Totally rework the math library, this time based on the MacOs X

math library (which is itself based on the math lib from FreeBSD).
 -Erik

1 files changed, 627 insertions, 0 deletions

diff --git a/libm/rndint.c b/libm/rndint.c
new file mode 100644
index 000000000..611fd9274
--- /dev/null
+++ b/libm/rndint.c
@@ -0,0 +1,627 @@
+/*******************************************************************************
+**      File:   rndint.c
+**      
+**      Contains: C source code for implementations of floating-point
+**                functions which round to integral value or format, as
+**                defined in header <fp.h>.  In particular, this file
+**                contains implementations of functions rint, nearbyint,
+**                rinttol, round, roundtol, trunc, modf and modfl.  This file
+**                targets PowerPC or Power platforms.
+**                        
+**      Written by: A. Sazegari, Apple AltiVec Group
+**	    Created originally by Jon Okada, Apple Numerics Group
+**      
+**      Copyright: © 1992-2001 by Apple Computer, Inc., all rights reserved
+**      
+**      Change History (most recent first):
+**
+**      13 Jul 01  ram  replaced --setflm calls with inline assembly
+**      03 Mar 01  ali	first port to os x using gcc, added the crucial __setflm
+**                      definition.
+**				1. removed double_t, put in double for now.
+**				2. removed iclass from nearbyint.
+**				3. removed wrong comments intrunc.
+**				4. 
+**      13 May 97  ali  made performance improvements in rint, rinttol, roundtol
+**                      and trunc by folding some of the taligent ideas into this
+**                      implementation.  nearbyint is faster than the one in taligent,
+**                      rint is more elegant, but slower by %30 than the taligent one.
+**      09 Apr 97  ali  deleted modfl and deferred to AuxiliaryDD.c
+**      15 Sep 94  ali  Major overhaul and performance improvements of all functions.
+**      20 Jul 94  PAF  New faster version
+**      16 Jul 93  ali  Added the modfl function.
+**      18 Feb 93  ali  Changed the return value of fenv functions
+**                      feclearexcept and feraiseexcept to their new
+**                      NCEG X3J11.1/93-001 definitions.
+**      16 Dec 92  JPO  Removed __itrunc implementation to a 
+**                      separate file.
+**      15 Dec 92  JPO  Added __itrunc implementation and modified
+**                      rinttol to include conversion from double
+**                      to long int format.  Modified roundtol to
+**                      call __itrunc.
+**      10 Dec 92  JPO  Added modf (double) implementation.
+**      04 Dec 92  JPO  First created.
+**                        
+*******************************************************************************/
+
+#include <limits.h>
+#include <math.h>
+
+#if !defined(__ppc__)
+#define asm(x)
+#endif
+
+#define      SET_INVALID      0x01000000UL
+
+typedef union
+      {
+      struct {
+#if defined(__BIG_ENDIAN__)
+        unsigned long int hi;
+        unsigned long int lo;
+#else
+        unsigned long int lo;
+        unsigned long int hi;
+#endif
+      } words;
+      double dbl;
+      } DblInHex;
+
+static const unsigned long int signMask = 0x80000000ul;
+static const double twoTo52      = 4503599627370496.0;
+static const double doubleToLong = 4503603922337792.0;	            // 2^52
+static const DblInHex Huge       = {{ 0x7FF00000, 0x00000000 }};
+static const DblInHex TOWARDZERO = {{ 0x00000000, 0x00000001 }};
+
+/*******************************************************************************
+*                                                                              *
+*     The function rint rounds its double argument to integral value           *
+*     according to the current rounding direction and returns the result in    *
+*     double format.  This function signals inexact if an ordered return       * 
+*     value is not equal to the operand.                                       *
+*                                                                              *
+********************************************************************************
+*                                                                              *
+*     This function calls:  fabs. 	                                           *
+*                                                                              *
+*******************************************************************************/
+
+/*******************************************************************************
+*     First, an elegant implementation.                                        *
+********************************************************************************
+*
+*double rint ( double x )
+*      {
+*      double y;
+*      
+*      y = twoTo52.fval;
+*      
+*      if ( fabs ( x ) >= y )                          // huge case is exact 
+*            return x;
+*      if ( x < 0 ) y = -y;                            // negative case 
+*      y = ( x + y ) - y;                              // force rounding 
+*      if ( y == 0.0 )                                 // zero results mirror sign of x 
+*            y = copysign ( y, x );
+*      return ( y );      
+*      }
+********************************************************************************
+*     Now a bit twidling version that is about %30 faster.                     *
+*******************************************************************************/
+
+#if defined(__ppc__)
+double rint ( double x )
+      {
+      DblInHex argument;
+      register double y;
+      unsigned long int xHead;
+      register long int target;
+      
+      argument.dbl = x;
+      xHead = argument.words.hi & 0x7fffffffUL;          // xHead <- high half of |x|
+      target = ( argument.words.hi < signMask );         // flags positive sign
+      
+      if ( xHead < 0x43300000ul ) 
+/*******************************************************************************
+*     Is |x| < 2.0^52?                                                         *
+*******************************************************************************/
+            {
+            if ( xHead < 0x3ff00000ul ) 
+/*******************************************************************************
+*     Is |x| < 1.0?                                                            *
+*******************************************************************************/
+                  {
+                  if ( target )
+                        y = ( x + twoTo52 ) - twoTo52;  // round at binary point
+                  else
+                        y = ( x - twoTo52 ) + twoTo52;  // round at binary point
+                  if ( y == 0.0 ) 
+                        {                               // fix sign of zero result
+                        if ( target )
+                              return ( 0.0 );
+                        else
+                              return ( -0.0 );
+                        }
+                  return y;
+                  }
+            
+/*******************************************************************************
+*     Is 1.0 < |x| < 2.0^52?                                                   *
+*******************************************************************************/
+
+            if ( target )
+                  return ( ( x + twoTo52 ) - twoTo52 ); //   round at binary pt.
