mirror of https://github.com/f4exb/sdrangel.git
Raw import of Anthony Williams' fixed point math library
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// Distributed under the Boost Software License, Version 1.0. (See
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// accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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// (C) Copyright 2007 Anthony Williams
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#include "fixed.hpp"
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// all constants are scaled to 2^28 (as 1)
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int64_t const internal_pi=0x3243f6a8;
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int64_t const internal_two_pi=0x6487ed51;
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int64_t const internal_half_pi=0x1921fb54;
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int64_t const internal_quarter_pi=0xc90fdaa;
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extern fixed const fixed_pi(fixed::internal(),internal_pi);
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extern fixed const fixed_two_pi(fixed::internal(),internal_two_pi);
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extern fixed const fixed_half_pi(fixed::internal(),internal_half_pi);
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extern fixed const fixed_quarter_pi(fixed::internal(),internal_quarter_pi);
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fixed& fixed::operator%=(fixed const& other)
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{
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m_nVal = m_nVal%other.m_nVal;
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return *this;
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}
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fixed& fixed::operator*=(fixed const& val)
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{
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bool const val_negative=val.m_nVal<0;
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bool const this_negative=m_nVal<0;
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bool const negate=val_negative ^ this_negative;
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uint64_t const other=val_negative?-val.m_nVal:val.m_nVal;
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uint64_t const self=this_negative?-m_nVal:m_nVal;
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if(uint64_t const self_upper=(self>>32))
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{
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m_nVal=(self_upper*other)<<(32-fixed_resolution_shift);
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}
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else
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{
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m_nVal=0;
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}
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if(uint64_t const self_lower=(self&0xffffffff))
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{
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uint64_t const other_upper=static_cast<uint64_t>(other>>32);
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uint64_t const other_lower=static_cast<uint64_t>(other&0xffffffff);
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uint64_t const lower_self_upper_other_res=self_lower*other_upper;
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uint64_t const lower_self_lower_other_res=self_lower*other_lower;
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m_nVal+=(lower_self_upper_other_res<<(32-fixed_resolution_shift))
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+ (lower_self_lower_other_res>>fixed_resolution_shift);
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}
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if(negate)
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{
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m_nVal=-m_nVal;
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}
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return *this;
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}
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fixed& fixed::operator/=(fixed const& divisor)
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{
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if( !divisor.m_nVal)
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{
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m_nVal=fixed_max.m_nVal;
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}
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else
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{
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bool const negate_this=(m_nVal<0);
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bool const negate_divisor=(divisor.m_nVal<0);
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bool const negate=negate_this ^ negate_divisor;
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uint64_t a=negate_this?-m_nVal:m_nVal;
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uint64_t b=negate_divisor?-divisor.m_nVal:divisor.m_nVal;
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uint64_t res=0;
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uint64_t temp=b;
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bool const a_large=a>b;
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unsigned shift=fixed_resolution_shift;
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if(a_large)
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{
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uint64_t const half_a=a>>1;
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while(temp<half_a)
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{
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temp<<=1;
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++shift;
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}
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}
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uint64_t d=1LL<<shift;
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if(a_large)
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{
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a-=temp;
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res+=d;
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}
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while(a && temp && shift)
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{
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unsigned right_shift=0;
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while(right_shift<shift && (temp>a))
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{
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temp>>=1;
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++right_shift;
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}
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d>>=right_shift;
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shift-=right_shift;
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a-=temp;
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res+=d;
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}
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m_nVal=(negate?-(int64_t)res:res);
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}
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return *this;
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}
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fixed fixed::sqrt() const
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{
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unsigned const max_shift=62;
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uint64_t a_squared=1LL<<max_shift;
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unsigned b_shift=(max_shift+fixed_resolution_shift)/2;
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uint64_t a=1LL<<b_shift;
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uint64_t x=m_nVal;
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while(b_shift && a_squared>x)
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{
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a>>=1;
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a_squared>>=2;
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--b_shift;
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}
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uint64_t remainder=x-a_squared;
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--b_shift;
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while(remainder && b_shift)
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{
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uint64_t b_squared=1LL<<(2*b_shift-fixed_resolution_shift);
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int const two_a_b_shift=b_shift+1-fixed_resolution_shift;
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uint64_t two_a_b=(two_a_b_shift>0)?(a<<two_a_b_shift):(a>>-two_a_b_shift);
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while(b_shift && remainder<(b_squared+two_a_b))
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{
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b_squared>>=2;
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two_a_b>>=1;
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--b_shift;
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}
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uint64_t const delta=b_squared+two_a_b;
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if((2*remainder)>delta)
