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270 lines
6.7 KiB
PHP
270 lines
6.7 KiB
PHP
{
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This file is part of the Free Pascal run time library.
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Copyright (c) 2008 by the Free Pascal development team.
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Implementation of mathematical Routines (only for real)
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See the file COPYING.FPC, included in this distribution,
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for details about the copyright.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
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**********************************************************************}
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// Based on restoring division algorithm
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// Algorithm source document: Lecture notes by S. Galal and D. Pham, Division algorithms and hardware implementations.
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// Link to documentation http://www.seas.ucla.edu/~ingrid/ee213a/lectures/division_presentV2.pdf
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// Also refer to description on Wikipedia: https://en.wikipedia.org/wiki/Division_algorithm#Restoring_division
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// Note that the algorithm automatically yields the following results for special cases:
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// z div 0 = MAX(type)
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// 0 div 0 = MAX(type)
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// 0 div n = 0
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// Checks for z = 0; n = [0,1]; n = z and n > z could shortcut the algorithm for speed-ups
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// but would add extra code
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// Perhaps add the checks depending on optimization settings?
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// z (dividend) = q(quotient) x n(divisor) + p(remainder)
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{$ifndef FPC_SYSTEM_HAS_DIV_BYTE}
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{$define FPC_SYSTEM_HAS_DIV_BYTE}
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// z in Ra, n in Rb, 0 in Rp
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function fpc_div_byte(n, z: byte): byte; assembler; nostackframe;
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{$ifdef FPC_IS_SYSTEM}[public,alias: 'FPC_DIV_BYTE'];{$endif}
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label
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start, div1, div2, div3, finish;
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asm
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// Symbol Name Register(s)
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// z (A) dividend R22
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// n (B) divisor R24
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// p (P) remainder R20
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// i counter R18
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cp R24, R1
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brne start
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{$ifdef CPUAVR_HAS_JMP_CALL}
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call get_pc_addr
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{$else CPUAVR_HAS_JMP_CALL}
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rcall get_pc_addr
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{$endif CPUAVR_HAS_JMP_CALL}
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movw R20, R24
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{$ifdef CPUAVR_HAS_JMP_CALL}
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call get_frame
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{$else CPUAVR_HAS_JMP_CALL}
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rcall get_frame
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{$endif CPUAVR_HAS_JMP_CALL}
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movw R18, R24
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ldi R22, 200
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clr R23
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clr R24
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clr R25
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{$ifdef CPUAVR_HAS_JMP_CALL}
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call HandleErrorAddrFrameInd
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{$else CPUAVR_HAS_JMP_CALL}
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rcall HandleErrorAddrFrameInd
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{$endif CPUAVR_HAS_JMP_CALL}
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start:
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clr R20 // clear remainder
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ldi R18, 8 // iterate over 8 bits
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div1:
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lsl R22 // shift left A
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rol R20 // shift left P with carry from A shift
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sub R20, R24 // Subtract B from P, P <= P - B
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brlo div2
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ori R22, 1 // Set A[0] = 1
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rjmp div3
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div2: // negative branch, A[0] = 0 (default after shift), restore P
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add R20, R24 // restore old value of P
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div3:
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dec R18
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brne div1
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finish:
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mov R24, R22 // Move result from R22 to R24
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end;
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{It is a compilerproc (systemh.inc), make an alias for internal use.}
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{$ifdef FPC_IS_SYSTEM}
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function fpc_div_byte(n, z: byte): byte; external name 'FPC_DIV_BYTE';
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{$endif FPC_IS_SYSTEM}
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{$endif FPC_SYSTEM_HAS_DIV_BYTE}
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{$ifndef FPC_SYSTEM_HAS_DIV_WORD}
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{$define FPC_SYSTEM_HAS_DIV_WORD}
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// z in Ra, n in Rb, 0 in Rp
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function fpc_div_word(n, z: word): word; assembler; nostackframe;
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{$ifdef FPC_IS_SYSTEM}[public,alias: 'FPC_DIV_WORD'];{$endif}
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label
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start, div1, div2, div3, finish;
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asm
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// Symbol Name Register(s)
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// z (A) dividend R23, R22
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// n (B) divisor R25, R24
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// p (P) remainder R21, R20
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// i counter R18
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cp R24, R1
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brne start
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{$ifdef CPUAVR_HAS_JMP_CALL}
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call get_pc_addr
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{$else CPUAVR_HAS_JMP_CALL}
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rcall get_pc_addr
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{$endif CPUAVR_HAS_JMP_CALL}
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movw R20, R24
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{$ifdef CPUAVR_HAS_JMP_CALL}
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call get_frame
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{$else CPUAVR_HAS_JMP_CALL}
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rcall get_frame
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{$endif CPUAVR_HAS_JMP_CALL}
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movw R18, R24
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ldi R22, 200
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clr R23
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clr R24
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clr R25
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{$ifdef CPUAVR_HAS_JMP_CALL}
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call HandleErrorAddrFrameInd
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{$else CPUAVR_HAS_JMP_CALL}
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rcall HandleErrorAddrFrameInd
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{$endif CPUAVR_HAS_JMP_CALL}
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start: // Start of division...