+            else
+                  return ( ( x - twoTo52 ) + twoTo52 );
+            }
+      
+/*******************************************************************************
+*     |x| >= 2.0^52 or x is a NaN.                                             *
+*******************************************************************************/
+      return ( x );
+      }
+#endif /* __ppc__ */
+
+/*******************************************************************************
+*                                                                              *
+*     The function nearbyint rounds its double argument to integral value      *
+*     according to the current rounding direction and returns the result in    *
+*     double format.  This function does not signal inexact.                   *
+*                                                                              *
+********************************************************************************
+*                                                                              *
+*     This function calls fabs and copysign.		                         *
+*                                                                              *
+*******************************************************************************/
+   
+double nearbyint ( double x )
+      {
+	double y, OldEnvironment;
+      
+	y = twoTo52;
+	
+	asm ("mffs %0" : "=f" (OldEnvironment));	/* get the environement */
+
+      if ( fabs ( x ) >= y )                          /* huge case is exact */
+            return x;
+      if ( x < 0 ) y = -y;                                   /* negative case */
+      y = ( x + y ) - y;                                    /* force rounding */
+      if ( y == 0.0 )                        /* zero results mirror sign of x */
+            y = copysign ( y, x );
+//	restore old flags
+	asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment ));
+      return ( y );      
+	}
+      
+/*******************************************************************************
+*                                                                              *
+*     The function rinttol converts its double argument to integral value      *
+*     according to the current rounding direction and returns the result in    *
+*     long int format.  This conversion signals invalid if the argument is a   *
+*     NaN or the rounded intermediate result is out of range of the            *
+*     destination long int format, and it delivers an unspecified result in    *
+*     this case.  This function signals inexact if the rounded result is       *
+*     within range of the long int format but unequal to the operand.          *
+*                                                                              *
+*******************************************************************************/
+
+long int rinttol ( double x )
+      {
+      register double y;
+      DblInHex argument, OldEnvironment;
+      unsigned long int xHead;
+      register long int target;
+      
+      argument.dbl = x;
+      target = ( argument.words.hi < signMask );        // flag positive sign
+      xHead = argument.words.hi & 0x7ffffffful;         // high 32 bits of x
+      
+      if ( target ) 
+/*******************************************************************************
+*    Sign of x is positive.                                                    *
+*******************************************************************************/
+            {
+            if ( xHead < 0x41dffffful ) 
+                  {                                    // x is safely in long range
+                  y = ( x + twoTo52 ) - twoTo52;       // round at binary point
+                  argument.dbl = y + doubleToLong;     // force result into argument.words.lo
+                  return ( ( long ) argument.words.lo );
+                  }
+            
+		asm ("mffs %0" : "=f" (OldEnvironment.dbl));	// get environment
+            
+            if ( xHead > 0x41dffffful ) 
+                  {                                    // x is safely out of long range
+                  OldEnvironment.words.lo |= SET_INVALID;
+			asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+                  return ( LONG_MAX );
+                  }
+            
+/*******************************************************************************
+*     x > 0.0 and may or may not be out of range of long.                      *
+*******************************************************************************/
+
+            y = ( x + twoTo52 ) - twoTo52;             // do rounding
+            if ( y > ( double ) LONG_MAX ) 
+                  {                                    // out of range of long
+                  OldEnvironment.words.lo |= SET_INVALID;
+			asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+                  return ( LONG_MAX );
+                  }
+            argument.dbl = y + doubleToLong;           // in range
+            return ( ( long ) argument.words.lo );      // return result & flags
+            }
+      
+/*******************************************************************************
+*    Sign of x is negative.                                                    *
+*******************************************************************************/
+      if ( xHead < 0x41e00000ul ) 
+            {                                          // x is safely in long range
+            y = ( x - twoTo52 ) + twoTo52;
+            argument.dbl = y + doubleToLong;
+            return ( ( long ) argument.words.lo );
+            }
+      
+	asm ("mffs %0" : "=f" (OldEnvironment.dbl));	// get environment
+      
+      if ( xHead > 0x41e00000ul ) 
+            {                                          // x is safely out of long range
+            OldEnvironment.words.lo |= SET_INVALID;
