diff options
author | Linus Torvalds <torvalds@ppc970.osdl.org> | 2005-04-16 15:20:36 -0700 |
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committer | Linus Torvalds <torvalds@ppc970.osdl.org> | 2005-04-16 15:20:36 -0700 |
commit | 1da177e4c3f41524e886b7f1b8a0c1fc7321cac2 (patch) | |
tree | 0bba044c4ce775e45a88a51686b5d9f90697ea9d /arch/m68k/math-emu/multi_arith.h |
Linux-2.6.12-rc2v2.6.12-rc2
Initial git repository build. I'm not bothering with the full history,
even though we have it. We can create a separate "historical" git
archive of that later if we want to, and in the meantime it's about
3.2GB when imported into git - space that would just make the early
git days unnecessarily complicated, when we don't have a lot of good
infrastructure for it.
Let it rip!
Diffstat (limited to 'arch/m68k/math-emu/multi_arith.h')
-rw-r--r-- | arch/m68k/math-emu/multi_arith.h | 819 |
1 files changed, 819 insertions, 0 deletions
diff --git a/arch/m68k/math-emu/multi_arith.h b/arch/m68k/math-emu/multi_arith.h new file mode 100644 index 00000000000..02251e5afd8 --- /dev/null +++ b/arch/m68k/math-emu/multi_arith.h @@ -0,0 +1,819 @@ +/* multi_arith.h: multi-precision integer arithmetic functions, needed + to do extended-precision floating point. + + (c) 1998 David Huggins-Daines. + + Somewhat based on arch/alpha/math-emu/ieee-math.c, which is (c) + David Mosberger-Tang. + + You may copy, modify, and redistribute this file under the terms of + the GNU General Public License, version 2, or any later version, at + your convenience. */ + +/* Note: + + These are not general multi-precision math routines. Rather, they + implement the subset of integer arithmetic that we need in order to + multiply, divide, and normalize 128-bit unsigned mantissae. */ + +#ifndef MULTI_ARITH_H +#define MULTI_ARITH_H + +#if 0 /* old code... */ + +/* Unsigned only, because we don't need signs to multiply and divide. */ +typedef unsigned int int128[4]; + +/* Word order */ +enum { + MSW128, + NMSW128, + NLSW128, + LSW128 +}; + +/* big-endian */ +#define LO_WORD(ll) (((unsigned int *) &ll)[1]) +#define HI_WORD(ll) (((unsigned int *) &ll)[0]) + +/* Convenience functions to stuff various integer values into int128s */ + +static inline void zero128(int128 a) +{ + a[LSW128] = a[NLSW128] = a[NMSW128] = a[MSW128] = 0; +} + +/* Human-readable word order in the arguments */ +static inline void set128(unsigned int i3, unsigned int i2, unsigned int i1, + unsigned int i0, int128 a) +{ + a[LSW128] = i0; + a[NLSW128] = i1; + a[NMSW128] = i2; + a[MSW128] = i3; +} + +/* Convenience functions (for testing as well) */ +static inline void int64_to_128(unsigned long long src, int128 dest) +{ + dest[LSW128] = (unsigned int) src; + dest[NLSW128] = src >> 32; + dest[NMSW128] = dest[MSW128] = 0; +} + +static inline void int128_to_64(const int128 src, unsigned long long *dest) +{ + *dest = src[LSW128] | (long long) src[NLSW128] << 32; +} + +static inline void put_i128(const int128 a) +{ + printk("%08x %08x %08x %08x\n", a[MSW128], a[NMSW128], + a[NLSW128], a[LSW128]); +} + +/* Internal shifters: + + Note that these are only good for 0 < count < 32. + */ + +static inline void _lsl128(unsigned int count, int128 a) +{ + a[MSW128] = (a[MSW128] << count) | (a[NMSW128] >> (32 - count)); + a[NMSW128] = (a[NMSW128] << count) | (a[NLSW128] >> (32 - count)); + a[NLSW128] = (a[NLSW128] << count) | (a[LSW128] >> (32 - count)); + a[LSW128] <<= count; +} + +static inline void _lsr128(unsigned int count, int128 a) +{ + a[LSW128] = (a[LSW128] >> count) | (a[NLSW128] << (32 - count)); + a[NLSW128] = (a[NLSW128] >> count) | (a[NMSW128] << (32 - count)); + a[NMSW128] = (a[NMSW128] >> count) | (a[MSW128] << (32 - count)); + a[MSW128] >>= count; +} + +/* Should be faster, one would hope */ + +static inline void lslone128(int128 a) +{ + asm volatile ("lsl.l #1,%0\n" + "roxl.l #1,%1\n" + "roxl.l #1,%2\n" + "roxl.l #1,%3\n" + : + "=d" (a[LSW128]), + "=d"(a[NLSW128]), + "=d"(a[NMSW128]), + "=d"(a[MSW128]) + : + "0"(a[LSW128]), + "1"(a[NLSW128]), + "2"(a[NMSW128]), + "3"(a[MSW128])); +} + +static inline void lsrone128(int128 a) +{ + asm volatile ("lsr.l #1,%0\n" + "roxr.l #1,%1\n" + "roxr.l #1,%2\n" + "roxr.l #1,%3\n" + : + "=d" (a[MSW128]), + "=d"(a[NMSW128]), + "=d"(a[NLSW128]), + "=d"(a[LSW128]) + : + "0"(a[MSW128]), + "1"(a[NMSW128]), + "2"(a[NLSW128]), + "3"(a[LSW128])); +} + +/* Generalized 128-bit shifters: + + These bit-shift to a multiple of 32, then move whole longwords. */ + +static inline void lsl128(unsigned int count, int128 a) +{ + int wordcount, i; + + if (count % 32) + _lsl128(count % 32, a); + + if (0 == (wordcount = count / 32)) + return; + + /* argh, gak, endian-sensitive */ + for (i = 0; i < 4 - wordcount; i++) { + a[i] = a[i + wordcount]; + } + for (i = 3; i >= 4 - wordcount; --i) { + a[i] = 0; + } +} + +static inline void lsr128(unsigned int count, int128 a) +{ + int wordcount, i; + + if (count % 32) + _lsr128(count % 32, a); + + if (0 == (wordcount = count / 32)) + return; + + for (i = 3; i >= wordcount; --i) { + a[i] = a[i - wordcount]; + } + for (i = 0; i < wordcount; i++) { + a[i] = 0; + } +} + +static inline int orl128(int a, int128 b) +{ + b[LSW128] |= a; +} + +static inline int btsthi128(const int128 a) +{ + return a[MSW128] & 0x80000000; +} + +/* test bits (numbered from 0 = LSB) up to and including "top" */ +static inline int bftestlo128(int top, const int128 a) +{ + int r = 0; + + if (top > 31) + r |= a[LSW128]; + if (top > 63) + r |= a[NLSW128]; + if (top > 95) + r |= a[NMSW128]; + + r |= a[3 - (top / 32)] & ((1 << (top % 32 + 1)) - 1); + + return (r != 0); +} + +/* Aargh. We need these because GCC is broken */ +/* FIXME: do them in assembly, for goodness' sake! */ +static inline void mask64(int pos, unsigned long long *mask) +{ + *mask = 0; + + if (pos < 32) { + LO_WORD(*mask) = (1 << pos) - 1; + return; + } + LO_WORD(*mask) = -1; + HI_WORD(*mask) = (1 << (pos - 32)) - 1; +} + +static inline void bset64(int pos, unsigned long long *dest) +{ + /* This conditional will be optimized away. Thanks, GCC! */ + if (pos < 32) + asm volatile ("bset %1,%0":"=m" + (LO_WORD(*dest)):"id"(pos)); + else + asm volatile ("bset %1,%0":"=m" + (HI_WORD(*dest)):"id"(pos - 32)); +} + +static inline int btst64(int pos, unsigned long long dest) +{ + if (pos < 32) + return (0 != (LO_WORD(dest) & (1 << pos))); + else + return (0 != (HI_WORD(dest) & (1 << (pos - 32)))); +} + +static inline void lsl64(int count, unsigned long long *dest) +{ + if (count < 32) { + HI_WORD(*dest) = (HI_WORD(*dest) << count) + | (LO_WORD(*dest) >> count); + LO_WORD(*dest) <<= count; + return; + } + count -= 32; + HI_WORD(*dest) = LO_WORD(*dest) << count; + LO_WORD(*dest) = 0; +} + +static inline void lsr64(int count, unsigned long long *dest) +{ + if (count < 32) { + LO_WORD(*dest) = (LO_WORD(*dest) >> count) + | (HI_WORD(*dest) << (32 - count)); + HI_WORD(*dest) >>= count; + return; + } + count -= 32; + LO_WORD(*dest) = HI_WORD(*dest) >> count; + HI_WORD(*dest) = 0; +} +#endif + +static inline void fp_denormalize(struct fp_ext *reg, unsigned int cnt) +{ + reg->exp += cnt; + + switch (cnt) { + case 0 ... 8: + reg->lowmant = reg->mant.m32[1] << (8 - cnt); + reg->mant.m32[1] = (reg->mant.m32[1] >> cnt) | + (reg->mant.m32[0] << (32 - cnt)); + reg->mant.m32[0] = reg->mant.m32[0] >> cnt; + break; + case 9 ... 32: + reg->lowmant = reg->mant.m32[1] >> (cnt - 8); + if (reg->mant.m32[1] << (40 - cnt)) + reg->lowmant |= 1; + reg->mant.m32[1] = (reg->mant.m32[1] >> cnt) | + (reg->mant.m32[0] << (32 - cnt)); + reg->mant.m32[0] = reg->mant.m32[0] >> cnt; + break; + case 33 ... 39: + asm volatile ("bfextu %1{%2,#8},%0" : "=d" (reg->lowmant) + : "m" (reg->mant.m32[0]), "d" (64 - cnt)); + if (reg->mant.m32[1] << (40 - cnt)) + reg->lowmant |= 1; + reg->mant.m32[1] = reg->mant.m32[0] >> (cnt - 32); + reg->mant.m32[0] = 0; + break; + case 40 ... 71: + reg->lowmant = reg->mant.m32[0] >> (cnt - 40); + if ((reg->mant.m32[0] << (72 - cnt)) || reg->mant.m32[1]) + reg->lowmant |= 1; + reg->mant.m32[1] = reg->mant.m32[0] >> (cnt - 32); + reg->mant.m32[0] = 0; + break; + default: + reg->lowmant = reg->mant.m32[0] || reg->mant.m32[1]; + reg->mant.m32[0] = 0; + reg->mant.m32[1] = 0; + break; + } +} + +static inline int fp_overnormalize(struct fp_ext *reg) +{ + int shift; + + if (reg->mant.m32[0]) { + asm ("bfffo %1{#0,#32},%0" : "=d" (shift) : "dm" (reg->mant.m32[0])); + reg->mant.m32[0] = (reg->mant.m32[0] << shift) | (reg->mant.m32[1] >> (32 - shift)); + reg->mant.m32[1] = (reg->mant.m32[1] << shift); + } else { + asm ("bfffo %1{#0,#32},%0" : "=d" (shift) : "dm" (reg->mant.m32[1])); + reg->mant.m32[0] = (reg->mant.m32[1] << shift); + reg->mant.m32[1] = 