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https://github.com/golang/go
synced 2024-11-21 23:24:41 -07:00
arm: precise float64 software floating point
Adds softfloat64 to generic runtime (will be discarded by linker when unused) and adds test for it. I used the test to check the software code against amd64 hardware and then check the software code against the arm and its simulation of hardware. The latter should have been a no-op (testing against itself) but turned up a bug in 5c causing the vlrt.c routines to miscompile. These changes make the cmath, math, and strconv tests pass without any special accommodations for arm. R=ken2 CC=golang-dev https://golang.org/cl/2713042
This commit is contained in:
Russ Cox
parent
e351533aab
commit
7c2b1597c6
@ -149,7 +149,6 @@ NOTEST=\
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image/jpeg\
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net/dict\
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rand\
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runtime\
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runtime/pprof\
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syscall\
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testing/iotest\
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@ -201,14 +200,6 @@ NOTEST+=syslog # no network
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NOTEST+=time # no syscall.Kill, syscall.SIGCHLD for sleep tests
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endif
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ifeq ($(GOARCH),arm)
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# Tests that fail, probably 5g bugs.
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# Disable so that dashboard all.bash can catch regressions.
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NOTEST+=cmath # software floating point (lack of) accuracy
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NOTEST+=math # software floating point (lack of) accuracy
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NOTEST+=strconv # software floating point (lack of) accuracy
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endif
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TEST=\
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$(filter-out $(NOTEST),$(DIRS))
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@ -25,6 +25,7 @@ GOFILES=\
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error.go\
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extern.go\
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sig.go\
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softfloat64.go\
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type.go\
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version.go\
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@ -2,6 +2,10 @@
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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// Software floating point interpretaton of ARM 7500 FP instructions.
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// The interpretation is not bit compatible with the 7500.
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// It uses true little-endian doubles, while the 7500 used mixed-endian.
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#include "runtime.h"
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void abort(void);
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@ -18,22 +22,6 @@ fabort(void)
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static uint32 doabort = 0;
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static uint32 trace = 0;
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#define DOUBLE_EXPBIAS 1023
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#define DOUBLE_MANT_MASK 0xfffffffffffffull
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#define DOUBLE_MANT_TOP_BIT 0x10000000000000ull
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#define DZERO 0x0000000000000000ull
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#define DNZERO 0x8000000000000000ull
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#define DONE 0x3ff0000000000000ull
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#define DINF 0x7ff0000000000000ull
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#define DNINF 0xfff0000000000000ull
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#define DNAN 0x7FF0000000000001ull
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#define SINGLE_EXPBIAS 127
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#define FINF 0x7f800000ul
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#define FNINF 0xff800000ul
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#define FNAN 0x7f800000ul
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static const int8* opnames[] = {
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// binary
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"adf",
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@ -115,24 +103,6 @@ frhs(uint32 rhs)
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}
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}
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static int32
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fexp(uint64 f)
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{
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return (int32)((uint32)(f >> 52) & 0x7ff) - DOUBLE_EXPBIAS;
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}
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static uint32
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fsign(uint64 f)
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{
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return (uint32)(f >> 63) & 0x1;
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}
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static uint64
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fmantissa(uint64 f)
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{
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return f &0x000fffffffffffffll;
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}
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static void
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fprint(void)
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{
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@ -145,42 +115,19 @@ fprint(void)
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static uint32
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d2s(uint64 d)
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{
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if ((d & ~(1ull << 63)) == 0)
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return (uint32)(d>>32);
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if (d == DINF)
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return FINF;
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if (d == DNINF)
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return FNINF;
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if ((d & ~(1ull << 63)) == DNAN)
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return FNAN;
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return (d>>32 & 0x80000000) | //sign
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((uint32)(fexp(d) + SINGLE_EXPBIAS) & 0xff) << 23 | // exponent
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(d >> 29 & 0x7fffff); // mantissa
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uint32 x;
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·f64to32c(d, &x);
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return x;
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}
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static uint64
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s2d(uint32 s)
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{
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if ((s & ~(1ul << 31)) == 0)
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return (uint64)(s) << 32;
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if (s == FINF)
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return DINF;
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if (s == FNINF)
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return DNINF;
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if ((s & ~(1ul << 31)) == FNAN)
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return DNAN;
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return (uint64)(s & 0x80000000) << 32 | // sign
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(uint64)((s >> 23 &0xff) + (DOUBLE_EXPBIAS - SINGLE_EXPBIAS)) << 52 | // exponent
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(uint64)(s & 0x7fffff) << 29; // mantissa
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}
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static int64
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rsh(int64 f, int32 s)
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{
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if (s >= 0)
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return f>>s;
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else
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return f<<-s;
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uint64 x;
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·f32to64c(s, &x);
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return x;
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}
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// cdp, data processing instructions
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@ -188,12 +135,8 @@ static void
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dataprocess(uint32* pc)
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{
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uint32 i, opcode, unary, dest, lhs, rhs, prec;
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uint32 high;
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int32 expd, exp0, exp1;
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uint64 fraw0, fraw1, exp, sign;
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uint64 fd, f0, f1;
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int64 fsd, fs0, fs1;
