AbaKus – a complex calculator
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 ``````/* HMath: C++ high precision math routines Copyright (C) 2004 Ariya Hidayat Last update: November 15, 2004 This file was copied from the SpeedCrunch program. Please visit http://speedcrunch.berlios.de/ for more information. This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, write to: The Free Software Foundation, Inc. 51 Franklin Street, Fifth Floor Boston, MA 02110-1301 USA. */ #include "hmath.h" #include "number.h" #include #include #include #include #include // internal number of decimal digits #define HMATH_MAX_PREC 150 // digits used for number comparison // (not all are used, to work around propagated error problem) #define HMATH_COMPARE_PREC 70 // maximum shown digits if prec is negative #define HMATH_MAX_SHOWN 20 // from number.c, need to be freed somehow extern bc_num _zero_; extern bc_num _one_; extern bc_num _two_; class HNumber::Private { public: bc_num num; bool nan; }; void out_of_memory(void){ return; } void rt_warn(char * ,...){ return; } void rt_error(char * ,...){ return; } static bc_num h_create( int len = 1, int scale = 0 ) { bc_num temp; temp = (bc_num) malloc( sizeof(bc_struct) ); temp->n_sign = PLUS; temp->n_len = len; temp->n_scale = scale; temp->n_refs = 1; temp->n_ptr = (char*) malloc( len+scale+1 ); temp->n_value = temp->n_ptr; temp->n_next = 0; memset (temp->n_ptr, 0, len+scale+1); return temp; } static void h_destroy( bc_num n ) { free( n->n_ptr ); free( n ); } // reclaim and free one bc_num from the freelist // workaround for number.c, because it doesn't really free a number // but instead put it in the pool of unused numbers // this function will take it back from that pool and set it really free static void h_grabfree() { bc_num t = bc_new_num( 1, 0 ); h_destroy( t ); } // make an exact (explicit) copy static bc_num h_copy( bc_num n ) { int len = n->n_len; int scale = n->n_scale; bc_num result = h_create( len, scale ); memcpy( result->n_ptr, n->n_value, len+scale+1 ); result->n_sign = n->n_sign; result->n_value = result->n_ptr; h_grabfree(); return result; } // same as copy, but readjust decimal digits static bc_num h_rescale( bc_num n, int sc ) { int len = n->n_len; int scale = MIN( sc, n->n_scale ); bc_num result = h_create( len, scale ); memcpy( result->n_ptr, n->n_value, len+scale+1 ); result->n_sign = n->n_sign; result->n_value = result->n_ptr; h_grabfree(); return result; } // convert simple string to number static bc_num h_str2num( const char* str, int scale = HMATH_MAX_PREC ) { int digits, strscale; const char *ptr; char *nptr; char zero_int; /* Check for valid number and count digits. */ ptr = str; digits = 0; strscale = 0; zero_int = FALSE; if ( (*ptr == '+') || (*ptr == '-')) ptr++; /* Sign */ while (*ptr == '0') ptr++; /* Skip leading zeros. */ while (isdigit((int)*ptr)) ptr++, digits++; /* digits */ if (*ptr == '.') ptr++; /* decimal point */ while (isdigit((int)*ptr)) ptr++, strscale++; /* digits */ if ((*ptr != '\0') || (digits+strscale == 0)) return h_create(); /* Adjust numbers and allocate storage and initialize fields. */ strscale = MIN(strscale, scale); if (digits == 0) { zero_int = TRUE; digits = 1; } bc_num num = h_create( digits, strscale ); ptr = str; if (*ptr == '-') { num->n_sign = MINUS; ptr++; } else { num->n_sign = PLUS; if (*ptr == '+') ptr++; } while (*ptr == '0') ptr++; nptr = num->n_value; if (zero_int) { *nptr++ = 0; digits = 0; } for (;digits > 0; digits--) *nptr++ = (char)CH_VAL(*ptr++); if (strscale > 0) { ptr++; for (;strscale > 0; strscale--) *nptr++ = (char)CH_VAL(*ptr++); } return num; } // add two numbers, return newly allocated number static bc_num h_add( bc_num n1, bc_num n2 ) { bc_num r = h_create(); bc_add( n1, n2, &r, 1 ); h_grabfree(); return r; } // subtract two numbers, return newly allocated number static bc_num h_sub( bc_num n1, bc_num n2 ) { bc_num r = h_create(); bc_sub( n1, n2, &r, 1 ); h_grabfree(); return r; } // multiply two numbers, return newly allocated number static bc_num h_mul( bc_num n1, bc_num n2 ) { bc_num r = h_create(); bc_multiply( n1, n2, &r, HMATH_MAX_PREC ); h_grabfree(); return r; } // divide two numbers, return newly allocated number static bc_num h_div( bc_num n1, bc_num n2 ) { bc_num r = h_create(); bc_divide( n1, n2, &r, HMATH_MAX_PREC ); h_grabfree(); return r; } // find 10 raise to num // e.g.: when num is 5, it results 100000 static bc_num h_raise10( int n ) { // calculate proper factor int len = abs(n)+2; char* sf = new char[len+1]; sf[len] = '\0'; if( n >= 0 ) { sf[0] = '1'; sf[len-1] = '\0'; sf[len-2] = '\0'; for( int i = 0; i < n; i++ ) sf[i+1] = '0'; } else { sf[0] = '0'; sf[1] = '.'; for( int i = 0; i < -n; i++ ) sf[i+2] = '0'; sf[len-1] = '1'; } bc_num factor = h_str2num( sf, abs(n) ); delete[] sf; return factor; } // round up to certain decimal digits static bc_num h_round( bc_num n, int prec ) { // no need to round? if( prec >= n->n_scale ) return h_copy( n ); // example: rounding "3.14159" to 4 decimal digits means // adding 0.5e-4 to 3.14159, it becomes 3.14164 // taking only 4 decimal digits, so it's now 3.1416 if( prec < 0 ) prec = 0; bc_num x = h_raise10( -prec-1 ); bc_num y = 0; bc_int2num( &y, 5 ); bc_num z = h_mul( x, y ); z->n_sign = n->n_sign; bc_num r = h_add( n, z ); h_destroy( x ); h_destroy( y ); h_destroy( z ); // only digits we are interested in bc_num v = h_rescale( r, prec ); h_destroy( r ); return v; } // remove trailing zeros static void h_trimzeros( bc_num num ) { while( ( num->n_scale > 0 ) && ( num->n_len+num->n_scale > 0 ) ) if( num->n_value[num->n_len+num->n_scale-1] == 0 ) num->n_scale--; else break; } static void h_init() { static bool h_initialized = false; if( !h_initialized ) { h_initialized = true; bc_init_numbers(); } } HNumber::HNumber() { h_init(); d = new Private; d->nan = false; d->num = h_create(); } HNumber::HNumber( const HNumber& hn ) { h_init(); d = new Private; d->nan = false; d->num = h_create(); operator=( hn ); } HNumber::HNumber( int i ) { h_init(); d = new Private; d->nan = false; d->num = h_create(); bc_int2num( &d->num, i ); } HNumber::HNumber( const char* str ) { h_init(); d = new Private; d->nan = false; d->num = h_create(); if( str ) if( strlen(str) == 3 ) if( tolower(str[0])=='n' ) if( tolower(str[1])=='a' ) if( tolower(str[2])=='n' ) d->nan = true; if( str && !d->nan ) { char* s = new char[ strlen(str)+1 ]; strcpy( s, str ); char* p = s; for( ;; p++ ) { if( *p != '+' ) if( *p != '-' ) if( *p != '.' ) if( !isdigit(*p) ) break; } int expd = 0; if( ( *p == 'e' ) || ( *p == 'E' ) ) { *p = '\0'; expd = atoi( p+1 ); } h_destroy( d->num ); d->num = h_str2num( s ); delete [] s; if( expd >= HMATH_MAX_PREC || // too large expd <= -HMATH_MAX_PREC ) // too small { d->nan = true; } if( expd != 0 ) { bc_num factor = h_raise10( expd ); bc_num nn = h_copy( d->num ); h_destroy( d->num ); d->num = h_mul( nn, factor ); h_destroy( nn ); h_destroy( factor ); } h_trimzeros( d->num ); } } HNumber::~HNumber() { h_destroy( d->num ); delete d; } bool HNumber::isNan() const { return d->nan; } bool HNumber::isZero() const { return !d->nan && ( bc_is_zero( d->num )!=0 ); } bool HNumber::isPositive() const { return !d->nan && !isNegative() && !isZero(); } bool HNumber::isNegative() const { return !d->nan && ( bc_is_neg( d->num )!=0 ); } HNumber HNumber::nan() { HNumber n; n.d->nan = true; return n; } HNumber& HNumber::operator=( const HNumber& hn ) { d->nan = hn.d->nan; h_destroy( d->num ); d->num = h_copy( hn.d->num ); return *this; } HNumber HNumber::operator+( const HNumber& num ) const { if( isNan() ) return HNumber( *this ); if( num.isNan() ) return HNumber( num ); HNumber result; h_destroy( result.d->num ); result.d->num = h_add( d->num, num.d->num ); return result; } HNumber& HNumber::operator+=( const HNumber& num ) { HNumber n = HNumber(*this) + num; operator=( n ); return *this; } HNumber HNumber::operator-( const HNumber& num ) const { if( isNan() ) return HNumber( *this ); if( num.isNan() ) return HNumber( num ); HNumber result; h_destroy( result.d->num ); result.d->num = h_sub( d->num, num.d->num ); return result; } HNumber& HNumber::operator-=( const HNumber& num ) { HNumber n = HNumber(*this) - num; operator=( n ); return *this; } HNumber HNumber::operator*( const HNumber& num ) const { if( isNan() ) return HNumber( *this ); if( num.isNan() ) return HNumber( num ); HNumber result; h_destroy( result.d->num ); result.d->num = h_mul( d->num, num.d->num ); return result; } HNumber& HNumber::operator*=( const HNumber& num ) { HNumber n = HNumber(*this) * num; operator=( n ); return *this; } HNumber HNumber::operator/( const HNumber& num ) const { if( isNan() ) return HNumber( *this ); if( num.isNan() ) return HNumber( num ); HNumber result; h_destroy( result.d->num ); result.d->num = h_div( d->num, num.d->num ); if(num == HNumber(0)) result.d->nan = true; return result; } HNumber& HNumber::operator/=( const HNumber& num ) { HNumber n = HNumber(*this) / num; operator=( n ); return *this; } bool HNumber::operator>( const HNumber& n ) const { return HMath::compare( *this, n ) > 0; } bool HNumber::operator<( const HNumber& n ) const { return HMath::compare( *this, n ) < 0; } bool HNumber::operator>=( const HNumber& n ) const { return HMath::compare( *this, n ) >= 0; } bool HNumber::operator<=( const HNumber& n ) const { return HMath::compare( *this, n ) <= 0; } bool HNumber::operator==( const HNumber& n ) const { return HMath::compare( *this, n ) == 0; } bool HNumber::operator!=( const HNumber& n ) const { return HMath::compare( *this, n ) != 0; } // format number with fixed number of decimal digits char* HMath::formatFixed( const HNumber& hn, int prec ) { if( hn.isNan() ) { char* str = (char*)malloc( 4 ); str[0] = 'N'; str[1] = 'a'; str[2] = 'N'; str[3] = '\0'; return str; } bc_num n = h_copy( hn.d->num ); h_trimzeros( n ); int oprec = prec; if( prec < 0 ) { prec = HMATH_MAX_SHOWN; if( n->n_scale < HMATH_MAX_SHOWN ) prec = n->n_scale; } // yes, this is necessary! bc_num m = h_round( n, prec ); h_trimzeros( m ); h_destroy( n ); n = m; if( oprec < 0 ) { prec = HMATH_MAX_SHOWN; if( n->n_scale < HMATH_MAX_SHOWN ) prec = n->n_scale; } // how many to allocate? int len = n->n_len + prec; if( n->n_sign != PLUS ) len++; if( prec > 0 ) len++; char* str = (char*)malloc( len+1 ); char* p = str; // the sign and the integer part // but avoid printing "-0" if( n->n_sign != PLUS ) if( !bc_is_zero( n ) ) *p++ = '-'; for( int c=0; cn_len; c++ ) *p++ = (char)BCD_CHAR( n->n_value[c] ); // the fraction part if( prec > 0 ) { *p++ = '.'; int k = (prec < n->n_scale) ? prec : n->n_scale; for( int d=0; dn_value[n->n_len+d] ); for( int r=n->n_scale; rnum->n_len+hn.d->num->n_scale; c++, tzeros++ ) if( hn.d->num->n_value[c]!= 0 ) break; int expd = hn.d->num->n_len - tzeros - 1; // extra digits needed for the exponent part int expn = 0; for( int e = ::abs(expd); e > 0; e/=10 ) expn++; if( expd <= 0 ) expn++; // scale the number by a new factor HNumber nn = hn * HMath::raise( 10, -expd ); // too close to zero? if( hn.isZero() || ( expd <= -HMATH_COMPARE_PREC ) ) { nn = HNumber(0); expd = 0; expn = 1; } char* str = formatFixed( nn, prec ); char* result = (char*) malloc( strlen(str)+expn+2 ); strcpy( result, str ); free( str ); // the exponential part char* p = result + strlen(result); *p++ = 'e'; p[expn] = '\0'; if( expd < 0 ) *p = '-'; for( int k=expn; k>0; k-- ) { int digit = expd % 10; p[k-1] = (char)('0' + ::abs( digit )); expd = expd / 10; if( expd == 0 ) break; } return result; } char* HMath::formatGeneral( const HNumber& hn, int prec ) { if( hn.isNan() ) { char* str = (char*)malloc( 4 ); str[0] = 'N'; str[1] = 'a'; str[2] = 'N'; str[3] = '\0'; return str; } // find the exponent and the factor int tzeros = 0; for( int c=0; cnum->n_len+hn.d->num->n_scale; c++, tzeros++ ) if( hn.d->num->n_value[c]!