dcomplex
csqrt(dcomplex z) {
dcomplex ans;
double x, y, t, ax, ay;
int n, ix, iy, hx, hy, lx, ly;
x = D_RE(z);
y = D_IM(z);
hx = HI_WORD(x);
lx = LO_WORD(x);
hy = HI_WORD(y);
ly = LO_WORD(y);
ix = hx & 0x7fffffff;
iy = hy & 0x7fffffff;
ay = fabs(y);
ax = fabs(x);
if (ix >= 0x7ff00000 || iy >= 0x7ff00000) {
/* x or y is Inf or NaN */
if (ISINF(iy, ly))
D_IM(ans) = D_RE(ans) = ay;
else if (ISINF(ix, lx)) {
if (hx > 0) {
D_RE(ans) = ax;
D_IM(ans) = ay * zero;
} else {
D_RE(ans) = ay * zero;
D_IM(ans) = ax;
}
} else
D_IM(ans) = D_RE(ans) = ax + ay;
} else if ((iy | ly) == 0) { /* y = 0 */
if (hx >= 0) {
D_RE(ans) = sqrt(ax);
D_IM(ans) = zero;
} else {
D_IM(ans) = sqrt(ax);
D_RE(ans) = zero;
}
} else if (ix >= iy) {
n = (ix - iy) >> 20;
if (n >= 30) { /* x >> y or y=0 */
t = sqrt(ax);
} else if (ix >= 0x5f300000) { /* x > 2**500 */
ax *= twom601;
y *= twom601;
t = two300 * sqrt(ax + sqrt(ax * ax + y * y));
} else if (iy < 0x20b00000) { /* y < 2**-500 */
ax *= two599;
y *= two599;
t = twom300 * sqrt(ax + sqrt(ax * ax + y * y));
} else
t = sqrt(half * (ax + sqrt(ax * ax + ay * ay)));
if (hx >= 0) {
D_RE(ans) = t;
D_IM(ans) = ay / (t + t);
} else {
D_IM(ans) = t;
D_RE(ans) = ay / (t + t);
}
} else {
/*
* arctan(x):
*
* if (x < 0) {
* x = abs(x);
* sign = 1;
* }
* y = arctan(x);
* if (sign) {
* y = -y;
* }
*/
struct fpn *
fpu_atan(struct fpemu *fe)
{
struct fpn a;
struct fpn x;
struct fpn v;
if (ISNAN(&fe->fe_f2))
return &fe->fe_f2;
if (ISZERO(&fe->fe_f2))
return &fe->fe_f2;
CPYFPN(&a, &fe->fe_f2);
if (ISINF(&fe->fe_f2)) {
/* f2 <- pi/2 */
fpu_const(&fe->fe_f2, FPU_CONST_PI);
fe->fe_f2.fp_exp--;
fe->fe_f2.fp_sign = a.fp_sign;
return &fe->fe_f2;
}
fpu_const(&x, FPU_CONST_1);
fpu_const(&fe->fe_f2, FPU_CONST_0);
CPYFPN(&v, &fe->fe_f2);
fpu_cordit1(fe, &x, &a, &fe->fe_f2, &v);
return &fe->fe_f2;
}
/*
* tan(x) = sin(x) / cos(x)
*/
struct fpn *
fpu_tan(struct fpemu *fe)
{
struct fpn x;
struct fpn s;
struct fpn *r;
if (ISNAN(&fe->fe_f2))
return &fe->fe_f2;
if (ISINF(&fe->fe_f2))
return fpu_newnan(fe);
/* if x is +0/-0, return +0/-0 */
if (ISZERO(&fe->fe_f2))
return &fe->fe_f2;
CPYFPN(&x, &fe->fe_f2);
/* sin(x) */
CPYFPN(&fe->fe_f2, &x);
r = fpu_sin(fe);
CPYFPN(&s, r);
/* cos(x) */
CPYFPN(&fe->fe_f2, &x);
r = fpu_cos(fe);
CPYFPN(&fe->fe_f2, r);
CPYFPN(&fe->fe_f1, &s);
r = fpu_div(fe);
return r;
}
/*
* arccos(x) = pi/2 - arcsin(x)
*/
struct fpn *
fpu_acos(struct fpemu *fe)
{
struct fpn *r;
if (ISNAN(&fe->fe_f2))
return &fe->fe_f2;
if (ISINF(&fe->fe_f2))
return fpu_newnan(fe);
r = fpu_asin(fe);
CPYFPN(&fe->fe_f2, r);
/* pi/2 - asin(x) */
fpu_const(&fe->fe_f1, FPU_CONST_PI);
fe->fe_f1.fp_exp--;
fe->fe_f2.fp_sign = !fe->fe_f2.fp_sign;
r = fpu_add(fe);
return r;
}
/*
* x
* arcsin(x) = arctan(---------------)
* sqrt(1 - x^2)
*/
struct fpn *
fpu_asin(struct fpemu *fe)
{
struct fpn x;
struct fpn *r;
if (ISNAN(&fe->fe_f2))
return &fe->fe_f2;
if (ISZERO(&fe->fe_f2))
return &fe->fe_f2;
if (ISINF(&fe->fe_f2))
return fpu_newnan(fe);
CPYFPN(&x, &fe->fe_f2);
/* x^2 */
CPYFPN(&fe->fe_f1, &fe->fe_f2);
r = fpu_mul(fe);
/* 1 - x^2 */
CPYFPN(&fe->fe_f2, r);
fe->fe_f2.fp_sign = 1;
fpu_const(&fe->fe_f1, FPU_CONST_1);
r = fpu_add(fe);
/* sqrt(1-x^2) */
CPYFPN(&fe->fe_f2, r);
r = fpu_sqrt(fe);
/* x/sqrt */
CPYFPN(&fe->fe_f2, r);
CPYFPN(&fe->fe_f1, &x);
r = fpu_div(fe);
/* arctan */
CPYFPN(&fe->fe_f2, r);
return fpu_atan(fe);
}
/*
* Our task is to calculate the square root of a floating point number x0.
