* mpfr/*: Update to mpfr 2001.

Tweaks applied to mpfr-impl.h for __gmp_allocate_func renaming, and to trunc.c
for OPERATION_$* scheme.

1 files changed, 42 insertions, 124 deletions

diff --git a/mpfr/exp.c b/mpfr/exp.c
index c3ec218a0..4dfb614c3 100644
--- a/mpfr/exp.c
+++ b/mpfr/exp.c
@@ -1,6 +1,6 @@
 /* mpfr_exp -- exponential of a floating-point number
 
-Copyright (C) 1999 PolKA project, Inria Lorraine and Loria
+Copyright (C) 1999 Free Software Foundation.
 
 This file is part of the MPFR Library.
 
@@ -20,14 +20,16 @@ the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
 MA 02111-1307, USA. */
 
 #include <stdio.h>
-#include <math.h>
 #include "gmp.h"
 #include "gmp-impl.h"
 #include "mpfr.h"
+#include "mpfr-impl.h"
 
 /* #define DEBUG */
 
-#define LOG2 0.69314718055994528622 /* log(2) rounded to zero on 53 bits */
+extern int mpfr_exp2 _PROTO((mpfr_ptr, mpfr_srcptr, mp_rnd_t)); 
+extern int mpfr_exp3 _PROTO((mpfr_ptr, mpfr_srcptr, mp_rnd_t)); 
+
 
 /* use Brent's formula exp(x) = (1+r+r^2/2!+r^3/3!+...)^(2^K)*2^n
    where x = n*log(2)+(2^K)*r
@@ -35,142 +37,58 @@ MA 02111-1307, USA. */
 */
 int 
 #if __STDC__
-mpfr_exp(mpfr_ptr y, mpfr_srcptr x, unsigned char rnd_mode) 
+mpfr_exp (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode) 
 #else
-mpfr_exp(y, x, rnd_mode)
-     mpfr_ptr y; 
-     mpfr_srcptr x; 
-     unsigned char rnd_mode; 
+mpfr_exp (y, x, rnd_mode)
+     mpfr_ptr y;
+     mpfr_srcptr x;
+     mp_rnd_t rnd_mode;
 #endif
 {
-  int n, expx, K, precy, q, k, l, expr, err; 
-  mpfr_t r, s, t;
-
-  if (FLAG_NAN(x)) { SET_NAN(y); return 1; }
-  if (!NOTZERO(x)) { mpfr_set_ui(y, 1, GMP_RNDN); return 0; }
-
-  expx = EXP(x);
-  precy = PREC(y);
-#ifdef DEBUG
-  printf("EXP(x)=%d\n",expx);
-#endif
+  int expx, precy; 
+
+  if (MPFR_IS_NAN(x)) { MPFR_SET_NAN(y); return 1; }
+
+  MPFR_CLEAR_NAN(y);
+
+  if (MPFR_IS_INF(x)) 
+    { 
+      if (MPFR_SIGN(x) > 0) {
+	MPFR_SET_INF(y);
+	if (MPFR_SIGN(y) < 0) MPFR_CHANGE_SIGN(y);
+      }
+      else {
+	MPFR_CLEAR_INF(y);
+	MPFR_SET_ZERO(y);
+	if (MPFR_SIGN(y) < 0) MPFR_CHANGE_SIGN(y);
+      }
+      /*    TODO: conflits entre infinis et zeros ? */
+      return 1;
+    }
+
+  MPFR_CLEAR_INF(y);
+      
+  if (!MPFR_NOTZERO(x)) { mpfr_set_ui(y, 1, GMP_RNDN); return 0; }
+
+  expx = MPFR_EXP(x);
+  precy = MPFR_PREC(y);
 
   /* if x > (2^31-1)*ln(2), then exp(x) > 2^(2^31-1) i.e. gives +infinity */
   if (expx > 30) {
-    if (SIGN(x)>0) { printf("+infinity"); return 1; }
-    else { SET_ZERO(y); return 1; }
+    if (MPFR_SIGN(x)>0) { printf("+infinity"); return 1; }
+    else { MPFR_SET_ZERO(y); return 1; }
   }
 
   /* if x < 2^(-precy), then exp(x) i.e. gives 1 +/- 1 ulp(1) */
-  if (expx < -precy) { int signx = SIGN(x);
+  if (expx < -precy) { int signx = MPFR_SIGN(x);
     mpfr_set_ui(y, 1, rnd_mode);
     if (signx>0 && rnd_mode==GMP_RNDU) mpfr_add_one_ulp(y);
     else if (signx<0 && (rnd_mode==GMP_RNDD || rnd_mode==GMP_RNDZ)) 
       mpfr_sub_one_ulp(y);
     return 1; }
 
