-/* origin: FreeBSD /usr/src/lib/msun/src/s_ceil.c */
-/*
- * ====================================================
- * 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.
- * ====================================================
- */
-/*
- * ceil(x)
- * Return x rounded toward -inf to integral value
- * Method:
- * Bit twiddling.
- * Exception:
- * Inexact flag raised if x not equal to ceil(x).
- */
-
#include "libm.h"
-static const double huge = 1.0e300;
-
double ceil(double x)
{
- int32_t i0,i1,j0;
- uint32_t i,j;
+ union {double f; uint64_t i;} u = {x};
+ int e = u.i >> 52 & 0x7ff;
+ double_t y;
- EXTRACT_WORDS(i0, i1, x);
- // FIXME signed shift
- j0 = ((i0>>20)&0x7ff) - 0x3ff;
- if (j0 < 20) {
- if (j0 < 0) {
- /* raise inexact if x != 0 */
- if (huge+x > 0.0) {
- if (i0 < 0) {
- i0 = 0x80000000;
- i1=0;
- } else if ((i0|i1) != 0) {
- i0=0x3ff00000;
- i1=0;
- }
- }
- } else {
- i = 0x000fffff>>j0;
- if (((i0&i)|i1) == 0) /* x is integral */
- return x;
- /* raise inexact flag */
- if (huge+x > 0.0) {
- if (i0 > 0)
- i0 += 0x00100000>>j0;
- i0 &= ~i;
- i1 = 0;
- }
- }
- } else if (j0 > 51) {
- if (j0 == 0x400) /* inf or NaN */
- return x+x;
- return x; /* x is integral */
- } else {
- i = (uint32_t)0xffffffff>>(j0-20);
- if ((i1&i) == 0)
- return x; /* x is integral */
- /* raise inexact flag */
- if (huge+x > 0.0) {
- if (i0 > 0) {
- if (j0 == 20)
- i0 += 1;
- else {
- j = i1 + (1<<(52-j0));
- if (j < i1) /* got a carry */
- i0 += 1;
- i1 = j;
- }
- }
- i1 &= ~i;
- }
+ if (e >= 0x3ff+52 || x == 0)
+ return x;
+ /* y = int(x) - x, where int(x) is an integer neighbor of x */
+ if (u.i >> 63)
+ y = (double)(x - 0x1p52) + 0x1p52 - x;
+ else
+ y = (double)(x + 0x1p52) - 0x1p52 - x;
+ /* special case because of non-nearest rounding modes */
+ if (e <= 0x3ff-1) {
+ FORCE_EVAL(y);
+ return u.i >> 63 ? -0.0 : 1;
}
- INSERT_WORDS(x, i0, i1);
- return x;
+ if (y < 0)
+ return x + y + 1;
+ return x + y;
}
-/* origin: FreeBSD /usr/src/lib/msun/src/s_ceilf.c */
-/*
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
- */
-/*
- * ====================================================
- * 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.
- * ====================================================
- */
-
#include "libm.h"
-static const float huge = 1.0e30;
-
float ceilf(float x)
{
- int32_t i0,j0;
- uint32_t i;
+ union {float f; uint32_t i;} u = {x};
+ int e = (int)(u.i >> 23 & 0xff) - 0x7f;
+ uint32_t m;
- GET_FLOAT_WORD(i0, x);
- j0 = ((i0>>23)&0xff) - 0x7f;
- if (j0 < 23) {
- if (j0 < 0) {
- /* raise inexact if x != 0 */
- if (huge+x > 0.0f) {
- if (i0 < 0)
- i0 = 0x80000000;
- else if(i0 != 0)
- i0 = 0x3f800000;
- }
- } else {
- i = 0x007fffff>>j0;
- if ((i0&i) == 0)
- return x; /* x is integral */
- /* raise inexact flag */
- if (huge+x > 0.0f) {
- if (i0 > 0)
- i0 += 0x00800000>>j0;
- i0 &= ~i;
- }
- }
+ if (e >= 23)
+ return x;
+ if (e >= 0) {
+ m = 0x007fffff >> e;
+ if ((u.i & m) == 0)
+ return x;
+ FORCE_EVAL(x + 0x1p120f);
+ if (u.i >> 31 == 0)
+ u.i += m;
+ u.i &= ~m;
} else {
- if (j0 == 0x80) /* inf or NaN */
- return x+x;
- return x; /* x is integral */
+ FORCE_EVAL(x + 0x1p120f);
+ if (u.i >> 31)
+ u.f = -0.0;
+ else if (u.i << 1)
+ u.f = 1.0;
}
- SET_FLOAT_WORD(x, i0);
- return x;
+ return u.f;
}
-/* origin: FreeBSD /usr/src/lib/msun/src/s_ceill.c */
-/*
- * ====================================================
- * 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.
