/*- * SPDX-License-Identifier: BSD-2-Clause-FreeBSD * * Copyright (c) 2004 David Schultz * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. * * $FreeBSD$ */ #include "platform_common.h" #define __FDLIBM_STDC__ #ifndef FLT_EVAL_METHOD #define FLT_EVAL_METHOD 0 #endif typedef uint32_t u_int32_t; typedef uint64_t u_int64_t; typedef union u32double_tag { int *pint; double *pdouble; } U32DOUBLE; static inline int * pdouble2pint(double *pdouble) { U32DOUBLE u; u.pdouble = pdouble; return u.pint; } typedef union { double value; struct { u_int32_t lsw; u_int32_t msw; } parts; struct { u_int64_t w; } xparts; } ieee_double_shape_type_little; typedef union { double value; struct { u_int32_t msw; u_int32_t lsw; } parts; struct { u_int64_t w; } xparts; } ieee_double_shape_type_big; typedef union { double d; struct { unsigned int manl : 32; unsigned int manh : 20; unsigned int exp : 11; unsigned int sign : 1; } bits; } IEEEd2bits_L; typedef union { double d; struct { unsigned int sign : 1; unsigned int exp : 11; unsigned int manh : 20; unsigned int manl : 32; } bits; } IEEEd2bits_B; typedef union { float f; struct { unsigned int man : 23; unsigned int exp : 8; unsigned int sign : 1; } bits; } IEEEf2bits_L; typedef union { float f; struct { unsigned int sign : 1; unsigned int exp : 8; unsigned int man : 23; } bits; } IEEEf2bits_B; static union { int a; char b; } __ue = { .a = 1 }; #define is_little_endian() (__ue.b == 1) #define __HIL(x) *(1 + pdouble2pint(&x)) #define __LOL(x) *(pdouble2pint(&x)) #define __HIB(x) *(pdouble2pint(&x)) #define __LOB(x) *(1 + pdouble2pint(&x)) /* Get two 32 bit ints from a double. */ #define EXTRACT_WORDS_L(ix0, ix1, d) \ do { \ ieee_double_shape_type_little ew_u; \ ew_u.value = (d); \ (ix0) = ew_u.parts.msw; \ (ix1) = ew_u.parts.lsw; \ } while (0) /* Set a double from two 32 bit ints. */ #define INSERT_WORDS_L(d, ix0, ix1) \ do { \ ieee_double_shape_type_little iw_u; \ iw_u.parts.msw = (ix0); \ iw_u.parts.lsw = (ix1); \ (d) = iw_u.value; \ } while (0) /* Get two 32 bit ints from a double. */ #define EXTRACT_WORDS_B(ix0, ix1, d) \ do { \ ieee_double_shape_type_big ew_u; \ ew_u.value = (d); \ (ix0) = ew_u.parts.msw; \ (ix1) = ew_u.parts.lsw; \ } while (0) /* Set a double from two 32 bit ints. */ #define INSERT_WORDS_B(d, ix0, ix1) \ do { \ ieee_double_shape_type_big iw_u; \ iw_u.parts.msw = (ix0); \ iw_u.parts.lsw = (ix1); \ (d) = iw_u.value; \ } while (0) /* Get the more significant 32 bit int from a double. */ #define GET_HIGH_WORD_L(i, d) \ do { \ ieee_double_shape_type_little gh_u; \ gh_u.value = (d); \ (i) = gh_u.parts.msw; \ } while (0) /* Get the more significant 32 bit int from a double. */ #define GET_HIGH_WORD_B(i, d) \ do { \ ieee_double_shape_type_big gh_u; \ gh_u.value = (d); \ (i) = gh_u.parts.msw; \ } while (0) /* Set the more significant 32 bits of a double from an int. */ #define SET_HIGH_WORD_L(d, v) \ do { \ ieee_double_shape_type_little sh_u; \ sh_u.value = (d); \ sh_u.parts.msw = (v); \ (d) = sh_u.value; \ } while (0) /* Set the more significant 32 bits of a double from an int. */ #define SET_HIGH_WORD_B(d, v) \ do { \ ieee_double_shape_type_big sh_u; \ sh_u.value = (d); \ sh_u.parts.msw = (v); \ (d) = sh_u.value; \ } while (0) /* Set the less significant 32 bits of a double from an int. */ #define SET_LOW_WORD_L(d, v) \ do { \ ieee_double_shape_type_little sh_u; \ sh_u.value = (d); \ sh_u.parts.lsw = (v); \ (d) = sh_u.value; \ } while (0) /* Set the more significant 32 bits of a double from an int. */ #define SET_LOW_WORD_B(d, v) \ do { \ ieee_double_shape_type_big sh_u; \ sh_u.value = (d); \ sh_u.parts.lsw = (v); \ (d) = sh_u.value; \ } while (0) /* Get the less significant 32 bit int from a double. */ #define GET_LOW_WORD_L(i, d) \ do { \ ieee_double_shape_type_little gl_u; \ gl_u.value = (d); \ (i) = gl_u.parts.lsw; \ } while (0) /* Get the less significant 