Floating point support functions

commands/i386/asmconv/asm86.h

@@ -89,7 +89,7 @@ typedef enum opcode {	/* 80486 opcodes, from the i486 reference manual.
 	FSIN,
 	FSINCOS,
 	FSQRT,
-	FSTD,	FSTS,	FSTPX,	FSTPD,	FSTPS,
+	FSTD,	FSTS,	FSTP,	FSTPX,	FSTPD,	FSTPS,
 	FSTCW,
 	FSTENV,
 	FSTSW,

commands/i386/asmconv/emit_gnu.c

@@ -151,6 +151,7 @@ static mnemonic_t mnemtab[] = {
 	{ FSTCW,	"fnstcw"	},
 	{ FSTD,		"fstl"		},
 	{ FSTENV,	"fnstenv"	},
+	{ FSTP,		"fstp"		},
 	{ FSTPD,	"fstpl"		},
 	{ FSTPS,	"fstps"		},
 	{ FSTPX,	"fstpt"		},

commands/i386/asmconv/parse_ack.c

@@ -160,6 +160,7 @@ static mnemonic_t mnemtab[] = {			/* This array is sorted. */
 	{ "fstcw",	FSTCW,		WORD },
 	{ "fstd",	FSTD,		WORD },
 	{ "fstenv",	FSTENV,		WORD },
+	{ "fstp",	FSTP,		WORD },
 	{ "fstpd",	FSTPD,		WORD },
 	{ "fstps",	FSTPS,		WORD },
 	{ "fstpx",	FSTPX,		WORD },

include/fenv.h

@@ -0,0 +1,21 @@
+#ifndef _FENV_H
+#define _FENV_H
+
+#include <stdint.h>
+
+#define FE_TONEAREST  1
+#define FE_DOWNWARD   2
+#define FE_UPWARD     3
+#define FE_TOWARDZERO 4
+
+typedef struct 
+{
+	u16_t cw;
+	u16_t sw;
+} fenv_t;
+
+int feholdexcept(fenv_t *envp);
+int fegetround(void);
+int fesetround(int round);
+
+#endif

include/math.h

@@ -7,11 +7,13 @@
 #include <ansi.h>
 #endif
 
-#define HUGE_VAL	(__huge_val())		/* may be infinity */
+#define INFINITY	(__infinity())
+#define NAN		(__qnan())
+#define HUGE_VAL	INFINITY
 
 /* Function Prototypes. */
-_PROTOTYPE( double __huge_val,	(void)					);
-_PROTOTYPE( int __IsNan,	(double _x)				);
+_PROTOTYPE( double __infinity,	(void)					);
+_PROTOTYPE( double __qnan,	(void)					);
 
 _PROTOTYPE( double acos,  (double _x)					);
 _PROTOTYPE( double asin,  (double _x)					);
@@ -40,6 +42,28 @@ _PROTOTYPE( double hypot, (double _x, double _y)			);
 
 #ifdef _POSIX_SOURCE	/* STD-C? */
 #include <mathconst.h>
+
+#define FP_INFINITE  1
+#define FP_NAN       2
+#define FP_NORMAL    3
+#define FP_SUBNORMAL 4
+#define FP_ZERO      5
+
+_PROTOTYPE( int fpclassify,     (double x)				);
+_PROTOTYPE( int isfinite,       (double x)				);
+_PROTOTYPE( int isinf,          (double x)				);
+_PROTOTYPE( int isnan,          (double x)				);
+_PROTOTYPE( int isnormal,       (double x)				);
+_PROTOTYPE( int signbit,        (double x)				);
+_PROTOTYPE( int isgreater,      (double x, double y)	);
+_PROTOTYPE( int isgreaterequal, (double x, double y)	);
+_PROTOTYPE( int isless,         (double x, double y)	);
+_PROTOTYPE( int islessequal,    (double x, double y)	);
+_PROTOTYPE( int islessgreater,  (double x, double y)	);
+_PROTOTYPE( int isunordered,    (double x, double y)	);
+_PROTOTYPE( double nearbyint,   (double x)				);
+_PROTOTYPE( double remainder,   (double x, double y)	);
+_PROTOTYPE( double trunc,       (double x)				);
 #endif
 
 #endif /* _MATH_H */

lib/ack/math/ldexp.c

@@ -14,7 +14,7 @@ ldexp(double fl, int exp)
 	int sign = 1;
 	int currexp;
 