+		asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+            return ( LONG_MIN );
+            }
+      
+/*******************************************************************************
+*    x < 0.0 and may or may not be out of range of long.                       *
+*******************************************************************************/
+
+      y = ( x - twoTo52 ) + twoTo52;                   // do rounding
+      if ( y < ( double ) LONG_MIN ) 
+            {                                          // out of range of long
+            OldEnvironment.words.lo |= SET_INVALID;
+		asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+            return ( LONG_MIN );
+            }
+      argument.dbl = y + doubleToLong;                       // in range
+      return ( ( long ) argument.words.lo );           // return result & flags
+      }
+
+/*******************************************************************************
+*                                                                              *
+*     The function round rounds its double argument to integral value          *
+*     according to the "add half to the magnitude and truncate" rounding of    *
+*     Pascal's Round function and FORTRAN's ANINT function and returns the     *
+*     result in double format.  This function signals inexact if an ordered    *
+*     return value is not equal to the operand.                                *
+*                                                                              *
+*******************************************************************************/
+   
+double round ( double x )
+      {      
+      DblInHex argument, OldEnvironment;
+      register double y, z;
+      register unsigned long int xHead;
+      register long int target;
+      
+      argument.dbl = x;
+      xHead = argument.words.hi & 0x7fffffffUL;      // xHead <- high half of |x|
+      target = ( argument.words.hi < signMask );     // flag positive sign
+      
+      if ( xHead < 0x43300000ul ) 
+/*******************************************************************************
+*     Is |x| < 2.0^52?                                                        *
+*******************************************************************************/
+            {
+            if ( xHead < 0x3ff00000ul ) 
+/*******************************************************************************
+*     Is |x| < 1.0?                                                           *
+*******************************************************************************/
+                  {
+			asm ("mffs %0" : "=f" (OldEnvironment.dbl));	// get environment
+                  if ( xHead < 0x3fe00000ul ) 
+/*******************************************************************************
+*     Is |x| < 0.5?                                                           *
+*******************************************************************************/
+                        {
+                        if ( ( xHead | argument.words.lo ) != 0ul )
+                              OldEnvironment.words.lo |= 0x02000000ul;
+				asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+                        if ( target ) 
+                              return ( 0.0 );
+                        else
+                              return ( -0.0 );
+                        }
+/*******************************************************************************
+*     Is 0.5 ² |x| < 1.0?                                                      *
+*******************************************************************************/
+                  OldEnvironment.words.lo |= 0x02000000ul;
+			asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+                  if ( target )
+                        return ( 1.0 );
+                  else
+                        return ( -1.0 );
+                  }
+/*******************************************************************************
+*     Is 1.0 < |x| < 2.0^52?                                                   *
+*******************************************************************************/
+            if ( target ) 
+                  {                                     // positive x
+                  y = ( x + twoTo52 ) - twoTo52;        // round at binary point
+                  if ( y == x )                         // exact case
+                        return ( x );
+                  z = x + 0.5;                          // inexact case
+                  y = ( z + twoTo52 ) - twoTo52;        // round at binary point
+                  if ( y > z )
+                        return ( y - 1.0 );
+                  else
+                        return ( y );
+                  }
+            
+/*******************************************************************************
+*     Is x < 0?                                                                *
+*******************************************************************************/
+            else 
+                  {
+                  y = ( x - twoTo52 ) + twoTo52;        // round at binary point
+                  if ( y == x )
+                        return ( x );
+                  z = x - 0.5;
+                  y = ( z - twoTo52 ) + twoTo52;        // round at binary point
+                  if ( y < z )
+                        return ( y + 1.0 );
+                  else
+                  return ( y );
+                  }
+            }
+/*******************************************************************************
+*      |x| >= 2.0^52 or x is a NaN.                                            *
+*******************************************************************************/
+      return ( x );
+      }
+
+/*******************************************************************************
+*                                                                              *
