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// TITLE("High-Performance Division")//++//// Copyright (c) 1993 Digital Equipment Corporation//// Module Name://// fastdiv.s//// Abstract://// This module implements a high-performance integer division routine// whose source is included from each of the division and remainder// functions.//// Author://// Thomas Van Baak (tvb) 12-Jan-1993// Ken Lesniak (lesniak) 04-Nov-1992//// Environment://// Any mode.//// Revision History:////--
//// Implementation Notes://// This code is the main "guts" of the eight divide and remainder routines// in the C library. It is intended to be included by a wrapper function// that defines options to control 32 vs. 64-bit, division vs. remainder,// and signed vs. unsigned. The wrapper function is responsible for the// prologue and epilogue sequences, as well as overflow checking and sign// adjustment on both input arguments and the return value.//// The algorithm used here is based on long division and a table for// approximating inverses as discussed in the paper "Division by a Constant"// by Mary Payne and Robert Gries. If the divisor inverse can be constructed// from the table without an error, the division is performed as described// in the paper with a multiplication and a shift.//// If the inverse can not be found in the table, we improve the inverse with// a linear approximation, "I". A multiplication by "I" and a shift by// log2(y) is used to obtain an approximate quotient, "Q". Now, like long// division, the most significant bits are correct, therefore if we// calculate the remainder R = x-Q*y, R will be smaller than x, and R will// contain the true remainder and the error in Q, "e" multiplied by y.//// So if we do the same multiplication and shift, we will get an// approximation for e. This is just long division, and it will finish// when R, the remainder, is less than y.//// Both the division algorithm code and the large division tables used by// the code are contained in this source file (to keep them together).// //// The code below requires that the wrapper function define register numbers// for each of the following symbolic register names://// Nu dividend (numerator)// Di divisor (denominator)// Qu quotient// Re remainder (may be the same as Qu)//// T0 temp// T1 temp// T2 temp// T3 temp// T4 temp// T5 temp// T6 temp (may be shared with Qu)//
//// The code below requires that the wrapper function define the symbol// FASTDIV_OPTIONS as the logical sum of the following names://
#define THIRTY_TWO_BIT 1 // perform 32-bit computations, otherwise
#define SIXTY_FOUR_BIT 0 // perform 64-bit computations
#define UNSIGNED 2 // treat operands as unsigned, otherwise
#define SIGNED 0 // treat operands as signed
#define DIVISION 4 // return quotient in Qu register, and/or
#define REMAINDER 8 // return remainder in Re register
//// Define the symbols that actually control the code generation.//
#define _THIRTYTWOBIT (FASTDIV_OPTIONS & THIRTY_TWO_BIT)
#define _SIXTYFOURBIT (!(FASTDIV_OPTIONS & THIRTY_TWO_BIT))