-	if (__IsNan(fl)) {
+	if (isnan(fl)) {
 		errno = EDOM;
 		return fl;
 	}

lib/i386/Makefile.in

@@ -2,6 +2,7 @@
 
 SUBDIRS="\
 	int64 \
+	math \
 	misc \
 	rts \
 	string"

lib/i386/math/Makefile.in

@@ -0,0 +1,17 @@
+# Makefile for lib/i386/math.
+
+CFLAGS="-O -D_MINIX -D_POSIX_SOURCE"
+
+LIBRARIES=libc
+
+libc_FILES="           \
+	arch_compare.c \
+	arch_round.c   \
+	fpu_cw.s       \
+	fpu_sw.s       \
+	fpu_round.s    \
+	fegetround.c   \
+	feholdexcept.c \
+	fesetround.c"
+
+TYPE=both

lib/i386/math/arch_compare.c

@@ -0,0 +1,118 @@
+#include <assert.h>
+#include <math.h>
+
+#include "fpu_cw.h"
+#include "fpu_sw.h"
+
+#define FPUSW_FLAG_MASK	\
+	(FPUSW_CONDITION_C0 | FPUSW_CONDITION_C2 | FPUSW_CONDITION_C3)
+
+#define DOUBLE_NORMAL_MIN 2.2250738585072013830902327173324e-308 /* 2^-1022 */
+
+int fpclassify(double x)
+{
+	/* use status word returned by fpu_xam to determine type */
+	switch (fpu_xam(x) & FPUSW_FLAG_MASK)
+	{
+		case FPUSW_CONDITION_C0:
+			return FP_NAN;
+
+		case FPUSW_CONDITION_C2:
+			/* 
+			 * unfortunately, fxam always operates on long doubles
+			 * regardless of the precision setting. This means some
+			 * subnormals are incorrectly classified as normals, 
+			 * since they can be normalized using the additional
+			 * exponent bits available. However, if we already know
+			 * that the number is normal as a long double, finding
+			 * out whether it would be subnormal as a double is just
+			 * a simple comparison.
+			 */
+			if (-DOUBLE_NORMAL_MIN < x && x < DOUBLE_NORMAL_MIN)
+				return FP_SUBNORMAL;
+			else
+				return FP_NORMAL;
+
+		case FPUSW_CONDITION_C0 | FPUSW_CONDITION_C2:
+			return FP_INFINITE;
+
+		case FPUSW_CONDITION_C3:
+			return FP_ZERO;
+
+		case FPUSW_CONDITION_C3 | FPUSW_CONDITION_C2:
+			return FP_SUBNORMAL;
+	}
+
+	/* we don't expect any other case: unsupported, emtpy or reserved */
+	assert(0);
+	return -1;
+}
+
+int signbit(double x)
+{
+	u16_t sw;
+
+	/* examine and use status word to determine sign */
+	sw = fpu_xam(x);
+	return (sw & FPUSW_CONDITION_C1) ? 1 : 0;
+}
+
+#define FPUSW_GREATER	0
+#define FPUSW_LESS	FPUSW_CONDITION_C0
+#define FPUSW_EQUAL	FPUSW_CONDITION_C3
+#define FPUSW_UNORDERED	\
+	(FPUSW_CONDITION_C0 | FPUSW_CONDITION_C2 | FPUSW_CONDITION_C3)
+
+static int fpcompare(double x, double y, u16_t sw1, u16_t sw2)
+{
+	u16_t sw;
+
+	/* compare and check sanity */
+	sw = fpu_compare(x, y) & FPUSW_FLAG_MASK;
+	switch (sw)
+	{
+		case FPUSW_GREATER:
+		case FPUSW_LESS:
+		case FPUSW_EQUAL:
+		case FPUSW_UNORDERED:
+			break;
+
+		default:
+			/* other values are not possible (see IA32 Dev Man) */
+			assert(0);
+			return -1;
+	}
+
+	/* test whether FPUSW equals either sw1 or sw2 */
+	return sw == sw1 || sw == sw2;
+}
+
+int isgreater(double x, double y)
+{
+	return fpcompare(x, y, FPUSW_GREATER, -1);
+}
+
+int isgreaterequal(double x, double y)
+{
+	return fpcompare(x, y, FPUSW_GREATER, FPUSW_EQUAL);
+}
+
+int isless(double x, double y)
+{
+	return fpcompare(x, y, FPUSW_LESS, -1);
+}
+
+int islessequal(double x, double y)
+{
+	return fpcompare(x, y, FPUSW_LESS, FPUSW_EQUAL);
+}
+
+int islessgreater(double x, double y)
+{
+	return fpcompare(x, y, FPUSW_LESS, FPUSW_GREATER);
+}
+
+int isunordered(double x, double y)
+{
+	return fpcompare(x, y, FPUSW_UNORDERED, -1);
+}

lib/i386/math/arch_round.c

@@ -0,0 +1,57 @@
+#include <errno.h>
+#include <fenv.h>
+#include <math.h>
+
+#include "fpu_cw.h"
+#include "fpu_round.h"
+
+static double rndint(double x, u16_t cw_bits, u16_t cw_mask)
+{
+	u16_t cw;
+
+	/* set FPUCW to the right value */
+	cw = fpu_cw_get();
+	fpu_cw_set((cw & cw_mask) | cw_bits);
+
+	/* perform the round */
+	fpu_rndint(&x);
+	
+	/* restore FPUCW */
+	fpu_cw_set(cw);
+	return x;
+}
+
+double nearbyint(double x)
+{
+	/* round, disabling floating point precision error */
+	return rndint(x, FPUCW_EXCEPTION_MASK_PM, ~0);
+}
+
+double remainder(double x, double y)
+{
+	int xclass, yclass;
+
+	/* check arguments */
+	xclass = fpclassify(x);
+	yclass = fpclassify(y);
+	if (xclass == FP_NAN || yclass == FP_NAN)
+		return NAN;
+
+	if (xclass == FP_INFINITE || yclass == FP_ZERO)
+	{
+		errno = EDOM;
+		return NAN;
+	}
+
+	/* call the assembly implementation */
+	fpu_remainder(&x, y);
+	return x;
+}
+
+double trunc(double x)
+{
+	/* round in truncate mode, disabling floating point precision error */
+	return rndint(x, 
+		FPUCW_EXCEPTION_MASK_PM | FPUCW_ROUNDING_CONTROL_TRUNC, 
+		~FPUCW_ROUNDING_CONTROL);
+}

