static inline DItype
__udivmoddi4 (UDItype x, UDItype y, DItype *res)
{
static unsigned char unrt[256] = {-2, -4, -6, -8, -10, -12, -14, -16, -18, -20, -22, -23, -25, -27, -29, -31, -32, -34, -36, -38, -39, -41, -43, -44, -46, -48,
-49, -51, -53, -54, -56, -57, -59, -61, -62, -64, -65, -67, -68, -70, -71, -73, -74, -76, -77, -78, -80, -81, -83, -84, -86,
-87, -88, -90, -91, -92, -94, -95, -96, -98, -99, -100, -102, -103, -104, -105, -107, -108, -109, -110, -112, -113, -114, -115,
-117, -118, -119, -120, -121, -122, -124, -125, -126, -127, -128, 127, 126, 125, 123, 122, 121, 120, 119, 118, 117, 116, 115,
114, 113, 112, 111, 110, 109, 108, 107, 106, 105, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 88,
87, 86, 85, 84, 83, 82, 81, 80, 80, 79, 78, 77, 76, 75, 74, 74, 73, 72, 71, 70, 70, 69, 68, 67, 66, 66, 65, 64, 63, 62, 62, 61,
60, 59, 59, 58, 57, 56, 56, 55, 54, 53, 53, 52, 51, 50, 50, 49, 48, 48, 47, 46, 46, 45, 44, 43, 43, 42, 41, 41, 40, 39, 39, 38,
37, 37, 36, 35, 35, 34, 33, 33, 32, 32, 31, 30, 30, 29, 28, 28, 27, 27, 26, 25, 25, 24, 24, 23, 22, 22, 21, 21, 20, 19, 19, 18,
18, 17, 17, 16, 15, 15, 14, 14, 13, 13, 12, 12, 11, 10, 10, 9, 9, 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 0, 0};
BIT_RESIZE(y,32);
// table lookup start
#define W 64
unsigned char k32 =__builtin_clz(y);
UDItype lshifted_y = ((UDItype)(((USItype)y) << k32))<<32;
/// remove the leading 1
lshifted_y = lshifted_y << 1;
UDItype ty = lsr64(lshifted_y, W-8 ); // prescaling
UDItype t = unrt[ ty ] | 256; // table lookup
UDItype z = lsr64(lsl64(t,W-9), (W-32-1)-k32 ); // postscaling
// z recurrence
UDItype my = 0-y;
//#define NR_UNROLLED
#ifdef NR_UNROLLED
z = z + umulh64(z,mul64(my,z));
z = z + umulh64(z,mul64(my,z));
z = z + umulh64(z,mul64(my,z));
#else
unsigned int index;
for (index = 0; index < 3; ++index) {
UDItype zd = umulh64(z,mul64(my,z));
//if (zd == 0) break;
z = z + zd;
}
#endif
// q estimate
UDItype q = umulh64(x,z);
UDItype r = x - mul64(y,q);
// q refinement
if (r >= y) {
r = r - y;
q = q + 1;
if (r >= y) {
r = r - y;
q = q + 1;
if (r >= y) { //add this in case of three iterations
r = r - y;
q = q + 1;
}
}
}
if (res != 0) *res = r;
return q;
}
PRIVATE void estimate_cpu_freq(void)
{
u64_t tsc_delta;
u64_t cpu_freq;
irq_hook_t calib_cpu;
/* set the probe, we use the legacy timer, IRQ 0 */
put_irq_handler(&calib_cpu, CLOCK_IRQ, calib_cpu_handler);
/* just in case we are in an SMP single cpu fallback mode */
BKL_UNLOCK();
/* set the PIC timer to get some time */
intr_enable();
/* loop for some time to get a sample */
while(probe_ticks < PROBE_TICKS) {
intr_enable();
}
intr_disable();
/* just in case we are in an SMP single cpu fallback mode */
BKL_LOCK();
/* remove the probe */
rm_irq_handler(&calib_cpu);
tsc_delta = sub64(tsc1, tsc0);
cpu_freq = mul64(div64u64(tsc_delta, PROBE_TICKS - 1), make64(system_hz, 0));
cpu_set_freq(cpuid, cpu_freq);
cpu_info[cpuid].freq = div64u(cpu_freq, 1000000);
BOOT_VERBOSE(cpu_print_freq(cpuid));
}
/* Unsigned 64x64 -> 128 multiplication */
void mulu64 (uint64_t *plow, uint64_t *phigh, uint64_t a, uint64_t b)
{
mul64(plow, phigh, a, b);
#if defined(DEBUG_MULDIV)
printf("mulu64: 0x%016llx * 0x%016llx = 0x%016llx%016llx\n",
a, b, *phigh, *plow);
#endif
}
static void testdiv(void)
{
u64_t q, r;
#if TIMED
struct timeval tvstart, tvend;
printf("i=0x%.8x%.8x; j=0x%.8x%.8x\n",
ex64hi(i), ex64lo(i),
ex64hi(j), ex64lo(j));
fflush(stdout);
if (gettimeofday(&tvstart, NULL) < 0) ERR;
#endif
/* division by zero has a separate test */
if (cmp64u(j, 0) == 0) {
testdiv0();
return;
}
/* perform division, store q in k to make ERR more informative */
q = div64(i, j);
r = rem64(i, j);
k = q;
#if TIMED
if (gettimeofday(&tvend, NULL) < 0) ERR;
tvend.tv_sec -= tvstart.tv_sec;
tvend.tv_usec -= tvstart.tv_usec;
if (tvend.tv_usec < 0) {
tvend.tv_sec -= 1;
tvend.tv_usec += 1000000;
}
printf("q=0x%.8x%.8x; r=0x%.8x%.8x; time=%d.%.6d\n",
ex64hi(q), ex64lo(q),
ex64hi(r), ex64lo(r),
tvend.tv_sec, tvend.tv_usec);
fflush(stdout);
#endif
/* compare to 64/32-bit division if possible */
if (!ex64hi(j)) {
if (cmp64(q, div64u64(i, ex64lo(j))) != 0) ERR;
if (!ex64hi(q)) {
if (cmp64u(q, div64u(i, ex64lo(j))) != 0) ERR;
}
if (cmp64u(r, rem64u(i, ex64lo(j))) != 0) ERR;
/* compare to 32-bit division if possible */
if (!ex64hi(i)) {
if (cmp64u(q, ex64lo(i) / ex64lo(j)) != 0) ERR;
if (cmp64u(r, ex64lo(i) % ex64lo(j)) != 0) ERR;
}
}
/* check results using i = q j + r and r < j */
if (cmp64(i, add64(mul64(q, j), r)) != 0) ERR;
if (cmp64(r, j) >= 0) ERR;
}
void SetIntNum16(void) { /* 1 */
/*
64 bit 演算のための数値をセット
var: 数値の入った変数
*/
int *var = getCaliVariable();
l_1000A0D8 = mul64(*var, numbase);
DEBUG_COMMAND("ShCalc.SetIntNum16 %p:\n", var);
}
void AddIntNum16(void) { /* 5 */
/*
64 bit 加算
var: 足す数の入った変数
*/
int *var = getCaliVariable();
l_1000A0D8 += mul64(*var, numbase);
DEBUG_COMMAND("ShCalc.AddIntNum16 %p:\n", var);
}
void MulIntNum16(void) { /* 9 */
/*
64 bit 乗算
var: 掛ける数の入った変数
*/
int *var = getCaliVariable();
l_1000A0D8 *= mul64(*var, numbase);
DEBUG_COMMAND("ShCalc.MulIntNum16: %p:\n", var);
}
CFixVector& CFixVector::Cross (CFixVector& dest, const CFixVector& v0, const CFixVector& v1)
{
#if 0
double x = (double (v0 [Y]) * double (v1 [Z]) - double (v0 [Z]) * double (v1 [Y])) / 65536.0;