- * ====================================================
- */
-/*
- * ceill(x)
- * Return x rounded toward -inf to integral value
- * Method:
- * Bit twiddling.
- * Exception:
- * Inexact flag raised if x not equal to ceill(x).
- */
-
#include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
return ceil(x);
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
-
-#ifdef LDBL_IMPLICIT_NBIT
-#define MANH_SIZE (LDBL_MANH_SIZE + 1)
-#define INC_MANH(u, c) do { \
- uint64_t o = u.bits.manh; \
- u.bits.manh += (c); \
- if (u.bits.manh < o) \
- u.bits.exp++; \
-} while (0)
-#else
-#define MANH_SIZE LDBL_MANH_SIZE
-#define INC_MANH(u, c) do { \
- uint64_t o = u.bits.manh; \
- u.bits.manh += (c); \
- if (u.bits.manh < o) { \
- u.bits.exp++; \
- u.bits.manh |= 1llu << (LDBL_MANH_SIZE - 1); \
- } \
-} while (0)
+#if LDBL_MANT_DIG == 64
+#define TOINT 0x1p63
+#elif LDBL_MANT_DIG == 113
+#define TOINT 0x1p112
#endif
-
-static const long double huge = 1.0e300;
-
long double ceill(long double x)
{
- union IEEEl2bits u = { .e = x };
- int e = u.bits.exp - LDBL_MAX_EXP + 1;
+ union ldshape u = {x};
+ int e = u.i.se & 0x7fff;
+ long double y;
- if (e < MANH_SIZE - 1) {
- if (e < 0) {
- /* raise inexact if x != 0 */
- if (huge + x > 0.0)
- if (u.bits.exp > 0 ||
- (u.bits.manh | u.bits.manl) != 0)
- u.e = u.bits.sign ? -0.0 : 1.0;
- } else {
- uint64_t m = ((1llu << MANH_SIZE) - 1) >> (e + 1);
- if (((u.bits.manh & m) | u.bits.manl) == 0)
- return x; /* x is integral */
- if (!u.bits.sign) {
-#ifdef LDBL_IMPLICIT_NBIT
- if (e == 0)
- u.bits.exp++;
- else
-#endif
- INC_MANH(u, 1llu << (MANH_SIZE - e - 1));
- }
- /* raise inexact flag */
- if (huge + x > 0.0) {
- u.bits.manh &= ~m;
- u.bits.manl = 0;
- }
- }
- } else if (e < LDBL_MANT_DIG - 1) {
- uint64_t m = (uint64_t)-1 >> (64 - LDBL_MANT_DIG + e + 1);
- if ((u.bits.manl & m) == 0)
- return x; /* x is integral */
- if (!u.bits.sign) {
- if (e == MANH_SIZE - 1)
- INC_MANH(u, 1);
- else {
- uint64_t o = u.bits.manl;
- u.bits.manl += 1llu << (LDBL_MANT_DIG - e - 1);
- if (u.bits.manl < o) /* got a carry */
- INC_MANH(u, 1);
- }
- }
- /* raise inexact flag */
- if (huge + x > 0.0)
- u.bits.manl &= ~m;
+ if (e >= 0x3fff+LDBL_MANT_DIG-1 || x == 0)
+ return x;
+ /* y = int(x) - x, where int(x) is an integer neighbor of x */
+ if (u.i.se >> 15)
+ y = x - TOINT + TOINT - x;
+ else
+ y = x + TOINT - TOINT - x;
+ /* special case because of non-nearest rounding modes */
+ if (e <= 0x3fff-1) {
+ FORCE_EVAL(y);
+ return u.i.se >> 15 ? -0.0 : 1;
}
- return u.e;
+ if (y < 0)
+ return x + y + 1;
+ return x + y;
}
#endif
-/* origin: FreeBSD /usr/src/lib/msun/src/s_floor.c */
-/*
- * ====================================================
- * 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.
- * ====================================================
- */
-/*
- * floor(x)
- * Return x rounded toward -inf to integral value
- * Method:
- * Bit twiddling.
- * Exception:
- * Inexact flag raised if x not equal to floor(x).