* This number x normally has the form:
*
* exp
* x = mant * 2 (where 1 <= mant < 2 and exp is an integer)
*
* This can be left as it stands, or the mantissa can be doubled and the
* exponent decremented:
*
* exp-1
* x = (2 * mant) * 2 (where 2 <= 2 * mant < 4)
*
* If the exponent `exp' is even, the square root of the number is best
* handled using the first form, and is by definition equal to:
*
* exp/2
* sqrt(x) = sqrt(mant) * 2
*
* If exp is odd, on the other hand, it is convenient to use the second
* form, giving:
*
* (exp-1)/2
* sqrt(x) = sqrt(2 * mant) * 2
*
* In the first case, we have
*
* 1 <= mant < 2
*
* and therefore
*
* sqrt(1) <= sqrt(mant) < sqrt(2)
*
* while in the second case we have
*
* 2 <= 2*mant < 4
*
* and therefore
*
* sqrt(2) <= sqrt(2*mant) < sqrt(4)
*
* so that in any case, we are sure that
*
* sqrt(1) <= sqrt(n * mant) < sqrt(4), n = 1 or 2
*
* or
*
* 1 <= sqrt(n * mant) < 2, n = 1 or 2.
*
* This root is therefore a properly formed mantissa for a floating
* point number. The exponent of sqrt(x) is either exp/2 or (exp-1)/2
* as above. This leaves us with the problem of finding the square root
* of a fixed-point number in the range [1..4).
*
* Though it may not be instantly obvious, the following square root
* algorithm works for any integer x of an even number of bits, provided
* that no overflows occur:
*
* let q = 0
* for k = NBITS-1 to 0 step -1 do -- for each digit in the answer...
* x *= 2 -- multiply by radix, for next digit
* if x >= 2q + 2^k then -- if adding 2^k does not
* x -= 2q + 2^k -- exceed the correct root,
* q += 2^k -- add 2^k and adjust x
* fi
* done
* sqrt = q / 2^(NBITS/2) -- (and any remainder is in x)
*
* If NBITS is odd (so that k is initially even), we can just add another
* zero bit at the top of x. Doing so means that q is not going to acquire
* a 1 bit in the first trip around the loop (since x0 < 2^NBITS). If the
* final value in x is not needed, or can be off by a factor of 2, this is
* equivalant to moving the `x *= 2' step to the bottom of the loop:
*
* for k = NBITS-1 to 0 step -1 do if ... fi; x *= 2; done
*
* and the result q will then be sqrt(x0) * 2^floor(NBITS / 2).
* (Since the algorithm is destructive on x, we will call x's initial
* value, for which q is some power of two times its square root, x0.)
*
* If we insert a loop invariant y = 2q, we can then rewrite this using
* C notation as:
*
* q = y = 0; x = x0;
* for (k = NBITS; --k >= 0;) {
* #if (NBITS is even)
* x *= 2;
* #endif
* t = y + (1 << k);
* if (x >= t) {
* x -= t;
* q += 1 << k;
* y += 1 << (k + 1);
* }
* #if (NBITS is odd)
* x *= 2;
* #endif
* }
*
* If x0 is fixed point, rather than an integer, we can simply alter the
* scale factor between q and sqrt(x0). As it happens, we can easily arrange
* for the scale factor to be 2**0 or 1, so that sqrt(x0) == q.
*
* In our case, however, x0 (and therefore x, y, q, and t) are multiword
* integers, which adds some complication. But note that q is built one
* bit at a time, from the top down, and is not used itself in the loop
* (we use 2q as held in y instead). This means we can build our answer
* in an integer, one word at a time, which saves a bit of work. Also,
* since 1 << k is always a `new' bit in q, 1 << k and 1 << (k+1) are
* `new' bits in y and we can set them with an `or' operation rather than
* a full-blown multiword add.
*
* We are almost done, except for one snag. We must prove that none of our
* intermediate calculations can overflow. We know that x0 is in [1..4)
* and therefore the square root in q will be in [1..2), but what about x,
* y, and t?