double y = (double (v0 [Z]) * double (v1 [X]) - double (v0 [X]) * double (v1 [Z])) / 65536.0;
double z = (double (v0 [X]) * double (v1 [Y]) - double (v0 [Y]) * double (v1 [X])) / 65536.0;
if (x > double (0x7fffffff))
x = double (0x7fffffff);
else if (x < double (-0x7fffffff))
x = double (-0x7fffffff);
if (y > double (0x7fffffff))
y = double (0x7fffffff);
else if (y < double (-0x7fffffff))
y = double (-0x7fffffff);
if (z > double (0x7fffffff))
z = double (0x7fffffff);
else if (z < double (-0x7fffffff))
z = double (-0x7fffffff);
dest.Set (fix (x), fix (y), fix (z));
#else
QLONG x, y, z;
x = mul64 (v0 [Y], v1 [Z]);
x += mul64 (-v0 [Z], v1 [Y]);
y = mul64 (v0 [Z], v1 [X]);
y += mul64 (-v0 [X], v1 [Z]);
z = mul64 (v0 [X], v1 [Y]);
z += mul64 (-v0 [Y], v1 [X]);
dest.Set (fix (x / 65536), fix (y / 65536), fix (z / 65536));
#endif
return dest;
}
void DivIntNum16(void) { /* 11 */
/*
64 bit 除算
var: 足す数の入った変数
*/
int *var = getCaliVariable();
gint64 i;
l_1000A0C8 = *var;
i = mul64(l_1000A0C8, numbase);
l_1000A0D8 = div64(l_1000A0D8, i);
DEBUG_COMMAND("ShCalc.DivIntNum16 %p:\n", var);
}
/* Signed 64x64 -> 128 multiplication */
void muls64 (uint64_t *plow, uint64_t *phigh, int64_t a, int64_t b)
{
int sa, sb;
sa = (a < 0);
if (sa)
a = -a;
sb = (b < 0);
if (sb)
b = -b;
mul64(plow, phigh, a, b);
if (sa ^ sb) {
neg128(plow, phigh);
}
#if defined(DEBUG_MULDIV)
printf("muls64: 0x%016llx * 0x%016llx = 0x%016llx%016llx\n",
a, b, *phigh, *plow);
#endif
}
PUBLIC short cpu_load(void)
{
u64_t current_tsc, *current_idle;
u64_t tsc_delta, idle_delta, busy;
struct proc *idle;
short load;
#ifdef CONFIG_SMP
unsigned cpu = cpuid;
#endif
u64_t *last_tsc, *last_idle;
last_tsc = get_cpu_var_ptr(cpu, cpu_last_tsc);
last_idle = get_cpu_var_ptr(cpu, cpu_last_idle);
idle = get_cpu_var_ptr(cpu, idle_proc);;
read_tsc_64(¤t_tsc);
current_idle = &idle->p_cycles; /* ptr to idle proc */
/* calculate load since last cpu_load invocation */
if (!is_zero64(*last_tsc)) {
tsc_delta = sub64(current_tsc, *last_tsc);
idle_delta = sub64(*current_idle, *last_idle);
busy = sub64(tsc_delta, idle_delta);
busy = mul64(busy, make64(100, 0));
load = ex64lo(div64(busy, tsc_delta));
if (load > 100)
load = 100;
} else
load = 0;
*last_tsc = current_tsc;
*last_idle = *current_idle;
return load;
}
/* BN_div_no_branch is a special version of BN_div. It does not contain
* branches that may leak sensitive information.
*/
static int BN_div_no_branch(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num,
const BIGNUM *divisor, BN_CTX *ctx)
{
int norm_shift,i,loop;
BIGNUM *tmp,wnum,*snum,*sdiv,*res;
BN_ULONG *resp,*wnump;
BN_ULONG d0,d1;
int num_n,div_n;
bn_check_top(dv);
bn_check_top(rm);
/* bn_check_top(num); */ /* 'num' has been checked in BN_div() */
bn_check_top(divisor);
if (BN_is_zero(divisor))
{
BNerr(BN_F_BN_DIV_NO_BRANCH,BN_R_DIV_BY_ZERO);
return(0);
}
BN_CTX_start(ctx);
tmp=BN_CTX_get(ctx);
snum=BN_CTX_get(ctx);
sdiv=BN_CTX_get(ctx);
if (dv == NULL)
res=BN_CTX_get(ctx);
else res=dv;
if (sdiv == NULL || res == NULL) goto err;
/* First we normalise the numbers */
norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
sdiv->neg=0;
norm_shift+=BN_BITS2;
if (!(BN_lshift(snum,num,norm_shift))) goto err;
snum->neg=0;
/* Since we don't know whether snum is larger than sdiv,
* we pad snum with enough zeroes without changing its
* value.
*/
if (snum->top <= sdiv->top+1)
{
if (bn_wexpand(snum, sdiv->top + 2) == NULL) goto err;
for (i = snum->top; i < sdiv->top + 2; i++) snum->d[i] = 0;
snum->top = sdiv->top + 2;
}
else
{
if (bn_wexpand(snum, snum->top + 1) == NULL) goto err;
snum->d[snum->top] = 0;
snum->top ++;
}
div_n=sdiv->top;
num_n=snum->top;
loop=num_n-div_n;
/* Lets setup a 'window' into snum
* This is the part that corresponds to the current
* 'area' being divided */
wnum.neg = 0;
wnum.d = &(snum->d[loop]);
wnum.top = div_n;
/* only needed when BN_ucmp messes up the values between top and max */
wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
/* Get the top 2 words of sdiv */
/* div_n=sdiv->top; */
d0=sdiv->d[div_n-1];
d1=(div_n == 1)?0:sdiv->d[div_n-2];
/* pointer to the 'top' of snum */
wnump= &(snum->d[num_n-1]);
/* Setup to 'res' */
res->neg= (num->neg^divisor->neg);
if (!bn_wexpand(res,(loop+1))) goto err;
res->top=loop-1;
resp= &(res->d[loop-1]);
/* space for temp */
if (!bn_wexpand(tmp,(div_n+1))) goto err;
/* if res->top == 0 then clear the neg value otherwise decrease
* the resp pointer */
if (res->top == 0)
res->neg = 0;
else
resp--;
for (i=0; i<loop-1; i++, wnump--, resp--)
{
BN_ULONG q,l0;
/* the first part of the loop uses the top two words of
* snum and sdiv to calculate a BN_ULONG q such that
* | wnum - sdiv * q | < sdiv */
#if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
q=bn_div_3_words(wnump,d1,d0);
#else
BN_ULONG n0,n1,rem=0;
n0=wnump[0];
n1=wnump[-1];
if (n0 == d0)
q=BN_MASK2;
else /* n0 < d0 */
{
#ifdef BN_LLONG
BN_ULLONG t2;
#if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
#else
q=bn_div_words(n0,n1,d0);
#ifdef BN_DEBUG_LEVITTE
TINYCLR_SSL_FPRINTF(OPENSSL_TYPE__FILE_STDERR,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
X) -> 0x%08X\n",
n0, n1, d0, q);
#endif
#endif
#ifndef REMAINDER_IS_ALREADY_CALCULATED
/*
* rem doesn't have to be BN_ULLONG. The least we
* know it's less that d0, isn't it?
