Szabolcs Nagy
c599f4f4d7
for these functions f(x)=x for small inputs, because f(0)=0 and f'(0)=1, but for subnormal values they should raise the underflow flag (required by annex F), if they are approximated by a polynomial around 0 then spurious underflow should be avoided (not required by annex F) all these functions should raise inexact flag for small x if x!=0, but it's not required by the standard and it does not seem a worthy goal, so support for it is removed in some cases. raising underflow: - x*x may not raise underflow for subnormal x if FLT_EVAL_METHOD!=0 - x*x may raise spurious underflow for normal x if FLT_EVAL_METHOD==0 - in case of double subnormal x, store x as float - in case of float subnormal x, store x*x as float
62 lines
1.4 KiB
C
62 lines
1.4 KiB
C
/* origin: FreeBSD /usr/src/lib/msun/src/e_asinf.c */
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/*
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* Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
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*/
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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#include "libm.h"
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static const double
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pio2 = 1.570796326794896558e+00;
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static const float
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/* coefficients for R(x^2) */
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pS0 = 1.6666586697e-01,
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pS1 = -4.2743422091e-02,
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pS2 = -8.6563630030e-03,
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qS1 = -7.0662963390e-01;
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static float R(float z)
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{
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float_t p, q;
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p = z*(pS0+z*(pS1+z*pS2));
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q = 1.0f+z*qS1;
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return p/q;
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}
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float asinf(float x)
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{
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double s;
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float z;
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uint32_t hx,ix;
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GET_FLOAT_WORD(hx, x);
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ix = hx & 0x7fffffff;
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if (ix >= 0x3f800000) { /* |x| >= 1 */
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if (ix == 0x3f800000) /* |x| == 1 */
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return x*pio2 + 0x1p-120f; /* asin(+-1) = +-pi/2 with inexact */
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return 0/(x-x); /* asin(|x|>1) is NaN */
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}
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if (ix < 0x3f000000) { /* |x| < 0.5 */
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/* if 0x1p-126 <= |x| < 0x1p-12, avoid raising underflow */
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if (ix < 0x39800000 && ix >= 0x00800000)
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return x;
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return x + x*R(x*x);
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}
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/* 1 > |x| >= 0.5 */
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z = (1 - fabsf(x))*0.5f;
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s = sqrt(z);
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x = pio2 - 2*(s+s*R(z));
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if (hx >> 31)
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return -x;
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return x;
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}
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