*
* We know that y = 2q at the beginning of each loop. (The relation only
* fails temporarily while y and q are being updated.) Since q < 2, y < 4.
* The sum in t can, in our case, be as much as y+(1<<1) = y+2 < 6, and.
* Furthermore, we can prove with a bit of work that x never exceeds y by
* more than 2, so that even after doubling, 0 <= x < 8. (This is left as
* an exercise to the reader, mostly because I have become tired of working
* on this comment.)
*
* If our floating point mantissas (which are of the form 1.frac) occupy
* B+1 bits, our largest intermediary needs at most B+3 bits, or two extra.
* In fact, we want even one more bit (for a carry, to avoid compares), or
* three extra. There is a comment in fpu_emu.h reminding maintainers of
* this, so we have some justification in assuming it.
*/
struct fpn *
fpu_sqrt(struct fpemu *fe)
{
struct fpn *x = &fe->fe_f1;
u_int bit, q, tt;
u_int x0, x1, x2, x3;
u_int y0, y1, y2, y3;
u_int d0, d1, d2, d3;
int e;
FPU_DECL_CARRY;
/*
* Take care of special cases first. In order:
*
* sqrt(NaN) = NaN
* sqrt(+0) = +0
* sqrt(-0) = -0
* sqrt(x < 0) = NaN (including sqrt(-Inf))
* sqrt(+Inf) = +Inf
*
* Then all that remains are numbers with mantissas in [1..2).
*/
DPRINTF(FPE_REG, ("fpu_sqer:\n"));
DUMPFPN(FPE_REG, x);
DPRINTF(FPE_REG, ("=>\n"));
if (ISNAN(x)) {
fe->fe_cx |= FPSCR_VXSNAN;
DUMPFPN(FPE_REG, x);
return (x);
}
if (ISZERO(x)) {
fe->fe_cx |= FPSCR_ZX;
x->fp_class = FPC_INF;
DUMPFPN(FPE_REG, x);
return (x);
}
if (x->fp_sign) {
return (fpu_newnan(fe));
}
if (ISINF(x)) {
fe->fe_cx |= FPSCR_VXSQRT;
DUMPFPN(FPE_REG, 0);
return (0);
}
/*
* Calculate result exponent. As noted above, this may involve
* doubling the mantissa. We will also need to double x each
* time around the loop, so we define a macro for this here, and
* we break out the multiword mantissa.
*/
#ifdef FPU_SHL1_BY_ADD
#define DOUBLE_X { \
FPU_ADDS(x3, x3, x3); FPU_ADDCS(x2, x2, x2); \
FPU_ADDCS(x1, x1, x1); FPU_ADDC(x0, x0, x0); \
}
#else
#define DOUBLE_X { \
x0 = (x0 << 1) | (x1 >> 31); x1 = (x1 << 1) | (x2 >> 31); \
x2 = (x2 << 1) | (x3 >> 31); x3 <<= 1; \
}
#endif
#if (FP_NMANT & 1) != 0
# define ODD_DOUBLE DOUBLE_X
# define EVEN_DOUBLE /* nothing */
#else
# define ODD_DOUBLE /* nothing */
# define EVEN_DOUBLE DOUBLE_X
#endif
x0 = x->fp_mant[0];
x1 = x->fp_mant[1];
x2 = x->fp_mant[2];
x3 = x->fp_mant[3];
e = x->fp_exp;
if (e & 1) /* exponent is odd; use sqrt(2mant) */
DOUBLE_X;
/* THE FOLLOWING ASSUMES THAT RIGHT SHIFT DOES SIGN EXTENSION */
x->fp_exp = e >> 1; /* calculates (e&1 ? (e-1)/2 : e/2 */
/*
* Now calculate the mantissa root. Since x is now in [1..4),
* we know that the first trip around the loop will definitely
* set the top bit in q, so we can do that manually and start
* the loop at the next bit down instead. We must be sure to
* double x correctly while doing the `known q=1.0'.
*
* We do this one mantissa-word at a time, as noted above, to
* save work. To avoid `(1U << 31) << 1', we also do the top bit
* outside of each per-word loop.
*
* The calculation `t = y + bit' breaks down into `t0 = y0, ...,
* t3 = y3, t? |= bit' for the appropriate word. Since the bit
* is always a `new' one, this means that three of the `t?'s are
* just the corresponding `y?'; we use `#define's here for this.
* The variable `tt' holds the actual `t?' variable.
