Adding upstream version 1:115.7.0.upstream/1%115.7.0upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 962 insertions, 0 deletions

diff --git a/modules/fdlibm/src/math_private.h b/modules/fdlibm/src/math_private.h
new file mode 100644
index 0000000000..f4373f2783
--- /dev/null
+++ b/modules/fdlibm/src/math_private.h
@@ -0,0 +1,962 @@
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+/*
+ * from: @(#)fdlibm.h 5.1 93/09/24
+ * $FreeBSD$
+ */
+
+#ifndef _MATH_PRIVATE_H_
+#define	_MATH_PRIVATE_H_
+
+#include <cfloat>
+#include <stdint.h>
+#include <sys/types.h>
+
+#include "mozilla/EndianUtils.h"
+
+#include "fdlibm.h"
+
+/*
+ * Emulate FreeBSD internal double types.
+ * Adapted from https://github.com/freebsd/freebsd-src/search?q=__double_t
+ */
+
+typedef double      __double_t;
+typedef __double_t  double_t;
+typedef float       __float_t;
+
+/*
+ * The original fdlibm code used statements like:
+ *	n0 = ((*(int*)&one)>>29)^1;		* index of high word *
+ *	ix0 = *(n0+(int*)&x);			* high word of x *
+ *	ix1 = *((1-n0)+(int*)&x);		* low word of x *
+ * to dig two 32 bit words out of the 64 bit IEEE floating point
+ * value.  That is non-ANSI, and, moreover, the gcc instruction
+ * scheduler gets it wrong.  We instead use the following macros.
+ * Unlike the original code, we determine the endianness at compile
+ * time, not at run time; I don't see much benefit to selecting
+ * endianness at run time.
+ */
+
+#ifndef u_int32_t
+#define u_int32_t uint32_t
+#endif
+#ifndef u_int64_t
+#define u_int64_t uint64_t
+#endif
+
+/* A union which permits us to convert between a long double and
+   four 32 bit ints.  */
+
+#if MOZ_BIG_ENDIAN()
+
+typedef union
+{
+  long double value;
+  struct {
+    u_int32_t mswhi;
+    u_int32_t mswlo;
+    u_int32_t lswhi;
+    u_int32_t lswlo;
+  } parts32;
+  struct {
+    u_int64_t msw;
+    u_int64_t lsw;
+  } parts64;
+} ieee_quad_shape_type;
+
+#endif
+
+#if MOZ_LITTLE_ENDIAN()
+
+typedef union
+{
+  long double value;
+  struct {
+    u_int32_t lswlo;
+    u_int32_t lswhi;
+    u_int32_t mswlo;
+    u_int32_t mswhi;
+  } parts32;
+  struct {
+    u_int64_t lsw;
+    u_int64_t msw;
+  } parts64;
+} ieee_quad_shape_type;
+
+#endif
+
+#if MOZ_BIG_ENDIAN()
+
+typedef union
+{
+  double value;
+  struct
+  {
+    u_int32_t msw;
+    u_int32_t lsw;
+  } parts;
+  struct
+  {
+    u_int64_t w;
+  } xparts;
+} ieee_double_shape_type;
+
+#endif
+
+#if MOZ_LITTLE_ENDIAN()
+
+typedef union
+{
+  double value;
+  struct
+  {
+    u_int32_t lsw;
+    u_int32_t msw;
+  } parts;
+  struct
+  {
+    u_int64_t w;
+  } xparts;
+} ieee_double_shape_type;
+
+#endif
+
+/* Get two 32 bit ints from a double.  */
+
+#define EXTRACT_WORDS(ix0,ix1,d)				\
+do {								\
+  ieee_double_shape_type ew_u;					\
+  ew_u.value = (d);						\
+  (ix0) = ew_u.parts.msw;					\
+  (ix1) = ew_u.parts.lsw;					\
+} while (0)
+
+/* Get a 64-bit int from a double. */
+#define EXTRACT_WORD64(ix,d)					\
+do {								\
+  ieee_double_shape_type ew_u;					\
+  ew_u.value = (d);						\
+  (ix) = ew_u.xparts.w;						\
+} while (0)
+
+/* Get the more significant 32 bit int from a double.  */
+
+#define GET_HIGH_WORD(i,d)					\
+do {								\
