float __expo2f(float);
float complex __ldexp_cexpf(float complex,int);
+int __rem_pio2l(long double, long double *);
long double __sinl(long double, long double, int);
long double __cosl(long double, long double);
long double __tanl(long double, long double, int);
--- /dev/null
+/* origin: FreeBSD /usr/src/lib/msun/ld80/e_rem_pio2.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ *
+ * Optimized by Bruce D. Evans.
+ */
+#include "libm.h"
+#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
+/* ld80 version of __rem_pio2(x,y)
+ *
+ * return the remainder of x rem pi/2 in y[0]+y[1]
+ * use __rem_pio2_large() for large x
+ */
+
+#define BIAS (LDBL_MAX_EXP - 1)
+
+/*
+ * invpio2: 64 bits of 2/pi
+ * pio2_1: first 39 bits of pi/2
+ * pio2_1t: pi/2 - pio2_1
+ * pio2_2: second 39 bits of pi/2
+ * pio2_2t: pi/2 - (pio2_1+pio2_2)
+ * pio2_3: third 39 bits of pi/2
+ * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
+ */
+static const double
+zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
+two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
+pio2_1 = 1.57079632679597125389e+00, /* 0x3FF921FB, 0x54444000 */
+pio2_2 = -1.07463465549783099519e-12, /* -0x12e7b967674000.0p-92 */
+pio2_3 = 6.36831716351370313614e-25; /* 0x18a2e037074000.0p-133 */
+
+static const long double
+invpio2 = 6.36619772367581343076e-01L, /* 0xa2f9836e4e44152a.0p-64 */
+pio2_1t = -1.07463465549719416346e-12L, /* -0x973dcb3b399d747f.0p-103 */
+pio2_2t = 6.36831716351095013979e-25L, /* 0xc51701b839a25205.0p-144 */
+pio2_3t = -2.75299651904407171810e-37L; /* -0xbb5bf6c7ddd660ce.0p-185 */
+
+int __rem_pio2l(long double x, long double *y)
+{
+ union IEEEl2bits u,u1;
+ long double z,w,t,r,fn;
+ double tx[3],ty[2];
+ int e0,ex,i,j,nx,n;
+ int16_t expsign;
+
+ u.e = x;
+ expsign = u.xbits.expsign;
+ ex = expsign & 0x7fff;
+ if (ex < BIAS + 25 || (ex == BIAS + 25 && u.bits.manh < 0xc90fdaa2)) {
+ union IEEEl2bits u2;
+ int ex1;
+
+ /* |x| ~< 2^25*(pi/2), medium size */
+ /* Use a specialized rint() to get fn. Assume round-to-nearest. */
+ fn = x*invpio2 + 0x1.8p63;
+ fn = fn - 0x1.8p63;
+// FIXME
+//#ifdef HAVE_EFFICIENT_IRINT
+// n = irint(fn);
+//#else
+ n = fn;
+//#endif
+ r = x-fn*pio2_1;
+ w = fn*pio2_1t; /* 1st round good to 102 bit */
+ j = ex;
+ y[0] = r-w;
+ u2.e = y[0];
+ ex1 = u2.xbits.expsign & 0x7fff;
+ i = j-ex1;
+ if (i > 22) { /* 2nd iteration needed, good to 141 */
+ t = r;
+ w = fn*pio2_2;
+ r = t-w;
+ w = fn*pio2_2t-((t-r)-w);
+ y[0] = r-w;
+ u2.e = y[0];
+ ex1 = u2.xbits.expsign & 0x7fff;
+ i = j-ex1;
+ if (i > 61) { /* 3rd iteration need, 180 bits acc */
+ t = r; /* will cover all possible cases */
+ w = fn*pio2_3;
+ r = t-w;
+ w = fn*pio2_3t-((t-r)-w);
+ y[0] = r-w;
+ }
+ }
+ y[1] = (r - y[0]) - w;
+ return n;
+ }
+ /*
+ * all other (large) arguments
+ */
+ if (ex == 0x7fff) { /* x is inf or NaN */
+ y[0] = y[1] = x - x;
+ return 0;
+ }
+ /* set z = scalbn(|x|,ilogb(x)-23) */
+ u1.e = x;
+ e0 = ex - BIAS - 23; /* e0 = ilogb(|x|)-23; */
+ u1.xbits.expsign = ex - e0;
+ z = u1.e;
+ for (i=0; i<2; i++) {
+ tx[i] = (double)(int32_t)z;
+ z = (z-tx[i])*two24;
+ }
+ tx[2] = z;
+ nx = 3;
+ while (tx[nx-1] == zero)
+ nx--; /* skip zero term */
+ n = __rem_pio2_large(tx,ty,e0,nx,2);
+ r = (long double)ty[0] + ty[1];
+ w = ty[1] - (r - ty[0]);
+ if (expsign < 0) {
+ y[0] = -r;
+ y[1] = -w;
+ return -n;
+ }
+ y[0] = r;
+ y[1] = w;
+ return n;
+}
+#endif
+++ /dev/null
-/* origin: FreeBSD /usr/src/lib/msun/ld80/e_rem_pio2.c */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
- *
- * Developed at SunSoft, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- *
- * Optimized by Bruce D. Evans.
