Initial import

libc/math/__cosl.c

@@ -0,0 +1,96 @@
+/* origin: FreeBSD /usr/src/lib/msun/ld80/k_cosl.c */
+/* origin: FreeBSD /usr/src/lib/msun/ld128/k_cosl.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.
+ * ====================================================
+ */
+
+
+#include "libc/math/libm.h"
+
+#if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
+#if LDBL_MANT_DIG == 64
+/*
+ * ld80 version of __cos.c.  See __cos.c for most comments.
+ */
+/*
+ * Domain [-0.7854, 0.7854], range ~[-2.43e-23, 2.425e-23]:
+ * |cos(x) - c(x)| < 2**-75.1
+ *
+ * The coefficients of c(x) were generated by a pari-gp script using
+ * a Remez algorithm that searches for the best higher coefficients
+ * after rounding leading coefficients to a specified precision.
+ *
+ * Simpler methods like Chebyshev or basic Remez barely suffice for
+ * cos() in 64-bit precision, because we want the coefficient of x^2
+ * to be precisely -0.5 so that multiplying by it is exact, and plain
+ * rounding of the coefficients of a good polynomial approximation only
+ * gives this up to about 64-bit precision.  Plain rounding also gives
+ * a mediocre approximation for the coefficient of x^4, but a rounding
+ * error of 0.5 ulps for this coefficient would only contribute ~0.01
+ * ulps to the final error, so this is unimportant.  Rounding errors in
+ * higher coefficients are even less important.
+ *
+ * In fact, coefficients above the x^4 one only need to have 53-bit
+ * precision, and this is more efficient.  We get this optimization
+ * almost for free from the complications needed to search for the best
+ * higher coefficients.
+ */
+static const long double
+C1 =  0.0416666666666666666136L;        /*  0xaaaaaaaaaaaaaa9b.0p-68 */
+static const double
+C2 = -0.0013888888888888874,            /* -0x16c16c16c16c10.0p-62 */
+C3 =  0.000024801587301571716,          /*  0x1a01a01a018e22.0p-68 */
+C4 = -0.00000027557319215507120,        /* -0x127e4fb7602f22.0p-74 */
+C5 =  0.0000000020876754400407278,      /*  0x11eed8caaeccf1.0p-81 */
+C6 = -1.1470297442401303e-11,           /* -0x19393412bd1529.0p-89 */
+C7 =  4.7383039476436467e-14;           /*  0x1aac9d9af5c43e.0p-97 */
+#define POLY(z) (z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*C7)))))))
+#elif LDBL_MANT_DIG == 113
+/*
+ * ld128 version of __cos.c.  See __cos.c for most comments.
+ */
+/*
+ * Domain [-0.7854, 0.7854], range ~[-1.80e-37, 1.79e-37]:
+ * |cos(x) - c(x))| < 2**-122.0
+ *
+ * 113-bit precision requires more care than 64-bit precision, since
+ * simple methods give a minimax polynomial with coefficient for x^2
+ * that is 1 ulp below 0.5, but we want it to be precisely 0.5.  See
+ * above for more details.
+ */
+static const long double
+C1 =  0.04166666666666666666666666666666658424671L,
+C2 = -0.001388888888888888888888888888863490893732L,
+C3 =  0.00002480158730158730158730158600795304914210L,
+C4 = -0.2755731922398589065255474947078934284324e-6L,
+C5 =  0.2087675698786809897659225313136400793948e-8L,
+C6 = -0.1147074559772972315817149986812031204775e-10L,
+C7 =  0.4779477332386808976875457937252120293400e-13L;
+static const double
+C8 = -0.1561920696721507929516718307820958119868e-15,
+C9 =  0.4110317413744594971475941557607804508039e-18,
+C10 = -0.8896592467191938803288521958313920156409e-21,
+C11 =  0.1601061435794535138244346256065192782581e-23;
+#define POLY(z) (z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*(C7+ \
+	z*(C8+z*(C9+z*(C10+z*C11)))))))))))
+#endif
+
+long double __cosl(long double x, long double y)
+{
+	long double hz,z,r,w;
+
+	z  = x*x;
+	r  = POLY(z);
+	hz = 0.5*z;
+	w  = 1.0-hz;
+	return w + (((1.0-w)-hz) + (z*r-x*y));
+}
+#endif