32 bit int from a double. */ #define GET_LOW_WORD_B(i, d) \ do { \ ieee_double_shape_type_big gl_u; \ gl_u.value = (d); \ (i) = gl_u.parts.lsw; \ } while (0) /* * A union which permits us to convert between a float and a 32 bit * int. */ typedef union { float value; /* FIXME: Assumes 32 bit int. */ unsigned int word; } ieee_float_shape_type; /* Get a 32 bit int from a float. */ #define GET_FLOAT_WORD(i, d) \ do { \ ieee_float_shape_type gf_u; \ gf_u.value = (d); \ (i) = gf_u.word; \ } while (0) /* Set a float from a 32 bit int. */ #define SET_FLOAT_WORD(d, i) \ do { \ ieee_float_shape_type sf_u; \ sf_u.word = (i); \ (d) = sf_u.value; \ } while (0) /* Macro wrappers. */ #define EXTRACT_WORDS(ix0, ix1, d) \ do { \ if (is_little_endian()) \ EXTRACT_WORDS_L(ix0, ix1, d); \ else \ EXTRACT_WORDS_B(ix0, ix1, d); \ } while (0) #define INSERT_WORDS(d, ix0, ix1) \ do { \ if (is_little_endian()) \ INSERT_WORDS_L(d, ix0, ix1); \ else \ INSERT_WORDS_B(d, ix0, ix1); \ } while (0) #define GET_HIGH_WORD(i, d) \ do { \ if (is_little_endian()) \ GET_HIGH_WORD_L(i, d); \ else \ GET_HIGH_WORD_B(i, d); \ } while (0) #define SET_HIGH_WORD(d, v) \ do { \ if (is_little_endian()) \ SET_HIGH_WORD_L(d, v); \ else \ SET_HIGH_WORD_B(d, v); \ } while (0) #define GET_LOW_WORD(d, v) \ do { \ if (is_little_endian()) \ GET_LOW_WORD_L(d, v); \ else \ GET_LOW_WORD_B(d, v); \ } while (0) #define SET_LOW_WORD(d, v) \ do { \ if (is_little_endian()) \ SET_LOW_WORD_L(d, v); \ else \ SET_LOW_WORD_B(d, v); \ } while (0) #define __HI(x) (is_little_endian() ? __HIL(x) : __HIB(x)) #define __LO(x) (is_little_endian() ? __LOL(x) : __LOB(x)) /* * Attempt to get strict C99 semantics for assignment with non-C99 compilers. */ #if FLT_EVAL_METHOD == 0 || __GNUC__ == 0 #define STRICT_ASSIGN(type, lval, rval) ((lval) = (rval)) #else #define STRICT_ASSIGN(type, lval, rval) \ do { \ volatile type __lval; \ \ if (sizeof(type) >= sizeof(long double)) \ (lval) = (rval); \ else { \ __lval = (rval); \ (lval) = __lval; \ } \ } while (0) #endif #ifdef __FDLIBM_STDC__ static const double huge = 1.0e300; #else static double huge = 1.0e300; #endif #ifdef __STDC__ static const double #else static double #endif tiny = 1.0e-300; #ifdef __STDC__ static const double #else static double #endif one = 1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */ #ifdef __STDC__ static const double #else static double #endif TWO52[2] = { 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ }; #ifdef __STDC__ static const double #else static double #endif atanhi[] = { 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */ 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */ 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */ }; #ifdef __STDC__ static const double #else static double #endif atanlo[] = { 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */ 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */ }; #ifdef __STDC__ static const double #else static double #endif aT[] = { 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */ -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */ 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */ -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */ 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */ -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */ 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */ -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ }; #ifdef __STDC__ static const double #else static double #endif zero = 0.0, pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ #ifdef __STDC__ static const double #else static double #endif bp[] = {1.0, 1.5,}, dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ two = 2.0, two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */ two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */ lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */ lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */ ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */ cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */ cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */ cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/ ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */ ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/ ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ static double freebsd_floor(double x); static double freebsd_ceil(double x); static double freebsd_fabs(double x); static double freebsd_rint(double x); static int freebsd_isnan(double x); static double freebsd_atan(double x); static double freebsd_atan2(double y, double x); static double freebsd_atan(double x) { double w, s1, s2, z; int32_t ix, hx, id; GET_HIGH_WORD(hx, x); ix = hx & 0x7fffffff; if (ix >= 0x44100000) { /* if |x| >= 2^66 */ u_int32_t low; GET_LOW_WORD(low, x); if (ix > 0x7ff00000 || (ix == 0x7ff00000 && (low != 0))) return x + x; /* NaN */ if (hx > 0) return atanhi[3] + *(volatile double *)&atanlo[3]; else return -atanhi[3] - *(volatile double *)&atanlo[3]; } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ if (ix < 0x3e400000) { /* |x| < 2^-27 */ if (huge + x > one) return x; /* raise inexact */ } id = -1; } else { x = freebsd_fabs(x); if (ix < 0x3ff30000) { /* |x| < 1.1875 */ if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */ id = 0; x = (2.0 * x - one) / (2.0 + x); } else { /* 11/16<=|x|< 19/16 */ id = 1; x = (x - one) / (x + one); } } else { if (ix < 0x40038000) { /* |x| < 2.4375 */ id = 2; x = (x - 1.5) / (one + 1.5 * x); } else { /* 2.4375 <= |x| < 2^66 */ id = 3; x = -1.0 / x; } } } /* end of argument reduction */ z = x * x; w = z * z; /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ s1 = z * (aT[0] + w * (aT[2] + w * (aT[4] + w * (aT[6] + w * (aT[8] + w * aT[10]))))); s2 = w * (aT[1] + w * (aT[3] + w * (aT[5] + w * (aT[7] + w * aT[9])))); if (id < 0) return x - x * (s1 + s2); else { z = atanhi[id] - ((x * (s1 + s2) - atanlo[id]) - x); return (hx < 0) ? -z : z; } } static double freebsd_atan2(double y, double x) { double z; int32_t k, m, hx, hy, ix, iy; u_int32_t lx, ly; EXTRACT_WORDS(hx, lx, x); ix = hx & 0x7fffffff; EXTRACT_WORDS(hy, ly, y); iy = hy & 0x7fffffff; if (((ix | ((lx | -lx) >> 31)) > 0x7ff00000) || ((iy | ((ly | -ly) >> 31)) > 0x7ff00000)) /* x or y is NaN */ return x + y; if (hx == 0x3ff00000 && lx == 0) return freebsd_atan(y); /* x=1.0 */ m = ((hy >> 31) & 1) | ((hx >> 30) & 2); /* 2*sign(x)+sign(y) */ /* when y = 0 */ if ((iy | ly) == 0) { switch (m) { case 0: case 1: return y; /* atan(+-0,+anything)=+-0 */ case 2: return pi + tiny; /* atan(+0,-anything) = pi */ case 3: default: return -pi - tiny; /* atan(-0,-anything) =-pi */ } } /* when x = 0 */ if ((ix | lx) == 0) return (hy < 0) ? -pi_o_2 - tiny : pi_o_2 + tiny; /* when x is INF */ if (ix == 0x7ff00000) { if (iy == 0x7ff00000) { switch (m) { case 0: return pi_o_4 + tiny; /* atan(+INF,+INF) */ case 1: return -pi_o_4 - tiny; /* atan(-INF,+INF) */ case 2: return 3.0 * pi_o_4 + tiny; /*atan(+INF,-INF)*/ case 3: default: return -3.0 * pi_o_4 - tiny; /*atan(-INF,-INF)*/ } } else { switch (m) { case 0: return zero; /* atan(+...,+INF) */ case 1: return -zero; /* atan(-...,+INF) */ case 2: return pi + tiny; /* atan(+...,-INF) */ case 3: default: return -pi - tiny; /* atan(-...,-INF) */ } } } /* when y is INF */ if (iy == 0x7ff00000) return (hy < 0) ? -pi_o_2 - tiny : pi_o_2 + tiny; /* compute y/x */ k = (iy - ix) >> 20; if (k > 60) { /* |y/x| > 2**60 */ z = pi_o_2 + 0.5 * pi_lo; m &= 1; } else if (hx < 0 && k < -60) z = 0.0; /* 0 > |y|/x > -2**-60 */ else z = freebsd_atan(fabs(y / x)); /* safe to do y/x */ switch (m) { case 0: return z; /* atan(+,+) */ case 1: return -z; /* atan(-,+) */ case 2: return pi - (z - pi_lo); /* atan(+,-) */ default: /* case 3 */ return (z - pi_lo) - pi; /* atan(-,-) */ } } #ifndef BH_HAS_SQRTF static float freebsd_sqrtf(float x) { float z; int32_t sign = (int)0x80000000; int32_t ix, s, q, m, t, i; u_int32_t r; GET_FLOAT_WORD(ix, x); /* take care of Inf and NaN */ if ((ix & 0x7f800000) == 0x7f800000) { return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf sqrt(-inf)=sNaN */ } /* take care of zero */ if (ix <= 0) { if ((ix & (~sign)) == 0) return x; /* sqrt(+-0) = +-0 */ else if (ix < 0) return (x - x) / (x - x); /* sqrt(-ve) = sNaN */ } /* normalize x */ m = (ix >> 23); if (m == 0) { /* subnormal x */ for (i = 0; (ix & 0x00800000) == 0; i++) ix <<= 1; m -= i - 1; } m -= 127; /* unbias exponent */ ix = (ix & 0x007fffff) | 0x00800000; if (m & 1) /* odd m, double x to make it even */ ix += ix; m >>= 1; /* m = [m/2] */ /* generate sqrt(x) bit by bit */ ix += ix; q = s = 0; /* q = sqrt(x) */ r = 0x01000000; /* r = moving bit from right to left */ while (r != 0) { t = s + r; if (t <= ix) { s = t + r; ix -= t; q += r; } ix += ix; r >>= 1; } /* use floating add to find out rounding direction */ if (ix != 0) { z = one - tiny; /* trigger inexact flag */ if (z >= one) { z = one + tiny; if (z > one) q += 2; else q += (q & 1); } } ix = (q >> 1) + 0x3f000000; ix += (m << 23); SET_FLOAT_WORD(z, ix); return z; } #endif /* end of BH_HAS_SQRTF */ #ifndef BH_HAS_SQRT static double freebsd_sqrt(double x) /* wrapper sqrt */ { double z; int32_t sign = (int)0x80000000; int32_t ix0, s0, q, m, t, i; u_int32_t r, t1, s1, ix1, q1; EXTRACT_WORDS(ix0, ix1, x); /* take care of Inf and NaN */ if ((ix0 & 0x7ff00000) == 0x7ff00000) { return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf sqrt(-inf)=sNaN */ } /* take care of zero */ if (ix0 <= 0) { if (((ix0 & (~sign)) | ix1) == 0) return x; /* sqrt(+-0) = +-0 */ else if (ix0 < 0) return (x - x) / (x - x); /* sqrt(-ve) = sNaN */ } /* normalize x */ m = (ix0 >> 20); if (m == 0) { /* subnormal x */ while (ix0 == 0) { m -= 21; ix0 |= (ix1 >> 11); ix1 <<= 21; } for (i = 0; (ix0 & 0x00100000) == 0; i++) ix0 <<= 1; m -= i - 1; ix0 |= (ix1 >> (32 - i)); ix1 <<= i; } m -= 1023; /* unbias exponent */ ix0 = (ix0 & 0x000fffff) | 0x00100000; if (m & 1) { /* odd m, double x to make it even */ ix0 += ix0 + ((ix1 & sign) >> 31); ix1 += ix1; } m >>= 1; /* m = [m/2] */ /* generate sqrt(x) bit by bit */ ix0 += ix0 + ((ix1 & sign) >> 31); ix1 += ix1; q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */ r = 0x00200000; /* r = moving bit from right to left */ while (r != 0) { t = s0 + r; if (t <= ix0) { s0 = t + r; ix0 -= t; q += r; } ix0 += ix0 + ((ix1 & sign) >> 31); ix1 += ix1; r >>= 1; } r = sign; while (r != 0) { t1 = s1 + r; t = s0; if ((t < ix0) || ((t == ix0) && (t1 <= ix1))) { s1 = t1 + r; if (((t1 & sign) == sign) && (s1 & sign) == 0) s0 += 1; ix0 -= t; if (ix1 < t1) ix0 -= 1; ix1 -= t1; q1 += r; } ix0 += ix0 + ((ix1 & sign) >> 31); ix1 += ix1; r >>= 1; } /* use floating add to find out rounding direction */ if ((ix0 | ix1) != 0) { z = one - tiny; /* trigger inexact flag */ if (z >= one) { z = one + tiny; if (q1 == (u_int32_t)0xffffffff) { q1 = 0; q += 1; } else if (z > one) { if (q1 == (u_int32_t)0xfffffffe) q += 1; q1 += 2; } else q1 += (q1 & 1); } } ix0 = (q >> 1) + 0x3fe00000; ix1 = q1 >> 1; if ((q & 1) == 1) ix1 |= sign; ix0 += (m << 20); INSERT_WORDS(z, ix0, ix1); return z; } #endif /* end of BH_HAS_SQRT */ static double freebsd_floor(double x) { int32_t i0, i1, j0; u_int32_t i, j; EXTRACT_WORDS(i0, i1, x); j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; if (j0 < 20) { if (j0 < 0) { /* raise inexact if x != 0 */ if (huge + x > 0.0) { /* return 0*sign(x) if |x|<1 */ if (i0 >= 0) { i0 = i1 = 0; } else if (((i0 & 0x7fffffff) | i1) != 0) { i0 = 0xbff00000; i1 = 0; } } } else { i = (0x000fffff) >> j0; if (((i0 & i) | i1) == 0) return x; /* x is integral */ if (huge + x > 0.0) { /* raise