*/
/* calculate q0 */
#define t0 tt
bit = FP_1;
EVEN_DOUBLE;
/* if (x >= (t0 = y0 | bit)) { */ /* always true */
q = bit;
x0 -= bit;
y0 = bit << 1;
/* } */
ODD_DOUBLE;
while ((bit >>= 1) != 0) { /* for remaining bits in q0 */
EVEN_DOUBLE;
t0 = y0 | bit; /* t = y + bit */
if (x0 >= t0) { /* if x >= t then */
x0 -= t0; /* x -= t */
q |= bit; /* q += bit */
y0 |= bit << 1; /* y += bit << 1 */
}
ODD_DOUBLE;
}
x->fp_mant[0] = q;
#undef t0
/* calculate q1. note (y0&1)==0. */
#define t0 y0
#define t1 tt
q = 0;
y1 = 0;
bit = 1 << 31;
EVEN_DOUBLE;
t1 = bit;
FPU_SUBS(d1, x1, t1);
FPU_SUBC(d0, x0, t0); /* d = x - t */
if ((int)d0 >= 0) { /* if d >= 0 (i.e., x >= t) then */
x0 = d0, x1 = d1; /* x -= t */
q = bit; /* q += bit */
y0 |= 1; /* y += bit << 1 */
}
ODD_DOUBLE;
while ((bit >>= 1) != 0) { /* for remaining bits in q1 */
EVEN_DOUBLE; /* as before */
t1 = y1 | bit;
FPU_SUBS(d1, x1, t1);
FPU_SUBC(d0, x0, t0);
if ((int)d0 >= 0) {
x0 = d0, x1 = d1;
q |= bit;
y1 |= bit << 1;
}
ODD_DOUBLE;
}
x->fp_mant[1] = q;
#undef t1
/* calculate q2. note (y1&1)==0; y0 (aka t0) is fixed. */
#define t1 y1
#define t2 tt
q = 0;
y2 = 0;
bit = 1 << 31;
EVEN_DOUBLE;
t2 = bit;
FPU_SUBS(d2, x2, t2);
FPU_SUBCS(d1, x1, t1);
FPU_SUBC(d0, x0, t0);
if ((int)d0 >= 0) {
x0 = d0, x1 = d1, x2 = d2;
q |= bit;
y1 |= 1; /* now t1, y1 are set in concrete */
}
ODD_DOUBLE;
while ((bit >>= 1) != 0) {
EVEN_DOUBLE;
t2 = y2 | bit;
FPU_SUBS(d2, x2, t2);
FPU_SUBCS(d1, x1, t1);
FPU_SUBC(d0, x0, t0);
if ((int)d0 >= 0) {
x0 = d0, x1 = d1, x2 = d2;
q |= bit;
y2 |= bit << 1;
}
ODD_DOUBLE;
}
x->fp_mant[2] = q;
#undef t2
/* calculate q3. y0, t0, y1, t1 all fixed; y2, t2, almost done. */
#define t2 y2
#define t3 tt
q = 0;
y3 = 0;
bit = 1 << 31;
EVEN_DOUBLE;
t3 = bit;
FPU_SUBS(d3, x3, t3);
FPU_SUBCS(d2, x2, t2);
FPU_SUBCS(d1, x1, t1);
FPU_SUBC(d0, x0, t0);
ODD_DOUBLE;
if ((int)d0 >= 0) {
x0 = d0, x1 = d1, x2 = d2;
q |= bit;
y2 |= 1;
}
while ((bit >>= 1) != 0) {
EVEN_DOUBLE;
t3 = y3 | bit;
FPU_SUBS(d3, x3, t3);
FPU_SUBCS(d2, x2, t2);
FPU_SUBCS(d1, x1, t1);
FPU_SUBC(d0, x0, t0);
if ((int)d0 >= 0) {
x0 = d0, x1 = d1, x2 = d2;
q |= bit;
y3 |= bit << 1;
}
ODD_DOUBLE;
}
x->fp_mant[3] = q;
/*
* The result, which includes guard and round bits, is exact iff
* x is now zero; any nonzero bits in x represent sticky bits.
*/
x->fp_sticky = x0 | x1 | x2 | x3;
DUMPFPN(FPE_REG, x);
return (x);
}
struct fpn *
fpu_div(struct fpemu *fe)
{
struct fpn *x = &fe->fe_f1, *y = &fe->fe_f2;
u_int q, bit;
u_int r0, r1, r2, r3, d0, d1, d2, d3, y0, y1, y2, y3;
FPU_DECL_CARRY
/*
* Since divide is not commutative, we cannot just use ORDER.
* Check either operand for NaN first; if there is at least one,
* order the signalling one (if only one) onto the right, then
* return it. Otherwise we have the following cases:
*
* Inf / Inf = NaN, plus NV exception
* Inf / num = Inf [i.e., return x]
* Inf / 0 = Inf [i.e., return x]
* 0 / Inf = 0 [i.e., return x]
* 0 / num = 0 [i.e., return x]
* 0 / 0 = NaN, plus NV exception
* num / Inf = 0
* num / num = num (do the divide)
* num / 0 = Inf, plus DZ exception
*/
DPRINTF(FPE_REG, ("fpu_div:\n"));
DUMPFPN(FPE_REG, x);
DUMPFPN(FPE_REG, y);
DPRINTF(FPE_REG, ("=>\n"));
if (ISNAN(x) || ISNAN(y)) {
ORDER(x, y);
fe->fe_cx |= FPSCR_VXSNAN;
DUMPFPN(FPE_REG, y);
return (y);
}
/*
* Need to split the following out cause they generate different
* exceptions.
