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 diff --git a/src/math/asin.c b/src/math/asin.cnew file mode 100644index 00000000..04bd0c14--- /dev/null+++ b/src/math/asin.c@@ -0,0 +1,109 @@+/* origin: FreeBSD /usr/src/lib/msun/src/e_asin.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.+ * ====================================================+ */+/* 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 "libm.h"++static const double+one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */+huge = 1.000e+300,+pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */+pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */+pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */+/* coefficients 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 */++double asin(double x)+{+ double t=0.0,w,p,q,c,r,s;+ int32_t hx,ix;++ GET_HIGH_WORD(hx, x);+ ix = hx & 0x7fffffff;+ if (ix >= 0x3ff00000) { /* |x|>= 1 */+ uint32_t lx;++ GET_LOW_WORD(lx, x);+ if ((ix-0x3ff00000 | lx) == 0)+ /* asin(1) = +-pi/2 with inexact */+ return x*pio2_hi + x*pio2_lo;+ return (x-x)/(x-x); /* asin(|x|>1) is NaN */+ } else if (ix < 0x3fe00000) { /* |x|<0.5 */+ if (ix < 0x3e500000) { /* if |x| < 2**-26 */+ if (huge+x > one)+ return x; /* return x with inexact if x!=0*/+ }+ 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;+ SET_LOW_WORD(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;+ return -t;+}