summaryrefslogtreecommitdiff
path: root/src/math/__rem_pio2.c
diff options
context:
space:
mode:
Diffstat (limited to 'src/math/__rem_pio2.c')
-rw-r--r--src/math/__rem_pio2.c176
1 files changed, 176 insertions, 0 deletions
diff --git a/src/math/__rem_pio2.c b/src/math/__rem_pio2.c
new file mode 100644
index 00000000..a7d779e0
--- /dev/null
+++ b/src/math/__rem_pio2.c
@@ -0,0 +1,176 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * 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.
+ */
+/* __rem_pio2(x,y)
+ *
+ * return the remainder of x rem pi/2 in y[0]+y[1]
+ * use __rem_pio2_large() for large x
+ */
+
+#include "libm.h"
+
+/*
+ * invpio2: 53 bits of 2/pi
+ * pio2_1: first 33 bit of pi/2
+ * pio2_1t: pi/2 - pio2_1
+ * pio2_2: second 33 bit of pi/2
+ * pio2_2t: pi/2 - (pio2_1+pio2_2)
+ * pio2_3: third 33 bit 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 */
+invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
+pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
+pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
+pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
+pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
+pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
+pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
+
+/* caller must handle the case when reduction is not needed: |x| ~<= pi/4 */
+int __rem_pio2(double x, double *y)
+{
+ double z,w,t,r,fn;
+ double tx[3],ty[2];
+ int32_t e0,i,j,nx,n,ix,hx;
+ uint32_t low;
+
+ GET_HIGH_WORD(hx,x);
+ ix = hx & 0x7fffffff;
+ if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */
+ if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */
+ goto medium; /* cancellation -- use medium case */
+ if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */
+ if (hx > 0) {
+ z = x - pio2_1; /* one round good to 85 bits */
+ y[0] = z - pio2_1t;
+ y[1] = (z-y[0]) - pio2_1t;
+ return 1;
+ } else {
+ z = x + pio2_1;
+ y[0] = z + pio2_1t;
+ y[1] = (z-y[0]) + pio2_1t;
+ return -1;
+ }
+ } else {
+ if (hx > 0) {
+ z = x - 2*pio2_1;
+ y[0] = z - 2*pio2_1t;
+ y[1] = (z-y[0]) - 2*pio2_1t;
+ return 2;
+ } else {
+ z = x + 2*pio2_1;
+ y[0] = z + 2*pio2_1t;
+ y[1] = (z-y[0]) + 2*pio2_1t;
+ return -2;
+ }
+ }
+ }
+ if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */
+ if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */
+ if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */
+ goto medium;
+ if (hx > 0) {
+ z = x - 3*pio2_1;
+ y[0] = z - 3*pio2_1t;
+ y[1] = (z-y[0]) - 3*pio2_1t;
+ return 3;
+ } else {
+ z = x + 3*pio2_1;
+ y[0] = z + 3*pio2_1t;
+ y[1] = (z-y[0]) + 3*pio2_1t;
+ return -3;
+ }
+ } else {
+ if (ix == 0x401921fb) /* |x| ~= 4pi/2 */
+ goto medium;
+ if (hx > 0) {
+ z = x - 4*pio2_1;
+ y[0] = z - 4*pio2_1t;
+ y[1] = (z-y[0]) - 4*pio2_1t;
+ return 4;
+ } else {
+ z = x + 4*pio2_1;
+ y[0] = z + 4*pio2_1t;
+ y[1] = (z-y[0]) + 4*pio2_1t;
+ return -4;
+ }
+ }
+ }
+ if (ix < 0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */
+ uint32_t high;
+medium:
+ /* Use a specialized rint() to get fn. Assume round-to-nearest. */
+ STRICT_ASSIGN(double, fn, x*invpio2 + 0x1.8p52);
+ fn = fn - 0x1.8p52;
+// FIXME
+#ifdef HAVE_EFFICIENT_IRINT
+ n = irint(fn);
+#else
+ n = (int32_t)fn;
+#endif
+ r = x - fn*pio2_1;
+ w = fn*pio2_1t; /* 1st round, good to 85 bits */
+ j = ix>>20;
+ y[0] = r - w;
+ GET_HIGH_WORD(high,y[0]);
+ i = j - ((high>>20)&0x7ff);
+ if (i > 16) { /* 2nd round, good to 118 bits */
+ t = r;
+ w = fn*pio2_2;
+ r = t - w;
+ w = fn*pio2_2t - ((t-r)-w);
+ y[0] = r - w;
+ GET_HIGH_WORD(high,y[0]);
+ i = j - ((high>>20)&0x7ff);
+ if (i > 49) { /* 3rd round, good to 151 bits, covers all cases */
+ t = r;
+ 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 (ix >= 0x7ff00000) { /* x is inf or NaN */
+ y[0] = y[1] = x - x;
+ return 0;
+ }
+ /* set z = scalbn(|x|,ilogb(x)-23) */
+ GET_LOW_WORD(low,x);
+ e0 = (ix>>20) - 1046; /* e0 = ilogb(z)-23; */
+ INSERT_WORDS(z, ix - ((int32_t)(e0<<20)), low);
+ 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,1);
+ if (hx < 0) {
+ y[0] = -ty[0];
+ y[1] = -ty[1];
+ return -n;
+ }
+ y[0] = ty[0];
+ y[1] = ty[1];
+ return n;
+}