Code coverage tests

This page documents the degree to which the PARI/GP source code is tested by our public test suite, distributed with the source distribution in directory src/test/. This is measured by the gcov utility; we then process gcov output using the lcov frond-end.

We test a few variants depending on Configure flags on the pari.math.u-bordeaux.fr machine (x86_64 architecture), and agregate them in the final report:

The target is to exceed 90% coverage for all mathematical modules (given that branches depending on DEBUGLEVEL or DEBUGMEM are not covered). This script is run to produce the results below.

LCOV - code coverage report
Current view: top level - kernel/none - mp_indep.c (source / functions) Hit Total Coverage
Test: PARI/GP v2.14.0 lcov report (development 27095-7e0f67a20c) Lines: 540 572 94.4 %
Date: 2021-11-29 07:04:58 Functions: 52 53 98.1 %
Legend: Lines: hit not hit

          Line data    Source code
       1             : #line 2 "../src/kernel/none/mp_indep.c"
       2             : /* Copyright (C) 2000  The PARI group.
       3             : 
       4             : This file is part of the PARI/GP package.
       5             : 
       6             : PARI/GP is free software; you can redistribute it and/or modify it under the
       7             : terms of the GNU General Public License as published by the Free Software
       8             : Foundation; either version 2 of the License, or (at your option) any later
       9             : version. It is distributed in the hope that it will be useful, but WITHOUT
      10             : ANY WARRANTY WHATSOEVER.
      11             : 
      12             : Check the License for details. You should have received a copy of it, along
      13             : with the package; see the file 'COPYING'. If not, write to the Free Software
      14             : Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. */
      15             : 
      16             : /* Find c such that 1=c*b mod 2^BITS_IN_LONG, assuming b odd (unchecked) */
      17             : ulong
      18    44994054 : invmod2BIL(ulong b)
      19             : {
      20             :   static int tab[] = { 0, 0, 0, 8, 0, 8, 0, 0 };
      21    44994054 :   ulong x = b + tab[b & 7]; /* b^(-1) mod 2^4 */
      22             : 
      23             :   /* Newton applied to 1/x - b = 0 */
      24             : #ifdef LONG_IS_64BIT
      25    44994054 :   x = x*(2-b*x); /* one more pass necessary */
      26             : #endif
      27    44994054 :   x = x*(2-b*x);
      28    44994054 :   x = x*(2-b*x); return x*(2-b*x);
      29             : }
      30             : 
      31             : void
      32   624149821 : affrr(GEN x, GEN y)
      33             : {
      34   624149821 :   long i, lx, ly = lg(y);
      35   624149821 :   if (!signe(x))
      36             :   {
      37      264396 :     y[1] = evalexpo(minss(expo(x), -bit_accuracy(ly)));
      38      264396 :     return;
      39             :   }
      40   623885425 :   y[1] = x[1]; lx = lg(x);
      41   623885425 :   if (lx <= ly)
      42             :   {
      43  2452351138 :     for (i=2; i<lx; i++) y[i]=x[i];
      44   598341924 :     for (   ; i<ly; i++) y[i]=0;
      45   493542718 :     return;
      46             :   }
      47   534173760 :   for (i=2; i<ly; i++) y[i]=x[i];
      48             :   /* lx > ly: round properly */
      49   130342707 :   if (x[ly] & HIGHBIT) roundr_up_ip(y, ly);
      50             : }
      51             : 
      52             : GEN
      53    58476300 : trunc2nr(GEN x, long n)
      54             : {
      55             :   long ex;
      56    58476300 :   if (!signe(x)) return gen_0;
      57    57968892 :   ex = expo(x) + n; if (ex < 0) return gen_0;
      58    55197899 :   return mantissa2nr(x, ex - bit_prec(x) + 1);
      59             : }
      60             : 
      61             : /* x a t_REAL, x = i/2^e, i a t_INT */
      62             : GEN
      63    34753661 : mantissa_real(GEN x, long *e)
      64             : {
      65    34753661 :   *e = bit_prec(x)-1-expo(x);
      66    34753633 :   return mantissa2nr(x, 0);
      67             : }
      68             : 
      69             : GEN
      70   808461345 : mului(ulong x, GEN y)
      71             : {
      72   808461345 :   long s = signe(y);
      73             :   GEN z;
      74             : 
      75   808461345 :   if (!s || !x) return gen_0;
      76   651815053 :   z = muluispec(x, y+2, lgefint(y)-2);
      77   649622094 :   setsigne(z,s); return z;
      78             : }
      79             : 
      80             : GEN
      81   493900492 : mulsi(long x, GEN y)
      82             : {
      83   493900492 :   long s = signe(y);
      84             :   GEN z;
      85             : 
      86   493900492 :   if (!s || !x) return gen_0;
      87   335379986 :   if (x<0) { s = -s; x = -x; }
      88   335379986 :   z = muluispec((ulong)x, y+2, lgefint(y)-2);
      89   335371048 :   setsigne(z,s); return z;
      90             : }
      91             : 
      92             : GEN
      93   195463366 : mulss(long x, long y)
      94             : {
      95             :   long p1;
      96             :   LOCAL_HIREMAINDER;
      97             : 
      98   195463366 :   if (!x || !y) return gen_0;
      99   195279068 :   if (x<0) {
     100      339506 :     x = -x;
     101      339506 :     if (y<0) { y = -y; p1 = mulll(x,y); return uutoi(hiremainder, p1); }
     102      225471 :     p1 = mulll(x,y); return uutoineg(hiremainder, p1);
     103             :   } else {
     104   194939562 :     if (y<0) { y = -y; p1 = mulll(x,y); return uutoineg(hiremainder, p1); }
     105   194935442 :     p1 = mulll(x,y); return uutoi(hiremainder, p1);
     106             :   }
     107             : }
     108             : GEN