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clr R20 // clear remainder low
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clr R21 // clear remainder hi
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ldi R18, 16 // iterate over 16 bits
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div1:
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lsl R22 // shift left A_L
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rol R23
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rol R20 // shift left P with carry from A shift
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rol R21
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sub R20, R24 // Subtract B from P, P <= P - B
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sbc R21, R25
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brlo div2
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ori R22, 1 // Set A[0] = 1
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rjmp div3
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div2: // negative branch, A[0] = 0 (default after shift), restore P
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add R20, R24 // restore old value of P
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adc R21, R25
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div3:
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dec R18
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brne div1
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finish:
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movw R24, R22 // Move result from R22:R23 to R24:R25
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end;
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{It is a compilerproc (systemh.inc), make an alias for internal use.}
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{$ifdef FPC_IS_SYSTEM}
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function fpc_div_word(n, z: word): word; external name 'FPC_DIV_WORD';
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{$endif FPC_IS_SYSTEM}
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{$endif FPC_SYSTEM_HAS_DIV_WORD}
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{$ifndef FPC_SYSTEM_HAS_DIV_DWORD}
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{$define FPC_SYSTEM_HAS_DIV_DWORD}
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// z in Ra, n in Rb, 0 in Rp
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function fpc_div_dword(n, z: dword): dword; assembler; nostackframe;
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{$ifdef FPC_IS_SYSTEM}[public,alias: 'FPC_DIV_DWORD'];{$endif}
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label
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start, div1, div2, div3, finish;
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asm
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// Symbol Name Register(s)
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// z (A) dividend R21, R20, R19, R18
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// n (B) divisor R25, R24, R23, R22
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// p (P) remainder R17, R16, R15, R14
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// i counter R26
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cp R24, R1
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cpc R25, R1
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cpc R22, R1
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cpc R23, R1
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brne .LNonZero
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{$ifdef CPUAVR_HAS_JMP_CALL}
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call get_pc_addr
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{$else CPUAVR_HAS_JMP_CALL}
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rcall get_pc_addr
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{$endif CPUAVR_HAS_JMP_CALL}
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movw R20, R24
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{$ifdef CPUAVR_HAS_JMP_CALL}
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call get_frame
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{$else CPUAVR_HAS_JMP_CALL}
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rcall get_frame
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{$endif CPUAVR_HAS_JMP_CALL}
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movw R18, R24
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ldi R22, 200
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clr R23
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clr R24
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clr R25
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{$ifdef CPUAVR_HAS_JMP_CALL}
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call HandleErrorAddrFrameInd
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{$else CPUAVR_HAS_JMP_CALL}
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rcall HandleErrorAddrFrameInd
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{$endif CPUAVR_HAS_JMP_CALL}
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.LNonZero:
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push R17
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push R16
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push R15
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push R14
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start: // Start of division...
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clr R14 // clear remainder
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clr R15 // clear remainder
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clr R16
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clr R17
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ldi R26, 32 // iterate over 32 bits
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div1:
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lsl R18 // shift left A_L
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rol R19
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rol R20
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rol R21
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rol R14 // shift left P with carry from A shift
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rol R15
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rol R16
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rol R17
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sub R14, R22 // Subtract B from P, P <= P - B
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sbc R15, R23
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sbc R16, R24
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sbc R17, R25
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brlo div2
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ori R18, 1 // Set A[0] = 1
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rjmp div3
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div2: // negative branch, A[0] = 0 (default after shift), restore P
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add R14, R22 // restore old value of P
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adc R15, R23
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adc R16, R24
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adc R17, R25
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div3:
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dec R26
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brne div1
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finish:
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movw R22, R18 // Move result from R18:R21 to R22:R25
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movw R24, R20
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pop R14
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pop R15
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pop R16
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pop R17
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end;
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{It is a compilerproc (systemh.inc), make an alias for internal use.}
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{$ifdef FPC_IS_SYSTEM}
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function fpc_div_dword(n, z: dword): dword; external name 'FPC_DIV_DWORD';
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{$endif FPC_IS_SYSTEM}
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{$endif FPC_SYSTEM_HAS_DIV_DWORD}
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