From 74e85423c8431e32447806a44ff0a4b3ed1da195 Mon Sep 17 00:00:00 2001 From: erdgeist Date: Sun, 5 Oct 2014 21:46:53 +0200 Subject: Initial version. Works. Untested. Unreviewed --- fixpow.c | 235 +++++++++++++++++++++++++++++++++++++++++++++++++++++++ generate_table.c | 34 ++++++++ 2 files changed, 269 insertions(+) create mode 100644 fixpow.c create mode 100644 generate_table.c diff --git a/fixpow.c b/fixpow.c new file mode 100644 index 0000000..be787b2 --- /dev/null +++ b/fixpow.c @@ -0,0 +1,235 @@ +/* Parts of this software was written by Dirk Engling + Those parts are considered beerware. Prost. Skol. Cheers or whatever. + + Original idea and the place where I heavily stole code from is + http://www.quinapalus.com/efunc.html + Dr Mark St John OWEN, E-mail: mail -at- quinapalus -dot- com +*/ + +#include +#include +#include +#include + +#define TO_Q16(X) ((int32_t)(65536.f*(X))) +#define FROM_Q16(X) ((double)((X)/65536.f)) + +// It works as follows: +// P = pow_QX_QY_QP( x, y ) == exp( ln(x) * y ) + +// Where if x is negative: +// * y must have no fractional part, +// * the result's sign is the lowest integral bit of y + +// We note that in every standard Q representation ln(x) will not exceed +// the value 22, so that we can safely work with a Q26 representation. +// +// if ln(x) * y would overflow in that representation, so would +// exp( ln(x) * y ) in Q16. +// +// Finally exp() is calculated in the domain specified by script + +#if 0 + The table[tm], generated from different versions of + generate_table, though. ++00,000000000465661287199 x = x + ( x >> 31 ) ++00,000000000931322574182 x = x + ( x >> 30 ) ++00,000000001862645147496 x = x + ( x >> 29 ) ++00,000000003725290291523 x = x + ( x >> 28 ) ++00,000000007450580569168 x = x + ( x >> 27 ) ++00,000000014901161082825 x = x + ( x >> 26 ) ++00,000000029802321943606 x = x + ( x >> 25 ) ++00,000000059604642999034 x = x + ( x >> 24 ) ++00,000000119209282445354 x = x + ( x >> 23 ) ++00,000000238418550679858 x = x + ( x >> 22 ) ++00,000000476837044516323 x = x + ( x >> 21 ) ++00,000000953673861659188 x = x + ( x >> 20 ) ++00,000001907346813825409 x = x + ( x >> 19 ) ++00,000003814689989685890 x = x + ( x >> 18 ) ++00,000007629365427567572 x = x + ( x >> 17 ) ++00,000015258672648362398 x = x + ( x >> 16 ) ++00,000030517112473186380 x = x + ( x >> 15 ) ++00,000061033293680638527 x = x + ( x >> 14 ) ++00,000122062862525677371 x = x + ( x >> 13 ) ++00,000244110827527362707 x = x + ( x >> 12 ) ++00,000488162079501351187 x = x + ( x >> 11 ) ++00,000976085973055458925 x = x + ( x >> 10 ) ++00,001951220131261749337 x = x + ( x >> 9 ) ++00,003898640415657322889 x = x + ( x >> 8 ) ++00,007782140442054948960 x = x + ( x >> 7 ) ++00,015504186535965254479 x = x + ( x >> 6 ) ++00,030771658666753687328 x = x + ( x >> 5 ) ++00,060624621816434839938 x = x + ( x >> 4 ) ++00,117783035656383455736 x = x + ( x >> 3 ) ++00,223143551314209764858 x = x + ( x >> 2 ) ++00,405465108108164384859 x = x + ( x >> 1 ) ++00,693147180559945286227 x = ( x << 1 ) ++01,386294361119890572454 x = ( x << 2 ) ++02,772588722239781144907 x = ( x << 4 ) ++05,545177444479562289814 x = ( x << 8 ) ++11,090354888959124579628 x = ( x << 16 ) ++21,487562597358305538364 x = ( x << 31 ) + +for negative values: + +-00,374693449441410697531 017FAFA3 x-= ( x >> 2 ) + ( x >> 4 ) +-00,207639364778244489562 00D49F69 x-= ( x >> 2 ) - ( x >> 4 ) +-00,115831815525121700761 00769C9D x-= ( x >> 3 ) - ( x >> 6 ) +-00,060380510988907482028 003DD463 x-= ( x >> 4 ) - ( x >> 8 ) +-00,031748698314580298119 002082BB x-= ( x >> 5 ) +-00,015996403602177928366 0010615C x-= ( x >> 6 ) + ( x >> 12 ) +-00,008089270731616965762 0008488D x-= ( x >> 7 ) + ( x >> 12 ) +-00,004159027401785260480 00044243 x-= ( x >> 8 ) + ( x >> 12 ) +-00,003423823349553609900 00038188 x-= ( x >> 8 ) - ( x >> 11 ) +-00,001832733117311761669 0001E070 x-= ( x >> 9 ) - ( x >> 13 ) +-00,000961766059678620302 0000FC1F x-= ( x >> 10 ) - ( x >> 16 ) +-00,000484583944571210926 00007F07 x-= ( x >> 11 ) - ( x >> 18 ) +-00,000243216525424976433 00003FC1 x-= ( x >> 12 ) - ( x >> 20 ) + +#endif + +// input is Q16, outputQ26 +static int32_t fixlog( int32_t x ) { + int32_t t,y; + + y = 0x2996BD9E; // ln(2^15) << 26 + if(x<0x00008000) x<<=16, y-= 0x2C5C85FD; + if(x<0x00800000) x<<= 8, y-= 0x162E42FE; + if(x<0x08000000) x<<= 4, y-= 0x0B17217F; + if(x<0x20000000) x<<= 2, y-= 0x058B90BF; + if(x<0x40000000) x<<= 1, y-= 0x02C5C85F; + t=x+(x>>1); if((t&0x80000000)==0) x=t, y-= 0x019F323E; + t=x+(x>>2); if((t&0x80000000)==0) x=t, y-= 0x00E47FBE; + t=x+(x>>3); if((t&0x80000000)==0) x=t, y-= 0x00789C1D; + t=x+(x>>4); if((t&0x80000000)==0) x=t, y-= 0x003E1461; + t=x+(x>>5); if((t&0x80000000)==0) x=t, y-= 0x001F829B; + t=x+(x>>6); if((t&0x80000000)==0) x=t, y-= 0x000FE054; + t=x+(x>>7); if((t&0x80000000)==0) x=t, y-= 0x0007F80A; + t=x+(x>>8); if((t&0x80000000)==0) x=t, y-= 0x0003FE01; + t=x+(x>>9); if((t&0x80000000)==0) x=t, y-= 0x0001FF80; + t=x+(x>>10);if((t&0x80000000)==0) x=t, y-= 0x0000FFE0; + t=x+(x>>11);if((t&0x80000000)==0) x=t, y-= 0x00007FF8; + t=x+(x>>12);if((t&0x80000000)==0) x=t, y-= 0x00003FFE; + t=x+(x>>13);if((t&0x80000000)==0) x=t, y-= 0x00001FFF; + x = 0x80000000-x; + y-= x>>5; + return y; +} + +// input is Q26, output Q16 +static uint32_t fixexp(int32_t x) { + int32_t t; + uint32_t y = 0x10000; + + if( (x & 0x80000000) == 0 ) { + t=x-0x162E42FE; if(t>=0) x=t,y<<=8; + t=x-0x0B17217F; if(t>=0) x=t,y<<=4; + t=x-0x058B90BF; if(t>=0) x=t,y<<=2; + t=x-0x02C5C85F; if(t>=0) x=t,y<<=1; + t=x-0x019F323E; if(t>=0) x=t,y+=y>>1; + t=x-0x00E47FBE; if(t>=0) x=t,y+=y>>2; + t=x-0x00789C1D; if(t>=0) x=t,y+=y>>3; + t=x-0x003E1461; if(t>=0) x=t,y+=y>>4; + t=x-0x001F829B; if(t>=0) x=t,y+=y>>5; + t=x-0x000FE054; if(t>=0) x=t,y+=y>>6; + t=x-0x0007F80A; if(t>=0) x=t,y+=y>>7; + t=x-0x0003FE01; if(t>=0) x=t,y+=y>>8; + t=x-0x0001FF80; if(t>=0) x=t,y+=y>>9; + t=x-0x0000FFE0; if(t>=0) x=t,y+=y>>10; + t=x-0x00007FF8; if(t>=0) x=t,y+=y>>11; + t=x-0x00003FFE; if(t>=0) x=t,y+=y>>12; + t=x-0x00001FFF; if(t>=0) x=t,y+=y>>13; + if(x&0x0001000) y+=y>>14; + if(x&0x0000800) y+=y>>15; + if(x&0x0000400) y+=y>>16; + if(x&0x0000200) y+=y>>17; + if(x&0x0000100) y+=y>>18; + if(x&0x0000080) y+=y>>19; + if(x&0x0000040) y+=y>>20; + if(x&0x0000020) y+=y>>21; + if(x&0x0000010) y+=y>>22; + if(x&0x0000008) y+=y>>23; + if(x&0x0000004) y+=y>>24; + if(x&0x0000002) y+=y>>25; + if(x&0x0000001) y+=y>>26; + } else { + x=-x; + t=x-0x162E42FE; if(t>=0) x=t,y>>=8; + t=x-0x0B17217F; if(t>=0) x=t,y>>=4; + t=x-0x058B90BF; if(t>=0) x=t,y>>=2; + t=x-0x02C5C85F; if(t>=0) x=t,y>>=1; + t=x-0x017FAFA3; if(t>=0) x=t,y-=(y>>2) + (y>>4); + t=x-0x00D49F69; if(t>=0) x=t,y-=(y>>2) - (y>>4); + t=x-0x00769C9D; if(t>=0) x=t,y-=(y>>3) - (y>>6); + t=x-0x003DD463; if(t>=0) x=t,y-=(y>>4) - (y>>8); + t=x-0x002082BB; if(t>=0) x=t,y-=y>>5; + t=x-0x0010615C; if(t>=0) x=t,y-=(y>>6) + (y>>12); + t=x-0x0008488D; if(t>=0) x=t,y-=(y>>7) + (y>>12); + t=x-0x00044243; if(t>=0) x=t,y-=(y>>8) + (y>>12); + t=x-0x00038188; if(t>=0) x=t,y-=(y>>8) - (y>>11); + t=x-0x0001E070; if(t>=0) x=t,y-=(y>>9) - (y>>13); + t=x-0x0000FC1F; if(t>=0) x=t,y-=(y>>10)- (y>>16); + t=x-0x00007F07; if(t>=0) x=t,y-=(y>>11)- (y>>18); + t=x-0x00003FC1; if(t>=0) x=t,y-=(y>>12)- (y>>20); + if(x&0x0002000) y-=y>>13; + if(x&0x0001000) y-=y>>14; + if(x&0x0000800) y-=y>>15; + if(x&0x0000400) y-=y>>16; + if(x&0x0000200) y-=y>>17; + if(x&0x0000100) y-=y>>18; + if(x&0x0000080) y-=y>>19; + if(x&0x0000040) y-=y>>20; + if(x&0x0000020) y-=y>>21; + if(x&0x0000010) y-=y>>22; + if(x&0x0000008) y-=y>>23; + if(x&0x0000004) y-=y>>24; + if(x&0x0000002) y-=y>>25; + if(x&0x0000001) y-=y>>26; + } + + return y; +} + +int fixpow(int32_t *pow, int32_t base, int32_t exponent ) +{ + int neg = 0; + int32_t log_base, res; + int64_t log_base_times_exponent; + + if( base < 0 ) { + // negative bases only can have integer exponents + if( exponent & 0xffff ) return -1; + // sign of power of a negative base is determined by + // wether exp is even + if( exponent & 0x10000 ) neg = 1; + base = abs(base); + } + + // To calculate pow(base,exp), we do exp( log(base) * exp ) + // which is mathematically the same. log_base is Q26 + log_base = fixlog( base ); + log_base_times_exponent = ( (int64_t)log_base * (int64_t)exponent ) >> 16; + + // fixexp overflows for values > 21,48756259689264 which + // in Q26 notation is 1442005916 + if( log_base_times_exponent > 1442005916 ) + return -2; + + res = (int32_t)log_base_times_exponent; + res = fixexp( res ); + if( neg ) res = -res; + *pow = res; + + return 0; +} + +int main() +{ + double base = -.5f; + double exponent = 10.f; + int32_t result; + int error = fixpow( &result, TO_Q16(base), TO_Q16(exponent) ); + + printf( "pow(%lf,%lf)=%lf (%s)\n", base, exponent, FROM_Q16(result), error?"ERROR":"OK" ); + return 0; +} diff --git a/generate_table.c b/generate_table.c new file mode 100644 index 0000000..c7a9d0c --- /dev/null +++ b/generate_table.c @@ -0,0 +1,34 @@ +#include +#include +#include + +// s(-1) n(14) off(+1) x = x - ( x >> 14 ) +// s( 1) n(-4) off( 0) x = ( x << 4 ) +// s( 1) n( 8) off(-1) x = - x + ( x << 8 ) + +int main() { + int n, m, nsign; + + // loop over all constructs in the form +-1*x^+-2n, n=-31..+31 + for (n=-31; n<= 31; ++n ) + for ( nsign=-1; nsign<=1; nsign+=2 ) + { + // The one term only case + double v = (double)nsign * pow( 2.f, (double)n ); + if( v > 0.f ) + printf( "%0+25.21lf %08X x = %s ( x %s %2d )%s\n", log(v), abs((int)(67108864.f*log(v))), nsign==-1?"-":" ", n>=0?"<<":">>", (int)abs(n), " !RECOMMENDED!" ); + + // Loop over second term + for (m=-31; m<=31; ++m ) + { + double v = pow( 2.f, (double)m ) + (double)nsign * pow( 2.f, (double)n ); + if( v > 0.f ) { + printf( "%0+25.21lf %08X x = ( x %s %2d ) %s ( x %s %2d )%s\n", log(v), abs((int)(67108864.f*log(v))), m>=0?"<<":">>", (int)abs(m), nsign==-1?"-":"+", n>=0?"<<":">>", (int)abs(n), n*m?"":" !RECOMMENDED!" ); + if( v < 1.f ) + printf( "%0+25.21lf %08X x-= ( x %s %2d ) %s ( x %s %2d )\n", log(1.0f - v), abs((int)(67108864.f*log(1.0f - v))), m>=0?"<<":">>", (int)abs(m), nsign==-1?"-":"+", n>=0?"<<":">>", (int)abs(n) ); + } + } + } + + return 0; +} -- cgit v1.2.3