*/
rem=(n1-q*d0)&BN_MASK2;
#endif
t2=(BN_ULLONG)d1*q;
for (;;)
{
if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
break;
q--;
rem += d0;
if (rem < d0) break; /* don't let rem overflow */
t2 -= d1;
}
#else /* !BN_LLONG */
BN_ULONG t2l,t2h;
q=bn_div_words(n0,n1,d0);
#ifdef BN_DEBUG_LEVITTE
TINYCLR_SSL_FPRINTF(OPENSSL_TYPE__FILE_STDERR,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
X) -> 0x%08X\n",
n0, n1, d0, q);
#endif
#ifndef REMAINDER_IS_ALREADY_CALCULATED
rem=(n1-q*d0)&BN_MASK2;
#endif
#if defined(BN_UMULT_LOHI)
BN_UMULT_LOHI(t2l,t2h,d1,q);
#elif defined(BN_UMULT_HIGH)
t2l = d1 * q;
t2h = BN_UMULT_HIGH(d1,q);
#else
{
BN_ULONG ql, qh;
t2l=LBITS(d1); t2h=HBITS(d1);
ql =LBITS(q); qh =HBITS(q);
mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
}
#endif
for (;;)
{
if ((t2h < rem) ||
((t2h == rem) && (t2l <= wnump[-2])))
break;
q--;
rem += d0;
if (rem < d0) break; /* don't let rem overflow */
if (t2l < d1) t2h--; t2l -= d1;
}
#endif /* !BN_LLONG */
}
#endif /* !BN_DIV3W */
l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
tmp->d[div_n]=l0;
wnum.d--;
/* ingore top values of the bignums just sub the two
* BN_ULONG arrays with bn_sub_words */
if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
{
/* Note: As we have considered only the leading
* two BN_ULONGs in the calculation of q, sdiv * q
* might be greater than wnum (but then (q-1) * sdiv
* is less or equal than wnum)
*/
q--;
if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
/* we can't have an overflow here (assuming
* that q != 0, but if q == 0 then tmp is
* zero anyway) */
(*wnump)++;
}
/* store part of the result */
*resp = q;
}
bn_correct_top(snum);
if (rm != NULL)
{
/* Keep a copy of the neg flag in num because if rm==num
* BN_rshift() will overwrite it.
*/
int neg = num->neg;
BN_rshift(rm,snum,norm_shift);
if (!BN_is_zero(rm))
rm->neg = neg;
bn_check_top(rm);
}
bn_correct_top(res);
BN_CTX_end(ctx);
return(1);
err:
bn_check_top(rm);
BN_CTX_end(ctx);
return(0);
}
int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
BN_CTX *ctx)
{
int norm_shift, i, j, loop;
BIGNUM *tmp, wnum, *snum, *sdiv, *res;
BN_ULONG *resp, *wnump;
BN_ULONG d0, d1;
int num_n, div_n;
bn_check_top(num);
bn_check_top(divisor);
if(BN_is_zero(divisor))
{
return (0);
}
if(BN_ucmp(num, divisor) < 0)
{
if(rm != NULL)
{
if(BN_copy(rm, num) == NULL) { return (0); }
}
if(dv != NULL) { BN_zero(dv); }
return (1);
}
BN_CTX_start(ctx);
tmp = BN_CTX_get(ctx);
snum = BN_CTX_get(ctx);
sdiv = BN_CTX_get(ctx);
if(dv == NULL)
{ res = BN_CTX_get(ctx); }
else { res = dv; }
if(sdiv == NULL || res == NULL) { goto err; }
tmp->neg = 0;
/* First we normalise the numbers */
norm_shift = BN_BITS2 - ((BN_num_bits(divisor)) % BN_BITS2);
BN_lshift(sdiv, divisor, norm_shift);
sdiv->neg = 0;
norm_shift += BN_BITS2;
BN_lshift(snum, num, norm_shift);
snum->neg = 0;
div_n = sdiv->top;
num_n = snum->top;
loop = num_n - div_n;
/* Lets setup a 'window' into snum
* This is the part that corresponds to the current
* 'area' being divided */
BN_init(&wnum);
wnum.d = &(snum->d[loop]);
wnum.top = div_n;
wnum.dmax = snum->dmax + 1; /* a bit of a lie */
/* Get the top 2 words of sdiv */
/* i=sdiv->top; */
d0 = sdiv->d[div_n - 1];
d1 = (div_n == 1) ? 0 : sdiv->d[div_n - 2];
/* pointer to the 'top' of snum */
wnump = &(snum->d[num_n - 1]);
/* Setup to 'res' */
res->neg = (num->neg ^ divisor->neg);
if(!bn_wexpand(res, (loop + 1))) { goto err; }
res->top = loop;
resp = &(res->d[loop - 1]);
/* space for temp */
if(!bn_wexpand(tmp, (div_n + 1))) { goto err; }
if(BN_ucmp(&wnum, sdiv) >= 0)
{
if(!BN_usub(&wnum, &wnum, sdiv)) { goto err; }
*resp = 1;
res->d[res->top - 1] = 1;
}
else
{ res->top--; }
resp--;
for(i = 0; i < loop - 1; i++)
{
BN_ULONG q, l0;
#if defined(BN_DIV3W) && !defined(NO_ASM)
BN_ULONG bn_div_3_words(BN_ULONG *, BN_ULONG, BN_ULONG);
q = bn_div_3_words(wnump, d1, d0);
#else
BN_ULONG n0, n1, rem = 0;
n0 = wnump[0];
n1 = wnump[-1];
if(n0 == d0)
{ q = BN_MASK2; }
else /* n0 < d0 */
{
#ifdef BN_LLONG
BN_ULLONG t2;
#if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
q = (BN_ULONG)(((((BN_ULLONG)n0) << BN_BITS2) | n1) / d0);
#else
q = bn_div_words(n0, n1, d0);
#endif
#ifndef REMAINDER_IS_ALREADY_CALCULATED
/*
* rem doesn't have to be BN_ULLONG. The least we
* know it's less that d0, isn't it?