0; + shift += 32; + } + + return shift; +} + +static inline int fp_addmant(struct fp_ext *dest, struct fp_ext *src) +{ + int carry; + + /* we assume here, gcc only insert move and a clr instr */ + asm volatile ("add.b %1,%0" : "=d,g" (dest->lowmant) + : "g,d" (src->lowmant), "0,0" (dest->lowmant)); + asm volatile ("addx.l %1,%0" : "=d" (dest->mant.m32[1]) + : "d" (src->mant.m32[1]), "0" (dest->mant.m32[1])); + asm volatile ("addx.l %1,%0" : "=d" (dest->mant.m32[0]) + : "d" (src->mant.m32[0]), "0" (dest->mant.m32[0])); + asm volatile ("addx.l %0,%0" : "=d" (carry) : "0" (0)); + + return carry; +} + +static inline int fp_addcarry(struct fp_ext *reg) +{ + if (++reg->exp == 0x7fff) { + if (reg->mant.m64) + fp_set_sr(FPSR_EXC_INEX2); + reg->mant.m64 = 0; + fp_set_sr(FPSR_EXC_OVFL); + return 0; + } + reg->lowmant = (reg->mant.m32[1] << 7) | (reg->lowmant ? 1 : 0); + reg->mant.m32[1] = (reg->mant.m32[1] >> 1) | + (reg->mant.m32[0] << 31); + reg->mant.m32[0] = (reg->mant.m32[0] >> 1) | 0x80000000; + + return 1; +} + +static inline void fp_submant(struct fp_ext *dest, struct fp_ext *src1, + struct fp_ext *src2) +{ + /* we assume here, gcc only insert move and a clr instr */ + asm volatile ("sub.b %1,%0" : "=d,g" (dest->lowmant) + : "g,d" (src2->lowmant), "0,0" (src1->lowmant)); + asm volatile ("subx.l %1,%0" : "=d" (dest->mant.m32[1]) + : "d" (src2->mant.m32[1]), "0" (src1->mant.m32[1])); + asm volatile ("subx.l %1,%0" : "=d" (dest->mant.m32[0]) + : "d" (src2->mant.m32[0]), "0" (src1->mant.m32[0])); +} + +#define fp_mul64(desth, destl, src1, src2) ({ \ + asm ("mulu.l %2,%1:%0" : "=d" (destl), "=d" (desth) \ + : "g" (src1), "0" (src2)); \ +}) +#define fp_div64(quot, rem, srch, srcl, div) \ + asm ("divu.l %2,%1:%0" : "=d" (quot), "=d" (rem) \ + : "dm" (div), "1" (srch), "0" (srcl)) +#define fp_add64(dest1, dest2, src1, src2) ({ \ + asm ("add.l %1,%0" : "=d,dm" (dest2) \ + : "dm,d" (src2), "0,0" (dest2)); \ + asm ("addx.l %1,%0" : "=d" (dest1) \ + : "d" (src1), "0" (dest1)); \ +}) +#define fp_addx96(dest, src) ({ \ + /* we assume here, gcc only insert move and a clr instr */ \ + asm volatile ("add.l %1,%0" : "=d,g" (dest->m32[2]) \ + : "g,d" (temp.m32[1]), "0,0" (dest->m32[2])); \ + asm volatile ("addx.l %1,%0" : "=d" (dest->m32[1]) \ + : "d" (temp.m32[0]), "0" (dest->m32[1])); \ + asm volatile ("addx.l %1,%0" : "=d" (dest->m32[0]) \ + : "d" (0), "0" (dest->m32[0])); \ +}) +#define fp_sub64(dest, src) ({ \ + asm ("sub.l %1,%0" : "=d,dm" (dest.m32[1]) \ + : "dm,d" (src.m32[1]), "0,0" (dest.m32[1])); \ + asm ("subx.l %1,%0" : "=d" (dest.m32[0]) \ + : "d" (src.m32[0]), "0" (dest.m32[0])); \ +}) +#define fp_sub96c(dest, srch, srcm, srcl) ({ \ + char carry; \ + asm ("sub.l %1,%0" : "=d,dm" (dest.m32[2]) \ + : "dm,d" (srcl), "0,0" (dest.m32[2])); \ + asm ("subx.l %1,%0" : "=d" (dest.m32[1]) \ + : "d" (srcm), "0" (dest.m32[1])); \ + asm ("subx.l %2,%1; scs %0" : "=d" (carry), "=d" (dest.m32[0]) \ + : "d" (srch), "1" (dest.m32[0])); \ + carry; \ +}) + +static inline void fp_multiplymant(union fp_mant128 *dest, struct fp_ext *src1, + struct fp_ext *src2) +{ + union fp_mant64 temp; + + fp_mul64(dest->m32[0], dest->m32[1], src1->mant.m32[0], src2->mant.m32[0]); + fp_mul64(dest->m32[2], dest->m32[3], src1->mant.m32[1], src2->mant.m32[1]); + + fp_mul64(temp.m32[0], temp.m32[1], src1->mant.m32[0], src2->mant.m32[1]); + fp_addx96(dest, temp); + + fp_mul64(temp.m32[0], temp.m32[1], src1->mant.m32[1], src2->mant.m32[0]); + fp_addx96(dest, temp); +} + +static inline void fp_dividemant(union fp_mant128 *dest, struct fp_ext *src, + struct fp_ext *div) +{ + union fp_mant128 tmp; + union fp_mant64 tmp64; + unsigned long *mantp = dest->m32; + unsigned long fix, rem, first, dummy; + int i; + + /* the algorithm below requires dest to be smaller than div, + but both have the high bit set */ + if (src->mant.m64 >= div->mant.m64) { + fp_sub64(src->mant, div->mant); + *mantp = 1; + } else + *mantp = 0; + mantp++; + + /* basic idea behind this algorithm: we can't divide two 64bit numbers + (AB/CD) directly, but we can calculate AB/C0, but this means this + quotient is off by C0/CD, so we have to multiply the first result + to fix the result, after that we have nearly the correct result + and only a few corrections are needed. */ + + /* C0/CD can be precalculated, but it's an 64bit division again, but + we can make it a bit easier, by dividing first through C so we get + 10/1D and now only a single shift and the value fits into 32bit. */ + fix = 0x80000000; + dummy = div->mant.m32[1] / div->mant.m32[0] + 1; + dummy = (dummy >> 1) | fix; + fp_div64(fix, dummy, fix, 0, dummy); + fix--; + + for (i = 0; i < 3; i++, mantp++) { + if (src->mant.m32[0] == div->mant.m32[0]) { + fp_div64(first, rem, 0, src->mant.m32[1], div->mant.m32[0]); + + fp_mul64(*mantp, dummy, first, fix); + *mantp += fix; + } else { + fp_div64(first, rem, src->mant.m32[0], src->mant.m32[1], div->mant.m32[0]); + + fp_mul64(*mantp, dummy, first, fix); + } + + fp_mul64(tmp.m32[0], tmp.m32[1], div->mant.m32[0], first - *mantp); + fp_add64(tmp.m32[0], tmp.m32[1], 0, rem); + tmp.m32[2] = 0; + + fp_mul64(tmp64.m32[0], tmp64.m32[1], *mantp, div->mant.m32[1]); + fp_sub96c(tmp, 0, tmp64.m32[0], tmp64.m32[1]); + + src->mant.m32[0] = tmp.m32[1]; + src->mant.m32[1] = tmp.m32[2]; + + while (!fp_sub96c(tmp, 0, div->mant.m32[0], div->mant.m32[1])) { + src->mant.m32[0] = tmp.m32[1]; + src->mant.m32[1] = tmp.m32[2]; + *mantp += 1; + } + } +} + +#if 0 +static inline unsigned int fp_fls128(union fp_mant128 *src) +{ + unsigned long data; + unsigned int res, off; + + if ((data = src->m32[0])) + off = 0; + else if ((data = src->m32[1])) + off = 32; + else if ((data = src->m32[2])) + off = 64; + else if ((data = src->m32[3])) + off = 96; + else + return 128; + + asm ("bfffo %1{#0,#32},%0" : "=d" (res) : "dm" (data)); + return res + off; +} + +static inline void fp_shiftmant128(union fp_mant128 *src, int shift) +{ + unsigned long sticky; + + switch (shift) { + case 0: + return; + case 1: + asm volatile ("lsl.l #1,%0" + : "=d" (src->m32[3]) : "0" (src->m32[3])); + asm volatile ("roxl.l #1,%0" + : "=d" (src->m32[2]) : "0" (src->m32[2])); + asm volatile ("roxl.l #1,%0" + : "=d" (src->m32[1]) : "0" (src->m32[1])); + asm volatile ("roxl.l #1,%0" + : "=d" (src->m32[0]) : "0" (src->m32[0])); + return; + case 2 ... 31: + src->m32[0] = (src->m32[0] << shift) | (src->m32[1] >> (32 - shift)); + src->m32[1] = (src->m32[1] << shift) | (src->m32[2] >> (32 - shift)); + src->m32[2] = (src->m32[2] << shift) | (src->m32[3] >> (32 - shift)); + src->m32[3] = (src->m32[3] << shift); + return; + case 32 ... 63: + shift -= 32; + src->m32[0] = (src->m32[1] << shift) | (src->m32[2] >> (32 - shift)); + src->m32[1] = (src->m32[2] << shift) | (src->m32[3] >> (32 - shift)); + src->m32[2] = (src->m32[3] << shift); + src->m32[3] = 0; + return; + case 64 ... 95: + shift -= 64; + src->m32[0] = (src->m32[2] << shift) | (src->m32[3] >> (32 - shift)); + src->m32[1] = (src->m32[3] << shift); + src->m32[2] = src->m32[3] = 0; + return; + case 96 ... 127: + shift -= 96; + src->m32[0] = (src->m32[3] << shift); + src->m32[1] = src->m32[2] = src->m32[3] = 0; + return; + case -31 ... -1: + shift = -shift; + sticky = 0; + if (src->m32[3] << (32 - shift)) + sticky = 1; + src->m32[3] = (src->m32[3] >> shift) | (src->m32[2] << (32 - shift)) | sticky; + src->m32[2] = (src->m32[2] >> shift) | (src->m32[1] << (32 - shift)); + src->m32[1] = (src->m32[1] >> shift) | (src->m32[0] << (32 - shift)); + src->m32[0] = (src->m32[0] >> shift); + return; + case -63 ... -32: + shift = -shift - 32; + sticky = 0; + if ((src->m32[2] << (32 - shift)) || src->m32[3]) + sticky = 1; + src->m32[3] = (src->m32[2] >> shift) | (src->m32[1] << (32 - shift)) | sticky; + src->m32[2] = (src->m32[1] >> shift) | (src->m32[0] << (32 - shift)); + src->m32[1] = (src->m32[0] >> shift); + src->m32[0] = 0; + return; + case -95 ... -64: + shift = -shift - 64; + sticky = 0; + if ((src->m32[1] << (32 - shift)) || src->m32[2] || src->m32[3]) + sticky = 1; + src->m32[3] = (src->m32[1] >> shift) | (src->m32[0] << (32 - shift)) | sticky; + src->m32[2] = (src->m32[0] >> shift); + src->m32[1] = src->m32[0] = 0; + return; + case -127 ... -96: + shift = -shift - 96; + sticky = 0; + if ((src->m32[0] << (32 - shift)) || src->m32[1] || src->m32[2] || src->m32[3]) + sticky = 1; + src->m32[3] = (src->m32[0] >> shift) | sticky; + src->m32[2] = src->m32[1] = src->m32[0] = 0; + return; + } + + if (shift < 0 && (src->m32[0] || src->m32[1] || src->m32[2] || src->m32[3])) + src->m32[3] = 1; + else + src->m32[3] = 0; + src->m32[2] = 0; + src->m32[1] = 0; + src->m32[0] = 0; +} +#endif + +static inline void fp_putmant128(struct fp_ext *dest, union fp_mant128 *src, + int shift) +{ + unsigned long tmp; + + switch (shift) { + case 0: + dest->mant.m64 = src->m64[0]; + dest->lowmant = src->m32[2] >> 24; + if (src->m32[3] || (src->m32[2] << 8)) + dest->lowmant |= 1; + break; + case 1: + asm volatile ("lsl.l #1,%0" + : "=d" (tmp) : "0" (src->m32[2])); + asm volatile ("roxl.l #1,%0" + : "=d" (dest->mant.m32[1]) : "0" (src->m32[1])); + asm volatile ("roxl.l #1,%0" + : "=d" (dest->mant.m32[0]) : "0" (src->m32[0])); + dest->lowmant = tmp >> 24; + if (src->m32[3] || (tmp << 8)) + dest->lowmant |= 1; + break; + case 31: + asm volatile ("lsr.l #1,%1; roxr.l #1,%0" + : "=d" (dest->mant.m32[0]) + : "d" (src->m32[0]), "0" (src->m32[1])); + asm volatile ("roxr.l #1,%0" + : "=d" (dest->mant.m32[1]) : "0" (src->m32[2])); + asm volatile ("roxr.l #1,%0" + : "=d" (tmp) : "0" (src->m32[3])); + dest->lowmant = tmp >> 24; + if (src->m32[3] << 7) + dest->lowmant |= 1; + break; + case 32: + dest->mant.m32[0] = src->m32[1]; + dest->mant.m32[1] = src->m32[2]; + dest->lowmant = src->m32[3] >> 24; + if (src->m32[3] << 8) + dest->lowmant |= 1; + break; + } +} + +#if 0 /* old code... */ +static inline int fls(unsigned int a) +{ + int r; + + asm volatile ("bfffo %1{#0,#32},%0" + : "=d" (r) : "md" (a)); + return r; +} + +/* fls = "find last set" (cf. ffs(3)) */ +static inline int fls128(const int128 a) +{ + if (a[MSW128]) + return fls(a[MSW128]); + if (a[NMSW128]) + return fls(a[NMSW128]) + 32; + /* XXX: it probably never gets beyond this point in actual + use, but that's indicative of a more general problem in the + algorithm (i.e. as per the actual 68881 implementation, we + really only need at most 67 bits of precision [plus + overflow]) so I'm not going to fix it. */ + if (a[NLSW128]) + return fls(a[NLSW128]) + 64; + if (a[LSW128]) + return fls(a[LSW128]) + 96; + else + return -1; +} + +static inline int zerop128(const int128 a) +{ + return !(a[LSW128] | a[NLSW128] | a[NMSW128] | a[MSW128]); +} + +static inline int nonzerop128(const int128 a) +{ + return (a[LSW128] | a[NLSW128] | a[NMSW128] | a[MSW128]); +} + +/* Addition and subtraction */ +/* Do these in "pure" assembly, because "extended" asm is unmanageable + here */ +static inline void add128(const int128 a, int128 b) +{ + /* rotating carry flags */ + unsigned int carry[2]; + + carry[0] = a[LSW128] > (0xffffffff - b[LSW128]); + b[LSW128] += a[LSW128]; + + carry[1] = a[NLSW128] > (0xffffffff - b[NLSW128] - carry[0]); + b[NLSW128] = a[NLSW128] + b[NLSW128] + carry[0]; + + carry[0] = a[NMSW128] > (0xffffffff - b[NMSW128] - carry[1]); + b[NMSW128] = a[NMSW128] + b[NMSW128] + carry[1]; + + b[MSW128] = a[MSW128] + b[MSW128] + carry[0]; +} + +/* Note: assembler semantics: "b -= a" */ +static inline void sub128(const int128 a, int128 b) +{ + /* rotating borrow flags */ + unsigned int