Initial revision

AUTHORS

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+David Defour and Catherine Daramy and Florent de Dinechin

ChangeLog

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+2003-04-18 : Florent de Dinechin
+	* initial autoconf/automake obsfuscation

Makefile.am

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+## Process this file with automake to produce Makefile.in
+
+lib_LIBRARIES = libcrlibm.a
+
+# shared libraries need libtool. We'll do it later.
+#lib_LTLIBRARIES = libcrlibm.la
+
+libcrlibm_a_SOURCES =  \
+	crlibm.h crlibm_private.h crlibm_private.c\
+	exp.h exp.c exp_fast.h exp_fast.c\
+	log.h log.c log_fast.c log_fast.h\
+	log10.h	log10.c\
+	log2.h  log2.c \
+	coefpi2.h rem_pio2.c\
+	sine.h sine.c\
+	cosine.h cosine.c\
+	tan.h tan.c cotan.c\
+	atan.h atan.c 
+
+# add all the scs_lib useful functions
+libcrlibm_a_LIBADD = scs_lib/addition_scs.o \
+	scs_lib/division_scs.o scs_lib/print_scs.o\
+	scs_lib/double2scs.o scs_lib/zero_scs.o\
+	scs_lib/multiplication_scs.o scs_lib/scs2double.o
+
+include_HEADERS = crlibm.h
+
+SUBDIRS = scs_lib . tests
+
+AM_CFLAGS =  -fPIC -Wall -Wshadow -Wpointer-arith  -Wcast-align -Wconversion -Waggregate-return -Wstrict-prototypes -Wnested-externs -Wlong-long -Winline 
+EXTRA_DIST = VERSION  

README

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+cr-libm, a portable, efficient, correctly rounded mathematical library.

README.DEV

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+Les commandes � taper la premi�re fois apr�s le cvs checkout sont
+(dans l'ordre)
+
+aclocal
+autoheader
+autoconf
+automake --add-missing
+./configure 
+
+Remarque : sur mon debian woody l'autoconf de service est trop vieux,
+il faut utiliser la commande autoconf2.50 ...
+

