576 lines
17 KiB
C
576 lines
17 KiB
C
#include "wcclibm.h"
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#include "math_private.h"
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/* e_rem_pio2f.c -- float version of e_rem_pio2.c
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Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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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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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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#if defined(LIBM_SCCS) && !defined(lint)
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static char rcsid[] =
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"$NetBSD: e_rem_pio2f.c,v 1.5 1995/05/10 20:46:03 jtc Exp $";
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#endif
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/* __ieee754_rem_pio2f(x,y)
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return the remainder of x rem pi/2 in y[ 0 ]+y[ 1 ]
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use __kernel_rem_pio2f()
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*/
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/* This array is like the one in e_rem_pio2.c, but the numbers are
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single precision and the last 8 bits are forced to 0. */
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#ifdef __STDC__
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static const int32_t fmref_npio2_hw[] = {
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#else
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static int32_t fmref_npio2_hw[] = {
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#endif
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0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00,
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0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00,
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0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100,
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0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00,
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0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00,
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0x4242c700, 0x42490f00};
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/*
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invpio2: 24 bits of 2/pi
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pio2_1: first 17 bit of pi/2
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pio2_1t: pi/2 - pio2_1
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pio2_2: second 17 bit of pi/2
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pio2_2t: pi/2 - (pio2_1+pio2_2)
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pio2_3: third 17 bit of pi/2
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pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
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*/
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#ifdef __STDC__
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static const float
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#else
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static float
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#endif
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/* zero = 0.0000000000e+00f, /\* 0x00000000 *\/ */
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/* half = 5.0000000000e-01f, /\* 0x3f000000 *\/ */
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/* two8 = 2.5600000000e+02f, /\* 0x43800000 *\/ */
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fmref_invpio2 = 6.3661980629e-01f, /* 0x3f22f984 */
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fmref_pio2_1 = 1.5707855225e+00f, /* 0x3fc90f80 */
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fmref_pio2_1t = 1.0804334124e-05f, /* 0x37354443 */
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fmref_pio2_2 = 1.0804273188e-05f, /* 0x37354400 */
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fmref_pio2_2t = 6.0770999344e-11f, /* 0x2e85a308 */
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fmref_pio2_3 = 6.0770943833e-11f, /* 0x2e85a300 */
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fmref_pio2_3t = 6.1232342629e-17f; /* 0x248d3132 */
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#ifdef __STDC__
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__attribute__((always_inline)) static inline int32_t
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fmref___ieee754_rem_pio2f(float x, float *y)
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#else
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__attribute__((always_inline)) static inline int32_t
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fmref___ieee754_rem_pio2f(x, y)
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float x, y[];
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#endif
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{
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float z, w, t, r, fn;
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int32_t i, j, n, ix, hx;
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GET_FLOAT_WORD(hx, x);
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ix = hx & 0x7fffffff;
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if (ix <= 0x3f490fd8) { /* |x| ~<= pi/4 , no need for reduction */
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y[0] = x;
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y[1] = 0;
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return 0;
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}
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if (ix < 0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */
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if (hx > 0) {
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z = x - fmref_pio2_1;
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if ((ix & 0xfffffff0) != 0x3fc90fd0) { /* 24+24 bit pi OK */
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y[0] = z - fmref_pio2_1t;
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y[1] = (z - y[0]) - fmref_pio2_1t;
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} else { /* near pi/2, use 24+24+24 bit pi */
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z -= fmref_pio2_2;
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y[0] = z - fmref_pio2_2t;
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y[1] = (z - y[0]) - fmref_pio2_2t;
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}
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return 1;
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} else { /* negative x */
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z = x + fmref_pio2_1;
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if ((ix & 0xfffffff0) != 0x3fc90fd0) { /* 24+24 bit pi OK */
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y[0] = z + fmref_pio2_1t;
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y[1] = (z - y[0]) + fmref_pio2_1t;
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} else { /* near pi/2, use 24+24+24 bit pi */
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z += fmref_pio2_2;
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y[0] = z + fmref_pio2_2t;
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y[1] = (z - y[0]) + fmref_pio2_2t;
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}
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return -1;
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}
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}
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if (ix <= 0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */
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t = fabsf(x);
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n = (int32_t) (t * fmref_invpio2 + fmref_half);
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fn = (float) n;
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r = t - fn * fmref_pio2_1;
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w = fn * fmref_pio2_1t; /* 1st round good to 40 bit */
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if (n < 32 && (int32_t) (ix & 0xffffff00) != fmref_npio2_hw[n - 1]) {
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y[0] = r - w; /* quick check no cancellation */
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} else {
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u_int32_t high;
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j = ix >> 23;
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y[0] = r - w;
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GET_FLOAT_WORD(high, y[0]);
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i = j - ((high >> 23) & 0xff);
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if (i > 8) { /* 2nd iteration needed, good to 57 */
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t = r;
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w = fn * fmref_pio2_2;
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r = t - w;
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w = fn * fmref_pio2_2t - ((t - r) - w);
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y[0] = r - w;
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GET_FLOAT_WORD(high, y[0]);
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i = j - ((high >> 23) & 0xff);
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if (i > 25) { /* 3rd iteration need, 74 bits acc */
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t = r; /* will cover all possible cases */
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w = fn * fmref_pio2_3;
