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ffa_ch9_exodus.kv       1 ------------------------------------------------------------------------------
ffa_ch9_exodus.kv 2 ------------------------------------------------------------------------------
ffa_ch9_exodus.kv 3 -- This file is part of 'Finite Field Arithmetic', aka 'FFA'. --
ffa_ch9_exodus.kv 4 -- --
ffa_ch9_exodus.kv 5 -- (C) 2018 Stanislav Datskovskiy ( www.loper-os.org ) --
ffa_ch9_exodus.kv 6 -- http://wot.deedbot.org/17215D118B7239507FAFED98B98228A001ABFFC7.html --
ffa_ch9_exodus.kv 7 -- --
ffa_ch9_exodus.kv 8 -- You do not have, nor can you ever acquire the right to use, copy or --
ffa_ch9_exodus.kv 9 -- distribute this software ; Should you use this software for any purpose, --
ffa_ch9_exodus.kv 10 -- or copy and distribute it to anyone or in any manner, you are breaking --
ffa_ch9_exodus.kv 11 -- the laws of whatever soi-disant jurisdiction, and you promise to --
ffa_ch9_exodus.kv 12 -- continue doing so for the indefinite future. In any case, please --
ffa_ch9_exodus.kv 13 -- always : read and understand any software ; verify any PGP signatures --
ffa_ch9_exodus.kv 14 -- that you use - for any purpose. --
ffa_ch9_exodus.kv 15 -- --
ffa_ch9_exodus.kv 16 -- See also http://trilema.com/2015/a-new-software-licensing-paradigm . --
ffa_ch9_exodus.kv 17 ------------------------------------------------------------------------------
ffa_ch9_exodus.kv 18 ------------------------------------------------------------------------------
ffa_ch9_exodus.kv 19
ffa_ch9_exodus.kv 20 with W_Shifts; use W_Shifts;
ffa_ch9_exodus.kv 21
ffa_ch9_exodus.kv 22
ffa_ch9_exodus.kv 23 package body W_Mul is
ffa_ch9_exodus.kv 24
ffa_ch10_karatsub... 25 function Mul_HalfWord_Iron(X : in HalfWord;
ffa_ch10_karatsub... 26 Y : in HalfWord) return Word is
ffa_ch10_karatsub... 27 begin
ffa_ch10_karatsub... 28 return X * Y;
ffa_ch10_karatsub... 29 end Mul_HalfWord_Iron;
ffa_ch10_karatsub... 30
ffa_ch10_karatsub... 31
ffa_ch9_exodus.kv 32 -- Multiply half-words X and Y, producing a Word-sized product
ffa_ch10_karatsub... 33 function Mul_HalfWord_Soft(X : in HalfWord; Y : in HalfWord) return Word is
ffa_ch9_exodus.kv 34
ffa_ch9_exodus.kv 35 -- X-Slide
ffa_ch9_exodus.kv 36 XS : Word := X;
ffa_ch9_exodus.kv 37
ffa_ch9_exodus.kv 38 -- Y-Slide
ffa_ch9_exodus.kv 39 YS : Word := Y;
ffa_ch9_exodus.kv 40
ffa_ch9_exodus.kv 41 -- Gate Mask
ffa_ch9_exodus.kv 42 GM : Word;
ffa_ch9_exodus.kv 43
ffa_ch9_exodus.kv 44 -- The Product
ffa_ch9_exodus.kv 45 XY : Word := 0;
ffa_ch9_exodus.kv 46
ffa_ch9_exodus.kv 47 -- Performed for each bit of HalfWord's bitness:
ffa_ch9_exodus.kv 48 procedure Bit is
ffa_ch9_exodus.kv 49 begin
ffa_ch9_exodus.kv 50
ffa_ch9_exodus.kv 51 -- Compute the gate mask
ffa_ch9_exodus.kv 52 GM := 0 - (YS and 1);
ffa_ch9_exodus.kv 53
ffa_ch9_exodus.kv 54 -- Perform the gated addition