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{
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a+=(1LL<<b_shift);
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remainder-=delta;
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if(b_shift)
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{
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--b_shift;
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}
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}
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}
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return fixed(internal(),a);
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}
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namespace
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{
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int const max_power=63-fixed_resolution_shift;
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// 35 values (63-28)
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int64_t const log_two_power_n_reversed[]={
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0x18429946ELL,0x1791272EFLL,0x16DFB516FLL,0x162E42FF0LL,0x157CD0E70LL,0x14CB5ECF1LL,0x1419ECB71LL,0x13687A9F2LL,
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0x12B708872LL,0x1205966F3LL,0x115424573LL,0x10A2B23F4LL,0xFF140274LL,0xF3FCE0F5LL,0xE8E5BF75LL,0xDDCE9DF6LL,
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0xD2B77C76LL,0xC7A05AF7LL,0xBC893977LL,0xB17217F8LL,0xA65AF679LL,0x9B43D4F9LL,0x902CB379LL,0x851591FaLL,
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0x79FE707bLL,0x6EE74EFbLL,0x63D02D7BLL,0x58B90BFcLL,0x4DA1EA7CLL,0x428AC8FdLL,0x3773A77DLL,0x2C5C85FeLL,
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0x2145647ELL,0x162E42FfLL,0xB17217FLL
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};
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// 28 values
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int64_t const log_one_plus_two_power_minus_n[]={
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0x67CC8FBLL,0x391FEF9LL,0x1E27077LL,0xF85186LL,
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0x7E0A6CLL,0x3F8151LL,0x1FE02ALL,0xFF805LL,0x7FE01LL,0x3FF80LL,0x1FFE0LL,0xFFF8LL,
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0x7FFELL,0x4000LL,0x2000LL,0x1000LL,0x800LL,0x400LL,0x200LL,0x100LL,
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0x80LL,0x40LL,0x20LL,0x10LL,0x8LL,0x4LL,0x2LL,0x1LL
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};
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// 28 values
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int64_t const log_one_over_one_minus_two_power_minus_n[]={
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0xB172180LL,0x49A5884LL,0x222F1D0LL,0x108598BLL,
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0x820AECLL,0x408159LL,0x20202BLL,0x100805LL,0x80201LL,0x40080LL,0x20020LL,0x10008LL,
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0x8002LL,0x4001LL,0x2000LL,0x1000LL,0x800LL,0x400LL,0x200LL,0x100LL,
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0x80LL,0x40LL,0x20LL,0x10LL,0x8LL,0x4LL,0x2LL,0x1LL
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};
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}
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fixed fixed::exp() const
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{
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if(m_nVal>=log_two_power_n_reversed[0])
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{
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return fixed_max;
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}
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if(m_nVal<-log_two_power_n_reversed[63-2*fixed_resolution_shift])
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{
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return fixed(internal(),0);
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}
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if(!m_nVal)
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{
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return fixed(internal(),fixed_resolution);
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}
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int64_t res=fixed_resolution;
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if(m_nVal>0)
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{
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int power=max_power;
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int64_t const* log_entry=log_two_power_n_reversed;
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int64_t temp=m_nVal;
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while(temp && power>(-(int)fixed_resolution_shift))
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{
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while(!power || (temp<*log_entry))
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{
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if(!power)
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{
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log_entry=log_one_plus_two_power_minus_n;
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}
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else
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{
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++log_entry;
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}
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--power;
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}
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temp-=*log_entry;
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if(power<0)
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{
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res+=(res>>(-power));
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}
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else
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{
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res<<=power;
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}
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}
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}
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else
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{
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int power=fixed_resolution_shift;
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int64_t const* log_entry=log_two_power_n_reversed+(max_power-power);
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int64_t temp=m_nVal;
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while(temp && power>(-(int)fixed_resolution_shift))
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{
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while(!power || (temp>(-*log_entry)))
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{
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if(!power)
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{
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log_entry=log_one_over_one_minus_two_power_minus_n;
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}
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else
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{
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++log_entry;
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}
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--power;
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}
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temp+=*log_entry;
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if(power<0)
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{
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res-=(res>>(-power));
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}
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else
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{
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res>>=power;
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}
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}
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}
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return fixed(internal(),res);
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}
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fixed fixed::log() const
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{
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if(m_nVal<=0)
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{
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return -fixed_max;
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}
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if(m_nVal==fixed_resolution)
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{
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return fixed_zero;
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}
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uint64_t temp=m_nVal;
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int left_shift=0;
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uint64_t const scale_position=0x8000000000000000;
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while(temp<scale_position)
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{
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++left_shift;
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temp<<=1;
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}
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int64_t res=(left_shift<max_power)?