= 0 ) break; int expd = hn.d->num->n_len - tzeros - 1; char* str; if( expd > 5 ) str = formatExp( hn, prec ); else if( ( expd < -4 ) && (expd>-HMATH_COMPARE_PREC ) ) str = formatExp( hn, prec ); else if ( (expd < 0) && (prec>0) && (expd < -prec) ) str = formatExp( hn, prec ); else str = formatFixed( hn, prec ); return str; } TQString HMath::formatGenString( const HNumber &n, int prec ) { char *foo = formatGeneral(n, prec); TQString s(foo); free(foo); return s; } char* HMath::format( const HNumber& hn, char format, int prec ) { if( hn.isNan() ) { char* str = (char*)malloc( 4 ); str[0] = 'N'; str[1] = 'a'; str[2] = 'N'; str[3] = '\0'; return str; } if( format=='g' ) return formatGeneral( hn, prec ); else if( format=='f' ) return formatFixed( hn, prec ); else if( format=='e' ) return formatExp( hn, prec ); // fallback to 'g' return formatGeneral( hn, prec ); } HNumber HMath::pi() { return HNumber("3.14159265358979323846264338327950288419716939937510" "58209749445923078164062862089986280348253421170679" "82148086513282306647093844609550582231725359408128" "48111745028410270193852110555964462294895493038196" "44288109756659334461284756482337867831652712019091" "45648566923460348610454326648213393607260249141273" "72458700660631558817488152092096282925409171536436" "78925903600113305305488204665213841469519415116094" "33057270365759591953092186117381932611793105118548" "07446237996274956735188575272489122793818301194912" "98336733624406566430860213949463952247371907021798" "60943702770539217176293176752384674818467669405132" "00056812714526356082778577134275778960917363717872" "14684409012249534301465495853710507922796892589235" "42019956112129021960864034418159813629774771309960" "51870721134999999837297804995105973173281609631859" "50244594553469083026425223082533446850352619311881" "71010003137838752886587533208381420617177669147303" "59825349042875546873115956286388235378759375195778" "1857780532171226806613001927876611195909216420198" ); } HNumber HMath::add( const HNumber& n1, const HNumber& n2 ) { HNumber result = n1 + n2; return result; } HNumber HMath::sub( const HNumber& n1, const HNumber& n2 ) { HNumber result = n1 - n2; return result; } HNumber HMath::mul( const HNumber& n1, const HNumber& n2 ) { HNumber result = n1 * n2; return result; } HNumber HMath::div( const HNumber& n1, const HNumber& n2 ) { HNumber result = n1 / n2; return result; } int HMath::compare( const HNumber& n1, const HNumber& n2 ) { if( n1.isNan() && n2.isNan() ) return 0; HNumber delta = sub( n1, n2 ); delta = HMath::round( delta, HMATH_COMPARE_PREC ); if( delta.isZero() ) return 0; else if( delta.isNegative() ) return -1; return 1; } HNumber HMath::abs( const HNumber& n ) { HNumber r( n ); r.d->num->n_sign = PLUS; return r; } HNumber HMath::negate( const HNumber& n ) { if( n.isNan() || n.isZero() ) return HNumber( n ); HNumber result( n ); result.d->num->n_sign = ( n.d->num->n_sign == PLUS ) ? MINUS : PLUS; return result; } HNumber HMath::round( const HNumber& n, int prec ) { if( n.isNan() ) return HNumber::nan(); HNumber result; h_destroy( result.d->num ); result.d->num = h_round( n.d->num, prec ); return result; } HNumber HMath::integer( const HNumber& n ) { if( n.isNan() ) return HNumber::nan(); if( n.isZero() ) return HNumber( 0 ); HNumber result; h_destroy( result.d->num ); result.d->num = h_rescale( n.d->num, 0 ); return result; } HNumber HMath::frac( const HNumber& n ) { if( n.isNan() ) return HNumber::nan(); return n - integer(n); } HNumber HMath::sqrt( const HNumber& n ) { if( n.isNan() ) return HNumber::nan(); if( n.isZero() ) return n; if( n.isNegative() ) return HNumber::nan(); // useful constant HNumber half("0.5"); // Use Netwon-Raphson algorithm HNumber r( 1 ); for( int i = 0; i < HMATH_MAX_PREC; i++ ) { HNumber q = n / r; if( r == q ) break; HNumber s = r + q; r = s * half; } return r; } HNumber HMath::raise( const HNumber& n1, int n ) { if( n1.isNan() ) return n1; if( n1.isZero() ) return n1; if( n1 == HNumber(1) ) return n1; if( n == 0 ) return HNumber(1); if( n == 1 ) return n1; HNumber result = n1; for( ; n > 1; n-- ) result *= n1; for( ; n < 1; n++ ) result /= n1; return result; } HNumber HMath::raise( const HNumber& n1, const HNumber& n2 ) { if( n1.isNan() ) return HNumber::nan(); if( n2.isNan() ) return HNumber::nan(); if( n1.isZero() ) return HNumber(0); if( n1 == HNumber(1) ) return n1; if( n2.isZero() ) return HNumber(1); if( n2 == HNumber(1) ) return n1; if( n2 == HMath::integer(n2) ) { // Evil hack. char *str = HMath::format( n2 ); int i = atoi(str); free (str); return HMath::raise( n1, i ); } // x^y = exp( y*ln(x) ) HNumber result = n2 * HMath::ln(n1); result = HMath::exp( result ); return result; } HNumber HMath::exp( const HNumber& x ) { if( x.isNan() ) return HNumber::nan(); bool negative = x.isNegative(); HNumber xs = HMath::abs( x ); // adjust so that x is less than 1 // Taylor expansion: e^x = 1 + x + x^2/2! + x^3/3! + ... HNumber num = xs; HNumber den = 1; HNumber sum = xs + 1; // now loop to sum the series for( int i = 2; i < HMATH_MAX_PREC; i++ ) { num *= xs; den *= HNumber(i); if( num.isZero() ) break; HNumber s = HMath::div( num, den ); if( s.isZero() ) break; sum += s; } HNumber result = sum; if( negative ) result = HMath::div( HNumber(1), result ); return result; }; HNumber HMath::ln( const HNumber& x ) { if( x.isNan() ) return HNumber::nan(); if( !x.isPositive() ) return HNumber::nan(); // short circuit if( x == HNumber(10) ) return HNumber("2.30258509299404568401799145468436420760110148862877" "29760333279009675726102948650438303813865953227795" "49054520440916779445247118780973037711833599749301" "72118016928228381938415404059160910960135436620869" ); // useful constants HNumber two(2); HNumber one(1); HNumber half("0.5"); // adjust so that x is between 0.5 and 2.0 // use the fact that ln(x^2) = 2*ln(x) HNumber xs( x ); unsigned factor = 2; while( xs >= two ) { factor *= 2; xs = HMath::sqrt( xs ); } while( xs <= half ) { factor *= 2; xs = HMath::sqrt( xs ); } // Taylor expansion: ln(x) = 2(a+a^3/3+a^5/5+...) // where a=(x-1)/(x+1) HNumber p = xs - 1; HNumber q = xs + 1; HNumber a = p / q; HNumber as = a*a; HNumber t = a; HNumber sum = a; // loop for the series (limited to avoid nasty cases) for( int i = 3; i < HMATH_MAX_PREC; i+= 2 ) { t *= as; if( t.isZero() ) break; HNumber s = HMath::div( t, HNumber(i) ); if( s.isZero() ) break; sum += s; } HNumber result = sum * HNumber( factor ); return result; } HNumber HMath::log( const HNumber& x ) { if( x.isNan() ) return HNumber::nan(); if( !x.isPositive() ) return HNumber::nan(); HNumber result = HMath::ln( x ) / HMath::ln(10); return result; } // ensure angle is within 0 to 2*pi // useful