- */
-
#include "libm.h"
-static const double huge = 1.0e300;
-
double floor(double x)
{
- int32_t i0,i1,j0;
- uint32_t i,j;
+ union {double f; uint64_t i;} u = {x};
+ int e = u.i >> 52 & 0x7ff;
+ double_t y;
- EXTRACT_WORDS(i0, i1, x);
- // FIXME: signed shift
- j0 = ((i0>>20)&0x7ff) - 0x3ff;
- if (j0 < 20) {
- if (j0 < 0) { /* |x| < 1 */
- /* raise inexact if x != 0 */
- if (huge+x > 0.0) {
- if (i0 >= 0) { /* x >= 0 */
- i0 = i1 = 0;
- } else if (((i0&0x7fffffff)|i1) != 0) {
- i0 = 0xbff00000;
- i1 = 0;
- }
- }
- } else {
- i = 0x000fffff>>j0;
- if (((i0&i)|i1) == 0)
- return x; /* x is integral */
- /* raise inexact flag */
- if (huge+x > 0.0) {
- if (i0 < 0)
- i0 += 0x00100000>>j0;
- i0 &= ~i;
- i1 = 0;
- }
- }
- } else if (j0 > 51) {
- if (j0 == 0x400)
- return x+x; /* inf or NaN */
- else
- return x; /* x is integral */
- } else {
- i = (uint32_t)0xffffffff>>(j0-20);
- if ((i1&i) == 0)
- return x; /* x is integral */
- /* raise inexact flag */
- if (huge+x > 0.0) {
- if (i0 < 0) {
- if (j0 == 20)
- i0++;
- else {
- j = i1+(1<<(52-j0));
- if (j < i1)
- i0++; /* got a carry */
- i1 = j;
- }
- }
- i1 &= ~i;
- }
+ if (e >= 0x3ff+52 || x == 0)
+ return x;
+ /* y = int(x) - x, where int(x) is an integer neighbor of x */
+ if (u.i >> 63)
+ y = (double)(x - 0x1p52) + 0x1p52 - x;
+ else
+ y = (double)(x + 0x1p52) - 0x1p52 - x;
+ /* special case because of non-nearest rounding modes */
+ if (e <= 0x3ff-1) {
+ FORCE_EVAL(y);
+ return u.i >> 63 ? -1 : 0;
}
- INSERT_WORDS(x, i0, i1);
- return x;
+ if (y > 0)
+ return x + y - 1;
+ return x + y;
}
-/* origin: FreeBSD /usr/src/lib/msun/src/s_floorf.c */
-/*
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
- */
-/*
- * ====================================================
- * 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.
- * ====================================================
- */
-/*
- * floorf(x)
- * Return x rounded toward -inf to integral value
- * Method:
- * Bit twiddling.
- * Exception:
- * Inexact flag raised if x not equal to floorf(x).
- */
-
#include "libm.h"
-static const float huge = 1.0e30;
-
float floorf(float x)
{
- int32_t i0,j0;
- uint32_t i;
+ union {float f; uint32_t i;} u = {x};
+ int e = (int)(u.i >> 23 & 0xff) - 0x7f;
+ uint32_t m;
- GET_FLOAT_WORD(i0, x);
- // FIXME: signed shift
- j0 = ((i0>>23)&0xff) - 0x7f;
- if (j0 < 23) {
- if (j0 < 0) { /* |x| < 1 */
- /* raise inexact if x != 0 */
- if (huge+x > 0.0f) {
- if (i0 >= 0) /* x >= 0 */
- i0 = 0;
- else if ((i0&0x7fffffff) != 0)
- i0 = 0xbf800000;
- }
- } else {
- i = 0x007fffff>>j0;
- if ((i0&i) == 0)
- return x; /* x is integral */
- /* raise inexact flag */
- if (huge+x > 0.0f) {
- if (i0 < 0)
- i0 += 0x00800000>>j0;
- i0 &= ~i;
- }
- }
+ if (e >= 23)
+ return x;
+ if (e >= 0) {
+ m = 0x007fffff >> e;
+ if ((u.i & m) == 0)
+ return x;
+ FORCE_EVAL(x + 0x1p120f);
+ if (u.i >> 31)
+ u.i += m;
+ u.i &= ~m;
} else {
- if (j0 == 0x80) /* inf or NaN */
- return x+x;
- else
- return x; /* x is integral */
+ FORCE_EVAL(x + 0x1p120f);
+ if (u.i >> 31 == 0)
+ u.i = 0;
+ else if (u.i << 1)
+ u.f = -1.0;
}
- SET_FLOAT_WORD(x, i0);
- return x;
+ return u.f;
}
-/* origin: FreeBSD /usr/src/lib/msun/src/s_floorl.c */
-/*
- * ====================================================
- * 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.