     109      963794 : sqrs(long x)
     110             : {
     111             :   long p1;
     112             :   LOCAL_HIREMAINDER;
     113             : 
     114      963794 :   if (!x) return gen_0;
     115      962870 :   if (x<0) x = -x;
     116      962870 :   p1 = mulll(x,x); return uutoi(hiremainder, p1);
     117             : }
     118             : GEN
     119  3290364849 : muluu(ulong x, ulong y)
     120             : {
     121             :   long p1;
     122             :   LOCAL_HIREMAINDER;
     123             : 
     124  3290364849 :   if (!x || !y) return gen_0;
     125  3290797112 :   p1 = mulll(x,y); return uutoi(hiremainder, p1);
     126             : }
     127             : GEN
     128   474436357 : sqru(ulong x)
     129             : {
     130             :   long p1;
     131             :   LOCAL_HIREMAINDER;
     132             : 
     133   474436357 :   if (!x) return gen_0;
     134   474105569 :   p1 = mulll(x,x); return uutoi(hiremainder, p1);
     135             : }
     136             : 
     137             : /* assume x > 1, y != 0. Return u * y with sign s */
     138             : static GEN
     139   456752240 : mulur_2(ulong x, GEN y, long s)
     140             : {
     141   456752240 :   long m, sh, i, lx = lg(y), e = expo(y);
     142   456752240 :   GEN z = cgetr(lx);
     143             :   ulong garde;
     144             :   LOCAL_HIREMAINDER;
     145             : 
     146   456407480 :   y--; garde = mulll(x,y[lx]);
     147  2570228460 :   for (i=lx-1; i>=3; i--) z[i]=addmul(x,y[i]);
     148   456407480 :   z[2]=hiremainder; /* != 0 since y normalized and |x| > 1 */
     149   456407480 :   sh = bfffo(hiremainder); m = BITS_IN_LONG-sh;
     150   456407480 :   if (sh) shift_left(z,z, 2,lx-1, garde,sh);
     151   456651781 :   z[1] = evalsigne(s) | evalexpo(m+e);
     152   456635741 :   if ((garde << sh) & HIGHBIT) roundr_up_ip(z, lx);
     153   456628324 :   return z;
     154             : }
     155             : 
     156             : INLINE GEN
     157      946069 : mul0r(GEN x)
     158             : {
     159      946069 :   long l = lg(x), e = expo(x);
     160      946069 :   e = (l > 2)? -prec2nbits(l) + e: (e < 0? 2*e: 0);
     161      946069 :   return real_0_bit(e);
     162             : }
     163             : /* lg(x) > 2 */
     164             : INLINE GEN
     165      185422 : div0r(GEN x) {
     166      185422 :   long l = lg(x), e = expo(x);
     167      185422 :   return real_0_bit(-prec2nbits(l) - e);
     168             : }
     169             : 
     170             : GEN
     171   112147522 : mulsr(long x, GEN y)
     172             : {
     173             :   long s;
     174             : 
     175   112147522 :   if (!x) return mul0r(y);
     176   112147474 :   s = signe(y);
     177   112147474 :   if (!s)
     178             :   {
     179      465343 :     if (x < 0) x = -x;
     180      465343 :     return real_0_bit( expo(y) + expu(x) );
     181             :   }
     182   111682131 :   if (x==1)  return rcopy(y);
     183   104114119 :   if (x==-1) return negr(y);
     184   102495729 :   if (x < 0)
     185    30969032 :     return mulur_2((ulong)-x, y, -s);
     186             :   else
     187    71526697 :     return mulur_2((ulong)x, y, s);
     188             : }
     189             : 
     190             : GEN
     191   567817197 : mulur(ulong x, GEN y)
     192             : {
     193             :   long s;
     194             : 
     195   567817197 :   if (!x) return mul0r(y);
     196   567817190 :   s = signe(y);
     197   567817190 :   if (!s) return real_0_bit( expo(y) + expu(x) );
     198   562805652 :   if (x==1) return rcopy(y);
     199   354145806 :   return mulur_2(x, y, s);
     200             : }
     201             : 
     202             : INLINE void
     203  3550946861 : mulrrz_end(GEN z, GEN hi, long lz, long sz, long ez, ulong garde)
     204             : {
     205             :   long i;
     206  3550946861 :   if (hi[2] < 0)
     207             :   {
     208  1726160110 :     if (z != hi)
     209  1023551169 :       for (i=2; i<lz ; i++) z[i] = hi[i];
     210  1726160110 :     ez++;
     211             :   }
     212             :   else
     213             :   {
     214  1824786751 :     shift_left(z,hi,2,lz-1, garde, 1);
     215  1825283222 :     garde <<= 1;
     216             :   }
     217  3551443332 :   if (garde & HIGHBIT)
     218             :   { /* round to nearest */
     219  1764653473 :     i = lz; do ((ulong*)z)[--i]++; while (i>1 && z[i]==0);
     220  1743060046 :     if (i == 1) { z[2] = (long)HIGHBIT; ez++; }
     221             :   }
     222  3551443332 :   z[1] = evalsigne(sz)|evalexpo(ez);
     223  3549131851 : }
     224             : /* mulrrz_end for lz = 3, minor simplifications. z[2]=hiremainder from mulll */
     225             : INLINE void
     226   598098272 : mulrrz_3end(GEN z, long sz, long ez, ulong garde)
     227             : {
     228   598098272 :   if (z[2] < 0)
     229             :   { /* z2 < (2^BIL-1)^2 / 2^BIL, hence z2+1 != 0 */
     230   280043321 :     if (garde & HIGHBIT) z[2]++; /* round properly */
     231   280043321 :     ez++;
     232             :   }
     233             :   else
     234             :   {
     235   318054951 :     uel(z,2) = (uel(z,2)<<1) | (garde>>(BITS_IN_LONG-1));
     236   318054951 :     if (garde & (1UL<<(BITS_IN_LONG-2)))
     237             :     {
     238   132695253 :       uel(z,2)++; /* round properly, z2+1 can overflow */
     239   132695253 :       if (!uel(z,2)) { uel(z,2) = HIGHBIT; ez++; }
     240             :     }
     241             :   }
     242   598098272 :   z[1] = evalsigne(sz)|evalexpo(ez);
     243   597714256 : }
     244             : 
     245             : /* set z <-- x^2 != 0, floating point multiplication.