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uint64 l, r;
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uint64 fd;
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i = *pc;
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// data processing
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@ -220,129 +163,25 @@ dataprocess(uint32* pc)
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goto undef;
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}
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} else {
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fraw0 = m->freg[lhs];
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fraw1 = frhs(rhs);
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if (isNaN(float64frombits(fraw0)) || isNaN(float64frombits(fraw1))) {
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m->freg[dest] = DNAN;
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goto ret;
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}
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l = m->freg[lhs];
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r = frhs(rhs);
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switch (opcode) {
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case 2: // suf
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fraw1 ^= 0x1ll << 63;
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// fallthrough
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case 0: // adf
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if (fraw0 == DZERO || fraw0 == DNZERO) {
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m->freg[dest] = fraw1;
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goto ret;
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}
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if (fraw1 == DZERO || fraw1 == DNZERO) {
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m->freg[dest] = fraw0;
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goto ret;
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}
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fs0 = fraw0 & DOUBLE_MANT_MASK | DOUBLE_MANT_TOP_BIT;
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fs1 = fraw1 & DOUBLE_MANT_MASK | DOUBLE_MANT_TOP_BIT;
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exp0 = fexp(fraw0);
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exp1 = fexp(fraw1);
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if (exp0 > exp1)
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fs1 = rsh(fs1, exp0-exp1);
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else
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fs0 = rsh(fs0, exp1-exp0);
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if (fraw0 & 0x1ll<<63)
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fs0 = -fs0;
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if (fraw1 & 0x1ll<<63)
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fs1 = -fs1;
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fsd = fs0 + fs1;
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if (fsd == 0) {
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m->freg[dest] = DZERO;
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goto ret;
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}
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sign = (uint64)fsd & 0x1ll<<63;
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if (fsd < 0)
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fsd = -fsd;
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for (expd = 55; expd > 0; expd--) {
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if (0x1ll<<expd & fsd)
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break;
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}
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if (expd - 52 < 0)
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fsd <<= -(expd - 52);
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else
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fsd >>= expd - 52;
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if (exp0 > exp1)
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exp = expd + exp0 - 52;
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else
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exp = expd + exp1 - 52;
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// too small value, can't represent
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if (1<<31 & expd) {
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m->freg[dest] = DZERO;
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goto ret;
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}
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// infinity
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if (expd > 1<<12) {
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m->freg[dest] = DINF;
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goto ret;
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}
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fd = sign | (exp + DOUBLE_EXPBIAS)<<52 | (uint64)fsd & DOUBLE_MANT_MASK;
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m->freg[dest] = fd;
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goto ret;
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case 4: //dvf
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if ((fraw1 & ~(1ull<<63)) == 0) {
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if ((fraw0 & ~(1ull<<63)) == 0) {
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m->freg[dest] = DNAN;
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} else {
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sign = fraw0 & 1ull<<63 ^ fraw1 & 1ull<<63;
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m->freg[dest] = sign | DINF;
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}
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goto ret;
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}
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// reciprocal for fraw1
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if (fraw1 == DONE)
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goto muf;
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f0 = 0x1ll << 63;
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f1 = fraw1 & DOUBLE_MANT_MASK | DOUBLE_MANT_TOP_BIT;
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f1 >>= 21;
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fd = f0/f1;
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fd <<= 21;
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fd &= DOUBLE_MANT_MASK;
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exp1 = -fexp(fraw1) - 1;
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sign = fraw1 & 0x1ll<<63;
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fraw1 = sign | (uint64)(exp1 + DOUBLE_EXPBIAS)<<52 | fd;
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// fallthrough
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case 1: // muf
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muf:
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if (fraw0 == DNZERO || fraw1 == DNZERO) {
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m->freg[dest] = DNZERO;
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goto ret;
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}
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if (fraw0 == DZERO || fraw1 == DZERO) {
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m->freg[dest] = DZERO;
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goto ret;
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}
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if (fraw0 == DONE) {
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m->freg[dest] = fraw1;
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goto ret;
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}
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if (fraw1 == DONE) {
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m->freg[dest] = fraw0;
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goto ret;
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}
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f0 = fraw0>>21 & 0x7fffffff | 0x1ll<<31;
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f1 = fraw1>>21 & 0x7fffffff | 0x1ll<<31;
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fd = f0*f1;
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high = fd >> 63;
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if (high)
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fd = fd >> 11 & DOUBLE_MANT_MASK;
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else
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fd = fd >> 10 & DOUBLE_MANT_MASK;
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exp = (uint64)(fexp(fraw0) + fexp(fraw1) + !!high + DOUBLE_EXPBIAS) & 0x7ff;
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sign = fraw0 >> 63 ^ fraw1 >> 63;
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fd = sign<<63 | exp<<52 | fd;
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m->freg[dest] = fd;
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goto ret;
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default:
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goto undef;
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case 0:
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·fadd64c(l, r, &m->freg[dest]);
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break;
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case 1:
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·fmul64c(l, r, &m->freg[dest]);
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break;
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case 2:
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·fsub64c(l, r, &m->freg[dest]);
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break;
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case 4:
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·fdiv64c(l, r, &m->freg[dest]);
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break;
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}
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goto ret;
