path: root/libm/rndint.c

/*******************************************************************************
**      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__ */