borrow[2]; + + borrow[0] = b[LSW128] < a[LSW128]; + b[LSW128] -= a[LSW128]; + + borrow[1] = b[NLSW128] < a[NLSW128] + borrow[0]; + b[NLSW128] = b[NLSW128] - a[NLSW128] - borrow[0]; + + borrow[0] = b[NMSW128] < a[NMSW128] + borrow[1]; + b[NMSW128] = b[NMSW128] - a[NMSW128] - borrow[1]; + + b[MSW128] = b[MSW128] - a[MSW128] - borrow[0]; +} + +/* Poor man's 64-bit expanding multiply */ +static inline void mul64(unsigned long long a, unsigned long long b, int128 c) +{ + unsigned long long acc; + int128 acc128; + + zero128(acc128); + zero128(c); + + /* first the low words */ + if (LO_WORD(a) && LO_WORD(b)) { + acc = (long long) LO_WORD(a) * LO_WORD(b); + c[NLSW128] = HI_WORD(acc); + c[LSW128] = LO_WORD(acc); + } + /* Next the high words */ + if (HI_WORD(a) && HI_WORD(b)) { + acc = (long long) HI_WORD(a) * HI_WORD(b); + c[MSW128] = HI_WORD(acc); + c[NMSW128] = LO_WORD(acc); + } + /* The middle words */ + if (LO_WORD(a) && HI_WORD(b)) { + acc = (long long) LO_WORD(a) * HI_WORD(b); + acc128[NMSW128] = HI_WORD(acc); + acc128[NLSW128] = LO_WORD(acc); + add128(acc128, c); + } + /* The first and last words */ + if (HI_WORD(a) && LO_WORD(b)) { + acc = (long long) HI_WORD(a) * LO_WORD(b); + acc128[NMSW128] = HI_WORD(acc); + acc128[NLSW128] = LO_WORD(acc); + add128(acc128, c); + } +} + +/* Note: unsigned */ +static inline int cmp128(int128 a, int128 b) +{ + if (a[MSW128] < b[MSW128]) + return -1; + if (a[MSW128] > b[MSW128]) + return 1; + if (a[NMSW128] < b[NMSW128]) + return -1; + if (a[NMSW128] > b[NMSW128]) + return 1; + if (a[NLSW128] < b[NLSW128]) + return -1; + if (a[NLSW128] > b[NLSW128]) + return 1; + + return (signed) a[LSW128] - b[LSW128]; +} + +inline void div128(int128 a, int128 b, int128 c) +{ + int128 mask; + + /* Algorithm: + + Shift the divisor until it's at least as big as the + dividend, keeping track of the position to which we've + shifted it, i.e. the power of 2 which we've multiplied it + by. + + Then, for this power of 2 (the mask), and every one smaller + than it, subtract the mask from the dividend and add it to + the quotient until the dividend is smaller than the raised + divisor. At this point, divide the dividend and the mask + by 2 (i.e. shift one place to the right). Lather, rinse, + and repeat, until there are no more powers of 2 left. */ + + /* FIXME: needless to say, there's room for improvement here too. */ + + /* Shift up */ + /* XXX: since it just has to be "at least as big", we can + probably eliminate this horribly wasteful loop. I will + have to prove this first, though */ + set128(0, 0, 0, 1, mask); + while (cmp128(b, a) < 0 && !btsthi128(b)) { + lslone128(b); + lslone128(mask); + } + + /* Shift down */ + zero128(c); + do { + if (cmp128(a, b) >= 0) { + sub128(b, a); + add128(mask, c); + } + lsrone128(mask); + lsrone128(b); + } while (nonzerop128(mask)); + + /* The remainder is in a... */ +} +#endif + +#endif /* MULTI_ARITH_H */ |