     246             :  * lz = lg(z) = lg(x) */
     247             : INLINE void
     248   407364963 : sqrz_i(GEN z, GEN x, long lz)
     249             : {
     250   407364963 :   long ez = 2*expo(x);
     251             :   long i, j, lzz, p1;
     252             :   ulong garde;
     253             :   GEN x1;
     254             :   LOCAL_HIREMAINDER;
     255             :   LOCAL_OVERFLOW;
     256             : 
     257   407364963 :   if (lz > SQRR_SQRI_LIMIT)
     258             :   {
     259    11639314 :     pari_sp av = avma;
     260    11639314 :     GEN hi = sqrispec_mirror(x+2, lz-2);
     261    11639314 :     mulrrz_end(z, hi, lz, 1, ez, hi[lz]);
     262    11639314 :     set_avma(av); return;
     263             :   }
     264   395725649 :   if (lz == 3)
     265             :   {
     266    90819642 :     garde = mulll(x[2],x[2]);
     267    90819642 :     z[2] = hiremainder;
     268    90819642 :     mulrrz_3end(z, 1, ez, garde);
     269    90854855 :     return;
     270             :   }
     271             : 
     272   304906007 :   lzz = lz-1; p1 = x[lzz];
     273   304906007 :   if (p1)
     274             :   {
     275   289433548 :     (void)mulll(p1,x[3]);
     276   289433548 :     garde = addmul(p1,x[2]);
     277   289433548 :     z[lzz] = hiremainder;
     278             :   }
     279             :   else
     280             :   {
     281    15472459 :     garde = 0;
     282    15472459 :     z[lzz] = 0;
     283             :   }
     284   822682738 :   for (j=lz-2, x1=x-j; j>=3; j--)
     285             :   {
     286   517776731 :     p1 = x[j]; x1++;
     287   517776731 :     if (p1)
     288             :     {
     289   503451291 :       (void)mulll(p1,x1[lz+1]);
     290   503451291 :       garde = addll(addmul(p1,x1[lz]), garde);
     291  1706566045 :       for (i=lzz; i>j; i--)
     292             :       {
     293  1203114754 :         hiremainder += overflow;
     294  1203114754 :         z[i] = addll(addmul(p1,x1[i]), z[i]);
     295             :       }
     296   503451291 :       z[j] = hiremainder+overflow;
     297             :     }
     298    14325440 :     else z[j]=0;
     299             :   }
     300   304906007 :   p1 = x[2]; x1++;
     301   304906007 :   garde = addll(mulll(p1,x1[lz]), garde);
     302  1127948589 :   for (i=lzz; i>2; i--)
     303             :   {
     304   823042582 :     hiremainder += overflow;
     305   823042582 :     z[i] = addll(addmul(p1,x1[i]), z[i]);
     306             :   }
     307   304906007 :   z[2] = hiremainder+overflow;
     308   304906007 :   mulrrz_end(z, z, lz, 1, ez, garde);
     309             : }
     310             : 
     311             : /* lz "large" = lg(y) = lg(z), lg(x) > lz if flag = 1 and >= if flag = 0 */
     312             : INLINE void
     313    25891261 : mulrrz_int(GEN z, GEN x, GEN y, long lz, long flag, long sz)
     314             : {
     315    25891261 :   pari_sp av = avma;
     316    25891261 :   GEN hi = muliispec_mirror(y+2, x+2, lz+flag-2, lz-2);
     317    25891261 :   mulrrz_end(z, hi, lz, sz, expo(x)+expo(y), hi[lz]);
     318    25891261 :   set_avma(av);
     319    25891261 : }
     320             : 
     321             : /* lz = 3 */
     322             : INLINE void
     323   507447288 : mulrrz_3(GEN z, GEN x, GEN y, long flag, long sz)
     324             : {
     325             :   ulong garde;
     326             :   LOCAL_HIREMAINDER;
     327   507447288 :   if (flag)
     328             :   {
     329    71123330 :     (void)mulll(x[2],y[3]);
     330    71123330 :     garde = addmul(x[2],y[2]);
     331             :   }
     332             :   else
     333   436323958 :     garde = mulll(x[2],y[2]);
     334   507447288 :   z[2] = hiremainder;
     335   507447288 :   mulrrz_3end(z, sz, expo(x)+expo(y), garde);
     336   507717129 : }
     337             : 
     338             : /* set z <-- x*y, floating point multiplication. Trailing 0s for x are
     339             :  * treated efficiently (important application: mulir).
     340             :  * lz = lg(z) = lg(x) <= ly <= lg(y), sz = signe(z). flag = lg(x) < lg(y) */
     341             : INLINE void
     342  3696831715 : mulrrz_i(GEN z, GEN x, GEN y, long lz, long flag, long sz)
     343             : {
     344             :   long ez, i, j, lzz, p1;
     345             :   ulong garde;
     346             :   GEN y1;
     347             :   LOCAL_HIREMAINDER;
     348             :   LOCAL_OVERFLOW;
     349             : 
     350  3696831715 :   if (x == y) { sqrz_i(z,x,lz); return; }
     351  3696831715 :   if (lz > MULRR_MULII_LIMIT) { mulrrz_int(z,x,y,lz,flag,sz); return; }
     352  3670940454 :   if (lz == 3) { mulrrz_3(z,x,y,flag,sz); return; }
     353  3163605013 :   ez = expo(x) + expo(y);
     354  3163605013 :   if (flag) { (void)mulll(x[2],y[lz]); garde = hiremainder; } else garde = 0;
     355  3163605013 :   lzz=lz-1; p1=x[lzz];
     356  3163605013 :   if (p1)
     357             :   {
     358  3057744183 :     (void)mulll(p1,y[3]);
     359  3057744183 :     garde = addll(addmul(p1,y[2]), garde);
     360  3057744183 :     z[lzz] = overflow+hiremainder;
     361             :   }
     362   105860830 :   else z[lzz]=0;
     363 10384085647 :   for (j=lz-2, y1=y-j; j>=3; j--)
     364             :   {
     365  7220480634 :     p1 = x[j]; y1++;
     366  7220480634 :     if (p1)
     367             :     {
     368  6983086954 :       (void)mulll(p1,y1[lz+1]);
     369  6983086954 :       garde = addll(addmul(p1,y1[lz]), garde);
     370 34297112904 :       for (i=lzz; i>j; i--)
     371             :       {
     372 27314025950 :         hiremainder += overflow;
     373 27314025950 :         z[i] = addll(addmul(p1,y1[i]), z[i]);
     374             :       }
     375  6983086954 :       z[j] = hiremainder+overflow;
     376             :     }
     377   237393680 :     else z[j]=0;
     378             :   }
     379  3163605013 :   p1 = x[2]; y1++;
     380  3163605013 :   garde = addll(mulll(p1,y1[lz]), garde);