- * ====================================================
- */
-/*
- * floorl(x)
- * Return x rounded toward -inf to integral value
- * Method:
- * Bit twiddling.
- * Exception:
- * Inexact flag raised if x not equal to floorl(x).
- */
-
#include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
return floor(x);
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
-
-#ifdef LDBL_IMPLICIT_NBIT
-#define MANH_SIZE (LDBL_MANH_SIZE + 1)
-#define INC_MANH(u, c) do { \
- uint64_t o = u.bits.manh; \
- u.bits.manh += (c); \
- if (u.bits.manh < o) \
- u.bits.exp++; \
-} while (0)
-#else
-#define MANH_SIZE LDBL_MANH_SIZE
-#define INC_MANH(u, c) do { \
- uint64_t o = u.bits.manh; \
- u.bits.manh += (c); \
- if (u.bits.manh < o) { \
- u.bits.exp++; \
- u.bits.manh |= 1llu << (LDBL_MANH_SIZE - 1); \
- } \
-} while (0)
+#if LDBL_MANT_DIG == 64
+#define TOINT 0x1p63
+#elif LDBL_MANT_DIG == 113
+#define TOINT 0x1p112
#endif
-
-static const long double huge = 1.0e300;
-
long double floorl(long double x)
{
- union IEEEl2bits u = { .e = x };
- int e = u.bits.exp - LDBL_MAX_EXP + 1;
+ union ldshape u = {x};
+ int e = u.i.se & 0x7fff;
+ long double y;
- if (e < MANH_SIZE - 1) {
- if (e < 0) {
- /* raise inexact if x != 0 */
- if (huge + x > 0.0)
- if (u.bits.exp > 0 ||
- (u.bits.manh | u.bits.manl) != 0)
- u.e = u.bits.sign ? -1.0 : 0.0;
- } else {
- uint64_t m = ((1llu << MANH_SIZE) - 1) >> (e + 1);
- if (((u.bits.manh & m) | u.bits.manl) == 0)
- return x; /* x is integral */
- if (u.bits.sign) {
-#ifdef LDBL_IMPLICIT_NBIT
- if (e == 0)
- u.bits.exp++;
- else
-#endif
- INC_MANH(u, 1llu << (MANH_SIZE - e - 1));
- }
- /* raise inexact flag */
- if (huge + x > 0.0) {
- u.bits.manh &= ~m;
- u.bits.manl = 0;
- }
- }
- } else if (e < LDBL_MANT_DIG - 1) {
- uint64_t m = (uint64_t)-1 >> (64 - LDBL_MANT_DIG + e + 1);
- if ((u.bits.manl & m) == 0)
- return x; /* x is integral */
- if (u.bits.sign) {
- if (e == MANH_SIZE - 1)
- INC_MANH(u, 1);
- else {
- uint64_t o = u.bits.manl;
- u.bits.manl += 1llu << (LDBL_MANT_DIG - e - 1);
- if (u.bits.manl < o) /* got a carry */
- INC_MANH(u, 1);
- }
- }
- /* raise inexact flag */
- if (huge + x > 0.0)
- u.bits.manl &= ~m;
+ if (e >= 0x3fff+LDBL_MANT_DIG-1 || x == 0)
+ return x;
+ /* y = int(x) - x, where int(x) is an integer neighbor of x */
+ if (u.i.se >> 15)
+ y = x - TOINT + TOINT - x;
+ else
+ y = x + TOINT - TOINT - x;
+ /* special case because of non-nearest rounding modes */
+ if (e <= 0x3fff-1) {
+ FORCE_EVAL(y);
+ return u.i.se >> 15 ? -1 : 0;
}
- return u.e;
+ if (y > 0)
+ return x + y - 1;
+ return x + y;
}
#endif
-/* origin: FreeBSD /usr/src/lib/msun/src/s_rint.c */
-/*
- * ====================================================
- * 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.
- * ====================================================
- */
-/*
- * rint(x)
- * Return x rounded to integral value according to the prevailing
- * rounding mode.
- * Method:
- * Using floating addition.
- * Exception:
- * Inexact flag raised if x not equal to rint(x).
