| /* SPDX-License-Identifier: GPL-2.0-or-later */ |
| /* 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. |
| |
| */ |
| |
| /* 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 |
| |
| 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) \ |
| : "dm" (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; |
| } |
| } |
| } |
| |
| 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; |
| } |
| } |
| |
| #endif /* MULTI_ARITH_H */ |