inexact flag */ if (i0 < 0) i0 += (0x00100000) >> j0; i0 &= (~i); i1 = 0; } } } else if (j0 > 51) { if (j0 == 0x400) return x + x; /* inf or NaN */ else return x; /* x is integral */ } else { i = ((u_int32_t)(0xffffffff)) >> (j0 - 20); if ((i1 & i) == 0) return x; /* x is integral */ if (huge + x > 0.0) { /* raise inexact flag */ if (i0 < 0) { if (j0 == 20) i0 += 1; else { j = i1 + (1 << (52 - j0)); if (j < i1) i0 += 1; /* got a carry */ i1 = j; } } i1 &= (~i); } } INSERT_WORDS(x, i0, i1); return x; } static double freebsd_ceil(double x) { int32_t i0, i1, j0; u_int32_t i, j; EXTRACT_WORDS(i0, i1, x); j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; if (j0 < 20) { if (j0 < 0) { /* raise inexact if x != 0 */ if (huge + x > 0.0) { /* return 0*sign(x) if |x|<1 */ if (i0 < 0) { i0 = 0x80000000; i1 = 0; } else if ((i0 | i1) != 0) { i0 = 0x3ff00000; i1 = 0; } } } else { i = (0x000fffff) >> j0; if (((i0 & i) | i1) == 0) return x; /* x is integral */ if (huge + x > 0.0) { /* raise inexact flag */ if (i0 > 0) i0 += (0x00100000) >> j0; i0 &= (~i); i1 = 0; } } } else if (j0 > 51) { if (j0 == 0x400) return x + x; /* inf or NaN */ else return x; /* x is integral */ } else { i = ((u_int32_t)(0xffffffff)) >> (j0 - 20); if ((i1 & i) == 0) return x; /* x is integral */ if (huge + x > 0.0) { /* raise inexact flag */ if (i0 > 0) { if (j0 == 20) i0 += 1; else { j = i1 + (1 << (52 - j0)); if (j < i1) i0 += 1; /* got a carry */ i1 = j; } } i1 &= (~i); } } INSERT_WORDS(x, i0, i1); return x; } static double freebsd_rint(double x) { int32_t i0, j0, sx; u_int32_t i, i1; double w, t; EXTRACT_WORDS(i0, i1, x); sx = (i0 >> 31) & 1; j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; if (j0 < 20) { if (j0 < 0) { if (((i0 & 0x7fffffff) | i1) == 0) return x; i1 |= (i0 & 0x0fffff); i0 &= 0xfffe0000; i0 |= ((i1 | -i1) >> 12) & 0x80000; SET_HIGH_WORD(x, i0); STRICT_ASSIGN(double, w, TWO52[sx] + x); t = w - TWO52[sx]; GET_HIGH_WORD(i0, t); SET_HIGH_WORD(t, (i0 & 0x7fffffff) | (sx << 31)); return t; } else { i = (0x000fffff) >> j0; if (((i0 & i) | i1) == 0) return x; /* x is integral */ i >>= 1; if (((i0 & i) | i1) != 0) { /* * Some bit is set after the 0.5 bit. To avoid the * possibility of errors from double rounding in * w = TWO52[sx]+x, adjust the 0.25 bit to a lower * guard bit. We do this for all j0<=51. The * adjustment is trickiest for j0==18 and j0==19 * since then it spans the word boundary. */ if (j0 == 19) i1 = 0x40000000; else if (j0 == 18) i1 = 0x80000000; else i0 = (i0 & (~i)) | ((0x20000) >> j0); } } } else if (j0 > 51) { if (j0 == 0x400) return x + x; /* inf or NaN */ else return x; /* x is integral */ } else { i = ((u_int32_t)(0xffffffff)) >> (j0 - 20); if ((i1 & i) == 0) return x; /* x is integral */ i >>= 1; if ((i1 & i) != 0) i1 = (i1 & (~i)) | ((0x40000000) >> (j0 - 20)); } INSERT_WORDS(x, i0, i1); STRICT_ASSIGN(double, w, TWO52[sx] + x); return w - TWO52[sx]; } static int freebsd_isnan(double d) { if (is_little_endian()) { IEEEd2bits_L u; u.d = d; return (u.bits.exp == 2047 && (u.bits.manl != 0 || u.bits.manh != 0)); } else { IEEEd2bits_B u; u.d = d; return (u.bits.exp == 2047 && (u.bits.manl != 0 || u.bits.manh != 0)); } } static float freebsd_fabsf(float x) { u_int32_t ix; GET_FLOAT_WORD(ix, x); SET_FLOAT_WORD(x, ix & 0x7fffffff); return x; } static double freebsd_fabs(double x) { u_int32_t high; GET_HIGH_WORD(high, x); SET_HIGH_WORD(x, high & 0x7fffffff); return x; } static const float huge_f = 1.0e30F; static const float TWO23[2] = { 8.3886080000e+06, /* 0x4b000000 */ -8.3886080000e+06, /* 0xcb000000 */ }; static float freebsd_truncf(float x) { int32_t i0, j0; u_int32_t i; GET_FLOAT_WORD(i0, x); j0 = ((i0 >> 23) & 0xff) - 0x7f; if (j0 < 23) { if (j0 < 0) { /* raise inexact if x != 0 */ if (huge_f + x > 0.0F) /* |x|<1, so return 0*sign(x) */ i0 &= 0x80000000; } else { i = (0x007fffff) >> j0; if ((i0 & i) == 0) return x; /* x is integral */ if (huge_f + x > 0.0F) /* raise inexact flag */ i0 &= (~i); } } else { if (j0 == 0x80) return x + x; /* inf or NaN */ else return x; /* x is integral */ } SET_FLOAT_WORD(x, i0); return x; } static float freebsd_rintf(float x) { int32_t i0, j0, sx; float w, t; GET_FLOAT_WORD(i0, x); sx = (i0 >> 31) & 1; j0 = ((i0 >> 23) & 0xff) - 0x7f; if (j0 < 23) { if (j0 < 0) { if ((i0 & 0x7fffffff) == 0) return x; STRICT_ASSIGN(float, w, TWO23[sx] + x); t = w - TWO23[sx]; GET_FLOAT_WORD(i0, t); SET_FLOAT_WORD(t, (i0 & 0x7fffffff) | (sx << 31)); return t; } STRICT_ASSIGN(float, w, TWO23[sx] + x); return w - TWO23[sx]; } if (j0 == 0x80) return x + x; /* inf or NaN */ else return x; /* x is integral */ } static float freebsd_ceilf(float x) { int32_t i0, j0; u_int32_t i; GET_FLOAT_WORD(i0, x); j0 = ((i0 >> 23) & 0xff) - 0x7f; if (j0 < 23) { if (j0 < 0) { /* raise inexact if x != 0 */ if (huge_f + x > (float)0.0) { /* return 0*sign(x) if |x|<1 */ if (i0 < 0) { i0 = 0x80000000; } else if (i0 != 0) { i0 = 0x3f800000; } } } else { i = (0x007fffff) >> j0; if ((i0 & i) == 0) return x; /* x is integral */ if (huge_f + x > (float)0.0) { /* raise inexact flag */ if (i0 > 0) i0 += (0x00800000) >> j0; i0 &= (~i); } } } else { if (j0 == 0x80) return x + x; /* inf or NaN */ else return x; /* x is integral */ } SET_FLOAT_WORD(x, i0); return x; } static float freebsd_floorf(float x) { int32_t i0, j0; u_int32_t i; GET_FLOAT_WORD(i0, x); j0 = ((i0 >> 23) & 0xff) - 0x7f; if (j0 < 23) { if (j0 < 0) { /* raise inexact if x != 0 */ if (huge_f + x > (float)0.0) { /* return 0*sign(x) if |x|<1 */ if (i0 >= 0) { i0 = 0; } else if ((i0 & 0x7fffffff) != 0) { i0 = 0xbf800000; } } } else { i = (0x007fffff) >> j0; if ((i0 & i) == 0) return x; /* x is integral */ if (huge_f + x > (float)0.0) { /* raise inexact flag */ if (i0 < 0) i0 += (0x00800000) >> j0; i0 &= (~i); } } } else { if (j0 == 0x80) return x + x; /* inf or NaN */ else return x; /* x is integral */ } SET_FLOAT_WORD(x, i0); return x; } static float freebsd_fminf(float x, float y) { if (is_little_endian()) { IEEEf2bits_L u[2] = { 0 }; u[0].f = x; u[1].f = y; /* Check for NaNs to avoid raising spurious exceptions. */ if (u[0].bits.exp == 255 && u[0].bits.man != 0) return (y); if (u[1].bits.exp == 255 && u[1].bits.man != 0) return (x); /* Handle comparisons of signed zeroes. */ if (u[0].bits.sign != u[1].bits.sign) return (u[u[1].bits.sign].f); } else { IEEEf2bits_B u[2] = { 0 }; u[0].f = x; u[1].f = y; /* Check for NaNs to avoid raising spurious exceptions. */ if (u[0].bits.exp == 255 && u[0].bits.man != 0) return (y); if (u[1].bits.exp == 255 && u[1].bits.man != 0) return (x); /* Handle comparisons of signed zeroes. */ if (u[0].bits.sign != u[1].bits.sign) return (u[u[1].bits.sign].f); } return (x < y ? x : y); } static float freebsd_fmaxf(float x, float y) { if (is_little_endian()) { IEEEf2bits_L u[2] = { 0 }; u[0].f = x; u[1].f = y; /* Check for NaNs to avoid raising spurious exceptions. */ if (u[0].bits.exp == 255 && u[0].bits.man != 0) return (y); if (u[1].bits.exp == 255 && u[1].bits.man != 0) return (x); /* Handle comparisons of signed zeroes. */ if (u[0].bits.sign != u[1].bits.sign) return (u[u[0].bits.sign].f); } else { IEEEf2bits_B u[2] = { 0 }; u[0].f = x; u[1].f = y; /* Check for NaNs to avoid raising spurious exceptions. */ if (u[0].bits.exp == 255 && u[0].bits.man != 0) return (y); if (u[1].bits.exp == 255 && u[1].bits.man != 0) return (x); /* Handle comparisons of signed zeroes. */ if (u[0].bits.sign != u[1].bits.sign) return (u[u[0].bits.sign].f); } return (x > y ? x : y); } static double freebsd_copysign(double x, double y) { u_int32_t hx, hy; GET_HIGH_WORD(hx, x); GET_HIGH_WORD(hy, y); SET_HIGH_WORD(x, (hx & 0x7fffffff) | (hy & 0x80000000)); return x; } static double freebsd_scalbn(double x, int n) { int32_t