#define _UNSIGNED (FASTDIV_OPTIONS & UNSIGNED)
#define _REMAINDER (FASTDIV_OPTIONS & REMAINDER)
#define _QUOTIENT (FASTDIV_OPTIONS & DIVISION)
//// These constants give the algorithm the best performance.//
#define BIT_LENGTH 8
#define BIT_VALUE (1 << BIT_LENGTH)
#define BIT_MASK (BIT_VALUE - 1)
#define K_BIT_LENGTH 8
#define K_BIT_VALUE (1 << K_BIT_LENGTH)
#define K_BIT_MASK (K_BIT_VALUE - 1)
#define TABLE_BIAS 16384
#define LOG2TAB -16384
#define INV_FLAG -15360
#define INV -14848
#define INV_M -14840
#ifndef FASTDIV_TABLES
.set noat
lda T3, __2divdata + TABLE_BIAS // set address of table beq Di, 30f // if zero divisor, generate trap
cmpule Nu, Di, T0 // check if dividend <= divisor#if _THIRTYTWOBIT
addl Di, 0, T1 // sign extend longword to quadword blt T1, 20f // high bit set so quotient <= 1#endif
#if _SIXTYFOURBIT
blt Di, 20f // high bit set so quotient <= 1#endif
cmpbge zero, Di, T2 // perform 8 byte parallel compare bne T0, 20f // dividend <= divisor so quotient <= 1
xor T2, 0xff, T0 // s4addq T0, T3, T0 // ldl AT, LOG2TAB(T0) // extbl Di, AT, T0 // s4addq T0, T3, T0 // ldl T0, LOG2TAB(T0) // s8addq AT, T0, AT // ornot zero, AT, T0 // sll Di, T0, T0 // sll T0, BIT_LENGTH + 1, T1 // bne T1, 40f //
//// Short case.//
subq Di, 1, T1 // compute divisor - 1 and Di, T1, T2 // divisor & (divisor - 1) srl T0, 63 - (BIT_LENGTH + 1), T6 // beq T2, 10f // divisor is a power of two
subq T6, BIT_VALUE + BIT_VALUE, T6 // bic T6, 1, T4 // s8addq T4, T3, T4 // ldq T5, INV(T4) // ldq T4, INV_M(T4) // subq T5, T4, T4 // cmovlbs T6, T4, T5 // addq T6, T3, T2 // ldq_u T0, INV_FLAG(T2) // extbl T0, T2, T2 // addq Nu, T2, T1 // umulh T1, T5, T3 //#if _SIXTYFOURBIT && _UNSIGNED
cmoveq T1, T5, T3 //#endif
srl T3, AT, Qu //#if _REMAINDER
mulq Qu, Di, T0 // subq Nu, T0, Re //#endif
br zero, 90f // all done, branch to epilogue code 10:
//// The divisor is now known to be a power of two.//// - The quotient is the dividend shifted right by exponent bits and// the remainder is the low order exponent bits of the dividend.//// AT = log2(divisor)// T1 = divisor - 1//
#if _REMAINDER
and Nu, T1, Re //#endif
#if _QUOTIENT
srl Nu, AT, Qu //#endif
br zero, 90f // all done, branch to epilogue code 20:
//// The quotient is now known to be either 0 or 1.//// - if the high bit of the divisor is set, the quotient must be less// than 2, so the quotient is 0 or 1.//// - if the dividend is less than the divisor, the quotient is 0 and// the remainder is the dividend.//// - if the dividend is equal to the divisor, the quotient is 1 and// the remainder is 0.//// - if the dividend is greater than the divisor, the quotient is 1// and the remainder is the dividend minus the divisor.//
#if _REMAINDER
cmpule Di, Nu, T0 // if divisor <= dividend subq Nu, Di, Re // then remainder is dividend, cmoveq T0, Nu, Re // else remainder is dividend - divisor#endif
#if _QUOTIENT
cmpule Di, Nu, Qu // if divisor <= dividend, 1, else 0#endif
br zero, 90f // all done, branch to epilogue code