lib/i386/math/fegetround.c

@@ -0,0 +1,23 @@
+#include <assert.h>
+#include <fenv.h>
+
+#include "fpu_cw.h"
+
+int fegetround(void)
+{
+	u16_t cw;
+
+	/* read and categorize FPUCW */
+	cw = fpu_cw_get();
+	switch (cw & FPUCW_ROUNDING_CONTROL)
+	{
+		case FPUCW_ROUNDING_CONTROL_NEAREST: return FE_TONEAREST;
+		case FPUCW_ROUNDING_CONTROL_DOWN:    return FE_DOWNWARD;
+		case FPUCW_ROUNDING_CONTROL_UP:      return FE_UPWARD;
+		case FPUCW_ROUNDING_CONTROL_TRUNC:   return FE_TOWARDZERO;
+	}
+
+	/* each case has been handled, otherwise the constants are wrong */
+	assert(0);
+	return -1;
+}

lib/i386/math/feholdexcept.c

@@ -0,0 +1,17 @@
+#include <errno.h>
+#include <fenv.h>
+
+#include "fpu_cw.h"
+#include "fpu_sw.h"
+
+int feholdexcept(fenv_t *envp)
+{
+	/* read FPUCW and FPUSW */
+	envp->cw = fpu_cw_get();
+	envp->sw = fpu_sw_get();
+	
+	/* update FPUCW to block exceptions */
+	fpu_cw_set(envp->cw | FPUCW_EXCEPTION_MASK);
+
+	return 0;
+}

lib/i386/math/fesetround.c

@@ -0,0 +1,27 @@
+#include <errno.h>
+#include <fenv.h>
+
+#include "fpu_cw.h"
+
+int fesetround(int round)
+{
+	u16_t cw;
+
+	/* read and update FPUCW */
+	cw = fpu_cw_get() & ~FPUCW_ROUNDING_CONTROL;
+	switch (round)
+	{
+		case FE_TONEAREST: cw |= FPUCW_ROUNDING_CONTROL_NEAREST; break;
+		case FE_DOWNWARD: cw |= FPUCW_ROUNDING_CONTROL_DOWN; break;
+		case FE_UPWARD: cw |= FPUCW_ROUNDING_CONTROL_UP; break;
+		case FE_TOWARDZERO: cw |= FPUCW_ROUNDING_CONTROL_TRUNC; break;
+
+		default:
+			errno = EINVAL;
+			return -1;
+	}
+
+	/* set FPUCW to the updated value */
+	fpu_cw_set(cw);
+	return 0;
+}

lib/i386/math/fpu_cw.h

@@ -0,0 +1,33 @@
+#ifndef __FPU_CW__
+#define __FPU_CW__
+
+#include <stdint.h>
+
+/* 
+ * see section 8.1.5 "x87 FPU Control Word" in "Intel 64 and IA-32 Architectures 
+ * Software Developer's Manual Volume 1 Basic Architecture" 
+ */
+#define FPUCW_EXCEPTION_MASK    0x003f
+#define FPUCW_EXCEPTION_MASK_IM 0x0001
+#define FPUCW_EXCEPTION_MASK_DM 0x0002
+#define FPUCW_EXCEPTION_MASK_ZM 0x0004
+#define FPUCW_EXCEPTION_MASK_OM 0x0008
+#define FPUCW_EXCEPTION_MASK_UM 0x0010
+#define FPUCW_EXCEPTION_MASK_PM 0x0020
+
+#define FPUCW_PRECISION_CONTROL         0x0300
+#define FPUCW_PRECISION_CONTROL_SINGLE  0x0000
+#define FPUCW_PRECISION_CONTROL_DOUBLE  0x0200
+#define FPUCW_PRECISION_CONTROL_XDOUBLE 0x0300
+
+#define FPUCW_ROUNDING_CONTROL         0x0c00
+#define FPUCW_ROUNDING_CONTROL_NEAREST 0x0000
+#define FPUCW_ROUNDING_CONTROL_DOWN    0x0400
+#define FPUCW_ROUNDING_CONTROL_UP      0x0800
+#define FPUCW_ROUNDING_CONTROL_TRUNC   0x0c00
+
+/* get and set FPU control word */
+u16_t fpu_cw_get(void);
+void fpu_cw_set(u16_t fpu_cw);
+
+#endif /* !defined(__FPU_CW__) */