for sin, cos static HNumber simplifyAngle( const HNumber& x ) { if( x.isNan() ) return HNumber::nan(); HNumber pi2 = HMath::pi() * 2; HNumber nn = x / pi2; HNumber xs = x - HMath::integer(nn)*pi2; if( xs.isNegative() ) xs += pi2; return xs; } HNumber HMath::sin( const HNumber& x ) { if( x.isNan() ) return HNumber::nan(); // short circuit if( x.isZero() ) return x; // adjust to small angle for speedup HNumber xs = simplifyAngle( x ); // Taylor expansion: sin(x) = x - x^3/3! + x^5/5! - x^7/7! ... HNumber xsq = xs*xs; HNumber num = xs; HNumber den = 1; HNumber sum = xs; // loop for the series (limited to avoid nasty cases) for( int i = 3; i < HMATH_MAX_PREC; i+=2 ) { num *= xsq; if( num.isZero() ) break; den *= HNumber(i-1); den *= HNumber(i); den = HMath::negate( den ); HNumber s = HMath::div( num, den ); if( s.isZero() ) break; sum += s; } HNumber result = sum; return result; } HNumber HMath::cos( const HNumber& x ) { if( x.isNan() ) return HNumber::nan(); // short circuit if( x.isZero() ) return HNumber( 1 ); // adjust to small angle for speedup HNumber xs = simplifyAngle( x ); // Taylor expansion: cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! ... HNumber xsq = xs*xs; HNumber num = 1; HNumber den = 1; HNumber sum = 1; // loop for the series (limited to avoid nasty cases) for( int i = 2; i < HMATH_MAX_PREC; i+=2 ) { num *= xsq; if( num.isZero() ) break; den *= HNumber(i-1); den *= HNumber(i); den = HMath::negate( den ); HNumber s = num / den; if( s.isZero() ) break; sum += s; } HNumber result = sum; return result; } HNumber HMath::tan( const HNumber& x ) { if( x.isNan() ) return HNumber::nan(); // tan(x) = cos(x)/sin(x) HNumber s = HMath::sin( x ); if( s.isZero() ) return s; HNumber c = HMath::cos( x ); if( c.isZero() ) return HNumber::nan(); HNumber result = s / c; return result; } HNumber HMath::atan( const HNumber& x ) { if( x.isNan() ) return HNumber::nan(); // useful constants HNumber one("1.0"); HNumber c( "0.2" ); // short circuit if( x == c ) return HNumber("0.19739555984988075837004976519479029344758510378785" "21015176889402410339699782437857326978280372880441" "12628118073691360104456479886794239355747565495216" "30327005221074700156450155600612861855266332573187" ); if( x == one ) // essentially equals to HMath::pi()/4; return HNumber("0.78539816339744830961566084581987572104929234984377" "64552437361480769541015715522496570087063355292669" "95537021628320576661773461152387645557931339852032" "12027936257102567548463027638991115573723873259549" ); bool negative = x.isNegative(); HNumber xs = HMath::abs( x ); // adjust so that x is less than c (we choose c = 0.2) // use the fact that atan(x) = atan(c) + atan((x-c)/(1+xc)) HNumber factor(0); HNumber base(0); while( xs > c ) { base = HMath::atan( c ); factor += one; HNumber p = xs - c; HNumber q = xs * c; xs = p / (q+one); } // Taylor series: atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ... HNumber num = xs; HNumber xsq = xs*xs; HNumber den = 1; HNumber sum = xs; // loop for the series (limited to avoid nasty cases) for( int i = 3; i < HMATH_MAX_PREC; i+=2 ) { num *= xsq; if( num.isZero() ) break; den = HNumber(i); int n = (i-1)/2; if( n&1 ) den = HNumber(-i); HNumber s = HMath::div( num, den ); if( s.isZero() ) break; sum += s; } HNumber result = factor*base + sum; if( negative ) result = HMath::negate( result ); return result; }; HNumber HMath::asin( const HNumber& x ) { if( x.isNan() ) return HNumber::nan(); // asin(x) = atan(x/sqrt(1-x*x)); HNumber d = HMath::sqrt( HNumber(1) - x*x ); if( d.isZero() ) { HNumber result = HMath::pi()/2; if( x.isNegative() ) result = HMath::negate( result ); return result; } HNumber result = HMath::atan( x / d ); return result; }; HNumber HMath::acos( const HNumber& x ) { if( x.isNan() ) return HNumber::nan(); if( x.isZero() ) return HMath::pi()/2; // acos(x) = atan(sqrt(1-x*x)/x); HNumber n = HMath::sqrt( HNumber(1) - x*x ); HNumber result = HMath::atan( n / x ); return result; }; HNumber HMath::sinh( const HNumber& x ) { if( x.isNan() ) return HNumber::nan(); // sinh(x) = 0.5*(e^x - e^(-x) ) HNumber result = HMath::exp(x) - HMath::exp( HMath::negate(x) ); result = result / 2; return result; } HNumber HMath::asinh( const HNumber& x ) { HNumber one(1); if(x.isNan()) return HNumber::nan(); return HMath::ln(x + HMath::sqrt(x * x + one)); } HNumber HMath::cosh( const HNumber& x ) { if( x.isNan() ) return HNumber::nan(); // cosh(x) = 0.5*(e^x - e^(-x) ) HNumber result = HMath::exp(x) + HMath::exp( HMath::negate(x) ); result = result / 2; return result; } HNumber HMath::acosh( const HNumber& x ) { HNumber one(1), zero(0); if(x.isNan() || x < one) return HNumber::nan(); // We always return the positive arc hyperbolic cosine. return HMath::ln(x + HMath::sqrt(x * x - one)); } HNumber HMath::tanh( const HNumber& x ) { if( x.isNan() ) return HNumber::nan(); // tanh(h) = sinh(x)/cosh(x) HNumber c = HMath::cosh( x ); if( c.isZero() ) return HNumber::nan(); HNumber s = HMath::sinh( x ); HNumber result = s / c; return result; } HNumber HMath::atanh( const HNumber& x ) { HNumber one(1), two(2); if(x.isNan() || HMath::abs(x) >= one) return HNumber::nan(); return HMath::ln((one + x) / (one - x)) / two; } void HMath::finalize() { bc_free_num( &_zero_ ); bc_free_num( &_one_ ); bc_free_num( &_two_ ); free( _one_ ); free( _zero_ ); free( _two_ ); h_grabfree(); h_grabfree(); h_grabfree(); h_grabfree(); } std::ostream& operator<<( std::ostream& s, HNumber num ) { char* str = HMath::formatFixed( num ); s << str; delete[] str; return s; } #ifdef HMATH_TEST #include #include static int hmath_total_tests = 0; static int hmath_failed_tests = 0; #define CHECK(x,y) check_value(__FILE__,__LINE__,#x,x,y) #define CHECK_FORMAT(f,p,x,y) check_format(__FILE__,__LINE__,#x,x,f,p,y) #define CHECK_PRECISE(x,y) check_precise(__FILE__,__LINE__,#x,x,y) static void check_value( const char *file, int line, const char* msg, const HNumber&n, const char* expected ) { hmath_total_tests++; char* result = HMath::formatFixed( n ); if( strcmp( result, expected ) ) { hmath_failed_tests++; std::cout << file << "["<< line <<"]: " << msg; std::cout << " Result: " << result; std::cout << ", "; std::cout << "Expected: " << expected; std::cout << std::endl; } free( result ); } static void check_format( const char *file, int line, const char* msg, const HNumber&n, char format, int prec, const char* expected ) { hmath_total_tests++; char* result = HMath::format( n, format, prec ); if( strcmp( result, expected ) ) { hmath_failed_tests++; std::cout << file << "["<< line <<"]: " << msg; std::cout << " Result: " << result; std::cout << ", "; std::cout << "Expected: " << expected; std::cout << std::endl; } free( result ); } static void check_precise( const char *file, int line, const char* msg, const HNumber&n, const char* expected ) { hmath_total_tests++; char* result = HMath::formatFixed( n, 50 ); if( strcmp( result, expected ) ) { hmath_failed_tests++; std::cout << file << "["<< line <<"]: " << msg; std::cout << " Result: " << result; std::cout << ", "; std::cout << "Expected: " << expected; std::cout << std::endl; } free( result ); } void test_create() { CHECK( HNumber("1.0"), "1" ); CHECK( HNumber("2.0"), "2" ); CHECK( HNumber("1e-3"), "0.001" ); // too large or small CHECK( HNumber("1e200"), "NaN" ); CHECK( HNumber("1e-200"), "NaN" ); } void test_format() { // fixed decimal digits CHECK_FORMAT( 'f', 0, HNumber("NaN"), "NaN" ); CHECK_FORMAT( 'f', 0, HNumber("0"), "0" ); CHECK_FORMAT( 'f', 0, HNumber("1.1"), "1" ); CHECK_FORMAT( 'f', 1, HNumber("2.11"), "2.1" ); CHECK_FORMAT( 'f', 2, HNumber("3.111"), "3.11" ); CHECK_FORMAT( 'f', 3, HNumber("4.1111"), "4.111" ); CHECK_FORMAT( 'f', 2, HNumber("3.14"), "3.14" ); CHECK_FORMAT( 'f', 3, HNumber("3.14"), "3.140" ); CHECK_FORMAT( 'f', 5, HNumber("3.14"), "3.14000" ); CHECK_FORMAT( 'f', 7, HNumber("3.14"), "3.1400000" ); CHECK_FORMAT( 'f', 7, HNumber("-0.001"), "-0.0010000" ); CHECK_FORMAT( 'f', 8, HNumber("-0.001"), "-0.00100000" ); CHECK_FORMAT( 'f', 9, HNumber("-0.001"), "-0.001000000" ); CHECK_FORMAT( 'f', 1, HNumber("4.001"), "4.0" ); CHECK_FORMAT( 'f', -1, HNumber("4.000000000000000000000000000000000000000000001"), "4" ); // exponential format CHECK_FORMAT( 'e', 0, HNumber("NaN"), "NaN" ); CHECK_FORMAT( 'e', 0, HNumber("0"), "0e0" ); CHECK_FORMAT( 'e', 0, HNumber("3.14"), "3e0" ); CHECK_FORMAT( 'e', 1, HNumber("3.14"), "3.1e0" ); CHECK_FORMAT( 'e', 2, HNumber("3.14"), "3.14e0" ); CHECK_FORMAT( 'e', 3, HNumber("3.14"), "3.140e0" ); CHECK_FORMAT( 'e', 5, HNumber("3.14"), "3.14000e0" ); CHECK_FORMAT( 'e', 7, HNumber("3.14"), "3.1400000e0" ); CHECK_FORMAT( 'e', 3, HNumber("-0.001"), "-1.000e-3" ); CHECK_FORMAT( 'e', 2, HNumber("0.0001"), "1.00e-4" ); CHECK_FORMAT( 'e', 2, HNumber("0.001"), "1.00e-3" ); CHECK_FORMAT( 'e', 2, HNumber("0.01"), "1.00e-2" ); CHECK_FORMAT( 'e', 2, HNumber("0.1"), "1.00e-1" ); CHECK_FORMAT( 'e', 2, HNumber("1"), "1.00e0" ); CHECK_FORMAT( 'e', 2, HNumber("10"), "1.00e1" ); CHECK_FORMAT( 'e', 2, HNumber("100"), "1.00e2" ); CHECK_FORMAT( 'e', 2, HNumber("1000"), "1.00e3" ); CHECK_FORMAT( 'e', 2, HNumber("10000"), "1.00e4" ); CHECK_FORMAT( 'e', 2, HNumber("100000"), "1.00e5" ); CHECK_FORMAT( 'e', 2, HNumber("1000000"), "1.00e6" ); CHECK_FORMAT( 'e', 2, HNumber("10000000"), "1.00e7" ); // general format CHECK_FORMAT( 'g', -1, HMath::pi(), "3.14159265358979323846" ); CHECK_FORMAT( 'g', 3, HNumber("0"), "0.000" ); CHECK_FORMAT( 'g', 3, HNumber("0.000000001"), "1.000e-9" ); CHECK_FORMAT( 'g', 3, HNumber("0.00000001"), "1.000e-8" ); CHECK_FORMAT( 'g', 3, HNumber("0.0000001"), "1.000e-7" ); CHECK_FORMAT( 'g', 3, HNumber("0.000001"), "1.000e-6" ); CHECK_FORMAT( 'g', 3, HNumber("0.00001"), "1.000e-5" ); CHECK_FORMAT( 'g', 3, HNumber("0.0001"), "1.000e-4" ); CHECK_FORMAT( 'g', 3, HNumber("0.001"), "0.001" ); CHECK_FORMAT( 'g', 3, HNumber("0.01"), "0.010" ); CHECK_FORMAT( 'g', 3, HNumber("0.1"), "0.100" ); CHECK_FORMAT( 'g', 3, HNumber("10"), "10.000" ); CHECK_FORMAT( 'g', 3, HNumber("100"), "100.000" ); CHECK_FORMAT( 'g', 3, HNumber("1000"), "1000.000" ); CHECK_FORMAT( 'g', 3, HNumber("10000"), "10000.000" ); CHECK_FORMAT( 'g', 3, HNumber("100000"), "100000.000" ); CHECK_FORMAT( 'g', 3, HNumber("1000000"), "1.000e6" ); CHECK_FORMAT( 'g', 3, HNumber("10000000"), "1.000e7" ); CHECK_FORMAT( 'g', 3, HNumber("100000000"), "1.000e8" ); CHECK_FORMAT( 'g', 3, HNumber("1403.1977"), "1403.198" ); CHECK_FORMAT( 'g', 3, HNumber("2604.1980"), "2604.198" ); CHECK_FORMAT( 'g', 3, HNumber("2.47e4"), "24700.000" ); } void test_op() { // addition CHECK( HNumber(0)+HNumber(0), "0" ); CHECK( HNumber(1)+HNumber(0), "1" ); CHECK( HNumber(1)+HNumber(1), "2" ); CHECK( HNumber(1)+HNumber(2), "3" ); CHECK( HNumber(1)+HNumber(10), "11" ); CHECK( HNumber(1)+HNumber(100), "101" ); CHECK( HNumber(1)+HNumber(1000), "1001" ); // subtraction CHECK( HNumber(0)-HNumber(0), "0" ); CHECK( HNumber(1)-HNumber(0), "1" ); CHECK( HNumber(1)-HNumber(2), "-1" ); // division CHECK( HNumber(1)/HNumber(2), "0.5" ); CHECK_PRECISE( HNumber(1)/HNumber(3), "0.33333333333333333333333333333333333333333333333333" ); CHECK_PRECISE( HNumber(2)/HNumber(3), "0.66666666666666666666666666666666666666666666666667" ); CHECK_PRECISE( HNumber(1)/HNumber(7), "0.14285714285714285714285714285714285714285714285714" ); CHECK_PRECISE( HNumber(2)/HNumber(7), "0.28571428571428571428571428571428571428571428571429" ); CHECK_PRECISE( HNumber(3)/HNumber(7), "0.42857142857142857142857142857142857142857142857143" ); CHECK_PRECISE( HNumber(4)/HNumber(7), "0.57142857142857142857142857142857142857142857142857" ); CHECK_PRECISE( HNumber(1)/HNumber(9), "0.11111111111111111111111111111111111111111111111111" ); // multiplication CHECK( HNumber(0)*HNumber(0), "0" ); CHECK( HNumber("1.0")*HNumber("0.0"), "0" ); CHECK( HNumber(1)*HNumber(1), "1" ); CHECK( HNumber(3)*HNumber(-4), "-12" ); CHECK( HNumber(-2)*HNumber(5), "-10" ); CHECK( HNumber(6)*HNumber(7), "42" ); CHECK( HNumber("1.5")*HNumber("1.5"), "2.25" ); } void test_functions() { // pi CHECK( HMath::pi(), "3.14159265358979323846" ); CHECK_PRECISE( HMath::pi(), "3.14159265358979323846264338327950288419716939937511" ); // abs CHECK( HMath::abs("0"), "0" ); CHECK( HMath::abs("1"), "1" ); CHECK( HMath::abs("100"), "100" ); CHECK( HMath::abs("-100"), "100" ); CHECK( HMath::abs("-3.14159"), "3.14159" ); CHECK( HMath::abs("NaN"), "NaN" ); // round