     381 13562122705 :   for (i=lzz; i>2; i--)
     382             :   {
     383 10398517692 :     hiremainder += overflow;
     384 10398517692 :     z[i] = addll(addmul(p1,y1[i]), z[i]);
     385             :   }
     386  3163605013 :   z[2] = hiremainder+overflow;
     387  3163605013 :   mulrrz_end(z, z, lz, sz, ez, garde);
     388             : }
     389             : 
     390             : GEN
     391  3713086378 : mulrr(GEN x, GEN y)
     392             : {
     393             :   long flag, ly, lz, sx, sy;
     394             :   GEN z;
     395             : 
     396  3713086378 :   if (x == y) return sqrr(x);
     397  3711862411 :   sx = signe(x); if (!sx) return real_0_bit(expo(x) + expo(y));
     398  3669194001 :   sy = signe(y); if (!sy) return real_0_bit(expo(x) + expo(y));
     399  3641522631 :   if (sy < 0) sx = -sx;
     400  3641522631 :   lz = lg(x);
     401  3641522631 :   ly = lg(y);
     402  3641522631 :   if (lz > ly) { lz = ly; swap(x, y); flag = 1; } else flag = (lz != ly);
     403  3641522631 :   z = cgetr(lz);
     404  3636974882 :   mulrrz_i(z, x,y, lz,flag, sx);
     405  3641869642 :   return z;
     406             : }
     407             : 
     408             : GEN
     409   423743697 : sqrr(GEN x)
     410             : {
     411   423743697 :   long lz, sx = signe(x);
     412             :   GEN z;
     413             : 
     414   423743697 :   if (!sx) return real_0_bit(2*expo(x));
     415   407616969 :   lz = lg(x); z = cgetr(lz);
     416   407372503 :   sqrz_i(z, x, lz);
     417   407532209 :   return z;
     418             : }
     419             : 
     420             : GEN
     421   634086961 : mulir(GEN x, GEN y)
     422             : {
     423   634086961 :   long sx = signe(x), sy;
     424   634086961 :   if (!sx) return mul0r(y);
     425   633140947 :   if (lgefint(x) == 3) {
     426   532868616 :     GEN z = mulur(uel(x,2), y);
     427   532505526 :     if (sx < 0) togglesign(z);
     428   532515696 :     return z;
     429             :   }
     430   100272331 :   sy = signe(y);
     431   100272331 :   if (!sy) return real_0_bit(expi(x) + expo(y));
     432    95101461 :   if (sy < 0) sx = -sx;
     433             :   {
     434    95101461 :     long lz = lg(y), lx = lgefint(x);
     435    95101461 :     GEN hi, z = cgetr(lz);
     436    95182159 :     pari_sp av = avma;
     437    95182159 :     if (lx < (lz>>1) || (lx < lz && lz > MULRR_MULII_LIMIT))
     438             :     { /* size mantissa of x < half size of mantissa z, or lx < lz so large
     439             :        * that mulrr will call mulii anyway: mulii */
     440    34946465 :       x = itor(x, lx);
     441    34946849 :       hi = muliispec_mirror(y+2, x+2, lz-2, lx-2);
     442    34946879 :       mulrrz_end(z, hi, lz, sx, expo(x)+expo(y), hi[lz]);
     443             :     }
     444             :     else /* dubious: complete x with 0s and call mulrr */
     445    60235694 :       mulrrz_i(z, itor(x,lz), y, lz, 0, sx);
     446    95188013 :     set_avma(av); return z;
     447             :   }
     448             : }
     449             : 
     450             : /* x + y*z, generic. If lgefint(z) <= 3, caller should use faster variants  */
     451             : static GEN
     452    90967156 : addmulii_gen(GEN x, GEN y, GEN z, long lz)
     453             : {
     454    90967156 :   long lx = lgefint(x), ly;
     455             :   pari_sp av;
     456             :   GEN t;
     457    90967156 :   if (lx == 2) return mulii(z,y);
     458    88055565 :   ly = lgefint(y);
     459    88055565 :   if (ly == 2) return icopy(x); /* y = 0, wasteful copy */
     460    87678995 :   av = avma; (void)new_chunk(lx+ly+lz); /*HACK*/
     461    87680182 :   t = mulii(z, y);
     462    87676114 :   set_avma(av); return addii(t,x);
     463             : }
     464             : /* x + y*z, lgefint(z) == 3 */
     465             : static GEN
     466   624913968 : addmulii_lg3(GEN x, GEN y, GEN z)
     467             : {
     468   624913968 :   long s = signe(z), lx, ly;
     469   624913968 :   ulong w = z[2];
     470             :   pari_sp av;
     471             :   GEN t;
     472   624913968 :   if (w == 1) return (s > 0)? addii(x,y): subii(x,y); /* z = +- 1 */
     473   508808141 :   lx = lgefint(x);
     474   508808141 :   ly = lgefint(y);
     475   508808141 :   if (lx == 2)
     476             :   { /* x = 0 */
     477    81407608 :     if (ly == 2) return gen_0;
     478    58002945 :     t = muluispec(w, y+2, ly-2);
     479    57947438 :     if (signe(y) < 0) s = -s;
     480    57947438 :     setsigne(t, s); return t;
     481             :   }
     482   427400533 :   if (ly == 2) return icopy(x); /* y = 0, wasteful copy */
     483   396222244 :   av = avma; (void)new_chunk(1+lx+ly);/*HACK*/
     484   397076321 :   t = muluispec(w, y+2, ly-2);
     485   396405981 :   if (signe(y) < 0) s = -s;
     486   396405981 :   setsigne(t, s);
     487   396405981 :   set_avma(av); return addii(x,t);
     488             : }
     489             : /* x + y*z */
     490             : GEN
     491   180960676 : addmulii(GEN x, GEN y, GEN z)
     492             : {
     493   180960676 :   long lz = lgefint(z);
     494   180960676 :   switch(lz)
     495             :   {
     496      471831 :     case 2: return icopy(x); /* z = 0, wasteful copy */
     497   135117972 :     case 3: return addmulii_lg3(x, y, z);
     498    45370873 :     default:return addmulii_gen(x, y, z, lz);
     499             :   }
     500             : }
     501             : /* x + y*z, returns x itself and not a copy when y*z = 0 */
     502             : GEN
     503  1801210741 : addmulii_inplace(GEN x, GEN y, GEN z)
     504             : {
     505             :   long lz;
     506  1801210741 :   if (lgefint(y) == 2) return x;
     507   533216754 :   lz = lgefint(z);
     508   533216754 :   switch(lz)
     509             :   {
     510        4587 :     case 2: return x;