lib/i386/math/fpu_cw.s

@@ -0,0 +1,20 @@
+!	fpu_cw_get() - get FPU control word	Author: Erik van der Kouwe
+!	fpu_cw_set() - set FPU control word	9 Dec 2009
+.sect .text
+.define _fpu_cw_get
+.define _fpu_cw_set
+
+! u16_t fpu_cw_get(void)
+_fpu_cw_get:
+	! clear unused bits just to be sure
+	xor	eax,	eax
+	push	eax
+	fstcw	(esp)
+	pop	eax
+	ret
+
+! void fpu_cw_set(u16_t fpu_cw)
+_fpu_cw_set:
+	! load control word from parameter
+	fldcw	4(esp)
+	ret

lib/i386/math/fpu_round.h

@@ -0,0 +1,7 @@
+#ifndef __FPU_RNDINT__
+#define __FPU_RNDINT__
+
+void fpu_rndint(double *value);
+void fpu_remainder(double *x, double y);
+
+#endif /* !defined(__FPU_RNDINT__) */

lib/i386/math/fpu_round.s

@@ -0,0 +1,36 @@
+!	fpu_rndint() - round integer	Author: Erik van der Kouwe
+!	                            	17 Dec 2009
+.sect .text
+.define _fpu_rndint
+.define _fpu_remainder
+
+! void fpu_rndint(double *value)
+_fpu_rndint:
+	! move the value onto the floating point stack
+	mov	eax,	4(esp)
+	fldd	(eax)
+
+	! round it (beware of precision exception!)
+	frndint
+
+	! store the result
+	fstpd	(eax)
+	ret
+
+! void fpu_remainder(double *x, double y)
+_fpu_remainder:
+	! move the values onto the floating point stack
+	fldd	8(esp)
+	mov	edx,	4(esp)
+	fldd	(edx)
+
+	! compute remainder, multiple iterations may be needed
+1:	fprem1
+	.data1	0xdf, 0xe0	! fnstsw	ax	
+	sahf
+	jp	1b
+
+	! store the result and pop the divisor
+	fstpd	(edx)
+	fstp	st
+	ret

lib/i386/math/fpu_sw.h

@@ -0,0 +1,26 @@
+#ifndef __FPU_SW__
+#define __FPU_SW__
+
+#include <stdint.h>
+
+#define FPUSW_EXCEPTION_IE  0x0001
+#define FPUSW_EXCEPTION_DE  0x0002
+#define FPUSW_EXCEPTION_ZE  0x0004
+#define FPUSW_EXCEPTION_OE  0x0008
+#define FPUSW_EXCEPTION_UE  0x0010
+#define FPUSW_EXCEPTION_PE  0x0020
+#define FPUSW_STACK_FAULT   0x0040
+#define FPUSW_ERROR_SUMMARY 0x0080
+#define FPUSW_CONDITION_C0  0x0100
+#define FPUSW_CONDITION_C1  0x0200
+#define FPUSW_CONDITION_C2  0x0400
+#define FPUSW_CONDITION_C3  0x4000
+#define FPUSW_BUSY          0x8000
+
+u16_t fpu_compare(double x, double y);
+u16_t fpu_sw_get(void);
+void fpu_sw_set(u16_t value);
+u16_t fpu_xam(double value);
+
+#endif /* !defined(__FPU_SW__) */
+

lib/i386/math/fpu_sw.s

@@ -0,0 +1,38 @@
+! fpu_compare() - compare doubles	Author: Erik van der Kouwe
+! fpu_sw_get() - get FPU status      	17 Dec 2009
+! fpu_xam() - examine double
+.sect .text
+.define _fpu_compare
+.define _fpu_sw_get
+.define _fpu_xam
+
+! u16_t fpu_compare(double x, double y)
+_fpu_compare:
+	! move the values onto the floating point stack
+	fldd	12(esp)
+	fldd	4(esp)
+
+	! compare values and return status word
+	fcompp
+	jmp	_fpu_sw_get
+
+! u16_t fpu_sw_get(void)
+_fpu_sw_get:
+	! clear unused high-order word and get status word
+	xor	eax,	eax
+	.data1	0xdf, 0xe0	! fnstsw	ax
+	ret
+	
+! u16_t fpu_xam(double value)
+_fpu_xam:
+	! move the value onto the floating point stack
+	fldd	4(esp)
+
+	! examine value and get status word
+	fxam
+	call	_fpu_sw_get
+
+	! pop the value
+	fstp	st
+	ret
+

lib/math/Makefile.in

@@ -9,6 +9,7 @@ libc_FILES=" \
 	atan.c \
 	atan2.c \
 	ceil.c \
+	compare.c \
 	exp.c \
 	fabs.c \
 	floor.c \

lib/math/compare.c

@@ -0,0 +1,39 @@
+#include <assert.h>
+#include <math.h>
+
+/* functions missing here are architecture-specific and are in i386/float */
+
+int isfinite(double x)
+{
+	/* return value based on classification */
+	switch (fpclassify(x))
+	{
+		case FP_INFINITE:
+		case FP_NAN:
+			return 0;
+
+		case FP_NORMAL:
+		case FP_SUBNORMAL:
+		case FP_ZERO:
+			return 1;
+	}
+
+	/* if we get here, fpclassify is buggy */
+	assert(0);
+	return -1;
+}
+
+int isinf(double x)
+{
+	return fpclassify(x) == FP_INFINITE;
+}
+
+int isnan(double x)
+{
+	return fpclassify(x) == FP_NAN;
+}
+
+int isnormal(double x)
+{
+	return fpclassify(x) == FP_NORMAL;
+}