*/
if (ISINF(x)) {
if (x->fp_class == y->fp_class) {
fe->fe_cx |= FPSCR_VXIDI;
return (fpu_newnan(fe));
}
DUMPFPN(FPE_REG, x);
return (x);
}
if (ISZERO(x)) {
fe->fe_cx |= FPSCR_ZX;
if (x->fp_class == y->fp_class) {
fe->fe_cx |= FPSCR_VXZDZ;
return (fpu_newnan(fe));
}
DUMPFPN(FPE_REG, x);
return (x);
}
/* all results at this point use XOR of operand signs */
x->fp_sign ^= y->fp_sign;
if (ISINF(y)) {
x->fp_class = FPC_ZERO;
DUMPFPN(FPE_REG, x);
return (x);
}
if (ISZERO(y)) {
fe->fe_cx = FPSCR_ZX;
x->fp_class = FPC_INF;
DUMPFPN(FPE_REG, x);
return (x);
}
/*
* Macros for the divide. See comments at top for algorithm.
* Note that we expand R, D, and Y here.
*/
#define SUBTRACT /* D = R - Y */ \
FPU_SUBS(d3, r3, y3); FPU_SUBCS(d2, r2, y2); \
FPU_SUBCS(d1, r1, y1); FPU_SUBC(d0, r0, y0)
#define NONNEGATIVE /* D >= 0 */ \
((int)d0 >= 0)
#ifdef FPU_SHL1_BY_ADD
#define SHL1 /* R <<= 1 */ \
FPU_ADDS(r3, r3, r3); FPU_ADDCS(r2, r2, r2); \
FPU_ADDCS(r1, r1, r1); FPU_ADDC(r0, r0, r0)
#else
#define SHL1 \
r0 = (r0 << 1) | (r1 >> 31), r1 = (r1 << 1) | (r2 >> 31), \
r2 = (r2 << 1) | (r3 >> 31), r3 <<= 1
#endif
#define LOOP /* do ... while (bit >>= 1) */ \
do { \
SHL1; \
SUBTRACT; \
if (NONNEGATIVE) { \
q |= bit; \
r0 = d0, r1 = d1, r2 = d2, r3 = d3; \
} \
} while ((bit >>= 1) != 0)
#define WORD(r, i) /* calculate r->fp_mant[i] */ \
q = 0; \
bit = 1 << 31; \
LOOP; \
(x)->fp_mant[i] = q
/* Setup. Note that we put our result in x. */
r0 = x->fp_mant[0];
r1 = x->fp_mant[1];
r2 = x->fp_mant[2];
r3 = x->fp_mant[3];
y0 = y->fp_mant[0];
y1 = y->fp_mant[1];
y2 = y->fp_mant[2];
y3 = y->fp_mant[3];
bit = FP_1;
SUBTRACT;
if (NONNEGATIVE) {
x->fp_exp -= y->fp_exp;
r0 = d0, r1 = d1, r2 = d2, r3 = d3;
q = bit;
bit >>= 1;
} else {
/*
* The multiplication algorithm for normal numbers is as follows:
*
* The fraction of the product is built in the usual stepwise fashion.
* Each step consists of shifting the accumulator right one bit
* (maintaining any guard bits) and, if the next bit in y is set,
* adding the multiplicand (x) to the accumulator. Then, in any case,
* we advance one bit leftward in y. Algorithmically:
*
* A = 0;
* for (bit = 0; bit < FP_NMANT; bit++) {
* sticky |= A & 1, A >>= 1;
* if (Y & (1 << bit))
* A += X;
* }
*
* (X and Y here represent the mantissas of x and y respectively.)
* The resultant accumulator (A) is the product's mantissa. It may
* be as large as 11.11111... in binary and hence may need to be
* shifted right, but at most one bit.
*
* Since we do not have efficient multiword arithmetic, we code the
* accumulator as four separate words, just like any other mantissa.
* We use local variables in the hope that this is faster than memory.
* We keep x->fp_mant in locals for the same reason.
*
* In the algorithm above, the bits in y are inspected one at a time.
* We will pick them up 32 at a time and then deal with those 32, one
* at a time. Note, however, that we know several things about y:
*
* - the guard and round bits at the bottom are sure to be zero;
*
* - often many low bits are zero (y is often from a single or double
* precision source);
*
* - bit FP_NMANT-1 is set, and FP_1*2 fits in a word.
*
* We can also test for 32-zero-bits swiftly. In this case, the center
* part of the loop---setting sticky, shifting A, and not adding---will
* run 32 times without adding X to A. We can do a 32-bit shift faster
* by simply moving words. Since zeros are common, we optimize this case.
* Furthermore, since A is initially zero, we can omit the shift as well
* until we reach a nonzero word.
*/
struct fpn *
fpu_mul(struct fpemu *fe)
{
struct fpn *x = &fe->fe_f1, *y = &fe->fe_f2;
u_int a3, a2, a1, a0, x3, x2, x1, x0, bit, m;
int sticky;
FPU_DECL_CARRY;
/*
* Put the `heavier' operand on the right (see fpu_emu.h).