     511   490035820 :     case 3: return addmulii_lg3(x, y, z);
     512    43176347 :     default:return addmulii_gen(x, y, z, lz);
     513             :   }
     514             : }
     515             : 
     516             : /* written by Bruno Haible following an idea of Robert Harley */
     517             : long
     518  2205995984 : vals(ulong z)
     519             : {
     520             :   static char tab[64]={-1,0,1,12,2,6,-1,13,3,-1,7,-1,-1,-1,-1,14,10,4,-1,-1,8,-1,-1,25,-1,-1,-1,-1,-1,21,27,15,31,11,5,-1,-1,-1,-1,-1,9,-1,-1,24,-1,-1,20,26,30,-1,-1,-1,-1,23,-1,19,29,-1,22,18,28,17,16,-1};
     521             : #ifdef LONG_IS_64BIT
     522             :   long s;
     523             : #endif
     524             : 
     525  2205995984 :   if (!z) return -1;
     526             : #ifdef LONG_IS_64BIT
     527  2010566793 :   if (! (z&0xffffffff)) { s = 32; z >>=32; } else s = 0;
     528             : #endif
     529  2205995984 :   z |= ~z + 1;
     530  2205995984 :   z += z << 4;
     531  2205995984 :   z += z << 6;
     532  2205995984 :   z ^= z << 16; /* or  z -= z<<16 */
     533             : #ifdef LONG_IS_64BIT
     534  2010566793 :   return s + tab[(z&0xffffffff)>>26];
     535             : #else
     536   195429191 :   return tab[z>>26];
     537             : #endif
     538             : }
     539             : 
     540             : GEN
     541          98 : divsi(long x, GEN y)
     542             : {
     543          98 :   long p1, s = signe(y);
     544             :   LOCAL_HIREMAINDER;
     545             : 
     546          98 :   if (!s) pari_err_INV("divsi",gen_0);
     547          98 :   if (!x || lgefint(y)>3 || ((long)y[2])<0) return gen_0;
     548          98 :   hiremainder=0; p1=divll(labs(x),y[2]);
     549          98 :   if (x<0) { hiremainder = -((long)hiremainder); p1 = -p1; }
     550          98 :   if (s<0) p1 = -p1;
     551          98 :   return stoi(p1);
     552             : }
     553             : 
     554             : GEN
     555     2940796 : divir(GEN x, GEN y)
     556             : {
     557             :   GEN z;
     558     2940796 :   long ly = lg(y), lx = lgefint(x);
     559             :   pari_sp av;
     560             : 
     561     2940796 :   if (ly == 2) pari_err_INV("divir",y);
     562     2940799 :   if (lx == 2) return div0r(y);
     563     2755377 :   if (lx == 3) {
     564     1519019 :     z = divur(x[2], y);
     565     1519009 :     if (signe(x) < 0) togglesign(z);
     566     1519009 :     return z;
     567             :   }
     568     1236358 :   z = cgetr(ly); av = avma;
     569     1236359 :   affrr(divrr(itor(x, ly+1), y), z);
     570     1236359 :   set_avma(av); return z;
     571             : }
     572             : 
     573             : GEN
     574     1824685 : divur(ulong x, GEN y)
     575             : {
     576             :   pari_sp av;
     577     1824685 :   long ly = lg(y);
     578             :   GEN z;
     579             : 
     580     1824685 :   if (ly == 2) pari_err_INV("divur",y);
     581     1824686 :   if (!x) return div0r(y);
     582     1824686 :   if (ly > INVNEWTON_LIMIT) {
     583         174 :     av = avma; z = invr(y);
     584         174 :     if (x == 1) return z;
     585         174 :     return gerepileuptoleaf(av, mulur(x, z));
     586             :   }
     587     1824512 :   z = cgetr(ly); av = avma;
     588     1824474 :   affrr(divrr(utor(x,ly+1), y), z);
     589     1824485 :   set_avma(av); return z;
     590             : }
     591             : 
     592             : GEN
     593         308 : divsr(long x, GEN y)
     594             : {
     595             :   pari_sp av;
     596         308 :   long ly = lg(y);
     597             :   GEN z;
     598             : 
     599         308 :   if (ly == 2) pari_err_INV("divsr",y);
     600         308 :   if (!x) return div0r(y);
     601         308 :   if (ly > INVNEWTON_LIMIT) {
     602           0 :     av = avma; z = invr(y);
     603           0 :     if (x == 1) return z;
     604           0 :     if (x ==-1) { togglesign(z); return z; }
     605           0 :     return gerepileuptoleaf(av, mulsr(x, z));
     606             :   }
     607         308 :   z = cgetr(ly); av = avma;
     608         308 :   affrr(divrr(stor(x,ly+1), y), z);
     609         308 :   set_avma(av); return z;
     610             : }
     611             : 
     612             : /* returns 1/y, assume y != 0 */
     613             : static GEN
     614    35439532 : invr_basecase(GEN y)
     615             : {
     616    35439532 :   long ly = lg(y);
     617    35439532 :   GEN z = cgetr(ly);
     618    35430505 :   pari_sp av = avma;
     619    35430505 :   affrr(divrr(real_1(ly+1), y), z);
     620    35436078 :   set_avma(av); return z;
     621             : }
     622             : /* returns 1/b, Newton iteration */
     623             : GEN
     624    35439403 : invr(GEN b)
     625             : {
     626    35439403 :   const long s = 6;
     627    35439403 :   long i, p, l = lg(b);
     628             :   GEN x, a;
     629             :   ulong mask;
     630             : 
     631    35439403 :   if (l <= maxss(INVNEWTON_LIMIT, (1L<<s) + 2)) {
     632    35303414 :     if (l == 2) pari_err_INV("invr",b);
     633    35303414 :     return invr_basecase(b);
     634             :   }
     635      136162 :   mask = quadratic_prec_mask(l-2);
     636      953463 :   for(i=0, p=1; i<s; i++) { p <<= 1; if (mask & 1) p--; mask >>= 1; }
     637      136209 :   x = cgetr(l);
     638      136209 :   a = rcopy(b); a[1] = _evalexpo(0) | evalsigne(1);
     639      136209 :   affrr(invr_basecase(rtor(a, p+2)), x);
     640      288890 :   while (mask > 1)
     641             :   {
     642      152681 :     p <<= 1; if (mask & 1) p--;
     643      152681 :     mask >>= 1;
     644      152681 :     setlg(a, p + 2);
     645      152681 :     setlg(x, p + 2);
     646             :     /* TODO: mulrr(a,x) should be a half product (the higher half is known).