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r = t - w;
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w = fn * fmref_pio2_3t - ((t - r) - w);
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y[0] = r - w;
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}
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}
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}
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y[1] = (r - y[0]) - w;
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if (hx < 0) {
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y[0] = -y[0];
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y[1] = -y[1];
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return -n;
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} else
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return n;
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}
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/*
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all other (large) arguments
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*/
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if (ix >= 0x7f800000) { /* x is inf or NaN */
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y[0] = y[1] = x - x;
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return 0;
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}
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y[0] = y[1] = x - x; /* dummy initialization */
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return 0; /* doesn't happen for our input */
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}
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/* k_cosf.c -- float version of k_cos.c
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Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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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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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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#if defined(LIBM_SCCS) && !defined(lint)
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static char rcsid[] = "$NetBSD: k_cosf.c,v 1.4 1995/05/10 20:46:23 jtc Exp $";
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#endif
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#ifdef __STDC__
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static const float
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#else
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static float
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#endif
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/* one = 1.0000000000e+00, /\* 0x3f800000 *\/ */
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fmref_C1 = 4.1666667908e-02f, /* 0x3d2aaaab */
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fmref_C2 = -1.3888889225e-03f, /* 0xbab60b61 */
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fmref_C3 = 2.4801587642e-05f, /* 0x37d00d01 */
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fmref_C4 = -2.7557314297e-07f, /* 0xb493f27c */
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fmref_C5 = 2.0875723372e-09f, /* 0x310f74f6 */
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fmref_C6 = -1.1359647598e-11f; /* 0xad47d74e */
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#ifdef __STDC__
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__attribute__((always_inline)) static inline float
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fmref___kernel_cosf(float x, float y)
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#else
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__attribute__((always_inline)) static inline float
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fmref___kernel_cosf(x, y)
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float x, y;
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#endif
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{
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float a, hz, z, r, qx;
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int32_t ix;
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GET_FLOAT_WORD(ix, x);
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ix &= 0x7fffffff; /* ix = |x|'s high word*/
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if (ix < 0x32000000) { /* if x < 2**27 */
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if (((int) x) == 0)
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return fmref_one; /* generate inexact */
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}
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z = x * x;
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r = z *
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(fmref_C1 +
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z * (fmref_C2 +
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z * (fmref_C3 + z * (fmref_C4 + z * (fmref_C5 + z * fmref_C6)))));
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if (ix < 0x3e99999a) /* if |x| < 0.3 */
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return fmref_one - ((float) 0.5f * z - (z * r - x * y));
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else {
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if (ix > 0x3f480000) /* x > 0.78125 */
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qx = (float) 0.28125f;
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else {
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SET_FLOAT_WORD(qx, ix - 0x01000000); /* x/4 */
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}
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hz = (float) 0.5f * z - qx;
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a = fmref_one - qx;
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return a - (hz - (z * r - x * y));
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}
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}
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/* k_sinf.c -- float version of k_sin.c
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Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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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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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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#if defined(LIBM_SCCS) && !defined(lint)
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static char rcsid[] = "$NetBSD: k_sinf.c,v 1.4 1995/05/10 20:46:33 jtc Exp $";
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#endif
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#ifdef __STDC__
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static const float
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#else
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static float
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#endif
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/* half = 5.0000000000e-01f,/\* 0x3f000000 *\/ */
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fmref_S1 = -1.6666667163e-01f, /* 0xbe2aaaab */
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fmref_S2 = 8.3333337680e-03f, /* 0x3c088889 */
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fmref_S3 = -1.9841270114e-04f, /* 0xb9500d01 */
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fmref_S4 = 2.7557314297e-06f, /* 0x3638ef1b */
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fmref_S5 = -2.5050759689e-08f, /* 0xb2d72f34 */
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fmref_S6 = 1.5896910177e-10f; /* 0x2f2ec9d3 */
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#ifdef __STDC__
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__attribute__((always_inline)) static inline float
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fmref___kernel_sinf(float x, float y, int iy)
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#else
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__attribute__((always_inline)) static inline float
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fmref___kernel_sinf(x, y, iy)
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float x, y;
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int iy; /* iy=0 if y is zero */
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#endif
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{
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float z, r, v;
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int32_t ix;
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GET_FLOAT_WORD(ix, x);
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ix &= 0x7fffffff; /* high word of x */
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if (ix < 0x32000000) { /* |x| < 2**-27 */
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if ((int) x == 0)
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return x; /* generate inexact */
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}
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z = x * x;
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v = z * x;
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r = fmref_S2 +
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z * (fmref_S3 + z * (fmref_S4 + z * (fmref_S5 + z * fmref_S6)));
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if (iy == 0)
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return x + v * (fmref_S1 + z * r);
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else
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return x - ((z * (fmref_half * y - v * r) - y) - v * fmref_S1);
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}
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/* s_atanf.c -- float version of s_atan.c.
