<4;i++) {
 131                 tx[i] = (double)((int32_t)(z));
 132                 z     = (z-tx[i])*two24;
 133         }
 134         tx[4] = z;
 135         nx = 5;
 136         while(tx[nx-1]==zero) nx--;     /* skip zero term */
 137         n  =  __kernel_rem_pio2(tx,ty,e0,nx,3);
 138         t = (long double)ty[2] + ty[1];
 139         r = t + ty[0];
 140         w = ty[0] - (r - t);
 141         if(expsign<0) {y[0] = -r; y[1] = -w; return -n;}
 142         y[0] = r; y[1] = w; return n;
 143 }