     647             :      * mulrr(x, ) already is */
     648      152681 :     affrr(addrr(x, mulrr(x, subsr(1, mulrr(a,x)))), x);
     649      152681 :     set_avma((pari_sp)a);
     650             :   }
     651      136209 :   x[1] = (b[1] & SIGNBITS) | evalexpo(expo(x)-expo(b));
     652      136209 :   set_avma((pari_sp)x); return x;
     653             : }
     654             : 
     655             : GEN
     656  2104069940 : modii(GEN x, GEN y)
     657             : {
     658  2104069940 :   switch(signe(x))
     659             :   {
     660   452395174 :     case 0: return gen_0;
     661  1224786398 :     case 1: return remii(x,y);
     662   426888368 :     default:
     663             :     {
     664   426888368 :       pari_sp av = avma;
     665   426888368 :       (void)new_chunk(lgefint(y));
     666   432047623 :       x = remii(x,y); set_avma(av);
     667   431948920 :       if (x==gen_0) return x;
     668   393189604 :       return subiispec(y+2,x+2,lgefint(y)-2,lgefint(x)-2);
     669             :     }
     670             :   }
     671             : }
     672             : 
     673             : void
     674      643008 : modiiz(GEN x, GEN y, GEN z)
     675             : {
     676      643008 :   const pari_sp av = avma;
     677      643008 :   affii(modii(x,y),z); set_avma(av);
     678      642989 : }
     679             : 
     680             : GEN
     681     8606885 : divrs(GEN x, long y)
     682             : {
     683             :   GEN z;
     684     8606885 :   if (y < 0)
     685             :   {
     686     2735560 :     z = divru(x, (ulong)-y);
     687     2735491 :     togglesign(z);
     688             :   }
     689             :   else
     690     5871325 :     z = divru(x, (ulong)y);
     691     8606747 :   return z;
     692             : }
     693             : 
     694             : GEN
     695   387897661 : divru(GEN x, ulong y)
     696             : {
     697   387897661 :   long i, lx, sh, e, s = signe(x);
     698             :   ulong garde;
     699             :   GEN z;
     700             :   LOCAL_HIREMAINDER;
     701             : 
     702   387897661 :   if (!y) pari_err_INV("divru",gen_0);
     703   387925295 :   if (!s) return real_0_bit(expo(x) - expu(y));
     704   387639039 :   if (!(y & (y-1))) /* power of 2 */
     705             :   {
     706    48656823 :     if (y == 1) return rcopy(x);
     707    47494765 :     return shiftr(x, -expu(y));
     708             :   }
     709   338982216 :   e = expo(x);
     710   338982216 :   lx = lg(x);
     711   338982216 :   z = cgetr(lx);
     712   338654380 :   if (lx == 3)
     713             :   {
     714    96068521 :     if (y <= uel(x,2))
     715             :     {
     716    96068269 :       hiremainder = 0;
     717    96068269 :       z[2] = divll(x[2],y);
     718             :       /* we may have hiremainder != 0 ==> garde */
     719    96068269 :       garde = divll(0,y);
     720             :     }
     721             :     else
     722             :     {
     723         252 :       hiremainder = x[2];
     724         252 :       z[2] = divll(0,y);
     725         252 :       garde = hiremainder;
     726         252 :       e -= BITS_IN_LONG;
     727             :     }
     728             :   }
     729             :   else
     730             :   {
     731   242585859 :     ulong yp = get_Fl_red(y);
     732   242891995 :     if (y <= uel(x,2))
     733             :     {
     734   242899650 :       hiremainder = 0;
     735  1406055856 :       for (i=2; i<lx; i++) z[i] = divll_pre(x[i],y,yp);
     736             :       /* we may have hiremainder != 0 ==> garde */
     737   243323802 :       garde = divll_pre(0,y,yp);
     738             :     }
     739             :     else
     740             :     {
     741        3290 :       long l = lx-1;
     742        3290 :       hiremainder = x[2];
     743       57029 :       for (i=2; i<l; i++) z[i] = divll_pre(x[i+1],y,yp);
     744        3290 :       z[i] = divll_pre(0,y,yp);
     745        3836 :       garde = hiremainder;
     746        3836 :       e -= BITS_IN_LONG;
     747             :     }
     748             :   }
     749   339494935 :   sh=bfffo(z[2]); /* z[2] != 0 */
     750   339494935 :   if (sh) shift_left(z,z, 2,lx-1, garde,sh);
     751   339772622 :   z[1] = evalsigne(s) | evalexpo(e-sh);
     752   339328695 :   if ((garde << sh) & HIGHBIT) roundr_up_ip(z, lx);
     753   339305994 :   return z;
     754             : }
     755             : 
     756             : GEN
     757   137097445 : truedvmdii(GEN x, GEN y, GEN *z)
     758             : {
     759             :   pari_sp av;
     760             :   GEN r, q, *gptr[2];
     761   137097445 :   if (!is_bigint(y)) return truedvmdis(x, itos(y), z);
     762     3486179 :   if (z == ONLY_REM) return modii(x,y);
     763             : 
     764     3486179 :   av = avma;
     765     3486179 :   q = dvmdii(x,y,&r); /* assume that r is last on stack */
     766     3486178 :   switch(signe(r))
     767             :   {
     768      765298 :     case 0:
     769      765298 :       if (z) *z = gen_0;
     770      765298 :       return q;
     771     1809355 :     case 1:
     772     1809355 :       if (z) *z = r; else cgiv(r);
     773     1809355 :       return q;
     774      911526 :     case -1: break;
     775             :   }
     776      911525 :   q = addis(q, -signe(y));
     777      911526 :   if (!z) return gerepileuptoint(av, q);
     778             : 
     779      460934 :   *z = subiispec(y+2,r+2, lgefint(y)-2,lgefint(r)-2);
     780      460934 :   gptr[0]=&q; gptr[1]=z; gerepilemanysp(av,(pari_sp)r,gptr,2);
     781      463026 :   return q;
     782             : }
     783             : GEN
     784   134133110 : truedvmdis(GEN x, long y, GEN *z)
     785             : {
     786   134133110 :   pari_sp av = avma;
     787             :   long r;
     788             :   GEN q;
     789             : 
     790   134133110 :   if (z == ONLY_REM) return modis(x, y);
     791   134133110 :   q = divis_rem(x,y,&r);
     792             : 
     793   134087618 :   if (r >= 0)
     794             :   {
     795   124147074 :     if (z) *z = utoi(r);
     796   124144598 :     return q;
     797             :   }
     798     9940544 :   q = gerepileuptoint(av, addis(q, (y < 0)? 1: -1));
     799     9961718 :   if (z) *z = utoi(r + labs(y));
     800     9961631 :   return q;
     801             : }
     802             : GEN
     803     6162526 : truedvmdsi(long x, GEN y, GEN *z)
     804             : {
     805             :   long q, r;
     806     6162526 :   if (z == ONLY_REM) return modsi(x, y);
     807     6162526 :   q = sdivsi_rem(x,y,&r);