CHECK( HMath::round( "3.14" ), "3" ); CHECK( HMath::round( "1.77" ), "2" ); CHECK( HMath::round( "3.14159", 4 ), "3.1416" ); CHECK( HMath::round( "3.14159", 3 ), "3.142" ); CHECK( HMath::round( "3.14159", 2 ), "3.14" ); CHECK( HMath::round( "3.14159", 1 ), "3.1" ); CHECK( HMath::round( "3.14159", 0 ), "3" ); CHECK( HMath::round( "-2.6041980", 4 ), "-2.6042" ); CHECK( HMath::round( "-2.6041980", 3 ), "-2.604" ); CHECK( HMath::round( "-2.6041980", 2 ), "-2.6" ); CHECK( HMath::round( "-2.6041980", 1 ), "-2.6" ); CHECK( HMath::round( "-2.6041980", 0 ), "-3" ); CHECK( HMath::round( "NaN" ), "NaN" ); // integer CHECK( HMath::integer( "0" ), "0" ); CHECK( HMath::integer( "0.25" ), "0" ); CHECK( HMath::integer( "0.85" ), "0" ); CHECK( HMath::integer( "14.0377" ), "14" ); CHECK( HMath::integer( "-0.25" ), "0" ); CHECK( HMath::integer( "-0.85" ), "0" ); CHECK( HMath::integer( "-14.0377" ), "-14" ); CHECK( HMath::integer( "NaN" ), "NaN" ); // frac CHECK( HMath::frac( "0" ), "0" ); CHECK( HMath::frac( "3.14159" ), "0.14159" ); CHECK( HMath::frac( "0.14159" ), "0.14159" ); CHECK( HMath::frac( "-3.14159" ), "-0.14159" ); CHECK( HMath::frac( "-0.14159" ), "-0.14159" ); CHECK( HMath::frac( "NaN" ), "NaN" ); // checking function 'sqrt' CHECK( HMath::sqrt(1), "1" ); CHECK( HMath::sqrt(4), "2" ); CHECK( HMath::sqrt(9), "3" ); CHECK( HMath::sqrt(16), "4" ); CHECK_PRECISE( HMath::sqrt(2), "1.41421356237309504880168872420969807856967187537695" ); CHECK_PRECISE( HMath::sqrt(3), "1.73205080756887729352744634150587236694280525381038" ); CHECK_PRECISE( HMath::sqrt(5), "2.23606797749978969640917366873127623544061835961153" ); CHECK_PRECISE( HMath::sqrt(7), "2.64575131106459059050161575363926042571025918308245" ); CHECK_PRECISE( HMath::sqrt(8), "2.82842712474619009760337744841939615713934375075390" ); CHECK_PRECISE( HMath::sqrt(10), "3.16227766016837933199889354443271853371955513932522" ); CHECK_PRECISE( HMath::sqrt(11), "3.31662479035539984911493273667068668392708854558935" ); CHECK_PRECISE( HMath::sqrt(12), "3.46410161513775458705489268301174473388561050762076" ); CHECK_PRECISE( HMath::sqrt(13), "3.60555127546398929311922126747049594625129657384525" ); CHECK_PRECISE( HMath::sqrt(14), "3.74165738677394138558374873231654930175601980777873" ); CHECK_PRECISE( HMath::sqrt(15), "3.87298334620741688517926539978239961083292170529159" ); CHECK_PRECISE( HMath::sqrt(17), "4.12310562561766054982140985597407702514719922537362" ); CHECK_PRECISE( HMath::sqrt(18), "4.24264068711928514640506617262909423570901562613084" ); CHECK_PRECISE( HMath::sqrt(19), "4.35889894354067355223698198385961565913700392523244" ); CHECK_PRECISE( HMath::sqrt(20), "4.47213595499957939281834733746255247088123671922305" ); CHECK( HMath::sqrt("0.04"), "0.2" ); CHECK( HMath::sqrt("0.09"), "0.3" ); CHECK( HMath::sqrt("0.16"), "0.4" ); CHECK( HMath::sqrt(-1), "NaN" ); CHECK( HMath::sqrt("NaN"), "NaN" ); // raise CHECK( HMath::raise(10,-3), "0.001" ); CHECK( HMath::raise(10,-2), "0.01" ); CHECK( HMath::raise(10,-1), "0.1" ); CHECK( HMath::raise(10,0), "1" ); CHECK( HMath::raise(10,1), "10" ); CHECK( HMath::raise(10,2), "100" ); CHECK( HMath::raise(10,3), "1000" ); CHECK( HMath::raise(10,4), "10000" ); CHECK( HMath::raise("2","2"), "4" ); CHECK( HMath::raise("3","3"), "27" ); CHECK( HMath::raise("4","4"), "256" ); CHECK_PRECISE( HMath::raise("2","0.1"), "1.07177346253629316421300632502334202290638460497756" ); CHECK_PRECISE( HMath::raise("2","0.2"), "1.14869835499703500679862694677792758944385088909780" ); CHECK_PRECISE( HMath::raise("2","0.3"), "1.23114441334491628449939306916774310987613776110082" ); CHECK( HMath::raise("NaN","0"), "NaN" ); CHECK( HMath::raise("-1","NaN"), "NaN" ); // exp CHECK_PRECISE( HMath::exp("0.1"), "1.10517091807564762481170782649024666822454719473752" ); CHECK_PRECISE( HMath::exp("0.2"), "1.22140275816016983392107199463967417030758094152050" ); CHECK_PRECISE( HMath::exp("0.3"), "1.34985880757600310398374431332800733037829969735937" ); CHECK_PRECISE( HMath::exp("0.4"), "1.49182469764127031782485295283722228064328277393743" ); CHECK_PRECISE( HMath::exp("0.5"), "1.64872127070012814684865078781416357165377610071015" ); CHECK_PRECISE( HMath::exp("0.6"), "1.82211880039050897487536766816286451338223880854644" ); CHECK_PRECISE( HMath::exp("0.7"), "2.01375270747047652162454938858306527001754239414587" ); CHECK_PRECISE( HMath::exp("0.8"), "2.22554092849246760457953753139507675705363413504848" ); CHECK_PRECISE( HMath::exp("0.9"), "2.45960311115694966380012656360247069542177230644008" ); CHECK_PRECISE( HMath::exp("1.0"), "2.71828182845904523536028747135266249775724709369996" ); // ln CHECK_PRECISE( HMath::ln("0.1"), "-2.30258509299404568401799145468436420760110148862877" ); CHECK_PRECISE( HMath::ln("0.2"), "-1.60943791243410037460075933322618763952560135426852" ); CHECK_PRECISE( HMath::ln("0.3"), "-1.20397280432593599262274621776183850295361093080602" ); CHECK_PRECISE( HMath::ln("0.4"), "-0.91629073187415506518352721176801107145010121990826" ); CHECK_PRECISE( HMath::ln("0.5"), "-0.69314718055994530941723212145817656807550013436026" ); CHECK_PRECISE( HMath::ln("0.6"), "-0.51082562376599068320551409630366193487811079644577" ); CHECK_PRECISE( HMath::ln("0.7"), "-0.35667494393873237891263871124118447796401675904691" ); CHECK_PRECISE( HMath::ln("0.8"), "-0.22314355131420975576629509030983450337460108554801" ); CHECK_PRECISE( HMath::ln("0.9"), "-0.10536051565782630122750098083931279830612037298327" ); CHECK_PRECISE( HMath::ln("1.0"), "0.00000000000000000000000000000000000000000000000000" ); CHECK_PRECISE( HMath::ln("1.1"), "0.09531017980432486004395212328076509222060536530864" ); CHECK_PRECISE( HMath::ln("1.2"), "0.18232155679395462621171802515451463319738933791449" ); CHECK_PRECISE( HMath::ln("1.3"), "0.26236426446749105203549598688095439720416645613143" ); CHECK_PRECISE( HMath::ln("1.4"), "0.33647223662121293050459341021699209011148337531334" ); CHECK_PRECISE( HMath::ln("1.5"), "0.40546510810816438197801311546434913657199042346249" ); CHECK_PRECISE( HMath::ln("1.6"), "0.47000362924573555365093703114834206470089904881225" ); CHECK_PRECISE( HMath::ln("1.7"), "0.53062825106217039623154316318876232798710152395697" ); CHECK_PRECISE( HMath::ln("1.8"), "0.58778666490211900818973114061886376976937976137698" ); CHECK_PRECISE( HMath::ln("1.9"), "0.64185388617239477599103597720348932963627777267036" ); CHECK_PRECISE( HMath::ln("2.0"), "0.69314718055994530941723212145817656807550013436026" ); CHECK_PRECISE( HMath::ln("3.0"), "1.09861228866810969139524523692252570464749055782275" ); CHECK_PRECISE( HMath::ln("4.0"), "1.38629436111989061883446424291635313615100026872051" ); CHECK_PRECISE( HMath::ln("100"), "4.60517018598809136803598290936872841520220297725755" ); // log