- */
-
-#include "libm.h"
-
-static const double
-TWO52[2] = {
- 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */
- -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */
-};
+#include <math.h>
+#include <stdint.h>
double rint(double x)
{
- int32_t i0,j0,sx;
- uint32_t i,i1;
- double w,t;
+ union {double f; uint64_t i;} u = {x};
+ int e = u.i>>52 & 0x7ff;
+ int s = u.i>>63;
+ double_t y;
- EXTRACT_WORDS(i0, i1, x);
- // FIXME: signed shift
- sx = (i0>>31) & 1;
- j0 = ((i0>>20)&0x7ff) - 0x3ff;
- if (j0 < 20) {
- if (j0 < 0) {
- if (((i0&0x7fffffff)|i1) == 0)
- return x;
- i1 |= i0 & 0x0fffff;
- i0 &= 0xfffe0000;
- i0 |= ((i1|-i1)>>12) & 0x80000;
- SET_HIGH_WORD(x, i0);
- STRICT_ASSIGN(double, w, TWO52[sx] + x);
- t = w - TWO52[sx];
- GET_HIGH_WORD(i0, t);
- SET_HIGH_WORD(t, (i0&0x7fffffff)|(sx<<31));
- return t;
- } else {
- i = 0x000fffff>>j0;
- if (((i0&i)|i1) == 0)
- return x; /* x is integral */
- i >>= 1;
- if (((i0&i)|i1) != 0) {
- /*
- * Some bit is set after the 0.5 bit. To avoid the
- * possibility of errors from double rounding in
- * w = TWO52[sx]+x, adjust the 0.25 bit to a lower
- * guard bit. We do this for all j0<=51. The
- * adjustment is trickiest for j0==18 and j0==19
- * since then it spans the word boundary.
- */
- if (j0 == 19)
- i1 = 0x40000000;
- else if (j0 == 18)
- i1 = 0x80000000;
- else
- i0 = (i0 & ~i)|(0x20000>>j0);
- }
- }
- } else if (j0 > 51) {
- if (j0 == 0x400)
- return x+x; /* inf or NaN */
- return x; /* x is integral */
- } else {
- i = (uint32_t)0xffffffff>>(j0-20);
- if ((i1&i) == 0)
- return x; /* x is integral */
- i >>= 1;
- if ((i1&i) != 0)
- i1 = (i1 & ~i)|(0x40000000>>(j0-20));
- }
- INSERT_WORDS(x, i0, i1);
- STRICT_ASSIGN(double, w, TWO52[sx] + x);
- return w - TWO52[sx];
+ if (e >= 0x3ff+52)
+ return x;
+ if (s)
+ y = (double)(x - 0x1p52) + 0x1p52;
+ else
+ y = (double)(x + 0x1p52) - 0x1p52;
+ if (y == 0)
+ return s ? -0.0 : 0;
+ return y;
}
-/* origin: FreeBSD /usr/src/lib/msun/src/s_rintf.c */
-/*
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
- */
-/*
- * ====================================================
- * 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.
- * ====================================================
- */
-
-#include "libm.h"
-
-static const float
-TWO23[2] = {
- 8.3886080000e+06, /* 0x4b000000 */
- -8.3886080000e+06, /* 0xcb000000 */
-};
+#include <math.h>
+#include <stdint.h>
float rintf(float x)
{
- int32_t i0,j0,sx;
- float w,t;
+ union {float f; uint32_t i;} u = {x};
+ int e = u.i>>23 & 0xff;
+ int s = u.i>>31;
+ float_t y;
- GET_FLOAT_WORD(i0, x);
- sx = (i0>>31) & 1;
- j0 = ((i0>>23)&0xff) - 0x7f;
- if (j0 < 23) {
- if (j0 < 0) {
- if ((i0&0x7fffffff) == 0)
- return x;
- STRICT_ASSIGN(float, w, TWO23[sx] + x);
- t = w - TWO23[sx];
- GET_FLOAT_WORD(i0, t);
- SET_FLOAT_WORD(t, (i0&0x7fffffff)|(sx<<31));
- return t;
- }
- STRICT_ASSIGN(float, w, TWO23[sx] + x);
- return w - TWO23[sx];
- }
- if (j0 == 0x80)
- return x+x; /* inf or NaN */
- return x; /* x is integral */
+ if (e >= 0x7f+23)
+ return x;
+ if (s)
+ y = (float)(x - 0x1p23f) + 0x1p23f;
+ else
+ y = (float)(x + 0x1p23f) - 0x1p23f;
+ if (y == 0)
+ return s ? -0.0f : 0.0f;
+ return y;
}
-/* origin: FreeBSD /usr/src/lib/msun/src/s_rintl.c */
-/*-
- * Copyright (c) 2008 David Schultz <das@FreeBSD.ORG>
- * All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