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log_two_power_n_reversed[left_shift]:
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-log_two_power_n_reversed[2*max_power-left_shift];
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unsigned right_shift=1;
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uint64_t shifted_temp=temp>>1;
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while(temp && (right_shift<fixed_resolution_shift))
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{
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while((right_shift<fixed_resolution_shift) && (temp<(shifted_temp+scale_position)))
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{
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shifted_temp>>=1;
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++right_shift;
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}
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temp-=shifted_temp;
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shifted_temp=temp>>right_shift;
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res+=log_one_over_one_minus_two_power_minus_n[right_shift-1];
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}
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return fixed(fixed::internal(),res);
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}
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namespace
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{
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const int64_t arctantab[32] = {
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297197971, 210828714, 124459457, 65760959, 33381290, 16755422, 8385879,
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4193963, 2097109, 1048571, 524287, 262144, 131072, 65536, 32768, 16384,
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8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1, 0, 0,
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};
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int64_t scale_cordic_result(int64_t a)
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{
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int64_t const cordic_scale_factor=0x22C2DD1C; /* 0.271572 * 2^31*/
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return (int64_t)((((int64_t)a)*cordic_scale_factor)>>31);
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}
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int64_t right_shift(int64_t val,int shift)
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{
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return (shift<0)?(val<<-shift):(val>>shift);
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}
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void perform_cordic_rotation(int64_t&px, int64_t&py, int64_t theta)
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{
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int64_t x = px, y = py;
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int64_t const *arctanptr = arctantab;
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for (int i = -1; i <= (int)fixed_resolution_shift; ++i)
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{
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int64_t const yshift=right_shift(y,i);
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int64_t const xshift=right_shift(x,i);
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if (theta < 0)
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{
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x += yshift;
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y -= xshift;
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theta += *arctanptr++;
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}
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else
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{
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x -= yshift;
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y += xshift;
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theta -= *arctanptr++;
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}
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}
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px = scale_cordic_result(x);
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py = scale_cordic_result(y);
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}
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void perform_cordic_polarization(int64_t& argx, int64_t&argy)
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{
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int64_t theta=0;
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int64_t x = argx, y = argy;
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int64_t const *arctanptr = arctantab;
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for(int i = -1; i <= (int)fixed_resolution_shift; ++i)
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{
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int64_t const yshift=right_shift(y,i);
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int64_t const xshift=right_shift(x,i);
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if(y < 0)
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{
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y += xshift;
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x -= yshift;
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theta -= *arctanptr++;
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}
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else
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{
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y -= xshift;
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x += yshift;
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theta += *arctanptr++;
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}
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}
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argx = scale_cordic_result(x);
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argy = theta;
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}
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}
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void fixed::sin_cos(fixed const& theta,fixed* s,fixed*c)
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{
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int64_t x=theta.m_nVal%internal_two_pi;
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if( x < 0 )
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x += internal_two_pi;
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bool negate_cos=false;
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bool negate_sin=false;
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if( x > internal_pi )
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{
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x =internal_two_pi-x;
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negate_sin=true;
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}
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if(x>internal_half_pi)
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{
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x=internal_pi-x;
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negate_cos=true;
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}
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int64_t x_cos=1<<28,x_sin=0;
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perform_cordic_rotation(x_cos,x_sin,(int64_t)x);
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if(s)
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{
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s->m_nVal=negate_sin?-x_sin:x_sin;
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}
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if(c)
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{
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c->m_nVal=negate_cos?-x_cos:x_cos;
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}
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}
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fixed fixed::atan() const
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{
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fixed r,theta;
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to_polar(1,*this,&r,&theta);
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return theta;
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}
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void fixed::to_polar(fixed const& x,fixed const& y,fixed* r,fixed*theta)
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{
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bool const negative_x=x.m_nVal<0;
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bool const negative_y=y.m_nVal<0;
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uint64_t a=negative_x?-x.m_nVal:x.m_nVal;
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uint64_t b=negative_y?-y.m_nVal:y.m_nVal;
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unsigned right_shift=0;
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unsigned const max_value=1U<<fixed_resolution_shift;
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while((a>=max_value) || (b>=max_value))
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{
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++right_shift;
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a>>=1;
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b>>=1;
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}
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int64_t xtemp=(int64_t)a;
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int64_t ytemp=(int64_t)b;
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perform_cordic_polarization(xtemp,ytemp);
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r->m_nVal=int64_t(xtemp)<<right_shift;
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theta->m_nVal=ytemp;
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if(negative_x && negative_y)
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{
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theta->m_nVal-=internal_pi;
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}
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else if(negative_x)
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{
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theta->m_nVal=internal_pi-theta->m_nVal;
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}
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else if(negative_y)
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{
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theta->m_nVal=-theta->m_nVal;
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}
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}
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