     808     6162526 :   if (r >= 0) {
     809     6162526 :     if (z) *z = utoi(r);
     810     6162526 :     return stoi(q);
     811             :   }
     812           0 :   q = q - signe(y);
     813           0 :   if (!z) return stoi(q);
     814             : 
     815           0 :   *z = subiuspec(y+2,(ulong)-r, lgefint(y)-2);
     816           0 :   return stoi(q);
     817             : }
     818             : 
     819             : /* 2^n = shifti(gen_1, n) */
     820             : GEN
     821    79363956 : int2n(long n) {
     822             :   long i, m, l;
     823             :   GEN z;
     824    79363956 :   if (n < 0) return gen_0;
     825    79345406 :   if (n == 0) return gen_1;
     826             : 
     827    77968895 :   l = dvmdsBIL(n, &m) + 3;
     828    77964567 :   z = cgetipos(l);
     829   358777213 :   for (i = 2; i < l; i++) z[i] = 0;
     830    77916558 :   *int_MSW(z) = 1UL << m; return z;
     831             : }
     832             : /* To avoid problems when 2^(BIL-1) < n. Overflow cleanly, where int2n
     833             :  * returns gen_0 */
     834             : GEN
     835    23650018 : int2u(ulong n) {
     836             :   ulong i, m, l;
     837             :   GEN z;
     838    23650018 :   if (n == 0) return gen_1;
     839             : 
     840    23650018 :   l = dvmduBIL(n, &m) + 3;
     841    23649985 :   z = cgetipos(l);
     842    47613331 :   for (i = 2; i < l; i++) z[i] = 0;
     843    23644450 :   *int_MSW(z) = 1UL << m; return z;
     844             : }
     845             : /* 2^n - 1 */
     846             : GEN
     847        9793 : int2um1(ulong n) {
     848             :   ulong i, m, l;
     849             :   GEN z;
     850        9793 :   if (n == 0) return gen_0;
     851             : 
     852        9793 :   l = dvmduBIL(n, &m);
     853        9793 :   l += m? 3: 2;
     854        9793 :   z = cgetipos(l);
     855       19725 :   for (i = 2; i < l; i++) z[i] = ~0UL;
     856        9793 :   if (m) *int_MSW(z) = (1UL << m) - 1;
     857        9793 :   return z;
     858             : }
     859             : 
     860             : GEN
     861  1669983275 : shifti(GEN x, long n)
     862             : {
     863  1669983275 :   long s = signe(x);
     864             :   GEN y;
     865             : 
     866  1669983275 :   if(s == 0) return gen_0;
     867  1424100642 :   y = shiftispec(x + 2, lgefint(x) - 2, n);
     868  1423471074 :   if (signe(y)) setsigne(y, s);
     869  1423471074 :   return y;
     870             : }
     871             : 
     872             : /* actual operations will take place on a+2 and b+2: we strip the codewords */
     873             : GEN
     874 14064620824 : mulii(GEN a,GEN b)
     875             : {
     876             :   long sa,sb;
     877             :   GEN z;
     878             : 
     879 14064620824 :   sa=signe(a); if (!sa) return gen_0;
     880 11201122472 :   sb=signe(b); if (!sb) return gen_0;
     881  7593667386 :   if (sb<0) sa = -sa;
     882  7593667386 :   z = muliispec(a+2,b+2, lgefint(a)-2,lgefint(b)-2);
     883  7620134076 :   setsigne(z,sa); return z;
     884             : }
     885             : 
     886             : GEN
     887  1575323502 : sqri(GEN a) { return sqrispec(a+2, lgefint(a)-2); }
     888             : 
     889             : /* sqrt()'s result may be off by 1 when a is not representable exactly as a
     890             :  * double [64bit machine] */
     891             : ulong
     892   223972721 : usqrt(ulong a)
     893             : {
     894   223972721 :   ulong x = (ulong)sqrt((double)a);
     895             : #ifdef LONG_IS_64BIT
     896   194213054 :   if (x > LOWMASK || x*x > a) x--;
     897             : #endif
     898   223972721 :   return x;
     899             : }
     900             : 
     901             : /********************************************************************/
     902             : /**                                                                **/
     903             : /**              EXPONENT / CONVERSION t_REAL --> double           **/
     904             : /**                                                                **/
     905             : /********************************************************************/
     906             : 
     907             : #ifdef LONG_IS_64BIT
     908             : long
     909     9630666 : dblexpo(double x)
     910             : {
     911             :   union { double f; ulong i; } fi;
     912     9630666 :   const int mant_len = 52;  /* mantissa bits (excl. hidden bit) */
     913     9630666 :   const int exp_mid = 0x3ff;/* exponent bias */
     914             : 
     915     9630666 :   if (x==0.) return -exp_mid;
     916     9630666 :   fi.f = x;
     917     9630666 :   return ((fi.i & (HIGHBIT-1)) >> mant_len) - exp_mid;
     918             : }
     919             : 
     920             : ulong
     921           0 : dblmantissa(double x)
     922             : {
     923             :   union { double f; ulong i; } fi;
     924           0 :   const int expo_len = 11; /* number of bits of exponent */
     925             : 
     926           0 :   if (x==0.) return 0;
     927           0 :   fi.f = x;
     928           0 :   return (fi.i << expo_len) | HIGHBIT;
     929             : }
     930             : 
     931             : GEN
     932     8447433 : dbltor(double x)
     933             : {
     934             :   GEN z;
     935             :   long e;
     936             :   union { double f; ulong i; } fi;
     937     8447433 :   const int mant_len = 52;  /* mantissa bits (excl. hidden bit) */
     938     8447433 :   const int exp_mid = 0x3ff;/* exponent bias */
     939     8447433 :   const int expo_len = 11; /* number of bits of exponent */
     940             : 
     941     8447433 :   if (x==0.) return real_0_bit(-exp_mid);
     942     8442581 :   fi.f = x; z = cgetr(DEFAULTPREC);
     943             :   {
     944     8439583 :     const ulong a = fi.i;
     945             :     ulong A;
     946     8439583 :     e = ((a & (HIGHBIT-1)) >> mant_len) - exp_mid;
     947     8439583 :     if (e == exp_mid+1) pari_err_OVERFLOW("dbltor [NaN or Infinity]");
     948     8439449 :     A = a << expo_len;
     949     8439449 :     if (e == -exp_mid)
     950             :     { /* unnormalized values */
     951           0 :       int sh = bfffo(A);
     952           0 :       e -= sh-1;
     953           0 :       z[2] = A << sh;
     954             :     }
     955             :     else
     956     8439449 :       z[2] = HIGHBIT | A;
     957     8439449 :     z[1] = _evalexpo(e) | evalsigne(x<0? -1: 1);