#include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
return rint(x);
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
-
-#define BIAS (LDBL_MAX_EXP - 1)
-
-static const float
-shift[2] = {
#if LDBL_MANT_DIG == 64
- 0x1.0p63, -0x1.0p63
+#define TOINT 0x1p63
#elif LDBL_MANT_DIG == 113
- 0x1.0p112, -0x1.0p112
+#define TOINT 0x1p112
#endif
-};
-static const float zero[2] = { 0.0, -0.0 };
-
long double rintl(long double x)
{
- union IEEEl2bits u;
- uint32_t expsign;
- int ex, sign;
-
- u.e = x;
- expsign = u.xbits.expsign;
- ex = expsign & 0x7fff;
-
- if (ex >= BIAS + LDBL_MANT_DIG - 1) {
- if (ex == BIAS + LDBL_MAX_EXP)
- return x + x; /* Inf, NaN, or unsupported format */
- return x; /* finite and already an integer */
- }
- sign = expsign >> 15;
-
- /*
- * The following code assumes that intermediate results are
- * evaluated in long double precision. If they are evaluated in
- * greater precision, double rounding may occur, and if they are
- * evaluated in less precision (as on i386), results will be
- * wildly incorrect.
- */
- x += shift[sign];
- x -= shift[sign];
-
- /*
- * If the result is +-0, then it must have the same sign as x, but
- * the above calculation doesn't always give this. Fix up the sign.
- */
- if (ex < BIAS && x == 0.0)
- return zero[sign];
-
- return x;
+ union ldshape u = {x};
+ int e = u.i.se & 0x7fff;
+ int s = u.i.se >> 15;
+ long double y;
+
+ if (e >= 0x3fff+LDBL_MANT_DIG-1)
+ return x;
+ if (s)
+ y = x - TOINT + TOINT;
+ else
+ y = x + TOINT - TOINT;
+ if (y == 0)
+ return 0*x;
+ return y;
}
#endif
-/* origin: FreeBSD /usr/src/lib/msun/src/s_round.c */
-/*-
- * Copyright (c) 2003, Steven G. Kargl
- * All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- * 1. Redistributions of source code must retain the above copyright
- * notice unmodified, this list of conditions, and the following
- * disclaimer.
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
- * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
- * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
- * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
- * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
- * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
- * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
- * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
- * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
- * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
- */
-
-#include <math.h>
+#include "libm.h"
double round(double x)
{
- double t;
+ union {double f; uint64_t i;} u = {x};
+ int e = u.i >> 52 & 0x7ff;
+ double_t y;
- if (!isfinite(x))
+ if (e >= 0x3ff+52)
return x;
-
- if (x >= 0.0) {
- t = floor(x);
- if (t - x <= -0.5)
- t += 1.0;
- return t;
- } else {
- t = floor(-x);
- if (t + x <= -0.5)
- t += 1.0;
- return -t;
+ if (u.i >> 63)
+ x = -x;
+ if (e < 0x3ff-1) {
+ /* raise inexact if x!=0 */
+ FORCE_EVAL(x + 0x1p52);
+ return 0*u.f;
}
+ y = (double)(x + 0x1p52) - 0x1p52 - x;
+ if (y > 0.5)
+ y = y + x - 1;
+ else if (y <= -0.5)
+ y = y + x + 1;
+ else
+ y = y + x;
+ if (u.i >> 63)
+ y = -y;
+ return y;
}
-/* origin: FreeBSD /usr/src/lib/msun/src/s_roundf.c */
-/*-
- * Copyright (c) 2003, Steven G. Kargl
- * All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- * 1. Redistributions of source code must retain the above copyright
- * notice unmodified, this list of conditions, and the following
- * disclaimer.