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Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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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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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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#if defined(LIBM_SCCS) && !defined(lint)
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static char rcsid[] = "$NetBSD: s_atanf.c,v 1.4 1995/05/10 20:46:47 jtc Exp $";
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#endif
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#ifdef __STDC__
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static const float fmref_atanhi[] = {
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#else
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static float fmref_atanhi[] = {
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#endif
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4.6364760399e-01f, /* atan(0.5)hi 0x3eed6338 */
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7.8539812565e-01f, /* atan(1.0)hi 0x3f490fda */
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9.8279368877e-01f, /* atan(1.5)hi 0x3f7b985e */
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1.5707962513e+00f, /* atan(inf)hi 0x3fc90fda */
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};
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#ifdef __STDC__
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static const float fmref_atanlo[] = {
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#else
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static float fmref_atanlo[] = {
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#endif
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5.0121582440e-09f, /* atan(0.5)lo 0x31ac3769 */
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3.7748947079e-08f, /* atan(1.0)lo 0x33222168 */
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3.4473217170e-08f, /* atan(1.5)lo 0x33140fb4 */
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7.5497894159e-08f, /* atan(inf)lo 0x33a22168 */
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};
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#ifdef __STDC__
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static const float fmref_aT[] = {
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#else
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static float fmref_aT[] = {
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#endif
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3.3333334327e-01f, /* 0x3eaaaaaa */
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-2.0000000298e-01f, /* 0xbe4ccccd */
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1.4285714924e-01f, /* 0x3e124925 */
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-1.1111110449e-01f, /* 0xbde38e38 */
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9.0908870101e-02f, /* 0x3dba2e6e */
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-7.6918758452e-02f, /* 0xbd9d8795 */
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6.6610731184e-02f, /* 0x3d886b35 */
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-5.8335702866e-02f, /* 0xbd6ef16b */
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4.9768779427e-02f, /* 0x3d4bda59 */
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-3.6531571299e-02f, /* 0xbd15a221 */
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1.6285819933e-02f, /* 0x3c8569d7 */
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};
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/* #ifdef __STDC__ */
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/* static const float */
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/* #else */
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/* static float */
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/* #endif */
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/* one = 1.0, */
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/* huge = 1.0e30; */
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#ifdef __STDC__
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__attribute__((always_inline)) static inline float
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fmref___atanf(float x)
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#else
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__attribute__((always_inline)) static inline float
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fmref___atanf(x)
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float x;
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#endif
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{
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float w, s1, s2, z;
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int32_t ix, hx, id;
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GET_FLOAT_WORD(hx, x);
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ix = hx & 0x7fffffff;
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if (ix >= 0x50800000) { /* if |x| >= 2^34 */
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if (ix > 0x7f800000)
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return x + x; /* NaN */
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if (hx > 0)
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return fmref_atanhi[3] + fmref_atanlo[3];
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else
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return -fmref_atanhi[3] - fmref_atanlo[3];
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}
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if (ix < 0x3ee00000) { /* |x| < 0.4375 */
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if (ix < 0x31000000) { /* |x| < 2^-29 */
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if (fmref_huge + x > fmref_one)
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return x; /* raise inexact */
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}
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id = -1;
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} else {
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x = fabsf(x);
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if (ix < 0x3f980000) { /* |x| < 1.1875 */
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if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */
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id = 0;
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x = ((float) 2.0f * x - fmref_one) / ((float) 2.0f + x);
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} else { /* 11/16<=|x|< 19/16 */
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id = 1;
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x = (x - fmref_one) / (x + fmref_one);
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}
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} else {
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if (ix < 0x401c0000) { /* |x| < 2.4375 */
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id = 2;
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x = (x - (float) 1.5f) / (fmref_one + (float) 1.5f * x);
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} else { /* 2.4375 <= |x| < 2^66 */
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id = 3;
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x = -(float) 1.0f / x;
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}
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}
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}
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/* end of argument reduction */
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z = x * x;
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w = z * z;
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/* break sum from i=0 to 10 aT[ i ]z**(i+1) into odd and even poly */
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s1 = z *
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(fmref_aT[0] +
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w * (fmref_aT[2] +
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w * (fmref_aT[4] +
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w * (fmref_aT[6] + w * (fmref_aT[8] + w * fmref_aT[10])))));
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s2 = w * (fmref_aT[1] +
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w * (fmref_aT[3] +
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w * (fmref_aT[5] + w * (fmref_aT[7] + w * fmref_aT[9]))));
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if (id < 0)
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return x - x * (s1 + s2);
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else {
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z = fmref_atanhi[id] - ((x * (s1 + s2) - fmref_atanlo[id]) - x);
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return (hx < 0) ? -z : z;
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}
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}
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// weak_alias (__atanf, atanf)
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/* s_cosf.c -- float version of s_cos.c.