*/
rem = (n1 - q * d0)&BN_MASK2;
#endif
t2 = (BN_ULLONG)d1 * q;
for(;;)
{
if(t2 <= ((((BN_ULLONG)rem) << BN_BITS2) | wnump[-2]))
{ break; }
q--;
rem += d0;
if(rem < d0) { break; } /* don't let rem overflow */
t2 -= d1;
}
#else /* !BN_LLONG */
BN_ULONG t2l, t2h, ql, qh;
q = bn_div_words(n0, n1, d0);
#ifndef REMAINDER_IS_ALREADY_CALCULATED
rem = (n1 - q * d0)&BN_MASK2;
#endif
#ifdef BN_UMULT_HIGH
t2l = d1 * q;
t2h = BN_UMULT_HIGH(d1, q);
#else
t2l = LBITS(d1);
t2h = HBITS(d1);
ql = LBITS(q);
qh = HBITS(q);
mul64(t2l, t2h, ql, qh); /* t2=(BN_ULLONG)d1*q; */
#endif
for(;;)
{
if((t2h < rem) ||
((t2h == rem) && (t2l <= wnump[-2])))
{ break; }
q--;
rem += d0;
if(rem < d0) { break; } /* don't let rem overflow */
if(t2l < d1) { t2h--; }
t2l -= d1;
}
#endif /* !BN_LLONG */
}
#endif /* !BN_DIV3W */
l0 = bn_mul_words(tmp->d, sdiv->d, div_n, q);
wnum.d--;
wnum.top++;
tmp->d[div_n] = l0;
for(j = div_n + 1; j > 0; j--)
if(tmp->d[j - 1]) { break; }
tmp->top = j;
j = wnum.top;
BN_sub(&wnum, &wnum, tmp);
snum->top = snum->top + wnum.top - j;
if(wnum.neg)
{
q--;
j = wnum.top;
BN_add(&wnum, &wnum, sdiv);
snum->top += wnum.top - j;
}
*(resp--) = q;
wnump--;
}
if(rm != NULL)
{
BN_rshift(rm, snum, norm_shift);
rm->neg = num->neg;
}
BN_CTX_end(ctx);
return (1);
err:
BN_CTX_end(ctx);
return (0);
}
int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
BN_CTX *ctx)
{
int norm_shift,i,loop;
BIGNUM *tmp,*snum,*sdiv,*res;
#ifdef BN_ALLOC /* pcg */
BIGNUM wnum;
#else
BN_ULONG *wnum_d;
#endif /* !BN_ALLOC */
BN_ULONG *resp,*wnump;
BN_ULONG d0,d1;
int num_n,div_n;
/* Invalid zero-padding would have particularly bad consequences
* in the case of 'num', so don't just rely on bn_check_top() for this one
* (bn_check_top() works only for BN_DEBUG builds) */
if (num->top > 0 && num->d[num->top - 1] == 0)
{
BNerr(BN_F_BN_DIV,BN_R_NOT_INITIALIZED);
return 0;
}
bn_check_top(num);
if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0))
{
return BN_div_no_branch(dv, rm, num, divisor, ctx);
}
bn_check_top(dv);
bn_check_top(rm);
/* bn_check_top(num); */ /* 'num' has been checked already */
bn_check_top(divisor);
if (BN_is_zero(divisor))
{
BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
return(0);
}
if (BN_ucmp(num,divisor) < 0)
{
if (rm != NULL)
{ if (BN_copy(rm,num) == NULL) return(0); }
if (dv != NULL) BN_zero(dv);
return(1);
}
BN_CTX_start(ctx);
tmp=BN_CTX_get(ctx);
snum=BN_CTX_get_ext( ctx, BIGNUM_EXT_MUL1 ); /* pcg */
sdiv=BN_CTX_get(ctx);
if (dv == NULL)
res=BN_CTX_get(ctx);
else res=dv;
if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL)
goto err;
/* First we normalise the numbers */
norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
sdiv->neg=0;
norm_shift+=BN_BITS2;
if (!(BN_lshift(snum,num,norm_shift))) goto err;
snum->neg=0;
div_n=sdiv->top;
num_n=snum->top;
loop=num_n-div_n;
/* Lets setup a 'window' into snum
* This is the part that corresponds to the current
* 'area' being divided */
#ifdef BN_ALLOC /* pcg */
wnum.neg = 0;
wnum.d = &(snum->d[loop]);
wnum.top = div_n;
/* only needed when BN_ucmp messes up the values between top and max */
wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
#else
wnum_d = &(snum->d[loop]);
#endif /* BN_ALLOC */
/* Get the top 2 words of sdiv */
/* div_n=sdiv->top; */
d0=sdiv->d[div_n-1];
d1=(div_n == 1)?0:sdiv->d[div_n-2];
/* pointer to the 'top' of snum */
wnump= &(snum->d[num_n-1]);
/* Setup to 'res' */
res->neg= (num->neg^divisor->neg);
if (!bn_wexpand(res,(loop+1))) goto err;
res->top=loop;
resp= &(res->d[loop-1]);
/* space for temp */
if( div_n+1 > BIGNUM_ALLOC_WORDS ) { assert( 0 ); goto err; }
if (BN_ucmp_word(wnum_d,div_n,sdiv) >= 0)
{
/* If BN_DEBUG_RAND is defined BN_ucmp changes (via
* bn_pollute) the const bignum arguments =>
* clean the values between top and max again */
bn_clear_top2max(&wnum);
bn_sub_words(wnum_d, wnum_d, sdiv->d, div_n);
*resp=1;
}
else
res->top--;
/* if res->top == 0 then clear the neg value otherwise decrease
* the resp pointer */
if (res->top == 0)
res->neg = 0;
else
resp--;
for (i=0; i<loop-1; i++, wnump--, resp--)
{
BN_ULONG q,l0;
/* the first part of the loop uses the top two words of
* snum and sdiv to calculate a BN_ULONG q such that
* | wnum - sdiv * q | < sdiv */
#if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
q=bn_div_3_words(wnump,d1,d0);
#else
BN_ULONG n0,n1,rem=0;
n0=wnump[0];
n1=wnump[-1];
if (n0 == d0)
q=BN_MASK2;
else /* n0 < d0 */
{
#ifdef BN_LLONG
BN_ULLONG t2;
#if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
#else
q=bn_div_words(n0,n1,d0);
#ifdef BN_DEBUG_LEVITTE
fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
X) -> 0x%08X\n",
n0, n1, d0, q);
#endif
#endif
#ifndef REMAINDER_IS_ALREADY_CALCULATED
/*
* rem doesn't have to be BN_ULLONG. The least we
* know it's less that d0, isn't it?
*/
rem=(n1-q*d0)&BN_MASK2;
#endif
t2=(BN_ULLONG)d1*q;
for (;;)
{
if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
break;
q--;
rem += d0;
if (rem < d0) break; /* don't let rem overflow */
t2 -= d1;
}
#else /* !BN_LLONG */
BN_ULONG t2l,t2h;
#if !defined( BN_UMULT_LOHI ) && !defined( BN_UMULT_HIGH ) /* pcg */
BN_ULONG ql,qh;
#endif
q=bn_div_words(n0,n1,d0);
#ifdef BN_DEBUG_LEVITTE
fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
X) -> 0x%08X\n",
n0, n1, d0, q);
#endif
#ifndef REMAINDER_IS_ALREADY_CALCULATED
rem=(n1-q*d0)&BN_MASK2;
#endif
#if defined(BN_UMULT_LOHI)
BN_UMULT_LOHI(t2l,t2h,d1,q);
#elif defined(BN_UMULT_HIGH)
t2l = d1 * q;
t2h = BN_UMULT_HIGH(d1,q);
#else
{
BN_ULONG ql, qh;
t2l=LBITS(d1); t2h=HBITS(d1);
ql =LBITS(q); qh =HBITS(q);
mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
}
#endif
for (;;)
{
if ((t2h < rem) ||
((t2h == rem) && (t2l <= wnump[-2])))
break;
q--;
rem += d0;
if (rem < d0) break; /* don't let rem overflow */
if (t2l < d1) t2h--; t2l -= d1;
}
#endif /* !BN_LLONG */
}
#endif /* !BN_DIV3W */
l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
tmp->d[div_n]=l0;
wnum_d--;
/* ingore top values of the bignums just sub the two
* BN_ULONG arrays with bn_sub_words */
if (bn_sub_words(wnum_d, wnum_d, tmp->d, div_n+1))
{
/* Note: As we have considered only the leading
* two BN_ULONGs in the calculation of q, sdiv * q
* might be greater than wnum (but then (q-1) * sdiv
* is less or equal than wnum)
*/
q--;
if (bn_add_words(wnum_d, wnum_d, sdiv->d, div_n))
/* we can't have an overflow here (assuming
* that q != 0, but if q == 0 then tmp is
* zero anyway) */
(*wnump)++;
}
/* store part of the result */
*resp = q;
}
bn_correct_top(snum);
if (rm != NULL)
{
/* Keep a copy of the neg flag in num because if rm==num
* BN_rshift() will overwrite it.