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}
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@ -375,61 +214,28 @@ ret:
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static void
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compare(uint32 *pc, uint32 *regs)
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{
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uint32 i, flags, lhs, rhs, sign0, sign1;
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uint64 f0, f1, mant0, mant1;
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int32 exp0, exp1;
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uint32 i, flags, lhs, rhs;
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uint64 l, r;
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int32 cmp;
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bool nan;
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i = *pc;
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flags = 0;
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lhs = i>>16 & 0x7;
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rhs = i & 0xf;
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f0 = m->freg[lhs];
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f1 = frhs(rhs);
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if (isNaN(float64frombits(f0)) || isNaN(float64frombits(f1))) {
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l = m->freg[lhs];
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r = frhs(rhs);
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·fcmp64c(l, r, &cmp, &nan);
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if (nan)
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flags = FLAGS_C | FLAGS_V;
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goto ret;
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}
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if (f0 == f1) {
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else if (cmp == 0)
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flags = FLAGS_Z | FLAGS_C;
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goto ret;
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}
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sign0 = fsign(f0);
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sign1 = fsign(f1);
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if (sign0 == 1 && sign1 == 0) {
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else if (cmp < 0)
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flags = FLAGS_N;
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goto ret;
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}
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if (sign0 == 0 && sign1 == 1) {
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else
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flags = FLAGS_C;
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goto ret;
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}
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if (sign0 == 0) {
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exp0 = fexp(f0);
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exp1 = fexp(f1);
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mant0 = fmantissa(f0);
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mant1 = fmantissa(f1);
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} else {
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exp0 = fexp(f1);
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exp1 = fexp(f0);
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mant0 = fmantissa(f1);
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mant1 = fmantissa(f0);
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}
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if (exp0 > exp1) {
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flags = FLAGS_C;
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} else if (exp0 < exp1) {
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flags = FLAGS_N;
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} else {
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if (mant0 > mant1)
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flags = FLAGS_C;
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else
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flags = FLAGS_N;
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}
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ret:
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if (trace) {
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printf(" %p %x\tcmf\tf%d, ", pc, *pc, lhs);
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if (rhs & 0x8)
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@ -503,9 +309,10 @@ ret:
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static void
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fltfix(uint32 *pc, uint32 *regs)
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{
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uint32 i, toarm, freg, reg, sign, val, prec;
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int32 rd, exp;
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uint64 fd, f0;
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uint32 i, toarm, freg, reg, prec;
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int64 val;
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uint64 f0;
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bool ok;
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i = *pc;
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toarm = i>>20 & 0x1;
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@ -513,33 +320,15 @@ fltfix(uint32 *pc, uint32 *regs)
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reg = i>>12 & 0xf;
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prec = precision(i);
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if (toarm) { //fix
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if (toarm) { // fix
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f0 = m->freg[freg];
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fd = f0 & DOUBLE_MANT_MASK | DOUBLE_MANT_TOP_BIT;
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exp = fexp(f0) - 52;
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if (exp < 0)
|
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fd = fd>>(-exp);
|
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else
|
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fd = fd<<exp;
|
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rd = ((int32)fd & 0x7fffffff);
|
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if (f0 & 0x1ll<<63)
|
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rd = -rd;
|
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regs[reg] = (uint32)rd;
|
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·f64tointc(f0, &val, &ok);
|
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if (!ok || (int32)val != val)
|
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val = 0;
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regs[reg] = val;
|
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} else { // flt
|
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if (regs[reg] == 0) {
|
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m->freg[freg] = DZERO;
|
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goto ret;
|
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}
|
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sign = regs[reg] >> 31 & 0x1;
|
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val = regs[reg];
|
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if (sign) val = -val;
|
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for (exp = 31; exp >= 0; exp--) {
|
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if (1<<(exp) & val)
|
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break;
|
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}
|
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fd = (uint64)val<<(52-exp) & DOUBLE_MANT_MASK;
|
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m->freg[freg] = (uint64)(sign) << 63 |
|
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(uint64)(exp + DOUBLE_EXPBIAS) << 52 | fd;
|
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·fintto64c((int32)regs[reg], &f0);
|
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m->freg[freg] = f0;
|
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}
|
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goto ret;
|
||||
|
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@ -581,7 +370,8 @@ stepflt(uint32 *pc, uint32 *regs)
|
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loadstore(pc, regs);
|
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return 1;
|
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case 7: // 111
|
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if (i>>24 & 1) return 0; // ignore swi
|
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if (i>>24 & 1)
|
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return 0; // ignore swi
|
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|
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if (i>>4 & 1) { //data transfer
|
||||
if ((i&0x00f0ff00) == 0x0090f100) {
|
||||
@ -606,6 +396,14 @@ stepflt(uint32 *pc, uint32 *regs)
|
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regs[11] = *(uint32*)((uint8*)pc + (i&0xfff) + 8);
|
||||
return 1;
|
||||
}
|
||||
|
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if(i == 0xe08bb00d) {
|
||||
// add sp to 11.
|
||||
// might be part of a large stack offset address
|
||||
// (or might not, but again no harm done).
|
||||
regs[11] += regs[13];
|
||||
return 1;
|
||||
}
|
||||
|
||||
return 0;
|
||||
}
|
||||
@ -615,11 +413,9 @@ uint32*
|
||||
_sfloat2(uint32 *lr, uint32 r0)
|
||||
{
|
||||
uint32 skip;
|
||||
// uint32 cpsr;
|
||||
|
||||
while(skip = stepflt(lr, &r0)) {
|
||||
while(skip = stepflt(lr, &r0))
|
||||
lr += skip;
|
||||
}
|
||||
return lr;
|
||||
}
|
||||
|
||||
|
||||
17
src/pkg/runtime/export_test.go
Normal file
17
src/pkg/runtime/export_test.go
Normal file
@ -0,0 +1,17 @@
|
||||
// Copyright 2010 The Go Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// Export guts for testing.
