Add a "fork" of musl as //fusl.

fusl/src/math/__rem_pio2.c

+/* 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"
+
+#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1
+#define EPS DBL_EPSILON
+#elif FLT_EVAL_METHOD==2
+#define EPS LDBL_EPSILON
+#endif
+
+/*
+ * 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
+toint   = 1.5/EPS,
+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)
+{
+        union {double f; uint64_t i;} u = {x};
+        double_t z,w,t,r,fn;
+        double tx[3],ty[2];
+        uint32_t ix;
+        int sign, n, ex, ey, i;
+
+        sign = u.i>>63;
+        ix = u.i>>32 & 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 (!sign) {
+                                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 (!sign) {
+                                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 (!sign) {
+                                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 (!sign) {
+                                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 */
+medium:
+                /* rint(x/(pi/2)), Assume round-to-nearest. */
+                fn = (double_t)x*invpio2 + toint - toint;
+                n = (int32_t)fn;
+                r = x - fn*pio2_1;
+                w = fn*pio2_1t;  /* 1st round, good to 85 bits */
+                y[0] = r - w;
+                u.f = y[0];
+                ey = u.i>>52 & 0x7ff;
+                ex = ix>>20;
+                if (ex - ey > 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;
+                        u.f = y[0];
+                        ey = u.i>>52 & 0x7ff;
+                        if (ex - ey > 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) */
+        u.f = x;
+        u.i &= (uint64_t)-1>>12;
+        u.i |= (uint64_t)(0x3ff + 23)<<52;
+        z = u.f;
+        for (i=0; i < 2; i++) {
+                tx[i] = (double)(int32_t)z;
+                z     = (z-tx[i])*0x1p24;
+        }
+        tx[i] = z;
+        /* skip zero terms, first term is non-zero */
+        while (tx[i] == 0.0)
+                i--;
+        n = __rem_pio2_large(tx,ty,(int)(ix>>20)-(0x3ff+23),i+1,1);
+        if (sign) {
+                y[0] = -ty[0];
+                y[1] = -ty[1];
+                return -n;
+        }
+        y[0] = ty[0];
+        y[1] = ty[1];
+        return n;
+}