+  ieee_double_shape_type gh_u;					\
+  gh_u.value = (d);						\
+  (i) = gh_u.parts.msw;						\
+} while (0)
+
+/* Get the less significant 32 bit int from a double.  */
+
+#define GET_LOW_WORD(i,d)					\
+do {								\
+  ieee_double_shape_type gl_u;					\
+  gl_u.value = (d);						\
+  (i) = gl_u.parts.lsw;						\
+} while (0)
+
+/* Set a double from two 32 bit ints.  */
+
+#define INSERT_WORDS(d,ix0,ix1)					\
+do {								\
+  ieee_double_shape_type iw_u;					\
+  iw_u.parts.msw = (ix0);					\
+  iw_u.parts.lsw = (ix1);					\
+  (d) = iw_u.value;						\
+} while (0)
+
+/* Set a double from a 64-bit int. */
+#define INSERT_WORD64(d,ix)					\
+do {								\
+  ieee_double_shape_type iw_u;					\
+  iw_u.xparts.w = (ix);						\
+  (d) = iw_u.value;						\
+} while (0)
+
+/* Set the more significant 32 bits of a double from an int.  */
+
+#define SET_HIGH_WORD(d,v)					\
+do {								\
+  ieee_double_shape_type sh_u;					\
+  sh_u.value = (d);						\
+  sh_u.parts.msw = (v);						\
+  (d) = sh_u.value;						\
+} while (0)
+
+/* Set the less significant 32 bits of a double from an int.  */
+
+#define SET_LOW_WORD(d,v)					\
+do {								\
+  ieee_double_shape_type sl_u;					\
+  sl_u.value = (d);						\
+  sl_u.parts.lsw = (v);						\
+  (d) = sl_u.value;						\
+} while (0)
+
+/*
+ * A union which permits us to convert between a float and a 32 bit
+ * int.
+ */
+
+typedef union
+{
+  float value;
+  /* FIXME: Assumes 32 bit int.  */
+  unsigned int word;
+} ieee_float_shape_type;
+
+/* Get a 32 bit int from a float.  */
+
+#define GET_FLOAT_WORD(i,d)					\
+do {								\
+  ieee_float_shape_type gf_u;					\
+  gf_u.value = (d);						\
+  (i) = gf_u.word;						\
+} while (0)
+
+/* Set a float from a 32 bit int.  */
+
+#define SET_FLOAT_WORD(d,i)					\
+do {								\
+  ieee_float_shape_type sf_u;					\
+  sf_u.word = (i);						\
+  (d) = sf_u.value;						\
+} while (0)
+
+/*
+ * Get expsign and mantissa as 16 bit and 64 bit ints from an 80 bit long
+ * double.
+ */
+
+#define	EXTRACT_LDBL80_WORDS(ix0,ix1,d)				\
+do {								\
+  union IEEEl2bits ew_u;					\
+  ew_u.e = (d);							\
+  (ix0) = ew_u.xbits.expsign;					\
+  (ix1) = ew_u.xbits.man;					\
+} while (0)
+
+/*
+ * Get expsign and mantissa as one 16 bit and two 64 bit ints from a 128 bit
+ * long double.
+ */
+
+#define	EXTRACT_LDBL128_WORDS(ix0,ix1,ix2,d)			\
+do {								\
+  union IEEEl2bits ew_u;					\
+  ew_u.e = (d);							\
+  (ix0) = ew_u.xbits.expsign;					\
+  (ix1) = ew_u.xbits.manh;					\
+  (ix2) = ew_u.xbits.manl;					\
+} while (0)
+
+/* Get expsign as a 16 bit int from a long double.  */
+
+#define	GET_LDBL_EXPSIGN(i,d)					\
+do {								\
+  union IEEEl2bits ge_u;					\
+  ge_u.e = (d);							\
+  (i) = ge_u.xbits.expsign;					\
+} while (0)
+
+/*
+ * Set an 80 bit long double from a 16 bit int expsign and a 64 bit int
+ * mantissa.
+ */
+
+#define	INSERT_LDBL80_WORDS(d,ix0,ix1)				\
+do {								\
+  union IEEEl2bits iw_u;					\
+  iw_u.xbits.expsign = (ix0);					\
+  iw_u.xbits.man = (ix1);					\
+  (d) = iw_u.e;							\
+} while (0)
+
+/*
+ * Set a 128 bit long double from a 16 bit int expsign and two 64 bit ints
+ * comprising the mantissa.