*/
int neg = num->neg;
BN_rshift(rm,snum,norm_shift);
if (!BN_is_zero(rm))
rm->neg = neg;
bn_check_top(rm);
}
BN_CTX_end_ext( ctx, BIGNUM_EXT_MUL1 ); /* pcg */
return(1);
err:
bn_check_top(rm);
BN_CTX_end_ext( ctx, BIGNUM_EXT_MUL1 ); /* pcg */
return(0);
}
/*--- poly_sine() -----------------------------------------------------------+
| |
+---------------------------------------------------------------------------*/
void poly_sine(FPU_REG const *arg, FPU_REG *result)
{
short exponent;
FPU_REG fixed_arg, arg_sqrd, arg_to_4, accum, negaccum;
exponent = arg->exp - EXP_BIAS;
if ( arg->tag == TW_Zero )
{
/* Return 0.0 */
reg_move(&CONST_Z, result);
return;
}
#ifdef PARANOID
if ( arg->sign != 0 ) /* Can't hack a number < 0.0 */
{
EXCEPTION(EX_Invalid);
reg_move(&CONST_QNaN, result);
return;
}
if ( exponent >= 0 ) /* Can't hack a number > 1.0 */
{
if ( (exponent == 0) && (arg->sigl == 0) && (arg->sigh == 0x80000000) )
{
reg_move(&CONST_1, result);
return;
}
EXCEPTION(EX_Invalid);
reg_move(&CONST_QNaN, result);
return;
}
#endif PARANOID
fixed_arg.sigl = arg->sigl;
fixed_arg.sigh = arg->sigh;
if ( exponent < -1 )
{
/* shift the argument right by the required places */
if ( shrx(&(fixed_arg.sigl), -1-exponent) >= 0x80000000U )
significand(&fixed_arg)++; /* round up */
}
mul64(&significand(&fixed_arg), &significand(&fixed_arg),
&significand(&arg_sqrd));
mul64(&significand(&arg_sqrd), &significand(&arg_sqrd),
&significand(&arg_to_4));
/* will be a valid positive nr with expon = 0 */
*(short *)&(accum.sign) = 0;
accum.exp = 0;
/* Do the basic fixed point polynomial evaluation */
polynomial(&(accum.sigl), &(arg_to_4.sigl), lterms, HIPOWER-1);
/* will be a valid positive nr with expon = 0 */
*(short *)&(negaccum.sign) = 0;
negaccum.exp = 0;
/* Do the basic fixed point polynomial evaluation */
polynomial(&(negaccum.sigl), &(arg_to_4.sigl), negterms, HIPOWER-1);
mul64(&significand(&arg_sqrd), &significand(&negaccum),
&significand(&negaccum));
/* Subtract the mantissas */
significand(&accum) -= significand(&negaccum);
/* Convert to 64 bit signed-compatible */
accum.exp = EXP_BIAS - 1 + accum.exp;
reg_move(&accum, result);
normalize(result);
reg_mul(result, arg, result, FULL_PRECISION);
reg_u_add(result, arg, result, FULL_PRECISION);
if ( result->exp >= EXP_BIAS )
{
/* A small overflow may be possible... but an illegal result. */
if ( (result->exp > EXP_BIAS) /* Larger or equal 2.0 */
|| (result->sigl > 1) /* Larger than 1.0+msb */
|| (result->sigh != 0x80000000) /* Much > 1.0 */
)
{
#ifdef DEBUGGING
RE_ENTRANT_CHECK_OFF;
printk("\nEXP=%d, MS=%08x, LS=%08x\n", result->exp,
result->sigh, result->sigl);
RE_ENTRANT_CHECK_ON;
#endif DEBUGGING
EXCEPTION(EX_INTERNAL|0x103);
}
#ifdef DEBUGGING
RE_ENTRANT_CHECK_OFF;
printk("\n***CORRECTING ILLEGAL RESULT*** in poly_sin() computation\n");
printk("EXP=%d, MS=%08x, LS=%08x\n", result->exp,
result->sigh, result->sigl);
RE_ENTRANT_CHECK_ON;
#endif DEBUGGING
result->sigl = 0; /* Truncate the result to 1.00 */
}
}
/*--- poly_atan() -----------------------------------------------------------+
| |
+---------------------------------------------------------------------------*/
void
poly_atan(FPU_REG * arg)
{
char recursions = 0;
short exponent;
FPU_REG odd_poly, even_poly, pos_poly, neg_poly;
FPU_REG argSq;
long long arg_signif, argSqSq;
#ifdef PARANOID
if (arg->sign != 0) { /* Can't hack a number < 0.0 */
arith_invalid(arg);
return;
} /* Need a positive number */
#endif /* PARANOID */
exponent = arg->exp - EXP_BIAS;
if (arg->tag == TW_Zero) {
/* Return 0.0 */
reg_move(&CONST_Z, arg);
return;
}
if (exponent >= -2) {
/* argument is in the range [0.25 .. 1.0] */
if (exponent >= 0) {
#ifdef PARANOID
if ((exponent == 0) &&
(arg->sigl == 0) && (arg->sigh == 0x80000000))
#endif /* PARANOID */
{
reg_move(&CONST_PI4, arg);
return;
}
#ifdef PARANOID
EXCEPTION(EX_INTERNAL | 0x104); /* There must be a logic
* error */
#endif /* PARANOID */
}
/* If the argument is greater than sqrt(2)-1 (=0.414213562...) */
/* convert the argument by an identity for atan */
if ((exponent >= -1) || (arg->sigh > 0xd413ccd0)) {
FPU_REG numerator, denom;
recursions++;
arg_signif = *(long long *) &(arg->sigl);
if (exponent < -1) {
if (shrx(&arg_signif, -1 - exponent) >= (unsigned)0x80000000)
arg_signif++; /* round up */
}
*(long long *) &(numerator.sigl) = -arg_signif;
numerator.exp = EXP_BIAS - 1;
normalize(&numerator); /* 1 - arg */
arg_signif = *(long long *) &(arg->sigl);
if (shrx(&arg_signif, -exponent) >= (unsigned)0x80000000)
arg_signif++; /* round up */
*(long long *) &(denom.sigl) = arg_signif;
denom.sigh |= 0x80000000; /* 1 + arg */
arg->exp = numerator.exp;
reg_u_div(&numerator, &denom, arg, FULL_PRECISION);
exponent = arg->exp - EXP_BIAS;
}
}
*(long long *) &arg_signif = *(long long *) &(arg->sigl);
#ifdef PARANOID
/* This must always be true */
if (exponent >= -1) {
EXCEPTION(EX_INTERNAL | 0x120); /* There must be a logic error */
}
#endif /* PARANOID */
/* shift the argument right by the required places */
if (shrx(&arg_signif, -1 - exponent) >= (unsigned)0x80000000)
arg_signif++; /* round up */
/* Now have arg_signif with binary point at the left .1xxxxxxxx */
mul64(&arg_signif, &arg_signif, (long long *) (&argSq.sigl));
mul64((long long *) (&argSq.sigl), (long long *) (&argSq.sigl), &argSqSq);
/* will be a valid positive nr with expon = 0 */
*(short *) &(pos_poly.sign) = 0;
pos_poly.exp = EXP_BIAS;
/* Do the basic fixed point polynomial evaluation */
polynomial(&pos_poly.sigl, (unsigned *) &argSqSq,
(unsigned short (*)[4]) oddplterms, HIPOWERop - 1);
mul64((long long *) (&argSq.sigl), (long long *) (&pos_poly.sigl),
(long long *) (&pos_poly.sigl));
/* will be a valid positive nr with expon = 0 */
*(short *) &(neg_poly.sign) = 0;
neg_poly.exp = EXP_BIAS;
/* Do the basic fixed point polynomial evaluation */
polynomial(&neg_poly.sigl, (unsigned *) &argSqSq,
(unsigned short (*)[4]) oddnegterms, HIPOWERon - 1);
/* Subtract the mantissas */
*((long long *) (&pos_poly.sigl)) -= *((long long *) (&neg_poly.sigl));
reg_move(&pos_poly, &odd_poly);
poly_add_1(&odd_poly);
/* The complete odd polynomial */
reg_u_mul(&odd_poly, arg, &odd_poly, FULL_PRECISION);
/* will be a valid positive nr with expon = 0 */
*(short *) &(even_poly.sign) = 0;
mul64((long long *) (&argSq.sigl),
(long long *) (&denomterm), (long long *) (&even_poly.sigl));
poly_add_1(&even_poly);
reg_div(&odd_poly, &even_poly, arg, FULL_PRECISION);
if (recursions)
reg_sub(&CONST_PI4, arg, arg, FULL_PRECISION);
}
size_t THSoundArchive::getSoundDuration(size_t iIndex)
{
SDL_RWops *pFile = loadSound(iIndex);
if(!pFile)
return 0;
uint16_t iWaveAudioFormat = 0;
uint16_t iWaveChannelCount = 0;
uint32_t iWaveSampleRate = 0;
uint32_t iWaveByteRate = 0;
uint16_t iWaveBlockAlign = 0;
uint16_t iWaveBitsPerSample = 0;
uint32_t iWaveDataLength = 0;
// This is a very crude RIFF parser, but it does the job.