//// Generate divide by zero exception. If execution is continued, return// a zero result.//
30: ldiq a0, GENTRAP_INTEGER_DIVIDE_BY_ZERO
GENERATE_TRAP
ldiq Qu, 0 // supply 0 result if continued br zero, 90f // branch to epilogue code //// Long case.//
40: srl T0, 63-(BIT_LENGTH+K_BIT_LENGTH), T6 // srl T6, K_BIT_LENGTH, T0 // and T6, K_BIT_MASK, T6 // addq T0, T0, T0 // s8addq T0, T3, T1 // ldq T2, INV-(16*BIT_VALUE)(T1) // ldq T0, INV_M-(16*BIT_VALUE)(T1) // mulq T0, T6, T0 // srl T0, K_BIT_LENGTH-1, T0 // subq T2, T0, T6 // umulh Nu, T6, T4 // srl T4, AT, T4 // mulq T4, Di, T5 // mov zero, T3 //#if _SIXTYFOURBIT
xor Nu, T5, T0 // bge T0, 50f //
umulh Di, T4, T3 //50:#endif
subq Nu, T5, T5 // beq T4, 70f //
cmpult Nu, T5, T0 // or T0, T3, T3 // negq T5, T1 // cmovne T3, T1, T5 // addq Di, Di, T0 // cmpule T0, T5, T0 // beq T0, 70f //
//// do {//
60: umulh T5, T6, T2 // srl T2, AT, T2 // negq T2, T0 // cmoveq T3, T2, T0 // addq T4, T0, T4 // mulq T2, Di, T1 // subq T5, T1, T5 //#if _SIXTYFOURBIT
ldiq T0, 1 // cmovne T3, 0, T0 // negq T5, T2 // cmovlt T5, T0, T3 // cmovlt T5, T2, T5 //#endif
addq Di, Di, T0 // cmpule T5, T0, T0 // cmovne T0, 0, T1 // bne T1, 60b //
//// } while//
70: cmpule Di, T5, T0 // beq T0, 80f //
subq T5, Di, T5 // subq T4, 1, T0 // addq T4, 1, T4 // cmovne T3, T0, T4 //80: cmoveq T5, 0, T3 //#if _REMAINDER
subq Di, T5, Re // cmoveq T3, T5, Re //#endif
#if _QUOTIENT
subq T4, 1, Qu // cmoveq T3, T4, Qu //#endif
90: .set at
#undef FASTDIV_OPTIONS
#else
//// The following data was machine generated. DO NOT EDIT MANUALLY.//
.globl __2divdata .rdata .align 4__2divdata:
//// LOG2TAB//
.align 2 .long 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3 .long 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 .long 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5 .long 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5 .long 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6 .long 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6 .long 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6 .long 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6 .long 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7 .long 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7 .long 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7 .long 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7 .long 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7 .long 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7 .long 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7 .long 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7
//// INV_FLAG//