|
||||
|
||||
package runtime
|
||||
|
||||
var Fadd64 = fadd64
|
||||
var Fsub64 = fsub64
|
||||
var Fmul64 = fmul64
|
||||
var Fdiv64 = fdiv64
|
||||
var F64to32 = f64to32
|
||||
var F32to64 = f32to64
|
||||
var Fcmp64 = fcmp64
|
||||
var Fintto64 = fintto64
|
||||
var F64toint = f64toint
|
||||
@ -558,6 +558,7 @@ void reflect·call(byte*, byte*, uint32);
|
||||
void ·panic(Eface);
|
||||
void ·panicindex(void);
|
||||
void ·panicslice(void);
|
||||
|
||||
/*
|
||||
* runtime c-called (but written in Go)
|
||||
*/
|
||||
@ -565,6 +566,16 @@ void ·newError(String, Eface*);
|
||||
void ·printany(Eface);
|
||||
void ·newTypeAssertionError(Type*, Type*, Type*, String*, String*, String*, String*, Eface*);
|
||||
void ·newErrorString(String, Eface*);
|
||||
void ·fadd64c(uint64, uint64, uint64*);
|
||||
void ·fsub64c(uint64, uint64, uint64*);
|
||||
void ·fmul64c(uint64, uint64, uint64*);
|
||||
void ·fdiv64c(uint64, uint64, uint64*);
|
||||
void ·fneg64c(uint64, uint64*);
|
||||
void ·f32to64c(uint32, uint64*);
|
||||
void ·f64to32c(uint64, uint32*);
|
||||
void ·fcmp64c(uint64, uint64, int32*, bool*);
|
||||
void ·fintto64c(int64, uint64*);
|
||||
void ·f64tointc(uint64, int64*, bool*);
|
||||
|
||||
/*
|
||||
* wrapped for go users
|
||||
|
||||
498
src/pkg/runtime/softfloat64.go
Normal file
498
src/pkg/runtime/softfloat64.go
Normal file
@ -0,0 +1,498 @@
|
||||
// Copyright 2010 The Go Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// Software IEEE754 64-bit floating point.
|
||||
// Only referred to (and thus linked in) by arm port
|
||||
// and by gotest in this directory.
|
||||
|
||||
package runtime
|
||||
|
||||
const (
|
||||
mantbits64 uint = 52
|
||||
expbits64 uint = 11
|
||||
bias64 = -1<<(expbits64-1) + 1
|
||||
|
||||
nan64 uint64 = (1<<expbits64-1)<<mantbits64 + 1
|
||||
inf64 uint64 = (1<<expbits64 - 1) << mantbits64
|
||||
neg64 uint64 = 1 << (expbits64 + mantbits64)
|
||||
|
||||
mantbits32 uint = 23
|
||||
expbits32 uint = 8
|
||||
bias32 = -1<<(expbits32-1) + 1
|
||||
|
||||
nan32 uint32 = (1<<expbits32-1)<<mantbits32 + 1
|
||||
inf32 uint32 = (1<<expbits32 - 1) << mantbits32
|
||||
neg32 uint32 = 1 << (expbits32 + mantbits32)
|
||||
)
|
||||
|
||||
func funpack64(f uint64) (sign, mant uint64, exp int, inf, nan bool) {
|
||||
sign = f & (1 << (mantbits64 + expbits64))
|
||||
mant = f & (1<<mantbits64 - 1)
|
||||
exp = int(f>>mantbits64) & (1<<expbits64 - 1)
|
||||
|
||||
switch exp {
|
||||
case 1<<expbits64 - 1:
|
||||
if mant != 0 {
|
||||
nan = true
|
||||
return
|
||||
}
|
||||
inf = true
|
||||
return
|
||||
|
||||
case 0:
|
||||
// denormalized
|
||||
if mant != 0 {
|
||||
exp += bias64 + 1
|
||||
for mant < 1<<mantbits64 {
|
||||
mant <<= 1
|
||||
exp--
|
||||
}
|
||||
}
|
||||
|
||||
default:
|
||||
// add implicit top bit
|
||||
mant |= 1 << mantbits64
|
||||
exp += bias64
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
func funpack32(f uint32) (sign, mant uint32, exp int, inf, nan bool) {
|
||||
sign = f & (1 << (mantbits32 + expbits32))
|
||||
mant = f & (1<<mantbits32 - 1)
|
||||
exp = int(f>>mantbits32) & (1<<expbits32 - 1)
|
||||
|
||||
switch exp {
|
||||
case 1<<expbits32 - 1:
|
||||
if mant != 0 {
|
||||
nan = true
|
||||
return
|
||||
}
|
||||
inf = true
|
||||
return
|
||||
|
||||
case 0:
|
||||
// denormalized
|
||||
if mant != 0 {
|
||||
exp += bias32 + 1
|
||||
for mant < 1<<mantbits32 {
|
||||
mant <<= 1
|
||||
exp--
|
||||
}
|
||||
}
|
||||
|
||||
default:
|
||||
// add implicit top bit
|
||||
mant |= 1 << mantbits32
|
||||
exp += bias32
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
func fpack64(sign, mant uint64, exp int, trunc uint64) uint64 {
|
||||
mant0, exp0, trunc0 := mant, exp, trunc
|
||||
if mant == 0 {
|
||||
return sign
|
||||
}
|
||||