+ */
+
+#define	INSERT_LDBL128_WORDS(d,ix0,ix1,ix2)			\
+do {								\
+  union IEEEl2bits iw_u;					\
+  iw_u.xbits.expsign = (ix0);					\
+  iw_u.xbits.manh = (ix1);					\
+  iw_u.xbits.manl = (ix2);					\
+  (d) = iw_u.e;							\
+} while (0)
+
+/* Set expsign of a long double from a 16 bit int.  */
+
+#define	SET_LDBL_EXPSIGN(d,v)					\
+do {								\
+  union IEEEl2bits se_u;					\
+  se_u.e = (d);							\
+  se_u.xbits.expsign = (v);					\
+  (d) = se_u.e;							\
+} while (0)
+
+#ifdef __i386__
+/* Long double constants are broken on i386. */
+#define	LD80C(m, ex, v) {						\
+	.xbits.man = __CONCAT(m, ULL),					\
+	.xbits.expsign = (0x3fff + (ex)) | ((v) < 0 ? 0x8000 : 0),	\
+}
+#else
+/* The above works on non-i386 too, but we use this to check v. */
+#define	LD80C(m, ex, v)	{ .e = (v), }
+#endif
+
+#ifdef FLT_EVAL_METHOD
+/*
+ * Attempt to get strict C99 semantics for assignment with non-C99 compilers.
+ */
+#if !defined(_MSC_VER) && (FLT_EVAL_METHOD == 0 || __GNUC__ == 0)
+#define	STRICT_ASSIGN(type, lval, rval)	((lval) = (rval))
+#else
+#define	STRICT_ASSIGN(type, lval, rval) do {	\
+	volatile type __lval;			\
+						\
+	if (sizeof(type) >= sizeof(long double))	\
+		(lval) = (rval);		\
+	else {					\
+		__lval = (rval);		\
+		(lval) = __lval;		\
+	}					\
+} while (0)
+#endif
+#else
+#define	STRICT_ASSIGN(type, lval, rval) do {	\
+	volatile type __lval;			\
+						\
+	if (sizeof(type) >= sizeof(long double))	\
+		(lval) = (rval);		\
+	else {					\
+		__lval = (rval);		\
+		(lval) = __lval;		\
+	}					\
+} while (0)
+#endif /* FLT_EVAL_METHOD */
+
+/* Support switching the mode to FP_PE if necessary. */
+#if defined(__i386__) && !defined(NO_FPSETPREC)
+#define	ENTERI() ENTERIT(long double)
+#define	ENTERIT(returntype)			\
+	returntype __retval;			\
+	fp_prec_t __oprec;			\
+						\
+	if ((__oprec = fpgetprec()) != FP_PE)	\
+		fpsetprec(FP_PE)
+#define	RETURNI(x) do {				\
+	__retval = (x);				\
+	if (__oprec != FP_PE)			\
+		fpsetprec(__oprec);		\
+	RETURNF(__retval);			\
+} while (0)
+#define	ENTERV()				\
+	fp_prec_t __oprec;			\
+						\
+	if ((__oprec = fpgetprec()) != FP_PE)	\
+		fpsetprec(FP_PE)
+#define	RETURNV() do {				\
+	if (__oprec != FP_PE)			\
+		fpsetprec(__oprec);		\
+	return;			\
+} while (0)
+#else
+#define	ENTERI()
+#define	ENTERIT(x)
+#define	RETURNI(x)	RETURNF(x)
+#define	ENTERV()
+#define	RETURNV()	return
+#endif
+
+/* Default return statement if hack*_t() is not used. */
+#define      RETURNF(v)      return (v)
+
+/*
+ * 2sum gives the same result as 2sumF without requiring |a| >= |b| or
+ * a == 0, but is slower.
+ */
+#define	_2sum(a, b) do {	\
+	__typeof(a) __s, __w;	\
+				\
+	__w = (a) + (b);	\
+	__s = __w - (a);	\
+	(b) = ((a) - (__w - __s)) + ((b) - __s); \
+	(a) = __w;		\
+} while (0)
+
+/*
+ * 2sumF algorithm.
+ *
+ * "Normalize" the terms in the infinite-precision expression a + b for
+ * the sum of 2 floating point values so that b is as small as possible
+ * relative to 'a'.  (The resulting 'a' is the value of the expression in
+ * the same precision as 'a' and the resulting b is the rounding error.)