     958             :   }
     959     8439449 :   return z;
     960             : }
     961             : 
     962             : double
     963   411448697 : rtodbl(GEN x)
     964             : {
     965   411448697 :   long ex,s=signe(x);
     966             :   ulong a;
     967             :   union { double f; ulong i; } fi;
     968   411448697 :   const int mant_len = 52;  /* mantissa bits (excl. hidden bit) */
     969   411448697 :   const int exp_mid = 0x3ff;/* exponent bias */
     970   411448697 :   const int expo_len = 11; /* number of bits of exponent */
     971             : 
     972   411448697 :   if (!s || (ex=expo(x)) < - exp_mid) return 0.0;
     973             : 
     974             :   /* start by rounding to closest */
     975   372215602 :   a = (x[2] & (HIGHBIT-1)) + 0x400;
     976   372215602 :   if (a & HIGHBIT) { ex++; a=0; }
     977   372215602 :   if (ex >= exp_mid) pari_err_OVERFLOW("t_REAL->double conversion");
     978   372217468 :   fi.i = ((ex + exp_mid) << mant_len) | (a >> expo_len);
     979   372217468 :   if (s<0) fi.i |= HIGHBIT;
     980   372217468 :   return fi.f;
     981             : }
     982             : 
     983             : #else /* LONG_IS_64BIT */
     984             : 
     985             : #if   PARI_DOUBLE_FORMAT == 1
     986             : #  define INDEX0 1
     987             : #  define INDEX1 0
     988             : #elif PARI_DOUBLE_FORMAT == 0
     989             : #  define INDEX0 0
     990             : #  define INDEX1 1
     991             : #endif
     992             : 
     993             : long
     994     1604173 : dblexpo(double x)
     995             : {
     996             :   union { double f; ulong i[2]; } fi;
     997     1604173 :   const int mant_len = 52;  /* mantissa bits (excl. hidden bit) */
     998     1604173 :   const int exp_mid = 0x3ff;/* exponent bias */
     999     1604173 :   const int shift = mant_len-32;
    1000             : 
    1001     1604173 :   if (x==0.) return -exp_mid;
    1002     1604173 :   fi.f = x;
    1003             :   {
    1004     1604173 :     const ulong a = fi.i[INDEX0];
    1005     1604173 :     return ((a & (HIGHBIT-1)) >> shift) - exp_mid;
    1006             :   }
    1007             : }
    1008             : 
    1009             : ulong
    1010           0 : dblmantissa(double x)
    1011             : {
    1012             :   union { double f; ulong i[2]; } fi;
    1013           0 :   const int expo_len = 11; /* number of bits of exponent */
    1014             : 
    1015           0 :   if (x==0.) return 0;
    1016           0 :   fi.f = x;
    1017             :   {
    1018           0 :     const ulong a = fi.i[INDEX0];
    1019           0 :     const ulong b = fi.i[INDEX1];
    1020           0 :     return HIGHBIT | b >> (BITS_IN_LONG-expo_len) | (a << expo_len);
    1021             :   }
    1022             : }
    1023             : 
    1024             : GEN
    1025     1356706 : dbltor(double x)
    1026             : {
    1027             :   GEN z;
    1028             :   long e;
    1029             :   union { double f; ulong i[2]; } fi;
    1030     1356706 :   const int mant_len = 52;  /* mantissa bits (excl. hidden bit) */
    1031     1356706 :   const int exp_mid = 0x3ff;/* exponent bias */
    1032     1356706 :   const int expo_len = 11; /* number of bits of exponent */
    1033     1356706 :   const int shift = mant_len-32;
    1034             : 
    1035     1356706 :   if (x==0.) return real_0_bit(-exp_mid);
    1036     1355910 :   fi.f = x; z = cgetr(DEFAULTPREC);
    1037             :   {
    1038     1355910 :     const ulong a = fi.i[INDEX0];
    1039     1355910 :     const ulong b = fi.i[INDEX1];
    1040             :     ulong A, B;
    1041     1355910 :     e = ((a & (HIGHBIT-1)) >> shift) - exp_mid;
    1042     1355910 :     if (e == exp_mid+1) pari_err_OVERFLOW("dbltor [NaN or Infinity]");
    1043     1355910 :     A = b >> (BITS_IN_LONG-expo_len) | (a << expo_len);
    1044     1355910 :     B = b << expo_len;
    1045     1355910 :     if (e == -exp_mid)
    1046             :     { /* unnormalized values */
    1047             :       int sh;
    1048           0 :       if (A)
    1049             :       {
    1050           0 :         sh = bfffo(A);
    1051           0 :         e -= sh-1;
    1052           0 :         z[2] = (A << sh) | (B >> (32-sh));
    1053           0 :         z[3] = B << sh;
    1054             :       }
    1055             :       else
    1056             :       {
    1057           0 :         sh = bfffo(B); /* B != 0 */
    1058           0 :         e -= sh-1 + 32;
    1059           0 :         z[2] = B << sh;
    1060           0 :         z[3] = 0;
    1061             :       }
    1062             :     }
    1063             :     else
    1064             :     {
    1065     1355910 :       z[3] = B;
    1066     1355910 :       z[2] = HIGHBIT | A;
    1067             :     }
    1068     1355910 :     z[1] = _evalexpo(e) | evalsigne(x<0? -1: 1);
    1069             :   }
    1070     1355910 :   return z;
    1071             : }
    1072             : 
    1073             : double
    1074    68741585 : rtodbl(GEN x)
    1075             : {
    1076    68741585 :   long ex,s=signe(x),lx=lg(x);
    1077             :   ulong a,b,k;
    1078             :   union { double f; ulong i[2]; } fi;
    1079    68741585 :   const int mant_len = 52;  /* mantissa bits (excl. hidden bit) */
    1080    68741585 :   const int exp_mid = 0x3ff;/* exponent bias */
    1081    68741585 :   const int expo_len = 11; /* number of bits of exponent */
    1082    68741585 :   const int shift = mant_len-32;
    1083             : 
    1084    68741585 :   if (!s || (ex=expo(x)) < - exp_mid) return 0.0;
    1085             : 
    1086             :   /* start by rounding to closest */
    1087    62176832 :   a = x[2] & (HIGHBIT-1);
    1088    62176832 :   if (lx > 3)
    1089             :   {
    1090    62033312 :     b = x[3] + 0x400UL; if (b < 0x400UL) a++;
    1091    62033312 :     if (a & HIGHBIT) { ex++; a=0; }
    1092             :   }
    1093      143520 :   else b = 0;
    1094    62176832 :   if (ex >= exp_mid) pari_err_OVERFLOW("t_REAL->double conversion");
    1095    62176832 :   ex += exp_mid;
    1096    62176832 :   k = (a >> expo_len) | (ex << shift);
    1097    62176832 :   if (s<0) k |= HIGHBIT;
    1098    62176832 :   fi.i[INDEX0] = k;
    1099    62176832 :   fi.i[INDEX1] = (a << (BITS_IN_LONG-expo_len)) | (b >> expo_len);
    1100    62176832 :   return fi.f;
    1101             : }
    1102             : #endif /* LONG_IS_64BIT */
    1103             : 

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