for mant < 1<<mantbits64 {
|
||||
mant <<= 1
|
||||
exp--
|
||||
}
|
||||
for mant >= 4<<mantbits64 {
|
||||
trunc |= mant & 1
|
||||
mant >>= 1
|
||||
exp++
|
||||
}
|
||||
if mant >= 2<<mantbits64 {
|
||||
if mant&1 != 0 && (trunc != 0 || mant&2 != 0) {
|
||||
mant++
|
||||
if mant >= 4<<mantbits64 {
|
||||
mant >>= 1
|
||||
exp++
|
||||
}
|
||||
}
|
||||
mant >>= 1
|
||||
exp++
|
||||
}
|
||||
if exp >= 1<<expbits64-1+bias64 {
|
||||
return sign ^ inf64
|
||||
}
|
||||
if exp < bias64+1 {
|
||||
if exp < bias64-int(mantbits64) {
|
||||
return sign | 0
|
||||
}
|
||||
// repeat expecting denormal
|
||||
mant, exp, trunc = mant0, exp0, trunc0
|
||||
for exp < bias64 {
|
||||
trunc |= mant & 1
|
||||
mant >>= 1
|
||||
exp++
|
||||
}
|
||||
if mant&1 != 0 && (trunc != 0 || mant&2 != 0) {
|
||||
mant++
|
||||
}
|
||||
mant >>= 1
|
||||
exp++
|
||||
if mant < 1<<mantbits64 {
|
||||
return sign | mant
|
||||
}
|
||||
}
|
||||
return sign | uint64(exp-bias64)<<mantbits64 | mant&(1<<mantbits64-1)
|
||||
}
|
||||
|
||||
func fpack32(sign, mant uint32, exp int, trunc uint32) uint32 {
|
||||
mant0, exp0, trunc0 := mant, exp, trunc
|
||||
if mant == 0 {
|
||||
return sign
|
||||
}
|
||||
for mant < 1<<mantbits32 {
|
||||
mant <<= 1
|
||||
exp--
|
||||
}
|
||||
for mant >= 4<<mantbits32 {
|
||||
trunc |= mant & 1
|
||||
mant >>= 1
|
||||
exp++
|
||||
}
|
||||
if mant >= 2<<mantbits32 {
|
||||
if mant&1 != 0 && (trunc != 0 || mant&2 != 0) {
|
||||
mant++
|
||||
if mant >= 4<<mantbits32 {
|
||||
mant >>= 1
|
||||
exp++
|
||||
}
|
||||
}
|
||||
mant >>= 1
|
||||
exp++
|
||||
}
|
||||
if exp >= 1<<expbits32-1+bias32 {
|
||||
return sign ^ inf32
|
||||
}
|
||||
if exp < bias32+1 {
|
||||
if exp < bias32-int(mantbits32) {
|
||||
return sign | 0
|
||||
}
|
||||
// repeat expecting denormal
|
||||
mant, exp, trunc = mant0, exp0, trunc0
|
||||
for exp < bias32 {
|
||||
trunc |= mant & 1
|
||||
mant >>= 1
|
||||
exp++
|
||||
}
|
||||
if mant&1 != 0 && (trunc != 0 || mant&2 != 0) {
|
||||
mant++
|
||||
}
|
||||
mant >>= 1
|
||||
exp++
|
||||
if mant < 1<<mantbits32 {
|
||||
return sign | mant
|
||||
}
|
||||
}
|
||||
return sign | uint32(exp-bias32)<<mantbits32 | mant&(1<<mantbits32-1)
|
||||
}
|
||||
|
||||
func fadd64(f, g uint64) uint64 {
|
||||
fs, fm, fe, fi, fn := funpack64(f)
|
||||
gs, gm, ge, gi, gn := funpack64(g)
|
||||
|
||||
// Special cases.
|
||||
switch {
|
||||
case fn || gn: // NaN + x or x + NaN = NaN
|
||||
return nan64
|
||||
|
||||
case fi && gi && fs != gs: // +Inf + -Inf or -Inf + +Inf = NaN
|
||||
return nan64
|
||||
|
||||
case fi: // ±Inf + g = ±Inf
|
||||
return f
|
||||
|
||||
case gi: // f + ±Inf = ±Inf
|
||||
return g
|
||||
|
||||
case fm == 0 && gm == 0 && fs != 0 && gs != 0: // -0 + -0 = -0
|
||||
return f
|
||||
|
||||
case fm == 0: // 0 + g = g but 0 + -0 = +0
|
||||
if gm == 0 {
|
||||
g ^= gs
|
||||
}
|
||||
return g
|
||||
|
||||
case gm == 0: // f + 0 = f
|
||||
return f
|
||||
|
||||
}
|
||||
|
||||
if fe < ge || fe == ge && fm < gm {
|
||||
f, g, fs, fm, fe, gs, gm, ge = g, f, gs, gm, ge, fs, fm, fe
|
||||
}
|
||||
|
||||
shift := uint(fe - ge)
|
||||
fm <<= 2
|
||||
gm <<= 2
|
||||
trunc := gm & (1<<shift - 1)
|
||||
gm >>= shift
|
||||
if fs == gs {
|
||||
fm += gm
|
||||
} else {
|
||||
fm -= gm
|
||||
if trunc != 0 {
|
||||
fm--
|
||||
}
|
||||
}
|
||||
if fm == 0 {
|
||||
fs = 0
|
||||
}
|
||||
return fpack64(fs, fm, fe-2, trunc)
|
||||
}
|
||||
|
||||
func fsub64(f, g uint64) uint64 {
|
||||
return fadd64(f, fneg64(g))
|
||||
}
|
||||
|
||||
func fneg64(f uint64) uint64 {
|
||||
return f ^ (1 << (mantbits64 + expbits64))
|
||||
}
|
||||
|
||||
func fmul64(f, g uint64) uint64 {
|
||||
fs, fm, fe, fi, fn := funpack64(f)
|
||||
gs, gm, ge, gi, gn := funpack64(g)
|
||||
|
||||
// Special cases.