lib/math/hugeval.c

@@ -9,7 +9,7 @@
 #include	<math.h>
 
 double
-__huge_val(void)
+__infinity(void)
 {
 #if (CHIP == INTEL)
 	static unsigned char ieee_infinity[] = { 
@@ -21,3 +21,18 @@ __huge_val(void)
 	return 1.0e+1000;	/* This will generate a warning */
 #endif
 }
+
+double
+__qnan(void)
+{
+#if (CHIP == INTEL)
+	static unsigned char ieee_qnan[] = { 
+		0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f };
+
+	assert(sizeof(double) == sizeof(ieee_qnan));
+	return *(double *) ieee_qnan;
+#else
+#error QNaN not defined on this architecture
+#endif
+}
+

lib/math/localmath.h

@@ -3,6 +3,8 @@
  */
 /* $Header$ */
 
+#define __IsNan isnan
+
 /* some constants (Hart & Cheney) */
 #define	M_PI		3.14159265358979323846264338327950288
 #define	M_2PI		6.28318530717958647692528676655900576

lib/math/sqrt.c

@@ -9,6 +9,7 @@
 #include	<math.h>
 #include	<float.h>
 #include	<errno.h>
+#include	"localmath.h"
 
 #define NITER	5
 

man/man3/feholdexcept.3

@@ -0,0 +1,28 @@
+.TH FEHOLDEXCEPT 3  "December 22, 2009"
+.UC 4
+.SH NAME
+feholdexcept \- disable floating point exceptions
+.SH SYNOPSIS
+.nf
+.ft B
+#include <fenv.h>
+
+int feholdexcept(fenv_t *\fIenvp\fP);
+.fi
+.SH DESCRIPTION
+The feholdexcept function disables floating point exceptions. The floating
+point environment prior to disabling exceptions is stored in the struct 
+pointed to by \fIenvp\fP. 
+.SH "RETURN VALUE"
+On x86, this function never fails and the return value is always 0. A portable
+program should, however, consider the possibility that this function may fail
+and will return -1 to indicate this.
+.SH "KNOWN ISSUES"
+POSIX requires the function to clear exception flags. However, as none of the
+other functions dealing with FPU flags and FPU state have been implemented this
+has no effect on MINIX. A full implementation may need to store more FPU state
+as there is no instruction to change the status word independent of the rest
+of the FPU state. Do not depend on the fields of fenv_t as they may change even
+on future versions of MINIX/x86.
+
+

man/man3/fesetround.3

@@ -0,0 +1,34 @@
+.TH FESETROUND 3  "December 18, 2009"
+.UC 4
+.SH NAME
+fegetround, fesetround \- floating point rounding mode control
+.SH SYNOPSIS
+.nf
+.ft B
+#include <fenv.h>
+
+int fegetround(void);
+int fesetround(int \fIround\fP);
+.fi
+.SH DESCRIPTION
+These functions control the floating point rounding mode. One can use 
+fegetround to determine the rounding mode currently in effect and fesetround
+the change the rounding mode. Four rounding modes are recognized: FE_TONEAREST,
+FE_DOWNWARD, FE_UPWARD and FE_TOWARDZERO. When rounding a value \fIx\fP to an 
+integer \fIn\fP, the following approaches can be taken: FE_TONEAREST selects 
+the \fIn\fP for which abs(fIx\fP - \fIn\fP) is minimal, preferring an even 
+\fIn\fP if there are two possibilities; FE_DOWNWARD selects the largest \fIn\fP
+for which \fIn\fP <= fIx\fP; FE_UPWARD selects the smallest \fIn\fP for which 
+\fIn\fP >= fIx\fP; and FE_TOWARDZERO selects \fIn\fP with the largest 
+abs(\fIn\fP) for which abs(\fIn\fP) <= abs(\fIx\fP).
+.SH "RETURN VALUE"
+fegetround returns the current rounding mode. fesetround returns 0 if it was 
+succesful in adjusting the rounding mode and -1 otherwise. The only possible
+reason for failure is an unsupported value for \fIround\fP, which is signalled
+by setting errno to EINVAL.
+.SH DIAGNOSTICS
+fegetround always succeeds. The only possible reason for failure of fesetround
+is an unsupported value for \fIround\fP, which is signalled by setting errno to
+EINVAL.
+.SH "SEE ALSO"
+nearbyint(3)

man/man3/fpclassify.3

@@ -0,0 +1,25 @@
+.TH FPCLASSIFY 3  "December 18, 2009"
+.UC 4
+.SH NAME
+fpclassify, isfinite, isinf, isnan, isnormal, signbit \- classify floating point numbers
+.SH SYNOPSIS
+.nf
+.ft B
+#include <math.h>
+
+int fpclassify(double \fIx\fP):
+int isfinite(double \fIx\fP);
+int isinf(double \fIx\fP);
+int isnan(double \fIx\fP);
+int isnormal(double \fIx\fP);
+int signbit(double \fIx\fP);
+.fi
+.SH DESCRIPTION
+These functions provide information about the specified floating point number 
+\fIx\fP. fpclassify returns one of the values FP_INFINITE, FP_NAN, FP_NORMAL,
+FP_SUBNORMAL and FP_ZERO depending on the type of number provided. The isinf,
+isinf, isnan and isnormal test for specific number classes, returning a 
+non-zero value is and only if the specified number belongs to the class 
+specified by the function name. The signbit function returns a non-zero value
+if and only if the sign bit is set, which for non-NaN values (including zero)
+means that the number is negative.