+ * |a| must be >= |b| or 0, b's type must be no larger than 'a's type, and
+ * exponent overflow or underflow must not occur.  This uses a Theorem of
+ * Dekker (1971).  See Knuth (1981) 4.2.2 Theorem C.  The name "TwoSum"
+ * is apparently due to Skewchuk (1997).
+ *
+ * For this to always work, assignment of a + b to 'a' must not retain any
+ * extra precision in a + b.  This is required by C standards but broken
+ * in many compilers.  The brokenness cannot be worked around using
+ * STRICT_ASSIGN() like we do elsewhere, since the efficiency of this
+ * algorithm would be destroyed by non-null strict assignments.  (The
+ * compilers are correct to be broken -- the efficiency of all floating
+ * point code calculations would be destroyed similarly if they forced the
+ * conversions.)
+ *
+ * Fortunately, a case that works well can usually be arranged by building
+ * any extra precision into the type of 'a' -- 'a' should have type float_t,
+ * double_t or long double.  b's type should be no larger than 'a's type.
+ * Callers should use these types with scopes as large as possible, to
+ * reduce their own extra-precision and efficiciency problems.  In
+ * particular, they shouldn't convert back and forth just to call here.
+ */
+#ifdef DEBUG
+#define	_2sumF(a, b) do {				\
+	__typeof(a) __w;				\
+	volatile __typeof(a) __ia, __ib, __r, __vw;	\
+							\
+	__ia = (a);					\
+	__ib = (b);					\
+	assert(__ia == 0 || fabsl(__ia) >= fabsl(__ib));	\
+							\
+	__w = (a) + (b);				\
+	(b) = ((a) - __w) + (b);			\
+	(a) = __w;					\
+							\
+	/* The next 2 assertions are weak if (a) is already long double. */ \
+	assert((long double)__ia + __ib == (long double)(a) + (b));	\
+	__vw = __ia + __ib;				\
+	__r = __ia - __vw;				\
+	__r += __ib;					\
+	assert(__vw == (a) && __r == (b));		\
+} while (0)
+#else /* !DEBUG */
+#define	_2sumF(a, b) do {	\
+	__typeof(a) __w;	\
+				\
+	__w = (a) + (b);	\
+	(b) = ((a) - __w) + (b); \
+	(a) = __w;		\
+} while (0)
+#endif /* DEBUG */
+
+/*
+ * Set x += c, where x is represented in extra precision as a + b.
+ * x must be sufficiently normalized and sufficiently larger than c,
+ * and the result is then sufficiently normalized.
+ *
+ * The details of ordering are that |a| must be >= |c| (so that (a, c)
+ * can be normalized without extra work to swap 'a' with c).  The details of
+ * the normalization are that b must be small relative to the normalized 'a'.
+ * Normalization of (a, c) makes the normalized c tiny relative to the
+ * normalized a, so b remains small relative to 'a' in the result.  However,
+ * b need not ever be tiny relative to 'a'.  For example, b might be about
+ * 2**20 times smaller than 'a' to give about 20 extra bits of precision.
+ * That is usually enough, and adding c (which by normalization is about
+ * 2**53 times smaller than a) cannot change b significantly.  However,
+ * cancellation of 'a' with c in normalization of (a, c) may reduce 'a'
+ * significantly relative to b.  The caller must ensure that significant
+ * cancellation doesn't occur, either by having c of the same sign as 'a',
+ * or by having |c| a few percent smaller than |a|.  Pre-normalization of
+ * (a, b) may help.
+ *
+ * This is a variant of an algorithm of Kahan (see Knuth (1981) 4.2.2
+ * exercise 19).  We gain considerable efficiency by requiring the terms to
+ * be sufficiently normalized and sufficiently increasing.
+ */
+#define	_3sumF(a, b, c) do {	\
+	__typeof(a) __tmp;	\
+				\
+	__tmp = (c);		\
+	_2sumF(__tmp, (a));	\
+	(b) += (a);		\
+	(a) = __tmp;		\
+} while (0)
+
+/*
+ * Common routine to process the arguments to nan(), nanf(), and nanl().
+ */
+void _scan_nan(uint32_t *__words, int __num_words, const char *__s);
+
+/*
+ * Mix 0, 1 or 2 NaNs.  First add 0 to each arg.  This normally just turns
+ * signaling NaNs into quiet NaNs by setting a quiet bit.  We do this
+ * because we want to never return a signaling NaN, and also because we
+ * don't want the quiet bit to affect the result.  Then mix the converted
+ * args using the specified operation.