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
- * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
- * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
- * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
- * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
- * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
- * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
- * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
- * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
- * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
- */
-
-#include <math.h>
+#include "libm.h"
float roundf(float x)
{
- float t;
+ union {float f; uint32_t i;} u = {x};
+ int e = u.i >> 23 & 0xff;
+ float_t y;
- if (!isfinite(x))
+ if (e >= 0x7f+23)
return x;
-
- if (x >= 0.0) {
- t = floorf(x);
- if (t - x <= -0.5)
- t += 1.0;
- return t;
- } else {
- t = floorf(-x);
- if (t + x <= -0.5)
- t += 1.0;
- return -t;
+ if (u.i >> 31)
+ x = -x;
+ if (e < 0x7f-1) {
+ FORCE_EVAL(x + 0x1p23f);
+ return 0*u.f;
}
+ y = (float)(x + 0x1p23f) - 0x1p23f - x;
+ if (y > 0.5f)
+ y = y + x - 1;
+ else if (y <= -0.5f)
+ y = y + x + 1;
+ else
+ y = y + x;
+ if (u.i >> 31)
+ y = -y;
+ return y;
}
-/* origin: FreeBSD /usr/src/lib/msun/src/s_roundl.c */
-/*-
- * Copyright (c) 2003, Steven G. Kargl
- * All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- * 1. Redistributions of source code must retain the above copyright
- * notice unmodified, this list of conditions, and the following
- * disclaimer.
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
- * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
- * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
- * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
- * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
- * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
- * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
- * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
- * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
- * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
- */
-
-#include <math.h>
-#include <float.h>
+#include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double roundl(long double x)
{
return round(x);
}
-#else
+#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
+#if LDBL_MANT_DIG == 64
+#define TOINT 0x1p63
+#elif LDBL_MANT_DIG == 113
+#define TOINT 0x1p112
+#endif
long double roundl(long double x)
{
- long double t;
+ union ldshape u = {x};
+ int e = u.i.se & 0x7fff;
+ long double y;
- if (!isfinite(x))
+ if (e >= 0x3fff+LDBL_MANT_DIG-1)
return x;
-
- if (x >= 0.0) {
- t = floorl(x);
- if (t - x <= -0.5)
- t += 1.0;
- return t;
- } else {
- t = floorl(-x);
- if (t + x <= -0.5)
- t += 1.0;
- return -t;
+ if (u.i.se >> 15)
+ x = -x;
+ if (e < 0x3fff-1) {
+ FORCE_EVAL(x + TOINT);
+ return 0*u.f;
}
+ y = x + TOINT - TOINT - x;
+ if (y > 0.5)
+ y = y + x - 1;
+ else if (y <= -0.5)
+ y = y + x + 1;
+ else
+ y = y + x;
+ if (u.i.se >> 15)
+ y = -y;
+ return y;
}
#endif
-/* origin: FreeBSD /usr/src/lib/msun/src/s_trunc.c */
-/*
- * ====================================================
- * 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.
- * ====================================================
- */
-/*
- * trunc(x)
- * Return x rounded toward 0 to integral value
- * Method:
- * Bit twiddling.
- * Exception:
- * Inexact flag raised if x not equal to trunc(x).
- */
-
#include "libm.h"
-static const double huge = 1.0e300;
-
double trunc(double x)
{
- int32_t i0,i1,j0;
- uint32_t i;
+ union {double f; uint64_t i;} u = {x};
+ int e = (int)(u.i >> 52 & 0x7ff) - 0x3ff + 12;
+ uint64_t m;
- EXTRACT_WORDS(i0, i1, x);
- j0 = ((i0>>20)&0x7ff) - 0x3ff;
- if (j0 < 20) {
- if (j0 < 0) { /* |x|<1, return 0*sign(x) */
- /* raise inexact if x != 0 */
- if (huge+x > 0.0) {
- i0 &= 0x80000000U;
- i1 = 0;
- }
- } else {
- i = 0x000fffff>>j0;
- if (((i0&i)|i1) == 0)
- return x; /* x is integral */
- /* raise inexact */
- if (huge+x > 0.0) {
- i0 &= ~i;
- i1 = 0;
- }
- }
- } else if (j0 > 51) {
- if (j0 == 0x400)
- return x + x; /* inf or NaN */
- return x; /* x is integral */
- } else {
- i = (uint32_t)0xffffffff>>(j0-20);
- if ((i1&i) == 0)
- return x; /* x is integral */
- /* raise inexact */
- if (huge+x > 0.0)
- i1 &= ~i;
- }
- INSERT_WORDS(x, i0, i1);
- return x;
+ if (e >= 52 + 12)
+ return x;
+ if (e < 12)
+ e = 1;
+ m = -1ULL >> e;
+ if ((u.i & m) == 0)
+ return x;
+ FORCE_EVAL(x + 0x1p120f);
+ u.i &= ~m;
+ return u.f;
}
-/* origin: FreeBSD /usr/src/lib/msun/src/s_truncf.c */
-/*
- * ====================================================
- * 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.