CHECK( HMath::log("1e-5"), "-5" ); CHECK( HMath::log("1e-4"), "-4" ); CHECK( HMath::log("1e-3"), "-3" ); CHECK( HMath::log("10"), "1" ); CHECK( HMath::log("100"), "2" ); CHECK( HMath::log("1000"), "3" ); CHECK( HMath::log("10000"), "4" ); CHECK( HMath::log("1e5"), "5" ); CHECK( HMath::log("1e6"), "6" ); CHECK( HMath::log("1e7"), "7" ); CHECK( HMath::log("1e8"), "8" ); CHECK( HMath::log("1e9"), "9" ); CHECK( HMath::log("1e10"), "10" ); CHECK( HMath::log("-1"), "NaN" ); CHECK( HMath::log("NaN"), "NaN" ); // sin CHECK( HMath::sin( "0" ), "0" ); CHECK( HMath::sin( HMath::pi()/4 ), "0.7071067811865475244" ); CHECK( HMath::sin( HMath::pi()/3 ), "0.86602540378443864676"); CHECK( HMath::sin( HMath::pi()/2 ), "1" ); CHECK( HMath::sin( HMath::pi()/1 ), "0" ); CHECK( HMath::sin( HMath::pi()*2/3 ), "0.86602540378443864676"); CHECK( HMath::sin( HMath::pi()*4/3 ), "-0.86602540378443864676"); CHECK( HMath::sin( HMath::pi()*5/3 ), "-0.86602540378443864676"); CHECK( HMath::sin( HMath::pi()*6/3 ), "0"); CHECK( HMath::sin( HMath::pi()*7/3 ), "0.86602540378443864676"); CHECK( HMath::sin( HMath::pi()*9/3 ), "0"); CHECK_PRECISE( HMath::sin("0.0"), "0.00000000000000000000000000000000000000000000000000" ); CHECK_PRECISE( HMath::sin("0.1"), "0.09983341664682815230681419841062202698991538801798" ); CHECK_PRECISE( HMath::sin("0.2"), "0.19866933079506121545941262711838975037020672954021" ); CHECK_PRECISE( HMath::sin("0.3"), "0.29552020666133957510532074568502737367783211174262" ); CHECK_PRECISE( HMath::sin("0.4"), "0.38941834230865049166631175679570526459306018344396" ); CHECK_PRECISE( HMath::sin("0.5"), "0.47942553860420300027328793521557138808180336794060" ); CHECK_PRECISE( HMath::sin("0.6"), "0.56464247339503535720094544565865790710988808499415" ); CHECK_PRECISE( HMath::sin("0.7"), "0.64421768723769105367261435139872018306581384457369" ); CHECK_PRECISE( HMath::sin("0.8"), "0.71735609089952276162717461058138536619278523779142" ); CHECK_PRECISE( HMath::sin("0.9"), "0.78332690962748338846138231571354862314014792572031" ); CHECK_PRECISE( HMath::sin("1.0"), "0.84147098480789650665250232163029899962256306079837" ); CHECK_PRECISE( HMath::sin("2.0"), "0.90929742682568169539601986591174484270225497144789" ); CHECK_PRECISE( HMath::sin("3.0"), "0.14112000805986722210074480280811027984693326425227" ); CHECK_PRECISE( HMath::sin("4.0"), "-0.75680249530792825137263909451182909413591288733647" ); CHECK_PRECISE( HMath::sin("5.0"), "-0.95892427466313846889315440615599397335246154396460" ); // cos CHECK( HMath::cos( "0" ), "1" ); CHECK( HMath::cos( HMath::pi()/4 ), "0.7071067811865475244" ); CHECK( HMath::cos( HMath::pi()/3 ), "0.5"); CHECK( HMath::cos( HMath::pi()/2 ), "0" ); CHECK( HMath::cos( HMath::pi()/1 ), "-1" ); CHECK( HMath::cos( HMath::pi()*2/3 ), "-0.5"); CHECK( HMath::cos( HMath::pi()*4/3 ), "-0.5"); CHECK( HMath::cos( HMath::pi()*5/3 ), "0.5"); CHECK( HMath::cos( HMath::pi()*6/3 ), "1"); CHECK( HMath::cos( HMath::pi()*7/3 ), "0.5"); CHECK( HMath::cos( HMath::pi()*9/3 ), "-1"); CHECK_PRECISE( HMath::cos("0.0"), "1.00000000000000000000000000000000000000000000000000" ); CHECK_PRECISE( HMath::cos("0.1"), "0.99500416527802576609556198780387029483857622541508" ); CHECK_PRECISE( HMath::cos("0.2"), "0.98006657784124163112419651674816887739352436080657" ); CHECK_PRECISE( HMath::cos("0.3"), "0.95533648912560601964231022756804989824421408263204" ); CHECK_PRECISE( HMath::cos("0.4"), "0.92106099400288508279852673205180161402585956931985" ); CHECK_PRECISE( HMath::cos("0.5"), "0.87758256189037271611628158260382965199164519710974" ); CHECK_PRECISE( HMath::cos("0.6"), "0.82533561490967829724095249895537603887809103918847" ); CHECK_PRECISE( HMath::cos("0.7"), "0.76484218728448842625585999019186490926821055037370" ); CHECK_PRECISE( HMath::cos("0.8"), "0.69670670934716542092074998164232492610178601370806" ); CHECK_PRECISE( HMath::cos("0.9"), "0.62160996827066445648471615140713350872176136659124" ); CHECK_PRECISE( HMath::cos("1.0"), "0.54030230586813971740093660744297660373231042061792" ); CHECK_PRECISE( HMath::cos("2.0"), "-0.41614683654714238699756822950076218976600077107554" ); CHECK_PRECISE( HMath::cos("3.0"), "-0.98999249660044545727157279473126130239367909661559" ); CHECK_PRECISE( HMath::cos("4.0"), "-0.65364362086361191463916818309775038142413359664622" ); // tan CHECK( HMath::tan( HMath::pi()/4 ), "1" ); CHECK( HMath::tan( HMath::pi()/3 ), "1.73205080756887729353"); CHECK( HMath::tan( HMath::pi()/1 ), "0" ); CHECK_PRECISE( HMath::tan("0.0"), "0.00000000000000000000000000000000000000000000000000" ); CHECK_PRECISE( HMath::tan("0.1"), "0.10033467208545054505808004578111153681900480457644" ); CHECK_PRECISE( HMath::tan("0.2"), "0.20271003550867248332135827164753448262687566965163" ); CHECK_PRECISE( HMath::tan("0.3"), "0.30933624960962323303530367969829466725781590680046" ); CHECK_PRECISE( HMath::tan("0.4"), "0.42279321873816176198163542716529033394198977271569" ); CHECK_PRECISE( HMath::tan("0.5"), "0.54630248984379051325517946578028538329755172017979" ); CHECK_PRECISE( HMath::tan("0.6"), "0.68413680834169231707092541746333574524265408075678" ); CHECK_PRECISE( HMath::tan("0.7"), "0.84228838046307944812813500221293771718722125080420" ); CHECK_PRECISE( HMath::tan("0.8"), "1.02963855705036401274636117282036528416821960677231" ); CHECK_PRECISE( HMath::tan("0.9"), "1.26015821755033913713457548539574847783362583439629" ); CHECK_PRECISE( HMath::tan("1.0"), "1.55740772465490223050697480745836017308725077238152" ); CHECK_PRECISE( HMath::tan("2.0"), "-2.18503986326151899164330610231368254343201774622766" ); CHECK_PRECISE( HMath::tan("3.0"), "-0.14254654307427780529563541053391349322609228490180" ); CHECK_PRECISE( HMath::tan("4.0"), "1.15782128234957758313734241826732392311976276736714" ); // atan