+ *
+ * When one arg is NaN, the result is typically that arg quieted.  When both
+ * args are NaNs, the result is typically the quietening of the arg whose
+ * mantissa is largest after quietening.  When neither arg is NaN, the
+ * result may be NaN because it is indeterminate, or finite for subsequent
+ * construction of a NaN as the indeterminate 0.0L/0.0L.
+ *
+ * Technical complications: the result in bits after rounding to the final
+ * precision might depend on the runtime precision and/or on compiler
+ * optimizations, especially when different register sets are used for
+ * different precisions.  Try to make the result not depend on at least the
+ * runtime precision by always doing the main mixing step in long double
+ * precision.  Try to reduce dependencies on optimizations by adding the
+ * the 0's in different precisions (unless everything is in long double
+ * precision).
+ */
+#define	nan_mix(x, y)		(nan_mix_op((x), (y), +))
+#define	nan_mix_op(x, y, op)	(((x) + 0.0L) op ((y) + 0))
+
+#ifdef _COMPLEX_H
+
+/*
+ * C99 specifies that complex numbers have the same representation as
+ * an array of two elements, where the first element is the real part
+ * and the second element is the imaginary part.
+ */
+typedef union {
+	float complex f;
+	float a[2];
+} float_complex;
+typedef union {
+	double complex f;
+	double a[2];
+} double_complex;
+typedef union {
+	long double complex f;
+	long double a[2];
+} long_double_complex;
+#define	REALPART(z)	((z).a[0])
+#define	IMAGPART(z)	((z).a[1])
+
+/*
+ * Inline functions that can be used to construct complex values.
+ *
+ * The C99 standard intends x+I*y to be used for this, but x+I*y is
+ * currently unusable in general since gcc introduces many overflow,
+ * underflow, sign and efficiency bugs by rewriting I*y as
+ * (0.0+I)*(y+0.0*I) and laboriously computing the full complex product.
+ * In particular, I*Inf is corrupted to NaN+I*Inf, and I*-0 is corrupted
+ * to -0.0+I*0.0.
+ *
+ * The C11 standard introduced the macros CMPLX(), CMPLXF() and CMPLXL()
+ * to construct complex values.  Compilers that conform to the C99
+ * standard require the following functions to avoid the above issues.
+ */
+
+#ifndef CMPLXF
+static __inline float complex
+CMPLXF(float x, float y)
+{
+	float_complex z;
+
+	REALPART(z) = x;
+	IMAGPART(z) = y;
+	return (z.f);
+}
+#endif
+
+#ifndef CMPLX
+static __inline double complex
+CMPLX(double x, double y)
+{
+	double_complex z;
+
+	REALPART(z) = x;
+	IMAGPART(z) = y;
+	return (z.f);
+}
+#endif
+
+#ifndef CMPLXL
+static __inline long double complex
+CMPLXL(long double x, long double y)
+{
+	long_double_complex z;
+
+	REALPART(z) = x;
+	IMAGPART(z) = y;
+	return (z.f);
+}
+#endif
+
+#endif /* _COMPLEX_H */
+ 
+/*
+ * The rnint() family rounds to the nearest integer for a restricted range
+ * range of args (up to about 2**MANT_DIG).  We assume that the current
+ * rounding mode is FE_TONEAREST so that this can be done efficiently.
+ * Extra precision causes more problems in practice, and we only centralize
+ * this here to reduce those problems, and have not solved the efficiency
+ * problems.  The exp2() family uses a more delicate version of this that
+ * requires extracting bits from the intermediate value, so it is not
+ * centralized here and should copy any solution of the efficiency problems.
+ */
+
+static inline double
+rnint(__double_t x)
+{
+	/*
+	 * This casts to double to kill any extra precision.  This depends
+	 * on the cast being applied to a double_t to avoid compiler bugs
+	 * (this is a cleaner version of STRICT_ASSIGN()).  This is
+	 * inefficient if there actually is extra precision, but is hard
+	 * to improve on.  We use double_t in the API to minimise conversions
+	 * for just calling here.  Note that we cannot easily change the
+	 * magic number to the one that works directly with double_t, since
+	 * the rounding precision is variable at runtime on x86 so the
+	 * magic number would need to be variable.  Assuming that the
+	 * rounding precision is always the default is too fragile.  This
+	 * and many other complications will move when the default is
+	 * changed to FP_PE.