* Then we will have one of the following cases, taken in the
* following order:
*
* - y = NaN. Implied: if only one is a signalling NaN, y is.
* The result is y.
* - y = Inf. Implied: x != NaN (is 0, number, or Inf: the NaN
* case was taken care of earlier).
* If x = 0, the result is NaN. Otherwise the result
* is y, with its sign reversed if x is negative.
* - x = 0. Implied: y is 0 or number.
* The result is 0 (with XORed sign as usual).
* - other. Implied: both x and y are numbers.
* The result is x * y (XOR sign, multiply bits, add exponents).
*/
DPRINTF(FPE_REG, ("fpu_mul:\n"));
DUMPFPN(FPE_REG, x);
DUMPFPN(FPE_REG, y);
DPRINTF(FPE_REG, ("=>\n"));
ORDER(x, y);
if (ISNAN(y)) {
y->fp_sign ^= x->fp_sign;
fe->fe_cx |= FPSCR_VXSNAN;
DUMPFPN(FPE_REG, y);
return (y);
}
if (ISINF(y)) {
if (ISZERO(x)) {
fe->fe_cx |= FPSCR_VXIMZ;
return (fpu_newnan(fe));
}
y->fp_sign ^= x->fp_sign;
DUMPFPN(FPE_REG, y);
return (y);
}
if (ISZERO(x)) {
x->fp_sign ^= y->fp_sign;
DUMPFPN(FPE_REG, x);
return (x);
}
/*
* Setup. In the code below, the mask `m' will hold the current
* mantissa byte from y. The variable `bit' denotes the bit
* within m. We also define some macros to deal with everything.
*/
x3 = x->fp_mant[3];
x2 = x->fp_mant[2];
x1 = x->fp_mant[1];
x0 = x->fp_mant[0];
sticky = a3 = a2 = a1 = a0 = 0;
#define ADD /* A += X */ \
FPU_ADDS(a3, a3, x3); \
FPU_ADDCS(a2, a2, x2); \
FPU_ADDCS(a1, a1, x1); \
FPU_ADDC(a0, a0, x0)
#define SHR1 /* A >>= 1, with sticky */ \
sticky |= a3 & 1, a3 = (a3 >> 1) | (a2 << 31), \
a2 = (a2 >> 1) | (a1 << 31), a1 = (a1 >> 1) | (a0 << 31), a0 >>= 1
#define SHR32 /* A >>= 32, with sticky */ \
sticky |= a3, a3 = a2, a2 = a1, a1 = a0, a0 = 0
#define STEP /* each 1-bit step of the multiplication */ \
SHR1; if (bit & m) { ADD; }; bit <<= 1
/*
* We are ready to begin. The multiply loop runs once for each
* of the four 32-bit words. Some words, however, are special.
* As noted above, the low order bits of Y are often zero. Even
* if not, the first loop can certainly skip the guard bits.
* The last word of y has its highest 1-bit in position FP_NMANT-1,
* so we stop the loop when we move past that bit.
*/
if ((m = y->fp_mant[3]) == 0) {
/* SHR32; */ /* unneeded since A==0 */
} else {
bit = 1 << FP_NG;
do {
STEP;
} while (bit != 0);
}
if ((m = y->fp_mant[2]) == 0) {
SHR32;
} else {
bit = 1;
do {
STEP;
} while (bit != 0);
}
if ((m = y->fp_mant[1]) == 0) {
SHR32;
} else {
bit = 1;
do {
STEP;
} while (bit != 0);
}
m = y->fp_mant[0]; /* definitely != 0 */
bit = 1;
do {
STEP;
} while (bit <= m);
/*
* Done with mantissa calculation. Get exponent and handle
* 11.111...1 case, then put result in place. We reuse x since
* it already has the right class (FP_NUM).