man/man3/islessgreater.3

@@ -0,0 +1,26 @@
+.TH ISLESSGREATER 3  "December 18, 2009"
+.UC 4
+.SH NAME
+isgreater, isgreaterequal, isless, islessequal, islessgreater, isunordered \- order floating point numbers
+.SH SYNOPSIS
+.nf
+.ft B
+#include <math.h>
+
+int isgreater(double \fIx\fP, double \fIy\fP);
+int isgreaterequal(double \fIx\fP, double \fIy\fP);
+int isless(double \fIx\fP, double \fIy\fP);
+int islessequal(double \fIx\fP, double \fIy\fP);
+int islessgreater(double \fIx\fP, double \fIy\fP);
+int isunordered(double \fIx\fP, double \fIy\fP);
+.fi
+.SH DESCRIPTION
+These functions compare the specified floating point numbers \fIx\fP and 
+\fIy\fP. They differ from the regular comparison operators in that they 
+recognize and additional 'unordered' relationship between the numbers if one of
+them is NaN. As a consequence, these functions do not raise floating point
+expceptions and can be safely used with NaN values.
+.SH "RETURN VALUE"
+The functions return a non-zero value if and only if the relationship specified
+in the name holds between \fIx\fP and \fIy\fP. All functions except for 
+'isunordered' return zero if either of the numbers is NaN.

man/man3/nearbyint.3

@@ -0,0 +1,28 @@
+.TH NEARBYINT 3  "December 18, 2009"
+.UC 4
+.SH NAME
+ceil, floor, nearbyint, trunc \- floating point rounding
+.SH SYNOPSIS
+.nf
+.ft B
+#include <math.h>
+
+double ceil(double \fIx\fP);
+double floor(double \fIx\fP);
+double nearbyint(double \fIx\fP);
+double trunc(double \fIx\fP);
+.fi
+.SH DESCRIPTION
+These functions round the specified floating point number to a nearby integer.
+For nearbyint, the rounding mode is determined by the value set using the
+fesetround function. The other functions are not influenced by the rounding 
+mode. The ceil function rounds upwards, selecting the smallest integer that is
+larger than or equal to \fIx\fP. The floor function rounds downwards, selecting
+the largest integer that is smaller than or equal to \fIx\fP. The trunc function
+rounds towards zero, selecting the largest integer with the largest absolute 
+value of which the absolute value is smaller than or equal to the absolute 
+value of \fIx\fP.
+.SH "RETURN VALUE"
+The functions return an integer close to \fIx\fP.
+.SH "SEE ALSO"
+fesetround(3)

man/man3/remainder.3

@@ -0,0 +1,20 @@
+.TH REMAINDER 3  "December 18, 2009"
+.UC 4
+.SH NAME
+remainder \- floating point remainder after division
+.SH SYNOPSIS
+.nf
+.ft B
+#include <math.h>
+
+double remainder(double \fIx\fP, double \fIy\fP);
+.fi
+.SH DESCRIPTION
+This function returns the remainder of a division of \fIx\fP by \fIy\fP. More
+formally, it computes which integer \fIn\fP is closest to the fraction 
+\fIx\fP/\fIy\fP and returns \fIx\fP - \fIn\fP*\fIy\fP. An even value for 
+\fIn\fP is preferred over an odd one if both are equally far away (that is, 
+banker's rounding is applied). If \fIx\fP is infinite or \fIy\fP is zero, 
+a NaN value is returned.
+.SH "RETURN VALUE"
+The function returns the remainder of a division of \fIx\fP by \fIy\fP.

test/Makefile

@@ -10,7 +10,7 @@ OBJ=	test1  test2  test3  test4  test5  test6  test7  test8  test9  \
 	       test21 test22 test23        test25 test26 test27 test28 test29 \
 	test30 test31 test32        test34 test35 test36 test37 test38 \
 	test39 t10a t11a t11b test40 t40a t40b t40c t40d t40e t40f test41 \
-	test42 test44 test45
+	test42 test44 test45 test47
 