k, hx, lx; EXTRACT_WORDS(hx, lx, x); k = (hx & 0x7ff00000) >> 20; /* extract exponent */ if (k == 0) { /* 0 or subnormal x */ if ((lx | (hx & 0x7fffffff)) == 0) return x; /* +-0 */ x *= two54; GET_HIGH_WORD(hx, x); k = ((hx & 0x7ff00000) >> 20) - 54; if (n < -50000) return tiny * x; /*underflow*/ } if (k == 0x7ff) return x + x; /* NaN or Inf */ k = k + n; if (k > 0x7fe) return huge * freebsd_copysign(huge, x); /* overflow */ if (k > 0) /* normal result */ { SET_HIGH_WORD(x, (hx & 0x800fffff) | (k << 20)); return x; } if (k <= -54) { if (n > 50000) /* in case integer overflow in n+k */ return huge * freebsd_copysign(huge, x); /*overflow*/ else return tiny * freebsd_copysign(tiny, x); /*underflow*/ } k += 54; /* subnormal result */ SET_HIGH_WORD(x, (hx & 0x800fffff) | (k << 20)); return x * twom54; } static double freebsd_pow(double x, double y) { double z, ax, z_h, z_l, p_h, p_l; double y1, t1, t2, r, s, t, u, v, w; int32_t i, j, k, yisint, n; int32_t hx, hy, ix, iy; u_int32_t lx, ly; EXTRACT_WORDS(hx, lx, x); EXTRACT_WORDS(hy, ly, y); ix = hx & 0x7fffffff; iy = hy & 0x7fffffff; /* y==zero: x**0 = 1 */ if ((iy | ly) == 0) return one; /* x==1: 1**y = 1, even if y is NaN */ if (hx == 0x3ff00000 && lx == 0) return one; /* y!=zero: result is NaN if either arg is NaN */ if (ix > 0x7ff00000 || ((ix == 0x7ff00000) && (lx != 0)) || iy > 0x7ff00000 || ((iy == 0x7ff00000) && (ly != 0))) return (x + 0.0) + (y + 0.0); /* determine if y is an odd int when x < 0 * yisint = 0 ... y is not an integer * yisint = 1 ... y is an odd int * yisint = 2 ... y is an even int */ yisint = 0; if (hx < 0) { if (iy >= 0x43400000) yisint = 2; /* even integer y */ else if (iy >= 0x3ff00000) { k = (iy >> 20) - 0x3ff; /* exponent */ if (k > 20) { j = ly >> (52 - k); if ((j << (52 - k)) == ly) yisint = 2 - (j & 1); } else if (ly == 0) { j = iy >> (20 - k); if ((j << (20 - k)) == iy) yisint = 2 - (j & 1); } } } /* special value of y */ if (ly == 0) { if (iy == 0x7ff00000) { /* y is +-inf */ if (((ix - 0x3ff00000) | lx) == 0) return one; /* (-1)**+-inf is NaN */ else if (ix >= 0x3ff00000) /* (|x|>1)**+-inf = inf,0 */ return (hy >= 0) ? y : zero; else /* (|x|<1)**-,+inf = inf,0 */ return (hy < 0) ? -y : zero; } if (iy == 0x3ff00000) { /* y is +-1 */ if (hy < 0) return one / x; else return x; } if (hy == 0x40000000) return x * x; /* y is 2 */ if (hy == 0x40080000) return x * x * x; /* y is 3 */ if (hy == 0x40100000) { /* y is 4 */ u = x * x; return u * u; } if (hy == 0x3fe00000) { /* y is 0.5 */ if (hx >= 0) /* x >= +0 */ return sqrt(x); } } ax = fabs(x); /* special value of x */ if (lx == 0) { if (ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000) { z = ax; /*x is +-0,+-inf,+-1*/ if (hy < 0) z = one / z; /* z = (1/|x|) */ if (hx < 0) { if (((ix - 0x3ff00000) | yisint) == 0) { z = (z - z) / (z - z); /* (-1)**non-int is NaN */ } else if (yisint == 1) z = -z; /* (x<0)**odd = -(|x|**odd) */ } return z; } } /* CYGNUS LOCAL + fdlibm-5.3 fix: This used to be n = (hx>>31)+1; but ANSI C says a right shift of a signed negative quantity is implementation defined. */ n = ((u_int32_t)hx >> 31) - 1; /* (x<0)**(non-int) is NaN */ if ((n | yisint) == 0) return (x - x) / (x - x); s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ if ((n | (yisint - 1)) == 0) s = -one; /* (-ve)**(odd int) */ /* |y| is huge */ if (iy > 0x41e00000) { /* if |y| > 2**31 */ if (iy > 0x43f00000) { /* if |y| > 2**64, must o/uflow */ if (ix <= 0x3fefffff) return (hy < 0) ? huge * huge : tiny * tiny; if (ix >= 0x3ff00000) return (hy > 0) ? huge * huge : tiny * tiny; } /* over/underflow if x is not close to one */ if (ix < 0x3fefffff) return (hy < 0) ? s * huge * huge : s * tiny * tiny; if (ix > 0x3ff00000) return (hy > 0) ? s * huge * huge : s * tiny * tiny; /* now |1-x| is tiny <= 2**-20, suffice to compute log(x) by x-x^2/2+x^3/3-x^4/4 */ t = ax - one; /* t has 20 trailing zeros */ w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25)); u = ivln2_h * t; /* ivln2_h has 21 sig. bits */ v = t * ivln2_l - w * ivln2; t1 = u + v; SET_LOW_WORD(t1, 0); t2 = v - (t1 - u); } else { double ss, s2, s_h, s_l, t_h, t_l; n = 0; /* take care subnormal number */ if (ix < 0x00100000) { ax *= two53; n -= 53; GET_HIGH_WORD(ix, ax); } n += ((ix) >> 20) - 0x3ff; j = ix & 0x000fffff; /* determine interval */ ix = j | 0x3ff00000; /* normalize ix */ if (j <= 0x3988E) k = 0; /* |x|> 1) | 0x20000000) + 0x00080000 + (k << 18)); t_l = ax - (t_h - bp[k]); s_l = v * ((u - s_h * t_h) - s_h * t_l); /* compute log(ax) */ s2 = ss * ss; r = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6))))); r += s_l * (s_h + ss); s2 = s_h * s_h; t_h = 3.0 + s2 + r; SET_LOW_WORD(t_h, 0); t_l = r - ((t_h - 3.0) - s2); /* u+v = ss*(1+...) */ u = s_h * t_h; v = s_l * t_h + t_l * ss; /* 2/(3log2)*(ss+...) */ p_h = u + v; SET_LOW_WORD(p_h, 0); p_l = v - (p_h - u); z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */ z_l = cp_l * p_h + p_l * cp + dp_l[k]; /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */ t = (double)n; t1 = (((z_h + z_l) + dp_h[k]) + t); SET_LOW_WORD(t1, 0); t2 = z_l - (((t1 - t) - dp_h[k]) - z_h); } /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ y1 = y; SET_LOW_WORD(y1, 0); p_l = (y - y1) * t1 + y * t2; p_h = y1 * t1; z = p_l + p_h; EXTRACT_WORDS(j, i, z); if (j >= 0x40900000) { /* z >= 1024 */ if (((j - 0x40900000) | i) != 0) /* if z > 1024 */ return s * huge * huge; /* overflow */ else { if (p_l + ovt > z - p_h) return s * huge * huge; /* overflow */ } } else if ((j & 0x7fffffff) >= 0x4090cc00) { /* z <= -1075 */ if (((j - 0xc090cc00) | i) != 0) /* z < -1075 */ return s * tiny * tiny; /* underflow */ else { if (p_l <= z - p_h) return s * tiny * tiny; /* underflow */ } } /* * compute 2**(p_h+p_l) */ i = j & 0x7fffffff; k = (i >> 20) - 0x3ff; n = 0; if (i > 0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ n = j + (0x00100000 >> (k + 1)); k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */ t = zero; SET_HIGH_WORD(t, n & ~(0x000fffff >> k)); n = ((n & 0x000fffff) | 0x00100000) >> (20 - k); if (j < 0) n = -n; p_h -= t; } t = p_l + p_h; SET_LOW_WORD(t, 0); u = t * lg2_h; v = (p_l - (t - p_h)) * lg2 + t * lg2_l; z = u + v; w = v - (z - u); t = z * z; t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5)))); r = (z * t1) / (t1 - two) - (w + z * w); z = one - (r - z); GET_HIGH_WORD(j, z); j += (n << 20); if ((j >> 20) <= 0) z = freebsd_scalbn(z, n); /* subnormal output */ else SET_HIGH_WORD(z, j); return s * z; } double atan(double x) { return freebsd_atan(x); } double atan2(double y, double x) { return freebsd_atan2(y, x); } #ifndef BH_HAS_SQRT double sqrt(double x) { return freebsd_sqrt(x); } #endif double floor(double x) { return freebsd_floor(x); } double ceil(double x) { return freebsd_ceil(x); } double fmin(double x, double y) { return x < y ? x : y; } double fmax(double x, double y) { return x > y ? x : y; } double rint(double x) { return freebsd_rint(x); } double fabs(double x) { return freebsd_fabs(x); } int isnan(double x) { return freebsd_isnan(x); } double trunc(double x) { return (x > 0) ? freebsd_floor(x) : freebsd_ceil(x); } int signbit(double x) { return ((__HI(x) & 0x80000000) >> 31); } float fabsf(float x) { return freebsd_fabsf(x); } float truncf(float x) { return freebsd_truncf(x); } float rintf(float x) { return freebsd_rintf(x); } float ceilf(float x) { return freebsd_ceilf(x); } float floorf(float x) { return freebsd_floorf(x); } float fminf(float x, float y) { return freebsd_fminf(x, y); } float fmaxf(float x, float y) { return freebsd_fmaxf(x, y); } #ifndef BH_HAS_SQRTF float sqrtf(float x) { return freebsd_sqrtf(x); } #endif double pow(double x, double y) { return freebsd_pow(x, y); } double scalbn(double x, int n) { return freebsd_scalbn(x, n); }