/*- * 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) /* * 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 __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 */ }; static double freebsd_sqrt(double x); 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_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>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; } 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>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>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 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]; 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]; 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]; 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]; 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); } double sqrt(double x) { return freebsd_sqrt(x); } 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 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); }