+*     The function roundtol converts its double argument to integral format    *
+*     according to the "add half to the magnitude and chop" rounding mode of   *
+*     Pascal's Round function and FORTRAN's NINT function.  This conversion    *
+*     signals invalid if the argument is a NaN or the rounded intermediate     *
+*     result is out of range of the destination long int format, and it        *
+*     delivers an unspecified result in this case.  This function signals      *
+*     inexact if the rounded result is within range of the long int format but *
+*     unequal to the operand.                                                  *
+*                                                                              *
+*******************************************************************************/
+
+long int roundtol ( double x )
+	{	
+	register double y, z;
+	DblInHex argument, OldEnvironment;
+	register unsigned long int xhi;
+	register long int target;
+	const DblInHex kTZ = {{ 0x0, 0x1 }};
+	const DblInHex kUP = {{ 0x0, 0x2 }};
+	
+	argument.dbl = x;
+	xhi = argument.words.hi & 0x7ffffffful;	        	// high 32 bits of x
+	target = ( argument.words.hi < signMask );         	// flag positive sign
+	
+	if ( xhi > 0x41e00000ul ) 
+/*******************************************************************************
+*     Is x is out of long range or NaN?                                        *
+*******************************************************************************/
+		{
+		asm ("mffs %0" : "=f" (OldEnvironment.dbl));	// get environment
+		OldEnvironment.words.lo |= SET_INVALID;
+		asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+		if ( target )			              	// pin result
+			return ( LONG_MAX );
+		else
+			return ( LONG_MIN );
+		}
+	
+	if ( target ) 
+/*******************************************************************************
+*     Is sign of x is "+"?                                                     *
+*******************************************************************************/
+		{
+		if ( x < 2147483647.5 ) 
+/*******************************************************************************
+*     x is in the range of a long.                                             *
+*******************************************************************************/
+			{
+			y = ( x + doubleToLong ) - doubleToLong; 	// round at binary point
+			if ( y != x )	
+				{		                    	// inexact case
+				asm ("mffs %0" : "=f" (OldEnvironment.dbl));	// save environment
+				asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( kTZ.dbl )); // truncate rounding
+				z = x + 0.5;		        	// truncate x + 0.5
+				argument.dbl = z + doubleToLong;
+				asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+				return ( ( long ) argument.words.lo );
+				}
+			
+			argument.dbl = y + doubleToLong;		// force result into argument.words.lo
+			return ( ( long ) argument.words.lo ); 	// return long result
+			}
+/*******************************************************************************
+*     Rounded positive x is out of the range of a long.                        *
+*******************************************************************************/
+		asm ("mffs %0" : "=f" (OldEnvironment.dbl));
+		OldEnvironment.words.lo |= SET_INVALID;
+		asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+		return ( LONG_MAX );		              	// return pinned result
+		}
+/*******************************************************************************
+*     x < 0.0 and may or may not be out of the range of a long.                *
+*******************************************************************************/
+	if ( x > -2147483648.5 ) 
+/*******************************************************************************
+*     x is in the range of a long.                                             *
+*******************************************************************************/
+		{
+		y = ( x + doubleToLong ) - doubleToLong;	  	// round at binary point
+		if ( y != x ) 
+			{			                    	// inexact case
+			asm ("mffs %0" : "=f" (OldEnvironment.dbl));	// save environment
+			asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( kUP.dbl )); // round up
+			z = x - 0.5;		              	// truncate x - 0.5
+			argument.dbl = z + doubleToLong;
+			asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+			return ( ( long ) argument.words.lo );
+			}
+		
+		argument.dbl = y + doubleToLong;
+		return ( ( long ) argument.words.lo );	  	//  return long result
+		}
+/*******************************************************************************
+*     Rounded negative x is out of the range of a long.                        *
+*******************************************************************************/
+	asm ("mffs %0" : "=f" (OldEnvironment.dbl));
+	OldEnvironment.words.lo |= SET_INVALID;
+	asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+	return ( LONG_MIN );			              	// return pinned result
+	}
+
+/*******************************************************************************
+*                                                                              *
+*     The function trunc truncates its double argument to integral value       *
+*     and returns the result in double format.  This function signals          *
+*     inexact if an ordered return value is not equal to the operand.          *
+*                                                                              *
+*******************************************************************************/
+   
+double trunc ( double x )
+      {	
+	DblInHex argument,OldEnvironment;
+	register double y;
+	register unsigned long int xhi;
+	register long int target;
+	
+	argument.dbl = x;
+	xhi = argument.words.hi & 0x7fffffffUL;	      	// xhi <- high half of |x|