CHECK_PRECISE( HMath::atan("0.0"), "0.00000000000000000000000000000000000000000000000000" ); CHECK_PRECISE( HMath::atan("0.1"), "0.09966865249116202737844611987802059024327832250431" ); CHECK_PRECISE( HMath::atan("0.2"), "0.19739555984988075837004976519479029344758510378785" ); CHECK_PRECISE( HMath::atan("0.3"), "0.29145679447786709199560462143289119350316759901207" ); CHECK_PRECISE( HMath::atan("0.4"), "0.38050637711236488630358791681043310449740571365810" ); CHECK_PRECISE( HMath::atan("0.5"), "0.46364760900080611621425623146121440202853705428612" ); CHECK_PRECISE( HMath::atan("0.6"), "0.54041950027058415544357836460859991013514825146259" ); CHECK_PRECISE( HMath::atan("1.0"), "0.78539816339744830961566084581987572104929234984378" ); CHECK_PRECISE( HMath::atan("-0.1"), "-0.09966865249116202737844611987802059024327832250431" ); CHECK_PRECISE( HMath::atan("-0.2"), "-0.19739555984988075837004976519479029344758510378785" ); CHECK_PRECISE( HMath::atan("-0.3"), "-0.29145679447786709199560462143289119350316759901207" ); CHECK_PRECISE( HMath::atan("-0.4"), "-0.38050637711236488630358791681043310449740571365810" ); CHECK_PRECISE( HMath::atan("-0.5"), "-0.46364760900080611621425623146121440202853705428612" ); CHECK_PRECISE( HMath::atan("-0.6"), "-0.54041950027058415544357836460859991013514825146259" ); CHECK_PRECISE( HMath::atan("-1.0"), "-0.78539816339744830961566084581987572104929234984378" ); // asin CHECK_PRECISE( HMath::asin("0.0"), "0.00000000000000000000000000000000000000000000000000" ); CHECK_PRECISE( HMath::asin("0.1"), "0.10016742116155979634552317945269331856867597222963" ); CHECK_PRECISE( HMath::asin("0.2"), "0.20135792079033079145512555221762341024003808140223" ); CHECK_PRECISE( HMath::asin("0.3"), "0.30469265401539750797200296122752916695456003170678" ); CHECK_PRECISE( HMath::asin("0.4"), "0.41151684606748801938473789761733560485570113512703" ); // acos CHECK_PRECISE( HMath::acos("0.1"), "1.47062890563333682288579851218705812352990872745792" ); CHECK_PRECISE( HMath::acos("0.2"), "1.36943840600456582777619613942212803185854661828532" ); CHECK_PRECISE( HMath::acos("0.3"), "1.26610367277949911125931873041222227514402466798078" ); CHECK_PRECISE( HMath::acos("0.4"), "1.15927948072740859984658379402241583724288356456053" ); // consistency: tan vs atan CHECK( HMath::atan("0.10033467208545054505808004578111153681900480457644"), "0.1" ); CHECK( HMath::atan("0.20271003550867248332135827164753448262687566965163"), "0.2" ); CHECK( HMath::atan("0.30933624960962323303530367969829466725781590680046"), "0.3" ); CHECK( HMath::atan("0.42279321873816176198163542716529033394198977271569"), "0.4" ); CHECK( HMath::atan("0.54630248984379051325517946578028538329755172017979"), "0.5" ); CHECK( HMath::atan("0.68413680834169231707092541746333574524265408075678"), "0.6" ); CHECK( HMath::atan("0.84228838046307944812813500221293771718722125080420"), "0.7" ); CHECK( HMath::atan("1.02963855705036401274636117282036528416821960677231"), "0.8" ); CHECK( HMath::atan("1.26015821755033913713457548539574847783362583439629"), "0.9" ); CHECK( HMath::atan("1.55740772465490223050697480745836017308725077238152"), "1" ); // consistency: sin vs asin for small angle CHECK( HMath::asin("0.09983341664682815230681419841062202698991538801798" ), "0.1"); CHECK( HMath::asin("0.19866933079506121545941262711838975037020672954021" ), "0.2"); CHECK( HMath::asin("0.29552020666133957510532074568502737367783211174262" ), "0.3"); CHECK( HMath::asin("0.38941834230865049166631175679570526459306018344396" ), "0.4"); CHECK( HMath::asin("0.47942553860420300027328793521557138808180336794060" ), "0.5"); CHECK( HMath::asin("0.56464247339503535720094544565865790710988808499415" ), "0.6"); CHECK( HMath::asin("0.64421768723769105367261435139872018306581384457369" ), "0.7"); CHECK( HMath::asin("0.71735609089952276162717461058138536619278523779142" ), "0.8"); // sinh CHECK_PRECISE( HMath::sinh("0.1"), "0.10016675001984402582372938352190502351492091687856" ); CHECK_PRECISE( HMath::sinh("0.2"), "0.20133600254109398762556824301031737297449484262574" ); CHECK_PRECISE( HMath::sinh("0.3"), "0.30452029344714261895843526700509522909802423268018" ); CHECK_PRECISE( HMath::sinh("0.4"), "0.41075232580281550854021001384469810435315092436331" ); CHECK_PRECISE( HMath::sinh("0.5"), "0.52109530549374736162242562641149155910592898261148" ); CHECK_PRECISE( HMath::sinh("0.6"), "0.63665358214824127112345437546514831902496342592790" ); CHECK_PRECISE( HMath::sinh("0.7"), "0.75858370183953350345987464759276815415493761421703" ); CHECK_PRECISE( HMath::sinh("0.8"), "0.88810598218762300657471757318975698055970959688815" ); CHECK_PRECISE( HMath::sinh("0.9"), "1.02651672570817527595833616197842235379403446513485" ); CHECK_PRECISE( HMath::sinh("1.0"), "1.17520119364380145688238185059560081515571798133410" ); // cosh CHECK_PRECISE( HMath::cosh("0.1"), "1.00500416805580359898797844296834164470962627785896" ); CHECK_PRECISE( HMath::cosh("0.2"), "1.02006675561907584629550375162935679733308609889476" ); CHECK_PRECISE( HMath::cosh("0.3"), "1.04533851412886048502530904632291210128027546467919" ); CHECK_PRECISE( HMath::cosh("0.4"), "1.08107237183845480928464293899252417629013184957412" ); CHECK_PRECISE( HMath::cosh("0.5"), "1.12762596520638078522622516140267201254784711809867" ); CHECK_PRECISE( HMath::cosh("0.6"), "1.18546521824226770375191329269771619435727538261853" ); CHECK_PRECISE( HMath::cosh("0.7"), "1.25516900563094301816467474099029711586260477992884" ); CHECK_PRECISE( HMath::cosh("0.8"), "1.33743494630484459800481995820531977649392453816033" ); CHECK_PRECISE( HMath::cosh("0.9"), "1.43308638544877438784179040162404834162773784130523" ); CHECK_PRECISE( HMath::cosh("1.0"), "1.54308063481524377847790562075706168260152911236586" ); } int test_hmath() { hmath_total_tests = 0; hmath_failed_tests = 0; test_create(); test_format(); test_op(); test_functions(); std::cout << hmath_total_tests << " total, "; std::cout << hmath_failed_tests << " failed\n"; HMath::finalize(); return hmath_failed_tests; }; #endif // vim: set et sw=2 ts=8:``````