+	 */
+	return ((double)(x + 0x1.8p52) - 0x1.8p52);
+}
+
+/*
+ * irint() and i64rint() give the same result as casting to their integer
+ * return type provided their arg is a floating point integer.  They can
+ * sometimes be more efficient because no rounding is required.
+ */
+#if defined(amd64) || defined(__i386__)
+#define	irint(x)						\
+    (sizeof(x) == sizeof(float) &&				\
+    sizeof(__float_t) == sizeof(long double) ? irintf(x) :	\
+    sizeof(x) == sizeof(double) &&				\
+    sizeof(__double_t) == sizeof(long double) ? irintd(x) :	\
+    sizeof(x) == sizeof(long double) ? irintl(x) : (int)(x))
+#else
+#define	irint(x)	((int)(x))
+#endif
+
+#define	i64rint(x)	((int64_t)(x))	/* only needed for ld128 so not opt. */
+
+#if defined(__i386__)
+static __inline int
+irintf(float x)
+{
+	int n;
+
+	__asm("fistl %0" : "=m" (n) : "t" (x));
+	return (n);
+}
+
+static __inline int
+irintd(double x)
+{
+	int n;
+
+	__asm("fistl %0" : "=m" (n) : "t" (x));
+	return (n);
+}
+#endif
+
+#if defined(__amd64__) || defined(__i386__)
+static __inline int
+irintl(long double x)
+{
+	int n;
+
+	__asm("fistl %0" : "=m" (n) : "t" (x));
+	return (n);
+}
+#endif
+
+#ifdef DEBUG
+#if defined(__amd64__) || defined(__i386__)
+#define	breakpoint()	asm("int $3")
+#else
+#include <signal.h>
+
+#define	breakpoint()	raise(SIGTRAP)
+#endif
+#endif
+
+/* Write a pari script to test things externally. */
+#ifdef DOPRINT
+#include <stdio.h>
+
+#ifndef DOPRINT_SWIZZLE
+#define	DOPRINT_SWIZZLE		0
+#endif
+
+#ifdef DOPRINT_LD80
+
+#define	DOPRINT_START(xp) do {						\
+	uint64_t __lx;							\
+	uint16_t __hx;							\
+									\
+	/* Hack to give more-problematic args. */			\
+	EXTRACT_LDBL80_WORDS(__hx, __lx, *xp);				\
+	__lx ^= DOPRINT_SWIZZLE;					\
+	INSERT_LDBL80_WORDS(*xp, __hx, __lx);				\
+	printf("x = %.21Lg; ", (long double)*xp);			\
+} while (0)
+#define	DOPRINT_END1(v)							\
+	printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
+#define	DOPRINT_END2(hi, lo)						\
+	printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n",		\
+	    (long double)(hi), (long double)(lo))
+
+#elif defined(DOPRINT_D64)
+
+#define	DOPRINT_START(xp) do {						\
+	uint32_t __hx, __lx;						\
+									\
+	EXTRACT_WORDS(__hx, __lx, *xp);					\
+	__lx ^= DOPRINT_SWIZZLE;					\
+	INSERT_WORDS(*xp, __hx, __lx);					\
+	printf("x = %.21Lg; ", (long double)*xp);			\
+} while (0)
+#define	DOPRINT_END1(v)							\
+	printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
+#define	DOPRINT_END2(hi, lo)						\
+	printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n",		\
+	    (long double)(hi), (long double)(lo))
+
+#elif defined(DOPRINT_F32)
+
+#define	DOPRINT_START(xp) do {						\
+	uint32_t __hx;							\
+									\
+	GET_FLOAT_WORD(__hx, *xp);					\
+	__hx ^= DOPRINT_SWIZZLE;					\
+	SET_FLOAT_WORD(*xp, __hx);					\
+	printf("x = %.21Lg; ", (long double)*xp);			\
+} while (0)
+#define	DOPRINT_END1(v)							\
+	printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
+#define	DOPRINT_END2(hi, lo)						\