 BIGOBJ=  test20 test24
 ROOTOBJ= test11 test33 test43 test46
@@ -94,4 +94,5 @@ test44: test44.c
 test45: test45.c test45.h
 test45-gcc: test45.c test45.h
 test46: test46.c
+test47: test47.c
 

test/run

@@ -19,7 +19,7 @@ echo " "
 # Run all the tests, keeping track of who failed.
 for i in  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 \
          21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 \
-         41 42 43 44 45 45-gcc 46 sh1.sh sh2.sh
+         41 42 43 44 45 45-gcc 46 47 sh1.sh sh2.sh
 do
    if [ -x ./test$i ]
    then

test/test47.c

@@ -0,0 +1,275 @@
+#include <assert.h>
+#include <fenv.h>
+#include <math.h>
+#include <signal.h>
+#include <stdlib.h>
+#include <stdio.h>
+#include <string.h>
+#include <sys/sigcontext.h>
+
+#define MAX_ERROR 4
+static int errct;
+
+/* maximum allowed FP difference for our tests */ 
+#define EPSILON 0.00000000023283064365386962890625 /* 2^(-32) */
+
+static void quit(void)
+{
+	if (errct == 0) 
+	{
+		printf("ok\n");
+		exit(0);
+	} 
+	else 
+	{
+		printf("%d errors\n", errct);
+		exit(1);
+	}
+}
+
+#define ERR(x, y) e(__LINE__, (x), (y))
+
+static void e(int n, double x, double y)
+{
+	printf("Line %d, x=%.20g, y=%.20g\n", n, x, y);
+	if (errct++ > MAX_ERROR) 
+	{
+		printf("Too many errors; test aborted\n");
+		exit(1);
+	}
+}
+
+static void signal_handler(int signum)
+{
+	struct sigframe *sigframe;
+	
+	/* report signal */
+	sigframe = (struct sigframe *) ((char *) &signum - 
+		(char *) &((struct sigframe *) NULL)->sf_signo);
+	printf("Signal %d at 0x%x\n", signum, sigframe->sf_scp->sc_regs.pc);
+	
+	/* count as error */
+	ERR(0, 0);
+	fflush(stdout);
+	
+	/* handle signa again next time */
+	signal(signum, signal_handler);
+}
+
+static void test_fpclassify(double value, int class, int test_sign)
+{
+	/* test fpclassify */
+	if (fpclassify(value) != class) ERR(value, 0);
+	if (test_sign) 
+	{
+		if (fpclassify(-value) != class) ERR(-value, 0);
+
+		/* test signbit */
+		if (signbit(value))   ERR(value, 0);
+		if (!signbit(-value)) ERR(-value, 0);
+	}
+}
+
+/* Maximum normal double: (2 - 2^(-53)) * 2^1023 */
+#define NORMAL_DOUBLE_MAX 1.797693134862315708145274237317e+308
+
+/* Minimum normal double: 2^(-1022) */
+#define NORMAL_DOUBLE_MIN 2.2250738585072013830902327173324e-308
+
+/* Maximum subnormal double: (1 - 2^(-53)) * 2^(-1022) */
+#define SUBNORMAL_DOUBLE_MAX 2.2250738585072008890245868760859e-308
+
+/* Minimum subnormal double: 2^(-52) * 2^(-1023) */
+#define SUBNORMAL_DOUBLE_MIN 4.9406564584124654417656879286822e-324
+
+static void test_fpclassify_values(void)
+{
+	double d;
+	char negzero[] = { 0, 0, 0, 0, 0, 0, 0, 0x80 };
+
+	/* test some corner cases for fpclassify and signbit */
+	test_fpclassify(INFINITY,             FP_INFINITE,    1);
+	test_fpclassify(NAN,                  FP_NAN,         0);
+	test_fpclassify(0,                    FP_ZERO,        0);
+	test_fpclassify(1,                    FP_NORMAL,      1);
+	test_fpclassify(NORMAL_DOUBLE_MAX,    FP_NORMAL,      1);
+	test_fpclassify(NORMAL_DOUBLE_MIN,    FP_NORMAL,      1);
+	test_fpclassify(SUBNORMAL_DOUBLE_MAX, FP_SUBNORMAL,   1);
+	test_fpclassify(SUBNORMAL_DOUBLE_MIN, FP_SUBNORMAL,   1);
+
+	/* 
+	 * unfortunately the minus operator does not change the sign of zero,
+	 * so a special case is needed to test it
+	 */
+	assert(sizeof(negzero) == sizeof(double));
+	test_fpclassify(*(double *) negzero, FP_ZERO, 0);
+	if (!signbit(*(double *) negzero)) ERR(0, 0);
+
+	/* test other small numbers for fpclassify and signbit */
+	d = 1;
+	while (d >= NORMAL_DOUBLE_MIN)
+	{
+		test_fpclassify(d, FP_NORMAL, 1);
+		d /= 10;
+	}
+	while (d >= SUBNORMAL_DOUBLE_MIN)
+	{
+		test_fpclassify(d, FP_SUBNORMAL, 1);
+		d /= 10;
+	}
+	test_fpclassify(d, FP_ZERO, 0);
+
+	/* test other large numbers for fpclassify and signbit */
+	d = 1;
+	while (d <= NORMAL_DOUBLE_MAX / 10)
+	{
+		test_fpclassify(d, FP_NORMAL, 1);
+		d *= 10;
+	}
+}
+
+/* expected rounding: up, down or identical */
+#define ROUND_EQ 1
+#define ROUND_DN 2
+#define ROUND_UP 3
+
