/* ceilf() * floorf() * frexpf() * ldexpf() * signbitf() * isnanf() * isfinitef() * * Single precision floating point numeric utilities * * * * SYNOPSIS: * * float x, y; * float ceilf(), floorf(), frexpf(), ldexpf(); * int signbit(), isnan(), isfinite(); * int expnt, n; * * y = floorf(x); * y = ceilf(x); * y = frexpf( x, &expnt ); * y = ldexpf( x, n ); * n = signbit(x); * n = isnan(x); * n = isfinite(x); * * * * DESCRIPTION: * * All four routines return a single precision floating point * result. * * sfloor() returns the largest integer less than or equal to x. * It truncates toward minus infinity. * * sceil() returns the smallest integer greater than or equal * to x. It truncates toward plus infinity. * * sfrexp() extracts the exponent from x. It returns an integer * power of two to expnt and the significand between 0.5 and 1 * to y. Thus x = y * 2**expn. * * ldexpf() multiplies x by 2**n. * * signbit(x) returns 1 if the sign bit of x is 1, else 0. * * These functions are part of the standard C run time library * for many but not all C compilers. The ones supplied are * written in C for either DEC or IEEE arithmetic. They should * be used only if your compiler library does not already have * them. * * The IEEE versions assume that denormal numbers are implemented * in the arithmetic. Some modifications will be required if * the arithmetic has abrupt rather than gradual underflow. */ /* Cephes Math Library Release 2.1: December, 1988 Copyright 1984, 1987, 1988 by Stephen L. Moshier Direct inquiries to 30 Frost Street, Cambridge, MA 02140 */ #include #ifdef DEC #undef DENORMAL #define DENORMAL 0 #endif #ifdef UNK #undef UNK #if BIGENDIAN #define MIEEE 1 #else #define IBMPC 1 #endif /* char *unkmsg = "ceil(), floor(), frexp(), ldexp() must be rewritten!\n"; */ #endif #define EXPMSK 0x807f #define MEXP 255 #define NBITS 24 extern float MAXNUMF; /* (2^24 - 1) * 2^103 */ #ifdef ANSIC float floorf(float); #else float floorf(); #endif float ceilf( float x ) { float y; #ifdef UNK printf( "%s\n", unkmsg ); return(0.0); #endif y = floorf( (float )x ); if( y < x ) y += 1.0; return(y); } /* Bit clearing masks: */ static unsigned short bmask[] = { 0xffff, 0xfffe, 0xfffc, 0xfff8, 0xfff0, 0xffe0, 0xffc0, 0xff80, 0xff00, 0xfe00, 0xfc00, 0xf800, 0xf000, 0xe000, 0xc000, 0x8000, 0x0000, }; float floorf( float x ) { unsigned short *p; union { float y; unsigned short i[2]; } u; int e; #ifdef UNK printf( "%s\n", unkmsg ); return(0.0); #endif u.y = x; /* find the exponent (power of 2) */ #ifdef DEC p = &u.i[0]; e = (( *p >> 7) & 0377) - 0201; p += 3; #endif #ifdef IBMPC p = &u.i[1]; e = (( *p >> 7) & 0xff) - 0x7f; p -= 1; #endif #ifdef MIEEE p = &u.i[0]; e = (( *p >> 7) & 0xff) - 0x7f; p += 1; #endif if( e < 0 ) { if( u.y < 0 ) return( -1.0 ); else return( 0.0 ); } e = (NBITS -1) - e; /* clean out 16 bits at a time */ while( e >= 16 ) { #ifdef IBMPC *p++ = 0; #endif #ifdef DEC *p-- = 0; #endif #ifdef MIEEE *p-- = 0; #endif e -= 16; } /* clear the remaining bits */ if( e > 0 ) *p &= bmask[e]; if( (x < 0) && (u.y != x) ) u.y -= 1.0; return(u.y); } float frexpf( float x, int *pw2 ) { union { float y; unsigned short i[2]; } u; int i, k; short *q; u.y = x; #ifdef UNK printf( "%s\n", unkmsg ); return(0.0); #endif #ifdef IBMPC q = &u.i[1]; #endif #ifdef DEC q = &u.i[0]; #endif #ifdef MIEEE q = &u.i[0]; #endif /* find the exponent (power of 2) */ i = ( *q >> 7) & 0xff; if( i == 0 ) { if( u.y == 0.0 ) { *pw2 = 0; return(0.0); } /* Number is denormal or zero */ #if DENORMAL /* Handle denormal number. */ do { u.y *= 2.0; i -= 1; k = ( *q >> 7) & 0xff; } while( k == 0 ); i = i + k; #else *pw2 = 0; return( 0.0 ); #endif /* DENORMAL */ } i -= 0x7e; *pw2 = i; *q &= 0x807f; /* strip all exponent bits */ *q |= 0x3f00; /* mantissa between 0.5 and 1 */ return( u.y ); } float ldexpf( float x, int pw2 ) { union { float y; unsigned short i[2]; } u; short *q; int e; #ifdef UNK printf( "%s\n", unkmsg ); return(0.0); #endif u.y = x; #ifdef DEC q = &u.i[0]; #endif #ifdef IBMPC q = &u.i[1]; #endif #ifdef MIEEE q = &u.i[0]; #endif while( (e = ( *q >> 7) & 0xff) == 0 ) { if( u.y == (float )0.0 ) { return( 0.0 ); } /* Input is denormal. */ if( pw2 > 0 ) { u.y *= 2.0; pw2 -= 1; } if( pw2 < 0 ) { if( pw2 < -24 ) return( 0.0 ); u.y *= 0.5; pw2 += 1; } if( pw2 == 0 ) return(u.y); } e += pw2; /* Handle overflow */ if( e > MEXP ) { return( MAXNUMF ); } *q &= 0x807f; /* Handle denormalized results */ if( e < 1 ) { #if DENORMAL if( e < -24 ) return( 0.0 ); *q |= 0x80; /* Set LSB of exponent. */ /* For denormals, significant bits may be lost even when dividing by 2. Construct 2^-(1-e) so the result is obtained with only one multiplication. */ u.y *= ldexpf(1.0f, e - 1); return(u.y); #else return( 0.0 ); #endif } *q |= (e & 0xff) << 7; return(u.y); } /* Return 1 if the sign bit of x is 1, else 0. */ int signbitf(x) float x; { union { float f; short s[4]; int i; } u; u.f = x; if( sizeof(int) == 4 ) { #ifdef IBMPC return( u.i < 0 ); #endif #ifdef DEC return( u.s[1] < 0 ); #endif #ifdef MIEEE return( u.i < 0 ); #endif } else { #ifdef IBMPC return( u.s[1] < 0 ); #endif #ifdef DEC return( u.s[1] < 0 ); #endif #ifdef MIEEE return( u.s[0] < 0 ); #endif } } /* Return 1 if x is a number that is Not a Number, else return 0. */ int isnanf(x) float x; { #ifdef NANS union { float f; unsigned short s[2]; unsigned int i; } u; u.f = x; if( sizeof(int) == 4 ) { #ifdef IBMPC if( ((u.i & 0x7f800000) == 0x7f800000) && ((u.i & 0x007fffff) != 0) ) return 1; #endif #ifdef DEC if( (u.s[1] & 0x7f80) == 0) { if( (u.s[1] | u.s[0]) != 0 ) return(1); } #endif #ifdef MIEEE if( ((u.i & 0x7f800000) == 0x7f800000) && ((u.i & 0x007fffff) != 0) ) return 1; #endif return(0); } else { /* size int not 4 */ #ifdef IBMPC if( (u.s[1] & 0x7f80) == 0x7f80) { if( ((u.s[1] & 0x007f) | u.s[0]) != 0 ) return(1); } #endif #ifdef DEC if( (u.s[1] & 0x7f80) == 0) { if( (u.s[1] | u.s[0]) != 0 ) return(1); } #endif #ifdef MIEEE if( (u.s[0] & 0x7f80) == 0x7f80) { if( ((u.s[0] & 0x000f) | u.s[1]) != 0 ) return(1); } #endif return(0); } /* size int not 4 */ #else /* No NANS. */ return(0); #endif } /* Return 1 if x is not infinite and is not a NaN. */ int isfinitef(x) float x; { #ifdef INFINITIES union { float f; unsigned short s[2]; unsigned int i; } u; u.f = x; if( sizeof(int) == 4 ) { #ifdef IBMPC if( (u.i & 0x7f800000) != 0x7f800000) return 1; #endif #ifdef DEC if( (u.s[1] & 0x7f80) == 0) { if( (u.s[1] | u.s[0]) != 0 ) return(1); } #endif #ifdef MIEEE if( (u.i & 0x7f800000) != 0x7f800000) return 1; #endif return(0); } else { #ifdef IBMPC if( (u.s[1] & 0x7f80) != 0x7f80) return 1; #endif #ifdef DEC if( (u.s[1] & 0x7f80) == 0) { if( (u.s[1] | u.s[0]) != 0 ) return(1); } #endif #ifdef MIEEE if( (u.s[0] & 0x7f80) != 0x7f80) return 1; #endif return(0); } #else /* No INFINITY. */ return(1); #endif }