+	printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n",		\
+	    (long double)(hi), (long double)(lo))
+
+#else /* !DOPRINT_LD80 && !DOPRINT_D64 (LD128 only) */
+
+#ifndef DOPRINT_SWIZZLE_HIGH
+#define	DOPRINT_SWIZZLE_HIGH	0
+#endif
+
+#define	DOPRINT_START(xp) do {						\
+	uint64_t __lx, __llx;						\
+	uint16_t __hx;							\
+									\
+	EXTRACT_LDBL128_WORDS(__hx, __lx, __llx, *xp);			\
+	__llx ^= DOPRINT_SWIZZLE;					\
+	__lx ^= DOPRINT_SWIZZLE_HIGH;					\
+	INSERT_LDBL128_WORDS(*xp, __hx, __lx, __llx);			\
+	printf("x = %.36Lg; ", (long double)*xp);					\
+} while (0)
+#define	DOPRINT_END1(v)							\
+	printf("y = %.36Lg; z = 0; show(x, y, z);\n", (long double)(v))
+#define	DOPRINT_END2(hi, lo)						\
+	printf("y = %.36Lg; z = %.36Lg; show(x, y, z);\n",		\
+	    (long double)(hi), (long double)(lo))
+
+#endif /* DOPRINT_LD80 */
+
+#else /* !DOPRINT */
+#define	DOPRINT_START(xp)
+#define	DOPRINT_END1(v)
+#define	DOPRINT_END2(hi, lo)
+#endif /* DOPRINT */
+
+#define	RETURNP(x) do {			\
+	DOPRINT_END1(x);		\
+	RETURNF(x);			\
+} while (0)
+#define	RETURNPI(x) do {		\
+	DOPRINT_END1(x);		\
+	RETURNI(x);			\
+} while (0)
+#define	RETURN2P(x, y) do {		\
+	DOPRINT_END2((x), (y));		\
+	RETURNF((x) + (y));		\
+} while (0)
+#define	RETURN2PI(x, y) do {		\
+	DOPRINT_END2((x), (y));		\
+	RETURNI((x) + (y));		\
+} while (0)
+#ifdef STRUCT_RETURN
+#define	RETURNSP(rp) do {		\
+	if (!(rp)->lo_set)		\
+		RETURNP((rp)->hi);	\
+	RETURN2P((rp)->hi, (rp)->lo);	\
+} while (0)
+#define	RETURNSPI(rp) do {		\
+	if (!(rp)->lo_set)		\
+		RETURNPI((rp)->hi);	\
+	RETURN2PI((rp)->hi, (rp)->lo);	\
+} while (0)
+#endif
+#define	SUM2P(x, y) ({			\
+	const __typeof (x) __x = (x);	\
+	const __typeof (y) __y = (y);	\
+					\
+	DOPRINT_END2(__x, __y);		\
+	__x + __y;			\
+})
+
+/*
+ * ieee style elementary functions
+ *
+ * We rename functions here to improve other sources' diffability
+ * against fdlibm.
+ */
+#define	__ieee754_sqrt	sqrt
+#define	__ieee754_acos	acos
+#define	__ieee754_acosh	acosh
+#define	__ieee754_log	log
+#define	__ieee754_log2	log2
+#define	__ieee754_atanh	atanh
+#define	__ieee754_asin	asin
+#define	__ieee754_atan2	atan2
+#define	__ieee754_exp	exp
+#define	__ieee754_cosh	cosh
+#define	__ieee754_fmod	fmod
+#define	__ieee754_pow	pow
+#define	__ieee754_lgamma lgamma
+#define	__ieee754_gamma	gamma
+#define	__ieee754_lgamma_r lgamma_r
+#define	__ieee754_gamma_r gamma_r
+#define	__ieee754_log10	log10
+#define	__ieee754_sinh	sinh
+#define	__ieee754_hypot	hypot
+#define	__ieee754_j0	j0
+#define	__ieee754_j1	j1
+#define	__ieee754_y0	y0
+#define	__ieee754_y1	y1
+#define	__ieee754_jn	jn
+#define	__ieee754_yn	yn
+#define	__ieee754_remainder remainder
+#define	__ieee754_scalb	scalb
+#define	__ieee754_sqrtf	sqrtf
+#define	__ieee754_acosf	acosf
+#define	__ieee754_acoshf acoshf
+#define	__ieee754_logf	logf
+#define	__ieee754_atanhf atanhf
+#define	__ieee754_asinf	asinf
+#define	__ieee754_atan2f atan2f
+#define	__ieee754_expf	expf
+#define	__ieee754_coshf	coshf
+#define	__ieee754_fmodf	fmodf
+#define	__ieee754_powf	powf