+static void test_round_value_mode_func(double value, int mode, double (*func)(double), int exp)
+{
+	int mode_old;
+	double rounded;
+
+	/* update and check rounding mode */
+	mode_old = fegetround();
+	fesetround(mode);
+	if (fegetround() != mode) ERR(0, 0);
+
+	/* perform rounding */
+	rounded = func(value);
+	
+	/* check direction of rounding */
+	switch (exp)
+	{
+		case ROUND_EQ: if (rounded != value) ERR(value, rounded); break;
+		case ROUND_DN: if (rounded >= value) ERR(value, rounded); break;
+		case ROUND_UP: if (rounded <= value) ERR(value, rounded); break;
+		default:       assert(0); 
+	}
+
+	/* check whether the number is sufficiently close */
+	if (fabs(value - rounded) >= 1) ERR(value, rounded);
+
+	/* check whether the number is integer */
+	if (remainder(rounded, 1)) ERR(value, rounded);
+
+	/* re-check and restore rounding mode */
+	if (fegetround() != mode) ERR(0, 0);
+	fesetround(mode_old);
+}
+
+static void test_round_value_mode(double value, int mode, int exp_nearbyint,
+	int exp_ceil, int exp_floor, int exp_trunc)
+{
+	/* test both nearbyint and trunc */
+	test_round_value_mode_func(value, mode, nearbyint, exp_nearbyint);
+	test_round_value_mode_func(value, mode, ceil,      exp_ceil);
+	test_round_value_mode_func(value, mode, floor,     exp_floor);
+	test_round_value_mode_func(value, mode, trunc,     exp_trunc);
+}
+
+static void test_round_value(double value, int exp_down, int exp_near, int exp_up, int exp_trunc)
+{
+	/* test each rounding mode */
+	test_round_value_mode(value, FE_DOWNWARD,   exp_down,  exp_up, exp_down, exp_trunc);
+	test_round_value_mode(value, FE_TONEAREST,  exp_near,  exp_up, exp_down, exp_trunc);
+	test_round_value_mode(value, FE_UPWARD,     exp_up,    exp_up, exp_down, exp_trunc);
+	test_round_value_mode(value, FE_TOWARDZERO, exp_trunc, exp_up, exp_down, exp_trunc);
+}
+
+static void test_round_values(void)
+{
+	int i;
+
+	/* test various values */
+	for (i = -100000; i < 100000; i++)
+	{
+		test_round_value(i + 0.00, ROUND_EQ, ROUND_EQ,                      ROUND_EQ, ROUND_EQ);
+		test_round_value(i + 0.25, ROUND_DN, ROUND_DN,                      ROUND_UP, (i >= 0) ? ROUND_DN : ROUND_UP);
+		test_round_value(i + 0.50, ROUND_DN, (i % 2) ? ROUND_UP : ROUND_DN, ROUND_UP, (i >= 0) ? ROUND_DN : ROUND_UP);
+		test_round_value(i + 0.75, ROUND_DN, ROUND_UP,                      ROUND_UP, (i >= 0) ? ROUND_DN : ROUND_UP);
+	}
+}
+
+static void test_remainder_value(double x, double y)
+{
+	int mode_old;
+	double r1, r2, z;
+
+	assert(y != 0);
+
+	/* compute remainder using the function */
+	r1 = remainder(x, y);
+
+	/* compute remainder using alternative approach */
+	mode_old = fegetround();
+	fesetround(FE_TONEAREST);
+	r2 = x - nearbyint(x / y) * y;
+	fesetround(mode_old);
+
+	/* Compare results */
+	if (fabs(r1 - r2) > EPSILON && fabs(r1 + r2) > EPSILON) 
+	{
+		printf("%.20g != %.20g\n", r1, r2);
+		ERR(x, y);
+	}
+}
+
+static void test_remainder_values_y(double x)
+{
+	int i, j;
+
+	/* try various rational and transcendental values for y (except zero) */
+	for (i = -50; i <= 50; i++)
+		if (i != 0)
+			for (j = 1; j < 10; j++)
+			{
+				test_remainder_value(x, (double) i / (double) j);
+				test_remainder_value(x, i * M_E + j * M_PI);
+			}
+}
+
+static void test_remainder_values_xy(void)
+{
+	int i, j;
+
+	/* try various rational and transcendental values for x */
+	for (i = -50; i <= 50; i++)
+		for (j = 1; j < 10; j++)
+		{
+			test_remainder_values_y((double) i / (double) j);
+			test_remainder_values_y(i * M_E + j * M_PI);
+		}
+}
+
+int main(int argc, char **argv)
+{
+	fenv_t fenv;
+	int i;
+	
+	printf("Test 47 ");
+	fflush(stdout);
+
+	/* no FPU errors, please */
+	if (feholdexcept(&fenv) < 0) ERR(0, 0);
+
+	/* some signals count as errors */
+	for (i = 0; i < _NSIG; i++)
+		if (i != SIGINT && i != SIGTERM && i != SIGKILL)
+			signal(i, signal_handler);
+		
+	/* test various floating point support functions */
+	test_fpclassify_values();
+	test_remainder_values_xy();
+	test_round_values();
+	quit();
+	return -1;
+}