- * ====================================================
- */
-/*
- * truncf(x)
- * Return x rounded toward 0 to integral value
- * Method:
- * Bit twiddling.
- * Exception:
- * Inexact flag raised if x not equal to truncf(x).
- */
-
#include "libm.h"
-static const float huge = 1.0e30f;
-
float truncf(float x)
{
- int32_t i0,j0;
- uint32_t i;
+ union {float f; uint32_t i;} u = {x};
+ int e = (int)(u.i >> 23 & 0xff) - 0x7f + 9;
+ uint32_t m;
- GET_FLOAT_WORD(i0, x);
- j0 = ((i0>>23)&0xff) - 0x7f;
- if (j0 < 23) {
- if (j0 < 0) { /* |x|<1, return 0*sign(x) */
- /* raise inexact if x != 0 */
- if (huge+x > 0.0f)
- i0 &= 0x80000000;
- } else {
- i = 0x007fffff>>j0;
- if ((i0&i) == 0)
- return x; /* x is integral */
- /* raise inexact */
- if (huge+x > 0.0f)
- i0 &= ~i;
- }
- } else {
- if (j0 == 0x80)
- return x + x; /* inf or NaN */
- return x; /* x is integral */
- }
- SET_FLOAT_WORD(x, i0);
- return x;
+ if (e >= 23 + 9)
+ return x;
+ if (e < 9)
+ e = 1;
+ m = -1U >> e;
+ if ((u.i & m) == 0)
+ return x;
+ FORCE_EVAL(x + 0x1p120f);
+ u.i &= ~m;
+ return u.f;
}
-/* origin: FreeBSD /usr/src/lib/msun/src/s_truncl.c */
-/*
- * ====================================================
- * 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.
- * ====================================================
- */
-/*
- * truncl(x)
- * Return x rounded toward 0 to integral value
- * Method:
- * Bit twiddling.
- * Exception:
- * Inexact flag raised if x not equal to truncl(x).
- */
-
#include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
return trunc(x);
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
-#ifdef LDBL_IMPLICIT_NBIT
-#define MANH_SIZE (LDBL_MANH_SIZE + 1)
-#else
-#define MANH_SIZE LDBL_MANH_SIZE
+#if LDBL_MANT_DIG == 64
+#define TOINT 0x1p63
+#elif LDBL_MANT_DIG == 113
+#define TOINT 0x1p112
#endif
-
-static const long double huge = 1.0e300;
-static const float zero[] = { 0.0, -0.0 };
-
long double truncl(long double x)
{
- union IEEEl2bits u = { .e = x };
- int e = u.bits.exp - LDBL_MAX_EXP + 1;
+ union ldshape u = {x};
+ int e = u.i.se & 0x7fff;
+ int s = u.i.se >> 15;
+ long double y;
- if (e < MANH_SIZE - 1) {
- if (e < 0) {
- /* raise inexact if x != 0 */
- if (huge + x > 0.0)
- u.e = zero[u.bits.sign];
- } else {
- uint64_t m = ((1llu << MANH_SIZE) - 1) >> (e + 1);
- if (((u.bits.manh & m) | u.bits.manl) == 0)
- return x; /* x is integral */
- /* raise inexact */
- if (huge + x > 0.0) {
- u.bits.manh &= ~m;
- u.bits.manl = 0;
- }
- }
- } else if (e < LDBL_MANT_DIG - 1) {
- uint64_t m = (uint64_t)-1 >> (64 - LDBL_MANT_DIG + e + 1);
- if ((u.bits.manl & m) == 0)
- return x; /* x is integral */
- /* raise inexact */
- if (huge + x > 0.0)
- u.bits.manl &= ~m;
+ if (e >= 0x3fff+LDBL_MANT_DIG-1)
+ return x;
+ if (e <= 0x3fff-1) {
+ FORCE_EVAL(x + 0x1p120f);
+ return x*0;
}
- return u.e;
+ /* y = int(|x|) - |x|, where int(|x|) is an integer neighbor of |x| */
+ if (s)
+ x = -x;
+ y = x + TOINT - TOINT - x;
+ if (y > 0)
+ y -= 1;
+ x += y;
+ return s ? -x : x;
}
#endif
projects / musl / commitdiff