.align 3 .byte 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1 .byte 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0 .byte 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1 .byte 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0 .byte 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0 .byte 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 .byte 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1 .byte 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0 .byte 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1 .byte 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1 .byte 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1 .byte 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1 .byte 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1 .byte 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0 .byte 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1 .byte 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0 .byte 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1 .byte 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0 .byte 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1 .byte 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0 .byte 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1 .byte 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1 .byte 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1 .byte 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1 .byte 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1 .byte 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0 .byte 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1 .byte 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1 .byte 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 .byte 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1 .byte 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1 .byte 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1
//// INV INV_M//
.align 4 .quad 0xffffffffffffffff, 0x007fc01ff007fc01, // 0 .quad 0xff00ff00ff00ff01, 0x007ec25bf68dabfe, // 1 .quad 0xfe03f80fe03f80fe, 0x007dc78930f5b971, // 2 .quad 0xfd08e5500fd08e55, 0x007ccf9c05f3157c, // 3 .quad 0xfc0fc0fc0fc0fc10, 0x007bda891528a983, // 4 .quad 0xfb18856506ddaba6, 0x007ae84535db391c, // 5 .quad 0xfa232cf252138ac0, 0x0079f8c575ac2ab0, // 6 .quad 0xf92fb2211855a865, 0x00790bff175cf1bf, // 7 .quad 0xf83e0f83e0f83e10, 0x007821e7919ad7f4, // 8 .quad 0xf74e3fc22c700f75, 0x00773a748dd2e48d, // 9 .quad 0xf6603d980f6603da, 0x0076559be70da3cb, // 10 .quad 0xf57403d5d00f5740, 0x00757353a8d2921b, // 11 .quad 0xf4898d5f85bb3950, 0x007493920e12f0da, // 12 .quad 0xf3a0d52cba872336, 0x0073b64d801bcc4b, // 13 .quad 0xf2b9d6480f2b9d65, 0x0072db7c958efc82, // 14 .quad 0xf1d48bcee0d399fa, 0x007203161162ec7b, // 15 .quad 0xf0f0f0f0f0f0f0f1, 0x00712d10e1e8f4b3, // 16 .quad 0xf00f00f00f00f00f, 0x007059641fda17d7, // 17 .quad 0xef2eb71fc4345238, 0x006f88070d69f229, // 18 .quad 0xee500ee500ee500f, 0x006eb8f1155fad72, // 19 .quad 0xed7303b5cc0ed730, 0x006dec19ca34cd01, // 20 .quad 0xec979118f3fc4da2, 0x006d2178e539a6a8, // 21 .quad 0xebbdb2a5c1619c8c, 0x006c590645bf5ef6, // 22 .quad 0xeae56403ab95900f, 0x006b92b9f0474060, // 23 .quad 0xea0ea0ea0ea0ea0f, 0x006ace8c0db7463d, // 24 .quad 0xe939651fe2d8d35c, 0x006a0c74ea93b5ce, // 25 .quad 0xe865ac7b7603a197, 0x00694c6cf63da0af, // 26 .quad 0xe79372e225fe30d9, 0x00688e6cc2362d3c, // 27 .quad 0xe6c2b4481cd85689, 0x0067d26d016682a0, // 28 .quad 0xe5f36cb00e5f36cb, 0x00671866876c373e, // 29 .quad 0xe525982af70c880e, 0x0066605247ea214c, // 30 .quad 0xe45932d7dc52100e, 0x0065aa2955dd6a6f, // 31 .quad 0xe38e38e38e38e38e, 0x0064f5e4e2f6c80c, // 32 .quad 0xe2c4a6886a4c2e10, 0x0064437e3ef7bb1b, // 33 .quad 0xe1fc780e1fc780e2, 0x006392eed713bb0b, // 34 .quad 0xe135a9c97500e136, 0x0062e43035553040, // 35 .quad 0xe070381c0e070382, 0x0062373c00062374, // 36 .quad 0xdfac1f74346c575f, 0x00618c0bf91c8837, // 37 .quad 0xdee95c4ca037ba57, 0x0060e299fdaa0972, // 38 .quad 0xde27eb2c41f3d9d1, 0x00603ae0054f3f9c, // 39 .quad 0xdd67c8a60dd67c8a, 0x005f94d821b23932, // 40 .quad 0xdca8f158c7f91ab8, 0x005ef07c7df83e6e, // 41 .quad 0xdbeb61eed19c5958, 0x005e4dc75e42ba41, // 42 .quad 0xdb2f171df7702919, 0x005dacb31f2f32ed, // 43 .quad 0xda740da740da740e, 0x005d0d3a355a3d88, // 44 .quad 0xd9ba4256c0366e91, 0x005c6f572ce55811, // 45 .quad 0xd901b2036406c80e, 0x005bd304a8ff968c, // 46 .quad 0xd84a598ec9151f43, 0x005b383d63711014, // 47 .quad 0xd79435e50d79435e, 0x005a9efc2c28f962, // 48 .quad 0xd6df43fca482f00d, 0x005a073be8ce5ae4, // 49 .quad 0xd62b80d62b80d62c, 0x005970f7945350f4, // 50 .quad 0xd578e97c3f5fe551, 0x0058dc2a3e8ac544, // 51 .quad 0xd4c77b03531dec0d, 0x005848cf0bc0912f, // 52 .quad 0xd4173289870ac52e, 0x0057b6e13453f8e0, // 53 .quad 0xd3680d3680d3680d, 0x0057265c04546fe2, // 54 .quad 0xd2ba083b445250ab, 0x0056973adb20982b, // 55 .quad 0xd20d20d20d20d20d, 0x005609792b076ce1, // 56 .quad 0xd161543e28e50274, 0x00557d1278eb8ad3, // 57 .quad 0xd0b69fcbd2580d0b, 0x0054f2025be888c5, // 58 .quad 0xd00d00d00d00d00d, 0x005468447cfa5248, // 59 .quad 0xcf6474a8819ec8e9, 0x0053dfd496a67807, // 60 .quad 0xcebcf8bb5b4169cb, 0x005358ae74a768fd, // 61 .quad 0xce168a7725080ce1, 0x0052d2cdf3998842, // 62 .quad 0xcd712752a886d242, 0x00524e2f00aa138f, // 63 .quad 0xcccccccccccccccd, 0x0051cacd9947cecc, // 64 .quad 0xcc29786c7607f99f, 0x005148a5cad5697f, // 65 .quad 0xcb8727c065c393e0, 0x0050c7b3b25d9315, // 66 .quad 0xcae5d85f1bbd6c95, 0x005047f37c48b368, // 67 .quad 0xca4587e6b74f0329, 0x004fc96164143d25, // 68 .quad 0xc9a633fcd967300d, 0x004f4bf9b40b9000, // 69 .quad 0xc907da4e871146ad, 0x004ecfb8c50260f1, // 70 .quad 0xc86a78900c86a789, 0x004e549afe109ef0, // 71 .quad 0xc7ce0c7ce0c7ce0c, 0x004dda9cd44fcaee, // 72 .quad 0xc73293d789b9f838, 0x004d61baca99ba10, // 73 .quad 0xc6980c6980c6980c, 0x004ce9f17148b95b, // 74 .quad 0xc5fe740317f9d00c, 0x004c733d65f90a5a, // 75 .quad 0xc565c87b5f9d4d1c, 0x004bfd9b534bb06e, // 76 .quad 0xc4ce07b00c4ce07b, 0x004b8907f0aa86ab, // 77 .quad 0xc4372f855d824ca6, 0x004b1580020d9680, // 78 .quad 0xc3a13de60495c773, 0x004aa30057c1a767, // 79 .quad 0xc30c30c30c30c30c, 0x004a3185ce30004a, // 80 .quad 0xc2780613c0309e02, 0x0049c10d4da7534b, // 81 .quad 0xc1e4bbd595f6e947, 0x00495193ca25cceb, // 82 .quad 0xc152500c152500c1, 0x0048e31643243fb8, // 83 .quad 0xc0c0c0c0c0c0c0c1, 0x00487591c36265c8, // 84 .quad 0xc0300c0300c0300c, 0x0048090360b4318c, // 85 .quad 