compiler/stdc/math/ld80/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/ld80/e_rem_pio2l.h,v 1.3 2011/06/18 13:56:33 benl Exp $");
  17
  18 /* ld80 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
  29 #define BIAS    (LDBL_MAX_EXP - 1)
  30
  31 /*
  32  * invpio2:  64 bits of 2/pi
  33  * pio2_1:   first  39 bits of pi/2
  34  * pio2_1t:  pi/2 - pio2_1
  35  * pio2_2:   second 39 bits of pi/2
  36  * pio2_2t:  pi/2 - (pio2_1+pio2_2)
  37  * pio2_3:   third  39 bits of pi/2
  38  * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
  39  */
  40
  41 static const double
  42 zero =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
  43 two24 =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
  44 pio2_1  =  1.57079632679597125389e+00,  /* 0x3FF921FB, 0x54444000 */
  45 pio2_2  = -1.07463465549783099519e-12,  /* -0x12e7b967674000.0p-92 */
  46 pio2_3  =  6.36831716351370313614e-25;  /*  0x18a2e037074000.0p-133 */
  47
  48 #if defined(__amd64__) || defined(__i386__)
  49 /* Long double constants are slow on these arches, and broken on i386. */
  50 static const volatile double
  51 invpio2hi __attribute__ ((__section__(".rodata"))) =  6.3661977236758138e-01,   /*  0x145f306dc9c883.0p-53 */
  52 invpio2lo __attribute__ ((__section__(".rodata"))) = -3.9356538861223811e-17,   /* -0x16b00000000000.0p-107 */
  53 pio2_1thi __attribute__ ((__section__(".rodata"))) = -1.0746346554971943e-12,   /* -0x12e7b9676733af.0p-92 */
  54 pio2_1tlo __attribute__ ((__section__(".rodata"))) =  8.8451028997905949e-29,   /*  0x1c080000000000.0p-146 */
  55 pio2_2thi __attribute__ ((__section__(".rodata"))) =  6.3683171635109499e-25,   /*  0x18a2e03707344a.0p-133 */
  56 pio2_2tlo __attribute__ ((__section__(".rodata"))) =  2.3183081793789774e-41,   /*  0x10280000000000.0p-187 */
  57 pio2_3thi __attribute__ ((__section__(".rodata"))) = -2.7529965190440717e-37,   /* -0x176b7ed8fbbacc.0p-174 */
  58 pio2_3tlo __attribute__ ((__section__(".rodata"))) = -4.2006647512740502e-54;   /* -0x19c00000000000.0p-230 */
  59 #define invpio2 ((long double)invpio2hi + invpio2lo)
  60 #define pio2_1t ((long double)pio2_1thi + pio2_1tlo)
  61 #define pio2_2t ((long double)pio2_2thi + pio2_2tlo)
  62 #define pio2_3t ((long double)pio2_3thi + pio2_3tlo)
  63 #else
  64 static const long double
  65 invpio2 =  6.36619772367581343076e-01L, /*  0xa2f9836e4e44152a.0p-64 */
  66 pio2_1t = -1.07463465549719416346e-12L, /* -0x973dcb3b399d747f.0p-103 */
  67 pio2_2t =  6.36831716351095013979e-25L, /*  0xc51701b839a25205.0p-144 */
  68 pio2_3t = -2.75299651904407171810e-37L; /* -0xbb5bf6c7ddd660ce.0p-185 */
  69 #endif
  70
  71 //VBS
  72 //static inline __always_inline int
  73 //__ieee754_rem_pio2l(long double x, long double *y)
  74
  75 static inline int
  76 __ieee754_rem_pio2l(long double x, long double *y)
  77 {
  78         union IEEEl2bits u,u1;
  79         long double z,w,t,r,fn;
  80         double tx[3],ty[2];
  81         int e0,ex,i,j,nx,n;
  82         int16_t expsign;
  83
  84         u.e = x;
  85         expsign = u.xbits.expsign;
  86         ex = expsign & 0x7fff;
  87         if (ex < BIAS + 25 || (ex == BIAS + 25 && u.bits.manh < 0xc90fdaa2)) {
  88             /* |x| ~< 2^25*(pi/2), medium size */
  89             /* Use a specialized rint() to get fn.  Assume round-to-nearest. */
  90             fn = x*invpio2+0x1.8p63;
  91             fn = fn-0x1.8p63;
  92 #ifdef HAVE_EFFICIENT_IRINT
  93             n  = irint(fn);
  94 #else
  95             n  = fn;
  96 #endif
  97             r  = x-fn*pio2_1;
  98             w  = fn*pio2_1t;    /* 1st round good to 102 bit */
  99             {
 100                 union IEEEl2bits u2;
 101                 int ex1;
 102                 j  = ex;
 103                 y[0] = r-w;
 104                 u2.e = y[0];
 105                 ex1 = u2.xbits.expsign & 0x7fff;
 106                 i = j-ex1;
 107                 if(i>22) {  /* 2nd iteration needed, good to 141 */
 108                     t  = r;
 109                     w  = fn*pio2_2;
 110                     r  = t-w;
 111                     w  = fn*pio2_2t-((t-r)-w);
 112                     y[0] = r-w;
 113                     u2.e = y[0];
 114                     ex1 = u2.xbits.expsign & 0x7fff;
 115                     i = j-ex1;
 116                     if(i>61) {  /* 3rd iteration need, 180 bits acc */
 117                         t  = r; /* will cover all possible cases */
 118                         w  = fn*pio2_3;
 119                         r  = t-w;
 120                         w  = fn*pio2_3t-((t-r)-w);
 121                         y[0] = r-w;
 122                     }
 123                 }
 124             }
 125             y[1] = (r-y[0])-w;
 126             return n;
 127         }
 128     /*
 129      * all other (large) arguments
 130      */
 131         if(ex==0x7fff) {                /* x is inf or NaN */
 132             y[0]=y[1]=x-x; return 0;
 133         }
 134     /* set z = scalbn(|x|,ilogb(x)-23) */
 135         u1.e = x;
 136         e0 = ex - BIAS - 23;            /* e0 = ilogb(|x|)-23; */
 137         u1.xbits.expsign = ex - e0;
 138         z = u1.e;
 139         for(i=0;i<2;i++) {
 140                 tx[i] = (double)((int32_t)(z));
 141                 z     = (z-tx[i])*two24;
 142         }
 143         tx[2] = z;
 144         nx = 3;
 145         while(tx[nx-1]==zero) nx--;     /* skip zero term */
 146         n  =  __kernel_rem_pio2(tx,ty,e0,nx,2);
 147         r = (long double)ty[0] + ty[1];
 148         w = ty[1] - (r - ty[0]);
 149         if(expsign<0) {y[0] = -r; y[1] = -w; return -n;}
 150         y[0] = r; y[1] = w; return n;
 151 }