|
||||
switch {
|
||||
case fn || gn: // NaN * g or f * NaN = NaN
|
||||
return nan64
|
||||
|
||||
case fi && gi: // Inf * Inf = Inf (with sign adjusted)
|
||||
return f ^ gs
|
||||
|
||||
case fi && gm == 0, fm == 0 && gi: // 0 * Inf = Inf * 0 = NaN
|
||||
return nan64
|
||||
|
||||
case fm == 0: // 0 * x = 0 (with sign adjusted)
|
||||
return f ^ gs
|
||||
|
||||
case gm == 0: // x * 0 = 0 (with sign adjusted)
|
||||
return g ^ fs
|
||||
}
|
||||
|
||||
// 53-bit * 53-bit = 107- or 108-bit
|
||||
lo, hi := mullu(fm, gm)
|
||||
shift := mantbits64 - 1
|
||||
trunc := lo & (1<<shift - 1)
|
||||
mant := hi<<(64-shift) | lo>>shift
|
||||
return fpack64(fs^gs, mant, fe+ge-1, trunc)
|
||||
}
|
||||
|
||||
func fdiv64(f, g uint64) uint64 {
|
||||
fs, fm, fe, fi, fn := funpack64(f)
|
||||
gs, gm, ge, gi, gn := funpack64(g)
|
||||
|
||||
// Special cases.
|
||||
switch {
|
||||
case fn || gn: // NaN / g = f / NaN = NaN
|
||||
return nan64
|
||||
|
||||
case fi && gi: // ±Inf / ±Inf = NaN
|
||||
return nan64
|
||||
|
||||
case !fi && !gi && fm == 0 && gm == 0: // 0 / 0 = NaN
|
||||
return nan64
|
||||
|
||||
case fi, !gi && gm == 0: // Inf / g = f / 0 = Inf
|
||||
return fs ^ gs ^ inf64
|
||||
|
||||
case gi, fm == 0: // f / Inf = 0 / g = Inf
|
||||
return fs ^ gs ^ 0
|
||||
}
|
||||
_, _, _, _ = fi, fn, gi, gn
|
||||
|
||||
// 53-bit<<54 / 53-bit = 53- or 54-bit.
|
||||
shift := mantbits64 + 2
|
||||
q, r := divlu(fm>>(64-shift), fm<<shift, gm)
|
||||
return fpack64(fs^gs, q, fe-ge-2, r)
|
||||
}
|
||||
|
||||
func f64to32(f uint64) uint32 {
|
||||
fs, fm, fe, fi, fn := funpack64(f)
|
||||
if fn {
|
||||
return nan32
|
||||
}
|
||||
fs32 := uint32(fs >> 32)
|
||||
if fi {
|
||||
return fs32 ^ inf32
|
||||
}
|
||||
const d = mantbits64 - mantbits32 - 1
|
||||
return fpack32(fs32, uint32(fm>>d), fe-1, uint32(fm&(1<<d-1)))
|
||||
}
|
||||
|
||||
func f32to64(f uint32) uint64 {
|
||||
const d = mantbits64 - mantbits32
|
||||
fs, fm, fe, fi, fn := funpack32(f)
|
||||
if fn {
|
||||
return nan64
|
||||
}
|
||||
fs64 := uint64(fs) << 32
|
||||
if fi {
|
||||
return fs64 ^ inf64
|
||||
}
|
||||
return fpack64(fs64, uint64(fm)<<d, fe, 0)
|
||||
}
|
||||
|
||||
func fcmp64(f, g uint64) (cmp int, isnan bool) {
|
||||
fs, fm, _, fi, fn := funpack64(f)
|
||||
gs, gm, _, gi, gn := funpack64(g)
|
||||
|
||||
switch {
|
||||
case fn, gn: // flag NaN
|
||||
return 0, true
|
||||
|
||||
case !fi && !gi && fm == 0 && gm == 0: // ±0 == ±0
|
||||
return 0, false
|
||||
|
||||
case fs > gs: // f < 0, g > 0
|
||||
return -1, false
|
||||
|
||||
case fs < gs: // f > 0, g < 0
|
||||
return +1, false
|
||||
|
||||
// Same sign, not NaN.
|
||||
// Can compare encodings directly now.
|
||||
// Reverse for sign.
|
||||
case fs == 0 && f < g, fs != 0 && f > g:
|
||||
return -1, false
|
||||
|
||||
case fs == 0 && f > g, fs != 0 && f < g:
|
||||
return +1, false
|
||||
}
|
||||
|
||||
// f == g
|
||||
return 0, false
|
||||
}
|
||||
|
||||
func f64toint(f uint64) (val int64, ok bool) {
|
||||
fs, fm, fe, fi, fn := funpack64(f)
|
||||
|
||||
switch {
|
||||
case fi, fn: // NaN
|
||||
return 0, false
|
||||
|
||||
case fe < -1: // f < 0.5
|
||||
return 0, false
|
||||
|
||||
case fe > 63: // f >= 2^63
|
||||
if fs != 0 && fm == 0 { // f == -2^63
|
||||
return -1 << 63, true
|
||||
}
|
||||
if fs != 0 {
|
||||
return 0, false
|
||||
}
|
||||
return 0, false
|
||||
}
|
||||
|
||||
for fe > int(mantbits64) {
|
||||
fe--
|
||||
fm <<= 1
|
||||
}
|
||||
for fe < int(mantbits64) {
|
||||
fe++
|
||||
fm >>= 1
|
||||
}
|
||||
val = int64(fm)
|
||||
if fs != 0 {
|
||||
val = -val
|
||||
}
|
||||
return val, true
|
||||
}
|
||||
|
||||
func fintto64(val int64) (f uint64) {
|
||||
fs := uint64(val) & (1 << 63)
|
||||
mant := uint64(val)
|
||||
if fs != 0 {
|
||||
mant = -mant
|
||||
}
|
||||
return fpack64(fs, mant, int(mantbits64), 0)
|
||||
}
|
||||
|
||||
// 64x64 -> 128 multiply.