+#define	__ieee754_lgammaf lgammaf
+#define	__ieee754_gammaf gammaf
+#define	__ieee754_lgammaf_r lgammaf_r
+#define	__ieee754_gammaf_r gammaf_r
+#define	__ieee754_log10f log10f
+#define	__ieee754_log2f log2f
+#define	__ieee754_sinhf	sinhf
+#define	__ieee754_hypotf hypotf
+#define	__ieee754_j0f	j0f
+#define	__ieee754_j1f	j1f
+#define	__ieee754_y0f	y0f
+#define	__ieee754_y1f	y1f
+#define	__ieee754_jnf	jnf
+#define	__ieee754_ynf	ynf
+#define	__ieee754_remainderf remainderf
+#define	__ieee754_scalbf scalbf
+
+#define acos fdlibm::acos
+#define acosf fdlibm::acosf
+#define asin fdlibm::asin
+#define asinf fdlibm::asinf
+#define atan fdlibm::atan
+#define atanf fdlibm::atanf
+#define atan2 fdlibm::atan2
+#define cos fdlibm::cos
+#define cosf fdlibm::cosf
+#define sin fdlibm::sin
+#define sinf fdlibm::sinf
+#define tan fdlibm::tan
+#define tanf fdlibm::tanf
+#define cosh fdlibm::cosh
+#define sinh fdlibm::sinh
+#define tanh fdlibm::tanh
+#define exp fdlibm::exp
+#define expf fdlibm::expf
+#define exp2 fdlibm::exp2
+#define exp2f fdlibm::exp2f
+#define log fdlibm::log
+#define logf fdlibm::logf
+#define log10 fdlibm::log10
+#define pow fdlibm::pow
+#define powf fdlibm::powf
+#define ceil fdlibm::ceil
+#define ceilf fdlibm::ceilf
+#define fabs fdlibm::fabs
+#define fabsf fdlibm::fabsf
+#define floor fdlibm::floor
+#define acosh fdlibm::acosh
+#define asinh fdlibm::asinh
+#define atanh fdlibm::atanh
+#define cbrt fdlibm::cbrt
+#define expm1 fdlibm::expm1
+#define hypot fdlibm::hypot
+#define log1p fdlibm::log1p
+#define log2 fdlibm::log2
+#define scalb fdlibm::scalb
+#define copysign fdlibm::copysign
+#define scalbn fdlibm::scalbn
+#define scalbnf fdlibm::scalbnf
+#define trunc fdlibm::trunc
+#define truncf fdlibm::truncf
+#define floorf fdlibm::floorf
+#define nearbyint fdlibm::nearbyint
+#define nearbyintf fdlibm::nearbyintf
+#define rint fdlibm::rint
+#define rintf fdlibm::rintf
+#define sqrtf fdlibm::sqrtf
+
+/* fdlibm kernel function */
+int	__kernel_rem_pio2(double*,double*,int,int,int);
+
+/* double precision kernel functions */
+#ifndef INLINE_REM_PIO2
+int	__ieee754_rem_pio2(double,double*);
+#endif
+double	__kernel_sin(double,double,int);
+double	__kernel_cos(double,double);
+double	__kernel_tan(double,double,int);
+double	__ldexp_exp(double,int);
+#ifdef _COMPLEX_H
+double complex __ldexp_cexp(double complex,int);
+#endif
+
+/* float precision kernel functions */
+#ifndef INLINE_REM_PIO2F
+int	__ieee754_rem_pio2f(float,double*);
+#endif
+#ifndef INLINE_KERNEL_SINDF
+float	__kernel_sindf(double);
+#endif
+#ifndef INLINE_KERNEL_COSDF
+float	__kernel_cosdf(double);
+#endif
+#ifndef INLINE_KERNEL_TANDF
+float	__kernel_tandf(double,int);
+#endif
+float	__ldexp_expf(float,int);
+#ifdef _COMPLEX_H
+float complex __ldexp_cexpf(float complex,int);
+#endif
+
+/* long double precision kernel functions */
+long double __kernel_sinl(long double, long double, int);
+long double __kernel_cosl(long double, long double);
+long double __kernel_tanl(long double, long double, int);
+
+#endif /* !_MATH_PRIVATE_H_ */