ffa_ch9_exodus.kv 55 XY := XY + (XS and GM);
ffa_ch9_exodus.kv 56
ffa_ch9_exodus.kv 57 -- Crank the next Y-slide bit into position
ffa_ch9_exodus.kv 58 YS := Shift_Right(YS, 1);
ffa_ch9_exodus.kv 59
ffa_ch9_exodus.kv 60 -- Advance the X-slide by 1 bit
ffa_ch9_exodus.kv 61 XS := Shift_Left(XS, 1);
ffa_ch9_exodus.kv 62
ffa_ch9_exodus.kv 63 end Bit;
ffa_ch9_exodus.kv 64
ffa_ch9_exodus.kv 65 begin
ffa_ch9_exodus.kv 66
ffa_ch9_exodus.kv 67 -- For each bit of the Y-Slide (unrolled) :
ffa_ch9_exodus.kv 68 for b in 1 .. HalfByteness loop
ffa_ch9_exodus.kv 69
ffa_ch9_exodus.kv 70 Bit; Bit; Bit; Bit; Bit; Bit; Bit; Bit;
ffa_ch9_exodus.kv 71
ffa_ch9_exodus.kv 72 end loop;
ffa_ch9_exodus.kv 73
ffa_ch9_exodus.kv 74 -- Return the Product
ffa_ch9_exodus.kv 75 return XY;
ffa_ch9_exodus.kv 76
ffa_ch10_karatsub... 77 end Mul_HalfWord_Soft;
ffa_ch9_exodus.kv 78
ffa_ch9_exodus.kv 79
ffa_ch9_exodus.kv 80 -- Get the bottom half of a Word
ffa_ch9_exodus.kv 81 function BottomHW(W : in Word) return HalfWord is
ffa_ch9_exodus.kv 82 begin
ffa_ch9_exodus.kv 83 return W and (2**HalfBitness - 1);
ffa_ch9_exodus.kv 84 end BottomHW;
ffa_ch9_exodus.kv 85
ffa_ch9_exodus.kv 86
ffa_ch9_exodus.kv 87 -- Get the top half of a Word
ffa_ch9_exodus.kv 88 function TopHW(W : in Word) return HalfWord is
ffa_ch9_exodus.kv 89 begin
ffa_ch9_exodus.kv 90 return Shift_Right(W, HalfBitness);
ffa_ch9_exodus.kv 91 end TopHW;
ffa_ch9_exodus.kv 92
ffa_ch9_exodus.kv 93
ffa_ch9_exodus.kv 94 -- Carry out X*Y mult, return lower word XY_LW and upper word XY_HW.
ffa_ch9_exodus.kv 95 procedure Mul_Word(X : in Word;
ffa_ch9_exodus.kv 96 Y : in Word;
ffa_ch9_exodus.kv 97 XY_LW : out Word;
ffa_ch9_exodus.kv 98 XY_HW : out Word) is
ffa_ch9_exodus.kv 99
ffa_ch9_exodus.kv 100 -- Bottom half of multiplicand X
ffa_ch9_exodus.kv 101 XL : constant HalfWord := BottomHW(X);
ffa_ch9_exodus.kv 102
ffa_ch9_exodus.kv 103 -- Top half of multiplicand X
ffa_ch9_exodus.kv 104 XH : constant HalfWord := TopHW(X);
ffa_ch9_exodus.kv 105
ffa_ch9_exodus.kv 106 -- Bottom half of multiplicand Y
ffa_ch9_exodus.kv 107 YL : constant HalfWord := BottomHW(Y);
ffa_ch9_exodus.kv 108
ffa_ch9_exodus.kv 109 -- Top half of multiplicand Y
ffa_ch9_exodus.kv 110 YH : constant HalfWord := TopHW(Y);
ffa_ch9_exodus.kv 111
ffa_ch9_exodus.kv 112 -- XL * YL
ffa_ch10_karatsub... 113 LL : constant Word := Mul_HalfWord_Iron(XL, YL);
ffa_ch9_exodus.kv 114
ffa_ch9_exodus.kv 115 -- XL * YH
ffa_ch10_karatsub... 116 LH : constant Word := Mul_HalfWord_Iron(XL, YH);
ffa_ch9_exodus.kv 117
ffa_ch9_exodus.kv 118 -- XH * YL
ffa_ch10_karatsub... 119 HL : constant Word := Mul_HalfWord_Iron(XH, YL);
ffa_ch9_exodus.kv 120
ffa_ch9_exodus.kv 121 -- XH * YH
ffa_ch10_karatsub... 122 HH : constant Word := Mul_HalfWord_Iron(XH, YH);
ffa_ch9_exodus.kv 123
ffa_ch9_exodus.kv 124 -- Carry
ffa_ch9_exodus.kv 125 CL : constant Word := TopHW(TopHW(LL) + BottomHW(LH) + BottomHW(HL));