|
||||
// adapted from hacker's delight.
|
||||
func mullu(u, v uint64) (lo, hi uint64) {
|
||||
const (
|
||||
s = 32
|
||||
mask = 1<<s - 1
|
||||
)
|
||||
u0 := u & mask
|
||||
u1 := u >> s
|
||||
v0 := v & mask
|
||||
v1 := v >> s
|
||||
w0 := u0 * v0
|
||||
t := u1*v0 + w0>>s
|
||||
w1 := t & mask
|
||||
w2 := t >> s
|
||||
w1 += u0 * v1
|
||||
return u * v, u1*v1 + w2 + w1>>s
|
||||
}
|
||||
|
||||
// 128/64 -> 64 quotient, 64 remainder.
|
||||
// adapted from hacker's delight
|
||||
func divlu(u1, u0, v uint64) (q, r uint64) {
|
||||
const b = 1 << 32
|
||||
|
||||
if u1 >= v {
|
||||
return 1<<64 - 1, 1<<64 - 1
|
||||
}
|
||||
|
||||
// s = nlz(v); v <<= s
|
||||
s := uint(0)
|
||||
for v&(1<<63) == 0 {
|
||||
s++
|
||||
v <<= 1
|
||||
}
|
||||
|
||||
vn1 := v >> 32
|
||||
vn0 := v & (1<<32 - 1)
|
||||
un32 := u1<<s | u0>>(64-s)
|
||||
un10 := u0 << s
|
||||
un1 := un10 >> 32
|
||||
un0 := un10 & (1<<32 - 1)
|
||||
q1 := un32 / vn1
|
||||
rhat := un32 - q1*vn1
|
||||
|
||||
again1:
|
||||
if q1 >= b || q1*vn0 > b*rhat+un1 {
|
||||
q1--
|
||||
rhat += vn1
|
||||
if rhat < b {
|
||||
goto again1
|
||||
}
|
||||
}
|
||||
|
||||
un21 := un32*b + un1 - q1*v
|
||||
q0 := un21 / vn1
|
||||
rhat = un21 - q0*vn1
|
||||
|
||||
again2:
|
||||
if q0 >= b || q0*vn0 > b*rhat+un0 {
|
||||
q0--
|
||||
rhat += vn1
|
||||
if rhat < b {
|
||||
goto again2
|
||||
}
|
||||
}
|
||||
|
||||
return q1*b + q0, (un21*b + un0 - q0*v) >> s
|
||||
}
|
||||
|
||||
// callable from C
|
||||
|
||||
func fadd64c(f, g uint64, ret *uint64) { *ret = fadd64(f, g) }
|
||||
func fsub64c(f, g uint64, ret *uint64) { *ret = fsub64(f, g) }
|
||||
func fmul64c(f, g uint64, ret *uint64) { *ret = fmul64(f, g) }
|
||||
func fdiv64c(f, g uint64, ret *uint64) { *ret = fdiv64(f, g) }
|
||||
func fneg64c(f uint64, ret *uint64) { *ret = fneg64(f) }
|
||||
func f32to64c(f uint32, ret *uint64) { *ret = f32to64(f) }
|
||||
func f64to32c(f uint64, ret *uint32) { *ret = f64to32(f) }
|
||||
func fcmp64c(f, g uint64, ret *int, retnan *bool) { *ret, *retnan = fcmp64(f, g) }
|
||||
func fintto64c(val int64, ret *uint64) { *ret = fintto64(val) }
|
||||
func f64tointc(f uint64, ret *int64, retok *bool) { *ret, *retok = f64toint(f) }
|
||||
198
src/pkg/runtime/softfloat64_test.go
Normal file
198
src/pkg/runtime/softfloat64_test.go
Normal file
@ -0,0 +1,198 @@
|
||||
// Copyright 2010 The Go Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package runtime_test
|
||||
|
||||
import (
|
||||
"math"
|
||||
"rand"
|
||||
. "runtime"
|
||||
"testing"
|
||||
)
|
||||
|
||||
// turn uint64 op into float64 op
|
||||
func fop(f func(x, y uint64) uint64) func(x, y float64) float64 {
|
||||
return func(x, y float64) float64 {
|
||||
bx := math.Float64bits(x)
|
||||
by := math.Float64bits(y)
|
||||
return math.Float64frombits(f(bx, by))
|
||||
}
|
||||
}
|
||||
|
||||
func add(x, y float64) float64 { return x + y }
|
||||
func sub(x, y float64) float64 { return x - y }
|
||||
func mul(x, y float64) float64 { return x * y }
|
||||
func div(x, y float64) float64 { return x / y }
|
||||
|
||||
func TestFloat64(t *testing.T) {
|
||||
base := []float64{
|
||||
0,
|
||||
math.Copysign(0, -1),
|
||||
-1,
|
||||
1,
|
||||
math.NaN(),
|
||||
math.Inf(+1),
|
||||
math.Inf(-1),
|
||||
0.1,
|
||||
1.5,
|
||||
1.9999999999999998, // all 1s mantissa
|
||||
1.3333333333333333, // 1.010101010101...
|
||||
1.1428571428571428, // 1.001001001001...