-  n = (int) floor(mpfr_get_d(x)/LOG2);
-
-  K = (int) sqrt( (double) precy );
-  l = (precy-1)/K + 1;
-  err = K + (int) ceil(log(2.0*(double)l+18.0)/LOG2);
-  /* add K extra bits, i.e. failure probability <= 1/2^K = O(1/precy) */
-  q = precy + err + K + 3;
-  mpfr_init2(r, q); mpfr_init2(s, q); mpfr_init2(t, q);
-  /* the algorithm consists in computing an upper bound of exp(x) using
-     a precision of q bits, and see if we can round to PREC(y) taking
-     into account the maximal error. Otherwise we increase q. */
-  do {
-#ifdef DEBUG
-  printf("n=%d K=%d l=%d q=%d\n",n,K,l,q);
-#endif
-
-  /* if n<0, we have to get an upper bound of log(2)
-     in order to get an upper bound of r = x-n*log(2) */
-  mpfr_log2(s, (n>=0) ? GMP_RNDZ : GMP_RNDU);
-#ifdef DEBUG
-  printf("n=%d log(2)=",n); mpfr_print_raw(s); putchar('\n');
-#endif
-  mpfr_mul_ui(r, s, (n<0) ? -n : n, (n>=0) ? GMP_RNDZ : GMP_RNDU); 
-  if (n<0) mpfr_neg(r, r, GMP_RNDD);
-  /* r = floor(n*log(2)) */
-
-#ifdef DEBUG
-  printf("x=%1.20e\n",mpfr_get_d(x));
-  printf(" ="); mpfr_print_raw(x); putchar('\n');
-  printf("r=%1.20e\n",mpfr_get_d(r));
-  printf(" ="); mpfr_print_raw(r); putchar('\n');
-#endif
-  mpfr_sub(r, x, r, GMP_RNDU);
-  if (SIGN(r)<0) { /* initial approximation n was too large */
-    n--;
-    mpfr_mul_ui(r, s, (n<0) ? -n : n, GMP_RNDZ);
-    if (n<0) mpfr_neg(r, r, GMP_RNDD);
-    mpfr_sub(r, x, r, GMP_RNDU);
-  }
-#ifdef DEBUG
-  printf("x-r=%1.20e\n",mpfr_get_d(r));
-  printf(" ="); mpfr_print_raw(r); putchar('\n');
-  if (SIGN(r)<0) { fprintf(stderr,"Error in mpfr_exp: r<0\n"); exit(1); }
-#endif
-  mpfr_div_2exp(r, r, K, GMP_RNDU); /* r = (x-n*log(2))/2^K */
-  mpfr_set_ui(s, 1, GMP_RNDU);
-  mpfr_set_ui(t, 1, GMP_RNDU);
-
-  l = 1; expr = EXP(r);
-  do {
-    mpfr_mul(t, t, r, GMP_RNDU);
-    mpfr_div_ui(t, t, l, GMP_RNDU);
-    mpfr_add(s, s, t, GMP_RNDU);
-#ifdef DEBUG
-    printf("l=%d t=%1.20e\n",l,mpfr_get_d(t)); 
-    printf("s=%1.20e\n",mpfr_get_d(s)); 
-#endif
-    l++;
-  } while (EXP(t)+expr > -q);
-#ifdef DEBUG
-  printf("l=%d q=%d (K+l)*q^2=%1.3e\n", l, q, (K+l)*(double)q*q);
-#endif
-
-  /* add 2 ulp to take into account rest of summation */
-  mpfr_add_one_ulp(s);
-  mpfr_add_one_ulp(s);
-  
-  for (k=0;k<K;k++) {
-    mpfr_mul(s, s, s, GMP_RNDU);
-#ifdef DEBUG
-    printf("k=%d s=%1.20e\n",k,mpfr_get_d(s)); 
-#endif
-  }
-
-  if (n>0) mpfr_mul_2exp(s, s, n, GMP_RNDU);
-  else mpfr_div_2exp(s, s, -n, GMP_RNDU);
-
-  /* error is at most 2^K*(2l+18) ulp */
-  l = 2*l+17; k=0; while (l) { k++; l >>= 1; }
-  /* now k = ceil(log(2l+18)/log(2)) */
-  K += k;
-#ifdef DEBUG
-    printf("after mult. by 2^n:\n");
-    if (EXP(s)>-1024) printf("s=%1.20e\n",mpfr_get_d(s)); 
-    printf(" ="); mpfr_print_raw(s); putchar('\n');
-    printf("err=%d bits\n", K);
-#endif
-
-  l = mpfr_can_round(s, q-K, GMP_RNDU, rnd_mode, precy);
-  if (l==0) {
-#ifdef DEBUG
-     printf("not enough precision, use %d\n", q+BITS_PER_MP_LIMB);
-     printf("q=%d q-K=%d precy=%d\n",q,q-K,precy);
-#endif
-     q += BITS_PER_MP_LIMB;
-     mpfr_set_prec(r, q); mpfr_set_prec(s, q); mpfr_set_prec(t, q);
-  }
-  } while (l==0);
-
-  mpfr_set(y, s, rnd_mode);
-
-  mpfr_clear(r); mpfr_clear(s); mpfr_clear(t);
+  if (precy > 13000) mpfr_exp3(y, x, rnd_mode); /* O(M(n) log(n)^2) */
+  else mpfr_exp2(y, x, rnd_mode); /* O(n^(1/3) M(n)) */
   return 1;
 }