uint32_t iFourCC;
uint32_t iChunkLength;
for(;;)
{
if(SDL_RWread(pFile, &iFourCC, 4, 1) != 1)
break;
if(SDL_RWread(pFile, &iChunkLength, 4, 1) != 1)
break;
if(iFourCC == FOURCC('R','I','F','F') || iFourCC == FOURCC('L','I','S','T'))
{
if(iChunkLength >= 4)
{
if(SDL_RWread(pFile, &iFourCC, 4, 1) != 1)
break;
else
continue;
}
}
if(iFourCC == FOURCC('f','m','t',' ') && iChunkLength >= 16)
{
if(SDL_RWread(pFile, &iWaveAudioFormat, 2, 1) != 1)
break;
if(SDL_RWread(pFile, &iWaveChannelCount, 2, 1) != 1)
break;
if(SDL_RWread(pFile, &iWaveSampleRate, 4, 1) != 1)
break;
if(SDL_RWread(pFile, &iWaveByteRate, 4, 1) != 1)
break;
if(SDL_RWread(pFile, &iWaveBlockAlign, 2, 1) != 1)
break;
if(SDL_RWread(pFile, &iWaveBitsPerSample, 2, 1) != 1)
break;
iChunkLength -= 16;
}
//Finally:
if(iFourCC == FOURCC('d','a','t','a'))
{
iWaveDataLength = iChunkLength;
break;
}
if(SDL_RWseek(pFile, iChunkLength + (iChunkLength & 1), RW_SEEK_CUR) == -1) {
break;
}
}
SDL_RWclose(pFile);
if(iWaveAudioFormat != 1 || iWaveChannelCount == 0 || iWaveSampleRate == 0
|| iWaveDataLength == 0 || iWaveBitsPerSample == 0)
{
return 0;
}
#define mul64(a, b) (static_cast<uint64_t>(a) * static_cast<uint64_t>(b))
return static_cast<size_t>(mul64(iWaveDataLength, 8000) /
mul64(mul64(iWaveBitsPerSample, iWaveChannelCount), iWaveSampleRate));
#undef mul64
}
/*--- poly_tan() ------------------------------------------------------------+
| |
+---------------------------------------------------------------------------*/
void
poly_tan(FPU_REG * arg, FPU_REG * y_reg)
{
char invert = 0;
short exponent;
FPU_REG odd_poly, even_poly, pos_poly, neg_poly;
FPU_REG argSq;
long long arg_signif, argSqSq;
exponent = arg->exp - EXP_BIAS;
if (arg->tag == TW_Zero) {
/* Return 0.0 */
reg_move(&CONST_Z, y_reg);
return;
}
if (exponent >= -1) {
/* argument is in the range [0.5 .. 1.0] */
if (exponent >= 0) {
#ifdef PARANOID
if ((exponent == 0) &&
(arg->sigl == 0) && (arg->sigh == 0x80000000))
#endif /* PARANOID */
{
arith_overflow(y_reg);
return;
}
#ifdef PARANOID
EXCEPTION(EX_INTERNAL | 0x104); /* There must be a logic
* error */
return;
#endif /* PARANOID */
}
/* The argument is in the range [0.5 .. 1.0) */
/* Convert the argument to a number in the range (0.0 .. 0.5] */
*((long long *) (&arg->sigl)) = -*((long long *) (&arg->sigl));
normalize(arg); /* Needed later */
exponent = arg->exp - EXP_BIAS;
invert = 1;
}
#ifdef PARANOID
if (arg->sign != 0) { /* Can't hack a number < 0.0 */
arith_invalid(y_reg);
return;
} /* Need a positive number */
#endif /* PARANOID */
*(long long *) &arg_signif = *(long long *) &(arg->sigl);
if (exponent < -1) {
/* shift the argument right by the required places */
if (shrx(&arg_signif, -1 - exponent) >= (unsigned)0x80000000)
arg_signif++; /* round up */
}
mul64(&arg_signif, &arg_signif, (long long *) (&argSq.sigl));
mul64((long long *) (&argSq.sigl), (long long *) (&argSq.sigl), &argSqSq);
/* will be a valid positive nr with expon = 0 */
*(short *) &(pos_poly.sign) = 0;
pos_poly.exp = EXP_BIAS;
/* Do the basic fixed point polynomial evaluation */
polynomial((u_int *) &pos_poly.sigl, (unsigned *) &argSqSq, oddplterms, HIPOWERop - 1);
/* will be a valid positive nr with expon = 0 */
*(short *) &(neg_poly.sign) = 0;
neg_poly.exp = EXP_BIAS;
/* Do the basic fixed point polynomial evaluation */
polynomial((u_int *) &neg_poly.sigl, (unsigned *) &argSqSq, oddnegterms, HIPOWERon - 1);
mul64((long long *) (&argSq.sigl), (long long *) (&neg_poly.sigl),
(long long *) (&neg_poly.sigl));
/* Subtract the mantissas */
*((long long *) (&pos_poly.sigl)) -= *((long long *) (&neg_poly.sigl));
/* Convert to 64 bit signed-compatible */
pos_poly.exp -= 1;
reg_move(&pos_poly, &odd_poly);
normalize(&odd_poly);
reg_mul(&odd_poly, arg, &odd_poly, FULL_PRECISION);
reg_u_add(&odd_poly, arg, &odd_poly, FULL_PRECISION); /* This is just the odd
* polynomial */
/* will be a valid positive nr with expon = 0 */
*(short *) &(pos_poly.sign) = 0;
pos_poly.exp = EXP_BIAS;
/* Do the basic fixed point polynomial evaluation */
polynomial((u_int *) &pos_poly.sigl, (unsigned *) &argSqSq, evenplterms, HIPOWERep - 1);
mul64((long long *) (&argSq.sigl),
(long long *) (&pos_poly.sigl), (long long *) (&pos_poly.sigl));
/* will be a valid positive nr with expon = 0 */
*(short *) &(neg_poly.sign) = 0;
neg_poly.exp = EXP_BIAS;
/* Do the basic fixed point polynomial evaluation */
polynomial((u_int *) &neg_poly.sigl, (unsigned *) &argSqSq, evennegterms, HIPOWERen - 1);
/* Subtract the mantissas */
*((long long *) (&neg_poly.sigl)) -= *((long long *) (&pos_poly.sigl));
/* and multiply by argSq */
/* Convert argSq to a valid reg number */
*(short *) &(argSq.sign) = 0;
argSq.exp = EXP_BIAS - 1;
normalize(&argSq);
/* Convert to 64 bit signed-compatible */
neg_poly.exp -= 1;
reg_move(&neg_poly, &even_poly);
normalize(&even_poly);
reg_mul(&even_poly, &argSq, &even_poly, FULL_PRECISION);