*/
m = x->fp_exp + y->fp_exp;
if (a0 >= FP_2) {
SHR1;
m++;
}
x->fp_sign ^= y->fp_sign;
x->fp_exp = m;
x->fp_sticky = sticky;
x->fp_mant[3] = a3;
x->fp_mant[2] = a2;
x->fp_mant[1] = a1;
x->fp_mant[0] = a0;
DUMPFPN(FPE_REG, x);
return (x);
}
int GDens2Update(GDens *ptr)
{
/*
update ptr
*/
double lpmax, lpsum, psum;
int i, n = ptr->n;
/*
compute various constants
*/
for(i=0;i<n;i++)
{
double s,
x0 = ptr->elm[i].xl, x1 = ptr->elm[i].xm, x2 = ptr->elm[i].xr,
f0 = ptr->elm[i].lfl, f1 = ptr->elm[i].lfm, f2 = ptr->elm[i].lfr;
ptr->elm[i].lfmax = f0; /* scale and shift */
f1 -= f0; f2 -= f0; f0 = 0.0;
x1 -= x0; x2 -= x0; x0 = 0.0;
s = 1./((-SQR(x2) + x2*x1)*x1);
ptr->elm[i].b = -s*(-f2*SQR(x1) +f1*SQR(x2));
ptr->elm[i].c = s*(-f2*x1 +f1*x2);
}
/*
compute the integral over each cell, unnormalized
*/
for(i=0;i<n;i++)
{
if (ISZERO(ptr->elm[i].c))
{
if (ISZERO(ptr->elm[i].b))
ptr->elm[i].lnormc = log(ptr->elm[i].xr-ptr->elm[i].xl);
else
{
double tmp = (ptr->elm[i].xr-ptr->elm[i].xl)*ptr->elm[i].b;
if (fabs(tmp) > FLT_EPSILON)
{
/*
all ok
*/
ptr->elm[i].lnormc = log(fabs(exp((ptr->elm[i].xr-ptr->elm[i].xl)*ptr->elm[i].b) -1.0))
- log(fabs(ptr->elm[i].b));
}
else
{
/*
this is the expansion for small 'tmp'
*/
ptr->elm[i].lnormc = log(fabs(tmp)) - log(fabs(ptr->elm[i].b));
}
}
}
else
{
/*
this can (and does) go wrong as the 'erf' and 'erfi' function may fail for high
values of the arguments. perhaps we need to intergrate directly
int(exp(x^2),x=low...high) ?
*/
double aa = 0.5*ptr->elm[i].b/sqrt(fabs(ptr->elm[i].c));
if (ptr->elm[i].c <= 0.0)
ptr->elm[i].lnormc = -0.25*SQR(ptr->elm[i].b)/ptr->elm[i].c +
log(1./(TWODIVSQRTPI*sqrt(-ptr->elm[i].c)))
+ lerf_diff(sqrt(-ptr->elm[i].c)*(ptr->elm[i].xr-ptr->elm[i].xl) -aa, -aa);
else
ptr->elm[i].lnormc = -0.25*SQR(ptr->elm[i].b)/ptr->elm[i].c +
log(1./(TWODIVSQRTPI*sqrt(ptr->elm[i].c)))
+ lerfi_diff(sqrt(ptr->elm[i].c)*(ptr->elm[i].xr-ptr->elm[i].xl) +aa, aa);
}
if (ISINF(ptr->elm[i].lnormc))
{
ptr->elm[i].lnormc = ptr->elm[i].b = ptr->elm[i].c = 0;
ptr->elm[i].lp = ptr->elm[i].lfl = ptr->elm[i].lfm = ptr->elm[i].lfr = ptr->elm[i].lfmax = -FLT_MAX;
}
else
{
ptr->elm[i].lp = ptr->elm[i].lnormc + ptr->elm[i].lfmax;
}
}
for(lpmax = ptr->elm[0].lp, i=1;i<n;i++) lpmax = MAX(lpmax, ptr->elm[i].lp);
for(i=0;i<n;i++) ptr->elm[i].lp -= lpmax;
for(i=0, psum=0.0;i<n;i++) psum += exp(ptr->elm[i].lp);
for(lpsum = log(psum), i=0;i<n;i++) ptr->elm[i].lp -= lpsum;
/*
speedup the search for regions and sampling
*/
qsort(ptr->elm, (size_t) ptr->n, sizeof(GDensElm), GDensElmCompare);
if (0)
{
for(i=0;i<n;i++)
{
printf("Gdens2 region %d\n", i);
printf("\txl %f xr %f\n", ptr->elm[i].xl, ptr->elm[i].xr);
printf("\tlnormc %f lp %f\n", ptr->elm[i].lnormc, ptr->elm[i].lp);
}
}
return 0;
}
/*
* Perform a compare instruction (with or without unordered exception).
* This updates the fcc field in the fsr.
*
* If either operand is NaN, the result is unordered. For cmpe, this
* causes an NV exception. Everything else is ordered:
* |Inf| > |numbers| > |0|.
* We already arranged for fp_class(Inf) > fp_class(numbers) > fp_class(0),
* so we get this directly. Note, however, that two zeros compare equal
* regardless of sign, while everything else depends on sign.
*
* Incidentally, two Infs of the same sign compare equal (per the 80387
* manual---it would be nice if the SPARC documentation were more
* complete).
*/
void
__fpu_compare(struct fpemu *fe, int cmpe, int fcc)
{
struct fpn *a, *b;
int cc;
FPU_DECL_CARRY
a = &fe->fe_f1;
b = &fe->fe_f2;
if (ISNAN(a) || ISNAN(b)) {
/*
* In any case, we already got an exception for signalling
* NaNs; here we may replace that one with an identical
* exception, but so what?.
*/
if (cmpe)
fe->fe_cx = FSR_NV;
cc = FSR_CC_UO;
goto done;
}
/*
* Must handle both-zero early to avoid sign goofs. Otherwise,
* at most one is 0, and if the signs differ we are done.