0xbfa02fe80bfa02ff, 0x00479d683bd0279f, // 86 .quad 0xbf112a8ad278e8dd, 0x004732bd801ebb67, // 87 .quad 0xbe82fa0be82fa0bf, 0x0046c900638aa88c, // 88 .quad 0xbdf59c91700bdf5a, 0x0046602e26524361, // 89 .quad 0xbd69104707661aa3, 0x0045f84412d9ba97, // 90 .quad 0xbcdd535db1cc5b7b, 0x0045913f7d7e44a5, // 91 .quad 0xbc52640bc52640bc, 0x00452b1dc46a3383, // 92 .quad 0xbbc8408cd63069a1, 0x0044c5dc4f69e972, // 93 .quad 0xbb3ee721a54d880c, 0x004461788fc1a9a5, // 94 .quad 0xbab656100bab6561, 0x0043fdf000043fdf, // 95 .quad 0xba2e8ba2e8ba2e8c, 0x00439b4023ea7a13, // 96 .quad 0xb9a7862a0ff46588, 0x00433966882b6f4f, // 97 .quad 0xb92143fa36f5e02e, 0x0042d860c2558f4d, // 98 .quad 0xb89bc36ce3e0453a, 0x0042782c70a87632, // 99 .quad 0xb81702e05c0b8170, 0x004218c739ef8000, // 100 .quad 0xb79300b79300b793, 0x0041ba2ecd5d1788, // 101 .quad 0xb70fbb5a19be3659, 0x00415c60e266bc99, // 102 .quad 0xb68d31340e4307d8, 0x0040ff5b38a1bd6e, // 103 .quad 0xb60b60b60b60b60b, 0x0040a31b97a09f52, // 104 .quad 0xb58a485518d1e7e4, 0x0040479fced1329a, // 105 .quad 0xb509e68a9b94821f, 0x003fece5b55b4e37, // 106 .quad 0xb48a39d44685fe97, 0x003f92eb2a002f2f, // 107 .quad 0xb40b40b40b40b40b, 0x003f39ae12fa7858, // 108 .quad 0xb38cf9b00b38cf9b, 0x003ee12c5ddecee8, // 109 .quad 0xb30f63528917c80b, 0x003e8963ff7d1056, // 110 .quad 0xb2927c29da5519cf, 0x003e3252f3c21e56, // 111 .quad 0xb21642c8590b2164, 0x003ddbf73d9a3d87, // 112 .quad 0xb19ab5c45606f00b, 0x003d864ee6d403ca, // 113 .quad 0xb11fd3b80b11fd3c, 0x003d31580003d316, // 114 .quad 0xb0a59b418d749d53, 0x003cdd10a067ddc1, // 115 .quad 0xb02c0b02c0b02c0b, 0x003c8976e5ccb15f, // 116 .quad 0xafb321a1496fdf0e, 0x003c3688f472452e, // 117 .quad 0xaf3addc680af3ade, 0x003be444f6f1897b, // 118 .quad 0xaec33e1f671529a5, 0x003b92a91e2274fb, // 119 .quad 0xae4c415c9882b931, 0x003b41b3a1028dad, // 120 .quad 0xadd5e6323fd48a86, 0x003af162bc9bea7b, // 121 .quad 0xad602b580ad602b6, 0x003aa1b4b3ecab20, // 122 .quad 0xaceb0f891e6551bb, 0x003a52a7cfcee3c6, // 123 .quad 0xac7691840ac76918, 0x003a043a5ee0fa15, // 124 .quad 0xac02b00ac02b00ac, 0x0039b66ab56e7112, // 125 .quad 0xab8f69e28359cd11, 0x003969372d5921bb, // 126 .quad 0xab1cbdd3e2970f60, 0x00391c9e2602ddfa, // 127 .quad 0xaaaaaaaaaaaaaaab, 0x0038d09e04377bbb, // 128 .quad 0xaa392f35dc17f00b, 0x003885353217460a, // 129 .quad 0xa9c84a47a07f5638, 0x00383a621f01d214, // 130 .quad 0xa957fab5402a55ff, 0x0037f0233f8135f4, // 131 .quad 0xa8e83f5717c0a8e8, 0x0037a6770d359f5a, // 132 .quad 0xa87917088e262b6f, 0x00375d5c06c14806, // 133 .quad 0xa80a80a80a80a80b, 0x003714d0afb4c633, // 134 .quad 0xa79c7b16ea64d422, 0x0036ccd3907bb709, // 135 .quad 0xa72f05397829cbc1, 0x003685633649c151, // 136 .quad 0xa6c21df6e1625c80, 0x00363e7e3307ee8e, // 137 .quad 0xa655c4392d7b73a8, 0x0035f8231d4258ba, // 138 .quad 0xa5e9f6ed347f0721, 0x0035b25090162b0e, // 139 .quad 0xa57eb50295fad40a, 0x00356d052b1ff400, // 140 .quad 0xa513fd6bb00a5140, 0x0035283f926a46f2, // 141 .quad 0xa4a9cf1d96833751, 0x0034e3fe6e5cabea, // 142 .quad 0xa44029100a440291, 