reg_add(&even_poly, &argSq, &even_poly, FULL_PRECISION);
reg_sub(&CONST_1, &even_poly, &even_poly, FULL_PRECISION); /* This is just the even
* polynomial */
/* Now ready to copy the results */
if (invert) {
reg_div(&even_poly, &odd_poly, y_reg, FULL_PRECISION);
} else {
reg_div(&odd_poly, &even_poly, y_reg, FULL_PRECISION);
}
}
int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
BN_CTX *ctx)
{
int norm_shift,i,j,loop;
BIGNUM *tmp,wnum,*snum,*sdiv,*res;
BN_ULONG *resp,*wnump;
BN_ULONG d0,d1;
int num_n,div_n;
bn_check_top(num);
bn_check_top(divisor);
if (BN_is_zero(divisor))
return(0);
if (BN_ucmp(num,divisor) < 0)
{
if (rm != NULL)
{ if (BN_copy(rm,num) == NULL) return(0); }
if (dv != NULL) BN_zero(dv);
return(1);
}
BN_CTX_start(ctx);
tmp=BN_CTX_get(ctx);
snum=BN_CTX_get(ctx);
sdiv=BN_CTX_get(ctx);
if (dv == NULL)
res=BN_CTX_get(ctx);
else res=dv;
if (sdiv==NULL || res == NULL) goto err;
tmp->neg=0;
/* First we normalise the numbers */
norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
sdiv->neg=0;
norm_shift+=BN_BITS2;
if (!(BN_lshift(snum,num,norm_shift))) goto err;
snum->neg=0;
div_n=sdiv->top;
num_n=snum->top;
loop=num_n-div_n;
/* Lets setup a 'window' into snum
* This is the part that corresponds to the current
* 'area' being divided */
BN_init(&wnum);
wnum.d= &(snum->d[loop]);
wnum.top= div_n;
wnum.dmax= snum->dmax+1; /* a bit of a lie */
/* Get the top 2 words of sdiv */
/* i=sdiv->top; */
d0=sdiv->d[div_n-1];
d1=(div_n == 1)?0:sdiv->d[div_n-2];
/* pointer to the 'top' of snum */
wnump= &(snum->d[num_n-1]);
/* Setup to 'res' */
res->neg= (num->neg^divisor->neg);
if (!bn_wexpand(res,(loop+1))) goto err;
res->top=loop;
resp= &(res->d[loop-1]);
/* space for temp */
if (!bn_wexpand(tmp,(div_n+1))) goto err;
if (BN_ucmp(&wnum,sdiv) >= 0)
{
if (!BN_usub(&wnum,&wnum,sdiv)) goto err;
*resp=1;
res->d[res->top-1]=1;
}
else
res->top--;
resp--;
for (i=0; i<loop-1; i++)
{
BN_ULONG q,l0;
BN_ULONG n0,n1,rem=0;
n0=wnump[0];
n1=wnump[-1];
if (n0 == d0)
q=BN_MASK2;
else /* n0 < d0 */
{
BN_ULONG t2l,t2h,ql,qh;
q=bn_div_words(n0,n1,d0);
rem=(n1-q*d0)&BN_MASK2;
t2l=LBITS(d1); t2h=HBITS(d1);
ql =LBITS(q); qh =HBITS(q);
mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
for (;;)
{
if ((t2h < rem) ||
((t2h == rem) && (t2l <= wnump[-2])))
break;
q--;
rem += d0;
if (rem < d0) break; /* don't let rem overflow */
if (t2l < d1) t2h--; t2l -= d1;
}
}
l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
wnum.d--; wnum.top++;
tmp->d[div_n]=l0;
for (j=div_n+1; j>0; j--)
if (tmp->d[j-1]) break;
tmp->top=j;
j=wnum.top;
if (!BN_sub(&wnum,&wnum,tmp)) goto err;
snum->top=snum->top+wnum.top-j;
if (wnum.neg)
{
q--;
j=wnum.top;
if (!BN_add(&wnum,&wnum,sdiv)) goto err;
snum->top+=wnum.top-j;
}
*(resp--)=q;
wnump--;
}
if (rm != NULL)
{
BN_rshift(rm,snum,norm_shift);
rm->neg=num->neg;
}
BN_CTX_end(ctx);
return(1);
err:
BN_CTX_end(ctx);
return(0);
}
/*-
* BN_div computes dv := num / divisor, rounding towards
* zero, and sets up rm such that dv*divisor + rm = num holds.
* Thus:
* dv->neg == num->neg ^ divisor->neg (unless the result is zero)
* rm->neg == num->neg (unless the remainder is zero)
* If 'dv' or 'rm' is NULL, the respective value is not returned.
*/
int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
BN_CTX *ctx)
{
int norm_shift, i, loop;
BIGNUM *tmp, wnum, *snum, *sdiv, *res;
BN_ULONG *resp, *wnump;
BN_ULONG d0, d1;
int num_n, div_n;
int no_branch = 0;
/*
* Invalid zero-padding would have particularly bad consequences so don't
* just rely on bn_check_top() here (bn_check_top() works only for
* BN_DEBUG builds)
*/
if ((num->top > 0 && num->d[num->top - 1] == 0) ||
(divisor->top > 0 && divisor->d[divisor->top - 1] == 0)) {
BNerr(BN_F_BN_DIV, BN_R_NOT_INITIALIZED);
return 0;
}
bn_check_top(num);
bn_check_top(divisor);
if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0)
|| (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0)) {
no_branch = 1;
}
bn_check_top(dv);
bn_check_top(rm);
/*- bn_check_top(num); *//*
* 'num' has been checked already
*/
/*- bn_check_top(divisor); *//*
* 'divisor' has been checked already
*/
if (BN_is_zero(divisor)) {
BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO);
return 0;
}
if (!no_branch && BN_ucmp(num, divisor) < 0) {
if (rm != NULL) {
if (BN_copy(rm, num) == NULL)
return 0;
}
if (dv != NULL)
BN_zero(dv);
return 1;
}
BN_CTX_start(ctx);
res = (dv == NULL) ? BN_CTX_get(ctx) : dv;
tmp = BN_CTX_get(ctx);
snum = BN_CTX_get(ctx);
sdiv = BN_CTX_get(ctx);
if (sdiv == NULL)
goto err;
/* First we normalise the numbers */
norm_shift = BN_BITS2 - ((BN_num_bits(divisor)) % BN_BITS2);
if (!(BN_lshift(sdiv, divisor, norm_shift)))
goto err;
sdiv->neg = 0;
norm_shift += BN_BITS2;
if (!(BN_lshift(snum, num, norm_shift)))
goto err;
snum->neg = 0;
if (no_branch) {
/*
* Since we don't know whether snum is larger than sdiv, we pad snum
* with enough zeroes without changing its value.
