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authormrb0nk500 <b0nk@b0nk.xyz>2023-02-02 17:29:19 -0400
committermrb0nk500 <b0nk@b0nk.xyz>2023-02-03 13:27:06 -0400
commitf2eabdb6257c09cf2890dac5e9737912728542af (patch)
tree3b46f6787185d65605651a0f48776dc9779ce648 /src/MSL_C.PPCEABI.bare.H/e_asin.c
parenteef1dd840b7cecac28c2e6b0574707b90a37d4e7 (diff)
global: Add rest of Dolphin SDK proper, add MSL, and MetroTRK
Finally, it links properly.
Diffstat (limited to 'src/MSL_C.PPCEABI.bare.H/e_asin.c')
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+/* @(#)e_asin.c 1.2 95/01/04 */
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+/* __ieee754_asin(x)
+ * Method :
+ * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
+ * we approximate asin(x) on [0,0.5] by
+ * asin(x) = x + x*x^2*R(x^2)
+ * where
+ * R(x^2) is a rational approximation of (asin(x)-x)/x^3
+ * and its remez error is bounded by
+ * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
+ *
+ * For x in [0.5,1]
+ * asin(x) = pi/2-2*asin(sqrt((1-x)/2))
+ * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
+ * then for x>0.98
+ * asin(x) = pi/2 - 2*(s+s*z*R(z))
+ * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
+ * For x<=0.98, let pio4_hi = pio2_hi/2, then
+ * f = hi part of s;
+ * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
+ * and
+ * asin(x) = pi/2 - 2*(s+s*z*R(z))
+ * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
+ * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
+ *
+ * Special cases:
+ * if x is NaN, return x itself;
+ * if |x|>1, return NaN with invalid signal.
+ *
+ */
+
+#include <fdlibm.h>
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+ one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+ big = 1.000e+300, pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
+ pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
+ pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
+ /* coefficient for R(x^2) */
+ pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
+ pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
+ pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
+ pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
+ pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
+ pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
+ qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
+ qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
+ qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
+ qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
+
+#ifdef __STDC__
+double __ieee754_asin(double x)
+#else
+double __ieee754_asin(x)
+double x;
+#endif
+{
+ double t, w, p, q, c, r, s;
+ _INT32 hx, ix;
+ hx = __HI(x);
+ ix = hx & 0x7fffffff;
+ if (ix >= 0x3ff00000) { /* |x|>= 1 */
+ if (((ix - 0x3ff00000) | __LO(x)) == 0)
+ /* asin(1)=+-pi/2 with inexact */
+ return x * pio2_hi + x * pio2_lo;
+ return NAN; /* asin(|x|>1) is NaN */
+ } else if (ix < 0x3fe00000) { /* |x|<0.5 */
+ if (ix < 0x3e400000) { /* if |x| < 2**-27 */
+ if (big + x > one)
+ return x; /* return x with inexact if x!=0*/
+ } else
+ t = x * x;
+ p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5)))));
+ q = one + t * (qS1 + t * (qS2 + t * (qS3 + t * qS4)));
+ w = p / q;
+ return x + x * w;
+ }
+ /* 1> |x|>= 0.5 */
+ w = one - fabs(x);
+ t = w * 0.5;
+ p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5)))));
+ q = one + t * (qS1 + t * (qS2 + t * (qS3 + t * qS4)));
+ s = sqrt(t);
+ if (ix >= 0x3FEF3333) { /* if |x| > 0.975 */
+ w = p / q;
+ t = pio2_hi - (2.0 * (s + s * w) - pio2_lo);
+ } else {
+ w = s;
+ __LO(w) = 0;
+ c = (t - w * w) / (s + w);
+ r = p / q;
+ p = 2.0 * s * r - (pio2_lo - 2.0 * c);
+ q = pio4_hi - 2.0 * w;
+ t = pio4_hi - (p - q);
+ }
+ if (hx > 0)
+ return t;
+ else
+ return -t;
+}