- */
-#include "libm.h"
-#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
-/* ld80 version of __rem_pio2(x,y)
- *
- * return the remainder of x rem pi/2 in y[0]+y[1]
- * use __rem_pio2_large() for large x
- */
-
-#define BIAS (LDBL_MAX_EXP - 1)
-
-/*
- * invpio2: 64 bits of 2/pi
- * pio2_1: first 39 bits of pi/2
- * pio2_1t: pi/2 - pio2_1
- * pio2_2: second 39 bits of pi/2
- * pio2_2t: pi/2 - (pio2_1+pio2_2)
- * pio2_3: third 39 bits of pi/2
- * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
- */
-static const double
-zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
-two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
-pio2_1 = 1.57079632679597125389e+00, /* 0x3FF921FB, 0x54444000 */
-pio2_2 = -1.07463465549783099519e-12, /* -0x12e7b967674000.0p-92 */
-pio2_3 = 6.36831716351370313614e-25; /* 0x18a2e037074000.0p-133 */
-
-static const long double
-invpio2 = 6.36619772367581343076e-01L, /* 0xa2f9836e4e44152a.0p-64 */
-pio2_1t = -1.07463465549719416346e-12L, /* -0x973dcb3b399d747f.0p-103 */
-pio2_2t = 6.36831716351095013979e-25L, /* 0xc51701b839a25205.0p-144 */
-pio2_3t = -2.75299651904407171810e-37L; /* -0xbb5bf6c7ddd660ce.0p-185 */
-
-static inline int __rem_pio2l(long double x, long double *y)
-{
- union IEEEl2bits u,u1;
- long double z,w,t,r,fn;
- double tx[3],ty[2];
- int e0,ex,i,j,nx,n;
- int16_t expsign;
-
- u.e = x;
- expsign = u.xbits.expsign;
- ex = expsign & 0x7fff;
- if (ex < BIAS + 25 || (ex == BIAS + 25 && u.bits.manh < 0xc90fdaa2)) {
- union IEEEl2bits u2;
- int ex1;
-
- /* |x| ~< 2^25*(pi/2), medium size */
- /* Use a specialized rint() to get fn. Assume round-to-nearest. */
- fn = x*invpio2 + 0x1.8p63;
- fn = fn - 0x1.8p63;
-// FIXME
-//#ifdef HAVE_EFFICIENT_IRINT
-// n = irint(fn);
-//#else
- n = fn;
-//#endif
- r = x-fn*pio2_1;
- w = fn*pio2_1t; /* 1st round good to 102 bit */
- j = ex;
- y[0] = r-w;
- u2.e = y[0];
- ex1 = u2.xbits.expsign & 0x7fff;
- i = j-ex1;
- if (i > 22) { /* 2nd iteration needed, good to 141 */
- t = r;
- w = fn*pio2_2;
- r = t-w;
- w = fn*pio2_2t-((t-r)-w);
- y[0] = r-w;
- u2.e = y[0];
- ex1 = u2.xbits.expsign & 0x7fff;
- i = j-ex1;
- if (i > 61) { /* 3rd iteration need, 180 bits acc */
- t = r; /* will cover all possible cases */
- w = fn*pio2_3;
- r = t-w;
- w = fn*pio2_3t-((t-r)-w);
- y[0] = r-w;
- }
- }
- y[1] = (r - y[0]) - w;
- return n;
- }
- /*
- * all other (large) arguments
- */
- if (ex == 0x7fff) { /* x is inf or NaN */
- y[0] = y[1] = x - x;
- return 0;
- }
- /* set z = scalbn(|x|,ilogb(x)-23) */
- u1.e = x;
- e0 = ex - BIAS - 23; /* e0 = ilogb(|x|)-23; */
- u1.xbits.expsign = ex - e0;
- z = u1.e;
- for (i=0; i<2; i++) {
- tx[i] = (double)(int32_t)z;
- z = (z-tx[i])*two24;
- }
- tx[2] = z;
- nx = 3;
- while (tx[nx-1] == zero)
- nx--; /* skip zero term */
- n = __rem_pio2_large(tx,ty,e0,nx,2);
- r = (long double)ty[0] + ty[1];
- w = ty[1] - (r - ty[0]);
- if (expsign < 0) {
- y[0] = -r;
- y[1] = -w;
- return -n;
- }
- y[0] = r;
- y[1] = w;
- return n;
-}
-#endif
return cos(x);
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
-#include "__rem_pio2l.h"
-
long double cosl(long double x)
{
union IEEEl2bits z;
*cos = c;
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
-#include "__rem_pio2l.h"
-
void sincosl(long double x, long double *sin, long double *cos)
{
union IEEEl2bits u;
return sin(x);
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
-#include "__rem_pio2l.h"
-
long double sinl(long double x)
{
union IEEEl2bits z;
return tan(x);
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
-#include "__rem_pio2l.h"
-
long double tanl(long double x)
{
union IEEEl2bits z;