ffa_ch9_exodus.kv 126
ffa_ch9_exodus.kv 127 begin
ffa_ch9_exodus.kv 128
ffa_ch9_exodus.kv 129 -- Get the bottom half of the Product:
ffa_ch9_exodus.kv 130 XY_LW := LL + Shift_Left(LH + HL, HalfBitness);
ffa_ch9_exodus.kv 131
ffa_ch9_exodus.kv 132 -- Get the top half of the Product:
ffa_ch9_exodus.kv 133 XY_HW := HH + TopHW(HL) + TopHW(LH) + CL;
ffa_ch9_exodus.kv 134
ffa_ch9_exodus.kv 135 end Mul_Word;
ffa_ch9_exodus.kv 136
ffa_ch12_karatsub... 137 ---------------------------------------------------------------------------
ffa_ch12_karatsub... 138 -- LET A CURSE FALL FOREVER on the authors of GCC, and on the Ada committee,
ffa_ch12_karatsub... 139 -- neither of whom saw it fit to decree a primitive which returns both
ffa_ch12_karatsub... 140 -- upper and lower halves of an iron MUL instruction's result. Consequently,
ffa_ch12_karatsub... 141 -- portable Mul_Word demands ~four~ MULs (and several additions and shifts);
ffa_ch12_karatsub... 142 -- while portable Sqr_Word demands ~three~ MULs (and likewise adds/shifts.)
ffa_ch12_karatsub... 143 -- If it were not for their idiocy, BOTH routines would weigh 1 CPU instr.!
ffa_ch12_karatsub... 144 ---------------------------------------------------------------------------
ffa_ch12_karatsub... 145
ffa_ch12_karatsub... 146 -- Carry out X*X squaring, return lower word XX_LW and upper word XX_HW.
ffa_ch12_karatsub... 147 procedure Sqr_Word(X : in Word;
ffa_ch12_karatsub... 148 XX_LW : out Word;
ffa_ch12_karatsub... 149 XX_HW : out Word) is
ffa_ch12_karatsub... 150
ffa_ch12_karatsub... 151 -- Bottom half of multiplicand X
ffa_ch12_karatsub... 152 XL : constant HalfWord := BottomHW(X);
ffa_ch12_karatsub... 153
ffa_ch12_karatsub... 154 -- Top half of multiplicand X
ffa_ch12_karatsub... 155 XH : constant HalfWord := TopHW(X);
ffa_ch12_karatsub... 156
ffa_ch12_karatsub... 157 -- XL^2
ffa_ch12_karatsub... 158 LL : constant Word := Mul_HalfWord_Iron(XL, XL);
ffa_ch12_karatsub... 159
ffa_ch12_karatsub... 160 -- XL * XH
ffa_ch12_karatsub... 161 LH : constant Word := Mul_HalfWord_Iron(XL, XH);
ffa_ch12_karatsub... 162
ffa_ch12_karatsub... 163 -- XH^2
ffa_ch12_karatsub... 164 HH : constant Word := Mul_HalfWord_Iron(XH, XH);
ffa_ch12_karatsub... 165
ffa_ch12_karatsub... 166 -- Carry
ffa_ch12_karatsub... 167 CL : constant Word := TopHW(TopHW(LL) + Shift_Left(BottomHW(LH), 1));
ffa_ch12_karatsub... 168
ffa_ch12_karatsub... 169 begin
ffa_ch12_karatsub... 170
ffa_ch12_karatsub... 171 -- Get the bottom half of the Product:
ffa_ch12_karatsub... 172 XX_LW := LL + Shift_Left(LH, HalfBitness + 1);
ffa_ch12_karatsub... 173
ffa_ch12_karatsub... 174 -- Get the top half of the Product:
ffa_ch12_karatsub... 175 XX_HW := HH + Shift_Left(TopHW(LH), 1) + CL;
ffa_ch12_karatsub... 176
ffa_ch12_karatsub... 177 end Sqr_Word;
ffa_ch12_karatsub... 178
ffa_ch9_exodus.kv 179 end W_Mul;