0x0034a0406baadbcc, // 143 .quad 0xa3d70a3d70a3d70a, 0x00345d043b44478a, // 144 .quad 0xa36e71a2cb033128, 0x00341a489243e8ca, // 145 .quad 0xa3065e3fae7cd0e0, 0x0033d80c29e05a93, // 146 .quad 0xa29ecf163bb6500a, 0x0033964dbf5c3891, // 147 .quad 0xa237c32b16cfd772, 0x0033550c13f6c382, // 148 .quad 0xa1d139855f7268ee, 0x00331445ecdcc986, // 149 .quad 0xa16b312ea8fc377d, 0x0032d3fa1319d0d6, // 150 .quad 0xa105a932f2ca891f, 0x00329427538983c8, // 151 .quad 0xa0a0a0a0a0a0a0a1, 0x003254cc7ec95ca2, // 152 .quad 0xa03c1688732b3032, 0x003215e8692a9028, // 153 .quad 0x9fd809fd809fd80a, 0x0031d779eaa43595, // 154 .quad 0x9f747a152d7836d0, 0x0031997fdec5aad6, // 155 .quad 0x9f1165e7254813e2, 0x00315bf924a933d8, // 156 .quad 0x9eaecc8d53ae2ddf, 0x00311ee49ee6d3cb, // 157 .quad 0x9e4cad23dd5f3a20, 0x0030e24133875f2f, // 158 .quad 0x9deb06c9194aa416, 0x0030a60dcbf7c5aa, // 159 .quad 0x9d89d89d89d89d8a, 0x00306a4954fc927a, // 160 .quad 0x9d2921c3d6411308, 0x00302ef2bea5a284, // 161 .quad 0x9cc8e160c3fb19b9, 0x002ff408fc420f05, // 162 .quad 0x9c69169b30446dfa, 0x002fb98b04544bcd, // 163 .quad 0x9c09c09c09c09c0a, 0x002f7f77d086781f, // 164 .quad 0x9baade8e4a2f6e10, 0x002f45ce5d9ee128, // 165 .quad 0x9b4c6f9ef03a3caa, 0x002f0c8dab74b53e, // 166 .quad 0x9aee72fcf957c10f, 0x002ed3b4bce4e6d7, // 167 .quad 0x9a90e7d95bc609a9, 0x002e9b4297c73e6e, // 168 .quad 0x9a33cd67009a33cd, 0x002e633644e39a62, // 169 .quad 0x99d722dabde58f06, 0x002e2b8ecfe75c01, // 170 .quad 0x997ae76b50efd00a, 0x002df44b475b00d8, // 171 .quad 0x991f1a515885fb37, 0x002dbd6abc97e780, // 172 .quad 0x98c3bac74f5db00a, 0x002d86ec43be3f17, // 173 .quad 0x9868c809868c8098, 0x002d50cef3ab208e, // 174 .quad 0x980e4156201301c8, 0x002d1b11e5eed122, // 175 .quad 0x97b425ed097b425f, 0x002ce5b436c32d10, // 176 .quad 0x975a750ff68a58af, 0x002cb0b5050239fa, // 177 .quad 0x97012e025c04b809, 0x002c7c13721ce019, // 178 .quad 0x96a850096a850097, 0x002c47cea211c9a1, // 179 .quad 0x964fda6c0964fda7, 0x002c13e5bb646783, // 180 .quad 0x95f7cc72d1b887e9, 0x002be057e7141b13, // 181 .quad 0x95a02568095a0257, 0x002bad24509383a7, // 182 .quad 0x9548e4979e0829fd, 0x002b7a4a25bfefbe, // 183 .quad 0x94f2094f2094f209, 0x002b47c896d8f0df, // 184 .quad 0x949b92ddc02526e5, 0x002b159ed67811bb, // 185 .quad 0x9445809445809446, 0x002ae3cc1988adbb, // 186 .quad 0x93efd1c50e726b7c, 0x002ab24f973fe99c, // 187 .quad 0x939a85c40939a85c, 0x002a81288914cc5b, // 188 .quad 0x93459be6b009345a, 0x002a50562ab877df, // 189 .quad 0x92f113840497889c, 0x002a1fd7ba0e80df, // 190 .quad 0x929cebf48bbd90e5, 0x0029efac7725656b, // 191 .quad 0x9249249249249249, 0x0029bfd3a42f218e, // 192 .quad 0x91f5bcb8bb02d9cd, 0x0029904c8579e17d, // 193 .quad 0x91a2b3c4d5e6f809, 0x002961166168d0d3, // 194 .quad 0x9150091500915009, 0x00293230806d0653, // 195 .quad 0x90fdbc090fdbc091, 0x0029039a2cfe8bab, // 196 .quad 0x90abcc0242af3009, 0x0028d552b39580c2, // 197 .quad 0x905a38633e06c43b, 0x0028a75962a35a0f, // 198 .quad 0x9009009009009009, 0x002879ad8a8c397c, // 199 .quad 0x8fb823ee08fb823f, 