+	target = ( argument.words.hi < signMask );	      	// flag positive sign
+	
+	if ( xhi < 0x43300000ul ) 
+/*******************************************************************************
+*     Is |x| < 2.0^53?                                                         *
+*******************************************************************************/
+		{
+		if ( xhi < 0x3ff00000ul ) 
+/*******************************************************************************
+*     Is |x| < 1.0?                                                            *
+*******************************************************************************/
+			{
+			if ( ( xhi | argument.words.lo ) != 0ul ) 
+				{                             	// raise deserved INEXACT
+				asm ("mffs %0" : "=f" (OldEnvironment.dbl));
+				OldEnvironment.words.lo |= 0x02000000ul;
+				asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl ));
+				}
+			if ( target )	                  	// return properly signed zero
+				return ( 0.0 );
+			else
+				return ( -0.0 );
+			}
+/*******************************************************************************
+*     Is 1.0 < |x| < 2.0^52?                                                   *
+*******************************************************************************/
+		if ( target ) 
+			{
+			y = ( x + twoTo52 ) - twoTo52;      	// round at binary point
+			if ( y > x )
+				return ( y - 1.0 );
+			else
+				return ( y );
+			}
+		
+		else 
+			{
+			y = ( x - twoTo52 ) + twoTo52;      	// round at binary point.
+			if ( y < x )
+				return ( y + 1.0 );
+			else
+				return ( y );
+			}
+		}
+/*******************************************************************************
+*      Is |x| >= 2.0^52 or x is a NaN.                                         *
+*******************************************************************************/
+	return ( x );
+	}
+
+/*******************************************************************************
+*     The modf family of functions separate a floating-point number into its   *
+*     fractional and integral parts, returning the fractional part and writing *
+*     the integral part in floating-point format to the object pointed to by a *
+*     pointer argument.  If the input argument is integral or infinite in      *
+*     value, the return value is a zero with the sign of the input argument.   *
+*     The modf family of functions raises no floating-point exceptions. older  *
+*     implemenation set the INVALID flag due to signaling NaN input.           *
+*                                                                              *
+*******************************************************************************/
+
+/*******************************************************************************
+*     modf is the double implementation.                                       *                             
+*******************************************************************************/
+
+#if defined(__ppc__)
+double modf ( double x, double *iptr )
+      {
+      register double OldEnvironment, xtrunc;
+      register unsigned long int xHead, signBit;
+      DblInHex argument;
+      
+      argument.dbl = x;
+      xHead = argument.words.hi & 0x7ffffffful;            // |x| high bit pattern
+      signBit = ( argument.words.hi & 0x80000000ul );      // isolate sign bit
+	  if (xHead == 0x7ff81fe0)
+			signBit = signBit | 0;
+      
+      if ( xHead < 0x43300000ul ) 
+/*******************************************************************************
+*     Is |x| < 2.0^53?                                                         *
+*******************************************************************************/
+            {
+            if ( xHead < 0x3ff00000ul )      
+/*******************************************************************************
+*     Is |x| < 1.0?                                                            *
+*******************************************************************************/
+                  {
+                  argument.words.hi = signBit;             // truncate to zero
+                  argument.words.lo = 0ul;
+                  *iptr = argument.dbl;
+                  return ( x );
+                  }
+/*******************************************************************************
+*     Is 1.0 < |x| < 2.0^52?                                                   *
+*******************************************************************************/
+			asm ("mffs %0" : "=f" (OldEnvironment));	// save environment
+			// round toward zero
+			asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( TOWARDZERO.dbl ));
+            if ( signBit == 0ul )                         // truncate to integer
+                  xtrunc = ( x + twoTo52 ) - twoTo52;
+            else
+                  xtrunc = ( x - twoTo52 ) + twoTo52;
+		// restore caller's env
+		asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment ));
+            *iptr = xtrunc;                               // store integral part
+            if ( x != xtrunc )                            // nonzero fraction
+                  return ( x - xtrunc );
+            else 
+                  {                                       // zero with x's sign
+                  argument.words.hi = signBit;
+                  argument.words.lo = 0ul;
+                  return ( argument.dbl );
+                  }
+            }
+      
+      *iptr = x;                                          // x is integral or NaN
+      if ( x != x )                                       // NaN is returned
+            return x;
+      else 
+            {                                             // zero with x's sign
+            argument.words.hi = signBit;
+            argument.words.lo = 0ul;
+            return ( argument.dbl );
+            }
+      }
+#endif /* __ppc__ */