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Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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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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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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/* #ifdef __STDC__ */
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/* static const float one=1.0; */
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/* #else */
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/* static float one=1.0; */
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/* #endif */
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#ifdef __STDC__
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__attribute__((always_inline)) static inline float
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fmref___cosf(float x)
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#else
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__attribute__((always_inline)) static inline float
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fmref___cosf(x)
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float x;
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#endif
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{
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float y[2], z = 0.0f;
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int32_t n, ix;
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GET_FLOAT_WORD(ix, x);
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/* |x| ~< pi/4 */
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ix &= 0x7fffffff;
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if (ix <= 0x3f490fd8)
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return fmref___kernel_cosf(x, z);
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/* cos(Inf or NaN) is NaN */
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else if (ix >= 0x7f800000)
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return x - x;
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|
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/* argument reduction needed */
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else {
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n = fmref___ieee754_rem_pio2f(x, y);
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switch (n & 3) {
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case 0:
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return fmref___kernel_cosf(y[0], y[1]);
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case 1:
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return -fmref___kernel_sinf(y[0], y[1], 1);
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case 2:
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return -fmref___kernel_cosf(y[0], y[1]);
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default:
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return fmref___kernel_sinf(y[0], y[1], 1);
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}
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}
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}
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/* s_sinf.c -- float version of s_sin.c.
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Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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|
*/
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|
|
|
/*
|
|
====================================================
|
|
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.
|
|
====================================================
|
|
*/
|
|
|
|
#ifdef __STDC__
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|
__attribute__((always_inline)) static inline float
|
|
fmref___sinf(float x)
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#else
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__attribute__((always_inline)) static inline float
|
|
fmref___sinf(x)
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float x;
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#endif
|
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{
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|
float y[2], z = 0.0;
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int32_t n, ix;
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GET_FLOAT_WORD(ix, x);
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|
|
/* |x| ~< pi/4 */
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ix &= 0x7fffffff;
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if (ix <= 0x3f490fd8)
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return fmref___kernel_sinf(x, z, 0);
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|
|
/* sin(Inf or NaN) is NaN */
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else if (ix >= 0x7f800000)
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return x - x;
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|
|
|
/* argument reduction needed */
|
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else {
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n = fmref___ieee754_rem_pio2f(x, y);
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|
switch (n & 3) {
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case 0:
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return fmref___kernel_sinf(y[0], y[1], 1);
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case 1:
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return fmref___kernel_cosf(y[0], y[1]);
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case 2:
|
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return -fmref___kernel_sinf(y[0], y[1], 1);
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default:
|
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return -fmref___kernel_cosf(y[0], y[1]);
|
|
}
|
|
}
|
|
}
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/* s_fabsf.c -- float version of s_fabs.c.
|
|
Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
|
*/
|
|
|
|
/*
|
|
====================================================
|
|
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.
|
|
====================================================
|
|
*/
|
|
|
|
/*
|
|
fabsf(x) returns the absolute value of x.
|
|
*/
|
|
|
|
#ifdef __STDC__
|
|
__attribute__((always_inline)) static inline float
|
|
fmref___fabsf(float x)
|
|
#else
|
|
__attribute__((always_inline)) static inline float
|
|
fmref___fabsf(x)
|
|
float x;
|
|
#endif
|
|
{
|
|
u_int32_t ix;
|
|
GET_FLOAT_WORD(ix, x);
|
|
SET_FLOAT_WORD(x, ix & 0x7fffffff);
|
|
return x;
|
|
}
|