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| 1 /* origin: FreeBSD /usr/src/lib/msun/src/e_asinl.c */ |
| 2 /* |
| 3 * ==================================================== |
| 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| 5 * |
| 6 * Developed at SunSoft, a Sun Microsystems, Inc. business. |
| 7 * Permission to use, copy, modify, and distribute this |
| 8 * software is freely granted, provided that this notice |
| 9 * is preserved. |
| 10 * ==================================================== |
| 11 */ |
| 12 /* |
| 13 * See comments in asin.c. |
| 14 * Converted to long double by David Schultz <das@FreeBSD.ORG>. |
| 15 */ |
| 16 |
| 17 #include "libm.h" |
| 18 |
| 19 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 |
| 20 long double asinl(long double x) |
| 21 { |
| 22 return asin(x); |
| 23 } |
| 24 #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 |
| 25 #include "__invtrigl.h" |
| 26 #if LDBL_MANT_DIG == 64 |
| 27 #define CLOSETO1(u) (u.i.m>>56 >= 0xf7) |
| 28 #define CLEARBOTTOM(u) (u.i.m &= -1ULL << 32) |
| 29 #elif LDBL_MANT_DIG == 113 |
| 30 #define CLOSETO1(u) (u.i.top >= 0xee00) |
| 31 #define CLEARBOTTOM(u) (u.i.lo = 0) |
| 32 #endif |
| 33 |
| 34 long double asinl(long double x) |
| 35 { |
| 36 union ldshape u = {x}; |
| 37 long double z, r, s; |
| 38 uint16_t e = u.i.se & 0x7fff; |
| 39 int sign = u.i.se >> 15; |
| 40 |
| 41 if (e >= 0x3fff) { /* |x| >= 1 or nan */ |
| 42 /* asin(+-1)=+-pi/2 with inexact */ |
| 43 if (x == 1 || x == -1) |
| 44 return x*pio2_hi + 0x1p-120f; |
| 45 return 0/(x-x); |
| 46 } |
| 47 if (e < 0x3fff - 1) { /* |x| < 0.5 */ |
| 48 if (e < 0x3fff - (LDBL_MANT_DIG+1)/2) { |
| 49 /* return x with inexact if x!=0 */ |
| 50 FORCE_EVAL(x + 0x1p120f); |
| 51 return x; |
| 52 } |
| 53 return x + x*__invtrigl_R(x*x); |
| 54 } |
| 55 /* 1 > |x| >= 0.5 */ |
| 56 z = (1.0 - fabsl(x))*0.5; |
| 57 s = sqrtl(z); |
| 58 r = __invtrigl_R(z); |
| 59 if (CLOSETO1(u)) { |
| 60 x = pio2_hi - (2*(s+s*r)-pio2_lo); |
| 61 } else { |
| 62 long double f, c; |
| 63 u.f = s; |
| 64 CLEARBOTTOM(u); |
| 65 f = u.f; |
| 66 c = (z - f*f)/(s + f); |
| 67 x = 0.5*pio2_hi-(2*s*r - (pio2_lo-2*c) - (0.5*pio2_hi-2*f)); |
| 68 } |
| 69 return sign ? -x : x; |
| 70 } |
| 71 #endif |
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