|
||||
1.112536929253601e-308, // first normal
|
||||
2,
|
||||
4,
|
||||
8,
|
||||
16,
|
||||
32,
|
||||
64,
|
||||
128,
|
||||
256,
|
||||
3,
|
||||
12,
|
||||
1234,
|
||||
123456,
|
||||
-0.1,
|
||||
-1.5,
|
||||
-1.9999999999999998,
|
||||
-1.3333333333333333,
|
||||
-1.1428571428571428,
|
||||
-2,
|
||||
-3,
|
||||
1e-200,
|
||||
1e-300,
|
||||
1e-310,
|
||||
5e-324,
|
||||
1e-105,
|
||||
1e-305,
|
||||
1e+200,
|
||||
1e+306,
|
||||
1e+307,
|
||||
1e+308,
|
||||
}
|
||||
all := make([]float64, 200)
|
||||
copy(all, base)
|
||||
for i := len(base); i < len(all); i++ {
|
||||
all[i] = rand.NormFloat64()
|
||||
}
|
||||
|
||||
test(t, "+", add, fop(Fadd64), all)
|
||||
test(t, "-", sub, fop(Fsub64), all)
|
||||
if GOARCH != "386" { // 386 is not precise!
|
||||
test(t, "*", mul, fop(Fmul64), all)
|
||||
test(t, "/", div, fop(Fdiv64), all)
|
||||
}
|
||||
}
|
||||
|
||||
// 64 -hw-> 32 -hw-> 64
|
||||
func trunc32(f float64) float64 {
|
||||
return float64(float32(f))
|
||||
}
|
||||
|
||||
// 64 -sw->32 -hw-> 64
|
||||
func to32sw(f float64) float64 {
|
||||
return float64(math.Float32frombits(F64to32(math.Float64bits(f))))
|
||||
}
|
||||
|
||||
// 64 -hw->32 -sw-> 64
|
||||
func to64sw(f float64) float64 {
|
||||
return math.Float64frombits(F32to64(math.Float32bits(float32(f))))
|
||||
}
|
||||
|
||||
// float64 -hw-> int64 -hw-> float64
|
||||
func hwint64(f float64) float64 {
|
||||
return float64(int64(f))
|
||||
}
|
||||
|
||||
// float64 -hw-> int32 -hw-> float64
|
||||
func hwint32(f float64) float64 {
|
||||
return float64(int32(f))
|
||||
}
|
||||
|
||||
// float64 -sw-> int64 -hw-> float64
|
||||
func toint64sw(f float64) float64 {
|
||||
i, ok := F64toint(math.Float64bits(f))
|
||||
if !ok {
|
||||
// There's no right answer for out of range.
|
||||
// Match the hardware to pass the test.
|
||||
i = int64(f)
|
||||
}
|
||||
return float64(i)
|
||||
}
|
||||
|
||||
// float64 -hw-> int64 -sw-> float64
|
||||
func fromint64sw(f float64) float64 {
|
||||
return math.Float64frombits(Fintto64(int64(f)))
|
||||
}
|
||||
|
||||
var nerr int
|
||||
|
||||
func err(t *testing.T, format string, args ...interface{}) {
|
||||
t.Errorf(format, args...)
|
||||
|
||||
// cut errors off after a while.
|
||||
// otherwise we spend all our time
|
||||
// allocating memory to hold the
|
||||
// formatted output.
|
||||
if nerr++; nerr >= 10 {
|
||||
t.Fatal("too many errors")
|
||||
}
|
||||
}
|
||||
|
||||
func test(t *testing.T, op string, hw, sw func(float64, float64) float64, all []float64) {
|
||||
for _, f := range all {
|
||||
for _, g := range all {
|
||||
h := hw(f, g)
|
||||
s := sw(f, g)
|
||||
if !same(h, s) {
|
||||
err(t, "%g %s %g = sw %g, hw %g\n", f, op, g, s, h)
|
||||
}
|
||||
testu(t, "to32", trunc32, to32sw, h)
|
||||
testu(t, "to64", trunc32, to64sw, h)
|
||||
testu(t, "toint64", hwint64, toint64sw, h)
|
||||
testu(t, "fromint64", hwint64, fromint64sw, h)
|
||||
testcmp(t, f, h)
|
||||
testcmp(t, h, f)
|
||||
testcmp(t, g, h)
|
||||
testcmp(t, h, g)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func testu(t *testing.T, op string, hw, sw func(float64) float64, v float64) {
|
||||
h := hw(v)
|
||||
s := sw(v)
|
||||
if !same(h, s) {
|
||||
err(t, "%s %g = sw %g, hw %g\n", op, v, s, h)
|
||||
}
|
||||
}
|
||||
|
||||
func hwcmp(f, g float64) (cmp int, isnan bool) {
|
||||
switch {
|
||||
case f < g:
|
||||
return -1, false
|
||||
case f > g:
|
||||
return +1, false
|
||||
case f == g:
|
||||
return 0, false
|
||||
}
|
||||
return 0, true // must be NaN
|
||||
}
|
||||
|
||||
func testcmp(t *testing.T, f, g float64) {
|
||||
hcmp, hisnan := hwcmp(f, g)
|
||||
scmp, sisnan := Fcmp64(math.Float64bits(f), math.Float64bits(g))
|
||||
if hcmp != scmp || hisnan != sisnan {
|
||||
err(t, "cmp(%g, %g) = sw %v, %v, hw %v, %v\n", f, g, scmp, sisnan, hcmp, hisnan)
|
||||
}
|
||||
}
|
||||
|
||||
func same(f, g float64) bool {
|
||||
if math.IsNaN(f) && math.IsNaN(g) {
|
||||
return true
|
||||
}
|
||||
if math.Copysign(1, f) != math.Copysign(1, g) {
|
||||
return false
|
||||
}
|
||||
return f == g
|
||||
}
|
||||
Loading…
Reference in New Issue
Block a user