*/
if (snum->top <= sdiv->top + 1) {
if (bn_wexpand(snum, sdiv->top + 2) == NULL)
goto err;
for (i = snum->top; i < sdiv->top + 2; i++)
snum->d[i] = 0;
snum->top = sdiv->top + 2;
} else {
if (bn_wexpand(snum, snum->top + 1) == NULL)
goto err;
snum->d[snum->top] = 0;
snum->top++;
}
}
div_n = sdiv->top;
num_n = snum->top;
loop = num_n - div_n;
/*
* Lets setup a 'window' into snum This is the part that corresponds to
* the current 'area' being divided
*/
wnum.neg = 0;
wnum.d = &(snum->d[loop]);
wnum.top = div_n;
wnum.flags = BN_FLG_STATIC_DATA;
/*
* only needed when BN_ucmp messes up the values between top and max
*/
wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
/* Get the top 2 words of sdiv */
/* div_n=sdiv->top; */
d0 = sdiv->d[div_n - 1];
d1 = (div_n == 1) ? 0 : sdiv->d[div_n - 2];
/* pointer to the 'top' of snum */
wnump = &(snum->d[num_n - 1]);
/* Setup to 'res' */
if (!bn_wexpand(res, (loop + 1)))
goto err;
res->neg = (num->neg ^ divisor->neg);
res->top = loop - no_branch;
resp = &(res->d[loop - 1]);
/* space for temp */
if (!bn_wexpand(tmp, (div_n + 1)))
goto err;
if (!no_branch) {
if (BN_ucmp(&wnum, sdiv) >= 0) {
/*
* If BN_DEBUG_RAND is defined BN_ucmp changes (via bn_pollute)
* the const bignum arguments => clean the values between top and
* max again
*/
bn_clear_top2max(&wnum);
bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
*resp = 1;
} else
res->top--;
}
/* Increase the resp pointer so that we never create an invalid pointer. */
resp++;
/*
* if res->top == 0 then clear the neg value otherwise decrease the resp
* pointer
*/
if (res->top == 0)
res->neg = 0;
else
resp--;
for (i = 0; i < loop - 1; i++, wnump--) {
BN_ULONG q, l0;
/*
* the first part of the loop uses the top two words of snum and sdiv
* to calculate a BN_ULONG q such that | wnum - sdiv * q | < sdiv
*/
# if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
BN_ULONG bn_div_3_words(BN_ULONG *, BN_ULONG, BN_ULONG);
q = bn_div_3_words(wnump, d1, d0);
# else
BN_ULONG n0, n1, rem = 0;
n0 = wnump[0];
n1 = wnump[-1];
if (n0 == d0)
q = BN_MASK2;
else { /* n0 < d0 */
# ifdef BN_LLONG
BN_ULLONG t2;
# if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
q = (BN_ULONG)(((((BN_ULLONG) n0) << BN_BITS2) | n1) / d0);
# else
q = bn_div_words(n0, n1, d0);
# endif
# ifndef REMAINDER_IS_ALREADY_CALCULATED
/*
* rem doesn't have to be BN_ULLONG. The least we
* know it's less that d0, isn't it?
*/
rem = (n1 - q * d0) & BN_MASK2;
# endif
t2 = (BN_ULLONG) d1 *q;
for (;;) {
if (t2 <= ((((BN_ULLONG) rem) << BN_BITS2) | wnump[-2]))
break;
q--;
rem += d0;
if (rem < d0)
break; /* don't let rem overflow */
t2 -= d1;
}
# else /* !BN_LLONG */
BN_ULONG t2l, t2h;
q = bn_div_words(n0, n1, d0);
# ifndef REMAINDER_IS_ALREADY_CALCULATED
rem = (n1 - q * d0) & BN_MASK2;
# endif
# if defined(BN_UMULT_LOHI)
BN_UMULT_LOHI(t2l, t2h, d1, q);
# elif defined(BN_UMULT_HIGH)
t2l = d1 * q;
t2h = BN_UMULT_HIGH(d1, q);
# else
{
BN_ULONG ql, qh;
t2l = LBITS(d1);
t2h = HBITS(d1);
ql = LBITS(q);
qh = HBITS(q);
mul64(t2l, t2h, ql, qh); /* t2=(BN_ULLONG)d1*q; */
}
# endif
for (;;) {
if ((t2h < rem) || ((t2h == rem) && (t2l <= wnump[-2])))
break;
q--;
rem += d0;
if (rem < d0)
break; /* don't let rem overflow */
if (t2l < d1)
t2h--;
t2l -= d1;
}
# endif /* !BN_LLONG */
}
# endif /* !BN_DIV3W */
l0 = bn_mul_words(tmp->d, sdiv->d, div_n, q);
tmp->d[div_n] = l0;
wnum.d--;
/*
* ingore top values of the bignums just sub the two BN_ULONG arrays
* with bn_sub_words
*/
if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n + 1)) {
/*
* Note: As we have considered only the leading two BN_ULONGs in
* the calculation of q, sdiv * q might be greater than wnum (but
* then (q-1) * sdiv is less or equal than wnum)
*/
q--;
if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
/*
* we can't have an overflow here (assuming that q != 0, but
* if q == 0 then tmp is zero anyway)
*/
(*wnump)++;
}
/* store part of the result */
resp--;
*resp = q;
}
bn_correct_top(snum);
if (rm != NULL) {
/*
* Keep a copy of the neg flag in num because if rm==num BN_rshift()
* will overwrite it.
*/
int neg = num->neg;
BN_rshift(rm, snum, norm_shift);
if (!BN_is_zero(rm))
rm->neg = neg;
bn_check_top(rm);
}
if (no_branch)
bn_correct_top(res);
BN_CTX_end(ctx);
return 1;
err:
bn_check_top(rm);
BN_CTX_end(ctx);
return 0;
}
static void testmul(void)
{
int kdone, kidx;
u32_t ilo = ex64lo(i), jlo = ex64lo(j);
u64_t prod = mul64(i, j);
int prodbits;
/* compute maximum index of highest-order bit */
prodbits = bsr64(i) + bsr64(j) + 1;
if (cmp64u(i, 0) == 0 || cmp64u(j, 0) == 0) prodbits = -1;
if (bsr64(prod) > prodbits) ERR;
/* compare to 32-bit multiplication if possible */
if (ex64hi(i) == 0 && ex64hi(j) == 0) {
if (cmp64(prod, mul64u(ilo, jlo)) != 0) ERR;
/* if there is no overflow we can check against pure 32-bit */
if (prodbits < 32 && cmp64u(prod, ilo * jlo) != 0) ERR;
}
/* in 32-bit arith low-order DWORD matches regardless of overflow */
if (ex64lo(prod) != ilo * jlo) ERR;
/* multiplication by zero yields zero */
if (prodbits < 0 && cmp64u(prod, 0) != 0) ERR;
/* if there is no overflow, check absence of zero divisors */
if (prodbits >= 0 && prodbits < 64 && cmp64u(prod, 0) == 0) ERR;
/* commutativity */
if (cmp64(prod, mul64(j, i)) != 0) ERR;
/* loop though all argument value combinations for third argument */
for (kdone = 0, kidx = 0; k = getargval(kidx, &kdone), !kdone; kidx++) {
/* associativity */
if (cmp64(mul64(mul64(i, j), k), mul64(i, mul64(j, k))) != 0) ERR;
/* left and right distributivity */
if (cmp64(mul64(add64(i, j), k), add64(mul64(i, k), mul64(j, k))) != 0) ERR;
if (cmp64(mul64(i, add64(j, k)), add64(mul64(i, j), mul64(i, k))) != 0) ERR;
}
}
int CRT(int x1, int x2) {
return (mul64(M1, x1, MM) + mul64(M2, x2, MM)) % MM % P;
}