VERSION

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+0.03

atan.c

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+/*
+ *  atan.c
+ *  
+ *
+ *  Created by cathydar on Thu Nov 07 2002.
+ *  Copyright (c) 2001 __MyCompanyName__. All rights reserved.
+ *
+ */
+#include <stdio.h>
+#include <stdlib.h>
+#include <atan.h>
+
+void atan(scs_ptr, scs_ptr);
+double atan_rd(double);
+double atan_ru(double);
+double atan_rn(double);
+
+/*
+ *  WHAT WE CAN DO :
+ *
+ * 1) Range reduction 
+ *
+ *	x > 0  because atan(-x) = - atan(x)
+ *	
+ *	we have built 50 intervals I(i), associated to a b(i) so that :
+ *	
+ *	For every x :
+ *	
+ *	we find the interval I(i) , as atan(x) = atan(b(i)) + atan( (x - b(i)) / (1 + x * b(i)) ) 
+ *	
+ *		so that X = (x - b(i)) / (1 + x * b(i))  be in interval [ -2^(-6) , 2^(-6) ] 
+ *		There is no cancellation because :
+ *		for every x in [ -2^(-6) , 2^(-6) ],
+ *		
+ *					     atan(x) <= 0.01562372862     in binary 0.000001111111111
+ *		AND for the smallest b(i)    atan(b(i)) = 0.04687118592   in binary 0.00001011111111 	   
+ *
+ *
+ * 2) Polynomial evaluation of atan(X), atan(b(i)) is tabulated.
+ *                  
+ *                                  (-???)  
+ *   Approximation error: |err| < 2^ 
+ *
+ *
+ * 3) Reconstruction:
+ *
+ *    atan(x) = atan(b(i)) + atan(X) 
+ *
+ *
+ * 4) Rounding:
+ *
+ *    when |x| is too big, the result is always sign(x) * Pi/2,
+ *    because Pi/2 is appromated by the biggest value smallest than Pi/2, 
+ *    in order not to have an atan > Pi/2.
+ */
+
+
+
+
+void atan(scs_ptr res_scs, scs_ptr x){
+    scs_t X_scs, denom1_scs, denom2_scs, num_scs, poly_scs, X2;
+    db_number db;
+    int k, ind = 100, j, intmid = 32;
+
+  scs_get_d(&db.d, x);  
+
+    /* Test if x need to be reduced */
+
+    if( db.i[0] >= borne_I[48]){
+      	if ( db.i[0]  < borne_I[49]){
+	    j = 48;}
+	else if( db.i[0] > borne_I[49]){
+	    j = 49;}
+	else {
+	    res_scs =  atan_bi_ptr[49];
+	    return;
+	}
+	ind = j;
+
+	/* evaluate X = (x - b(j)) / (1 + x*b(j)) */
+
+	scs_mul(denom1_scs,bsc_ptr[ind],x);
+	scs_add(denom2_scs,denom1_scs,SCS_ONE);
+	scs_sub(X_scs,x,bsc_ptr[ind]);
+	scs_div(X_scs,X_scs,denom2_scs);
+    }
+    else if (((int) db.i[0]) == borne_I[48]) {
+	res_scs = atan_bi_ptr[48];
+	return ;
+    }
+    else if ( db.i[0] < borne_I[0]){
+	scs_set(X_scs, x);
+	ind = 60;
+    }
+    else{	/* First reduction : find the interval including x, "save" j to have b(j)  and then being able to calculate X */
+	j = 32;
+	for (k=1;k<=5;k++){
+	    if (db.i[0] < borne_I[j]){
+		j -= (intmid >> k);
+            }
+            else if(db.i[0] > borne_I[j]){
+		j += (intmid >>  k);	    
+	    }
+	    else {res_scs = atan_bi_ptr[j];
+		  return ;
+	    }
+	}
+	if (db.i[0] < borne_I[j]){
+	    ind = j-1;
+	}
+	else{
+	    ind = j;
+	}
+
+    /* evaluate X = (x - b(j)) / (1 + x*b(j)) */
+
+	scs_mul(denom1_scs,bsc_ptr[ind],x);
+	scs_add(denom2_scs,denom1_scs,SCS_ONE);   
+	scs_sub(num_scs,x,bsc_ptr[ind]);
+	scs_div(X_scs,num_scs,denom2_scs);
+    } 
+printf("ind = %d\n", ind);
+
+/* Polynomial evaluation of atan(X) , X = (x-b(i)) / (1+ x*b(i)) */ 
+
+    scs_square(X2, X_scs);
+    scs_set(res_scs, constant_poly_ptr[0]);
+    for(k=1; k < 13; k++){
+	scs_mul(res_scs, res_scs, X2);		/* we use Horner expression */
+    	scs_add(res_scs, constant_poly_ptr[k], res_scs);
+
+    }
+    scs_mul(poly_scs, res_scs, X_scs);
+
+    if(ind == 60){ 
+	scs_set(res_scs, poly_scs);
+	return;
+    }else{
+	printf("on ajoute l' atan de b(j)\n"); 
+	/*scs_set(denom_scs, res_scs);*/
+	scs_add(res_scs,atan_bi_ptr[ind], poly_scs); 
+    }
+    return;
+}	
+
+/*************************************************************
+ *************************************************************
+ *               ROUNDED  TO NEAREST
+ *************************************************************
+ *************************************************************/
+
+double sn_atan(double x){ 
+  scs_t sc1;
+  scs_t res_scs;
+  db_number res;
+  int sign =1;
+
+   res.d = x;
+
+    /* Filter cases */
+    if((res.l & 0x7fffffffffffffffULL) > larg_int.l) 
+    {
+	if (x > 0){
+	    return pio2.d;
+	}
+	else{
+            return mpio2.d;
+	}
+    }
+    else if ((res.l & 0x7fffffffffffffffULL) < tiny_int.l) {
+	    return 0.0;
+    }
+    else{
+	 if (x < 0){
+	    sign = -1;
+	    x *= -1;
+	}
+	scs_set_d(sc1, x);
+	atan(res_scs, sc1);
+	scs_get_d(&res.d, res_scs);
+	if (sign == -1){
+	    res.d *= -1;
+	    return res.d;
+	}
+	return res.d;
+    }
+}
+
+/*************************************************************
+ *************************************************************
+ *               ROUNDED  TOWARD  -INFINITY
+ *************************************************************
+ *************************************************************/
+
+double atan_rd(double x){ 
+  scs_t sc1;
+  scs_t res_scs;
+  db_number res;
+  int sign = 1;
+
+  res.d = x;
+
+    /* Filter cases */
+    if((res.l & 0x7fffffffffffffffULL) > larg_int.l) 
+    {
+	if (x < 0){
+	    return mpio2.d;
+	}
+	else{
+		return pio2.d;
+	}
+    }
+    else {  
+	if (x < 0){
+	    sign = -1;
+	    x *= -1;
+	}
+	scs_set_d(sc1, x);
+	atan(res_scs, sc1);
+	if (sign == -1){
+	    scs_get_d_pinf(&res.d, res_scs);
+	    res.d *= -1;
+	    return res.d;
+	}
+	else{
+	    scs_get_d_minf(&res.d, res_scs);		
+	    return res.d;
+	}
+    }
+}
+
+/*************************************************************
+ *************************************************************
+ *               ROUNDED  TOWARD  +INFINITY
+ *************************************************************
+ *************************************************************/
+
+double atan_ru(double x){ 
+  scs_t sc1;
+  scs_t res_scs;
+  db_number res;
+  int sign = 1;
+
+  res.d = x;
+
+    /* Filter cases */
+    if((res.l & 0x7fffffffffffffffULL) > larg_int.l) 
+    {
+	if (x > 0)
+        {
+	    return pio2.d;
+	}
+	else
+	{
+            return mpio2.d; 		
+	}
+    }
+    else 
+	{
+	   if (x < 0){
+		sign = -1;
+		x *= -1;
+	    }
+
+	    scs_set_d(sc1, x);
+	    atan(res_scs, sc1);
+	    	    if (sign == -1){
+		scs_get_d_minf(&res.d, res_scs);
+		res.d *= -1;
+		return res.d;
+	    }
+	    else{
+		scs_get_d_pinf(&res.d, res_scs);		
+		return res.d;
+	    }
+	}
+}
+