0x00284c4e7da06171, // 200 .quad 0x8f67a1e3fdc26178, 0x00281f3b9015c16f, // 201 .quad 0x8f1779d9fdc3a219, 0x0027f27418019bf5, // 202 .quad 0x8ec7ab397255e41d, 0x0027c5f76d52450e, // 203 .quad 0x8e78356d1408e783, 0x002799c4e9c8f94d, // 204 .quad 0x8e2917e0e702c6cd, 0x00276ddbe8f3cca0, // 205 .quad 0x8dda520237694809, 0x0027423bc827b0a6, // 206 .quad 0x8d8be33f95d71590, 0x002716e3e67a921c, // 207 .quad 0x8d3dcb08d3dcb08d, 0x0026ebd3a4bd8d01, // 208 .quad 0x8cf008cf008cf009, 0x0026c10a657736fa, // 209 .quad 0x8ca29c046514e023, 0x002696878cddffb1, // 210 .quad 0x8c55841c815ed5ca, 0x00266c4a80d2a6b2, // 211 .quad 0x8c08c08c08c08c09, 0x00264252a8dac681, // 212 .quad 0x8bbc50c8deb420c0, 0x0026189f6e1b7473, // 213 .quad 0x8b70344a139bc75a, 0x0025ef303b53f50e, // 214 .quad 0x8b246a87e19008b2, 0x0025c6047cd8847d, // 215 .quad 0x8ad8f2fba9386823, 0x00259d1ba08d32c5, // 216 .quad 0x8a8dcd1feeae465c, 0x0025747515e0d378, // 217 .quad 0x8a42f8705669db46, 0x00254c104dc80080, // 218 .quad 0x89f87469a23920e0, 0x002523ecbab82fae, // 219 .quad 0x89ae4089ae4089ae, 0x0024fc09d0a2dace, // 220 .quad 0x89645c4f6e055dec, 0x0024d46704f0b9de, // 221 .quad 0x891ac73ae9819b50, 0x0024ad03ce7d0f24, // 222 .quad 0x88d180cd3a4133d7, 0x002485dfa59104dc, // 223 .quad 0x8888888888888889, 0x00245efa03df1c1d, // 224 .quad 0x883fddf00883fddf, 0x00243852647eaccb, // 225 .quad 0x87f78087f78087f8, 0x002411e843e77632, // 226 .quad 0x87af6fd5992d0d40, 0x0023ebbb1fed4014, // 227 .quad 0x8767ab5f34e47ef1, 0x0023c5ca77bb8be3, // 228 .quad 0x872032ac13008720, 0x0023a015cbd155d3, // 229 .quad 0x86d905447a34acc6, 0x00237a9c9dfce59b, // 230 .quad 0x869222b1acf1ce96, 0x0023555e7157ae8e, // 231 .quad 0x864b8a7de6d1d608, 0x0023305aca423ed8, // 232 .quad 0x86053c345a0b8473, 0x00230b912e603d96, // 233 .quad 0x85bf37612cee3c9b, 0x0022e70124947795, // 234 .quad 0x85797b917765ab89, 0x0022c2aa34fcfa72, // 235 .quad 0x8534085340853408, 0x00229e8be8ef3de8, // 236 .quad 0x84eedd357c1b0085, 0x00227aa5caf45b0a, // 237 .quad 0x84a9f9c8084a9f9d, 0x002256f766c5512f, // 238 .quad 0x84655d9bab2f1008, 0x002233804947585d, // 239 .quad 0x8421084210842108, 0x0022104000884100, // 240 .quad 0x83dcf94dc7570ce1, 0x0021ed361bbae0a0, // 241 .quad 0x839930523fbe3368, 0x0021ca622b338b7a, // 242 .quad 0x8355ace3c897db10, 0x0021a7c3c0649abe, // 243 .quad 0x83126e978d4fdf3b, 0x0021855a6ddaff33, // 244 .quad 0x82cf750393ac3319, 0x00216325c73ae026, // 245 .quad 0x828cbfbeb9a020a3, 0x00214125613c4656, // 246 .quad 0x824a4e60b3262bc5, 0x00211f58d1a7d2cb, // 247 .quad 0x8208208208208208, 0x0020fdbfaf538145, // 248 .quad 0x81c635bc123fdf8e, 0x0020dc59921f7638, // 249 .quad 0x81848da8faf0d277, 0x0020bb2612f2d806, // 250 .quad 0x814327e3b94f462f, 0x00209a24cbb8b365, // 251 .quad 0x8102040810204081, 0x00207955575ceaab, // 252 .quad 0x80c121b28bd1ba98, 0x002058b751c92feb, // 253 .quad 0x8080808080808081, 0x0020384a57e209a8, // 254 .quad 0x8040201008040201, 0x0020180e0783e1f9, // 255
#endif // FASTDIV_TABLES
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