*/
if (ISZERO(a) && ISZERO(b)) {
cc = FSR_CC_EQ;
goto done;
}
if (a->fp_sign) { /* a < 0 (or -0) */
if (!b->fp_sign) { /* b >= 0 (or if a = -0, b > 0) */
cc = FSR_CC_LT;
goto done;
}
} else { /* a > 0 (or +0) */
if (b->fp_sign) { /* b <= -0 (or if a = +0, b < 0) */
cc = FSR_CC_GT;
goto done;
}
}
/*
* Now the signs are the same (but may both be negative). All
* we have left are these cases:
*
* |a| < |b| [classes or values differ]
* |a| > |b| [classes or values differ]
* |a| == |b| [classes and values identical]
*
* We define `diff' here to expand these as:
*
* |a| < |b|, a,b >= 0: a < b => FSR_CC_LT
* |a| < |b|, a,b < 0: a > b => FSR_CC_GT
* |a| > |b|, a,b >= 0: a > b => FSR_CC_GT
* |a| > |b|, a,b < 0: a < b => FSR_CC_LT
*/
#define opposite_cc(cc) ((cc) == FSR_CC_LT ? FSR_CC_GT : FSR_CC_LT)
#define diff(magnitude) (a->fp_sign ? opposite_cc(magnitude) : (magnitude))
if (a->fp_class < b->fp_class) { /* |a| < |b| */
cc = diff(FSR_CC_LT);
goto done;
}
if (a->fp_class > b->fp_class) { /* |a| > |b| */
cc = diff(FSR_CC_GT);
goto done;
}
/* now none can be 0: only Inf and numbers remain */
if (ISINF(a)) { /* |Inf| = |Inf| */
cc = FSR_CC_EQ;
goto done;
}
/*
* Only numbers remain. To compare two numbers in magnitude, we
* simply subtract them.
*/
a = __fpu_sub(fe);
if (a->fp_class == FPC_ZERO)
cc = FSR_CC_EQ;
else
cc = diff(FSR_CC_GT);
done:
fe->fe_fsr = (fe->fe_fsr & fcc_nmask[fcc]) |
((u_long)cc << fcc_shift[fcc]);
}
int pvsnfmt_double(pvsnfmt_vars *info, double d) {
char *digits;
int sign = 0;
int dec;
double value = d;
int len;
int pad = 0;
//int signwidth = 0;
int totallen;
char signchar = 0;
int leadingzeros = 0;
int printdigits; /* temporary var used in different contexts */
int flags = info->flags;
int width = info->width;
const char fmt = *(info->fmt);
int precision = info->precision;
/* Check for special values first */
char *special = 0;
if(ISSNAN(value)) {
special = "NaN";
}
else if(ISQNAN(value)) {
special = "NaN";
}
else if(ISINF(value)) {
if(value < 0) {
sign = 1;
}
special = "Inf";
}
if(special) {
totallen = len = strlen(special);
/* Sign (this is silly for NaN but conforming to printf */
if(flags & (FLAG_SIGNED | FLAG_SIGN_PAD) || sign) {
if(sign) {
signchar = '-';
}
else if(flags & FLAG_SIGN_PAD) {
signchar = ' ';
}
else {
signchar = '+';
}
totallen++;
}
/* Padding */
if(totallen < width) {
pad = width - totallen;
}
else {
pad = 0;
}
totallen += pad ;
// haleyjd 05/07/08: this was forgotten!
if(info->nmax <= 1) {
return totallen;
}
/* Sign now if zeropad */
if(flags & FLAG_ZERO_PAD && signchar) {
if(info->nmax > 1) {
*(info->pinsertion) = signchar;
info->pinsertion += 1;
info->nmax -= 1;
}
}
/* Right align */
if(!(flags & FLAG_LEFT_ALIGN)) {
if(info->nmax <= 1) {
pad = 0;
}
else if((int) info->nmax - 1 < pad) {
pad = info->nmax - 1;
}
if(flags & FLAG_ZERO_PAD) {
memset(info->pinsertion, '0', pad);
}
else {
memset(info->pinsertion, ' ', pad);
}
info->pinsertion += pad ;
info->nmax -= pad ;
}
/* Sign now if not zeropad */
if(!(flags & FLAG_ZERO_PAD) && signchar) {
if(info->nmax > 1) {
*(info->pinsertion) = signchar;
info->pinsertion += 1;
info->nmax -= 1;
}
}
if(info->nmax <= 0) {
len = 0;
}
else if((int) info->nmax - 1 < len) {
len = info->nmax - 1;
}
memcpy(info->pinsertion, special, len);
info->pinsertion += len;
info->nmax -= len;
/* Left align */
if(flags & FLAG_LEFT_ALIGN) {
if(info->nmax <= 1) {
pad = 0;
}
else if((int) info->nmax - 1 < pad) {
pad = info->nmax - 1;
}
memset(info->pinsertion, ' ', pad);
info->pinsertion += pad ;
info->nmax -= pad ;
}
return totallen;
}
if(fmt == 'f') {
if(precision == UNKNOWN_PRECISION) {
precision = 6;
}
digits = FCVT(value, precision, &dec, &sign);
len = strlen(digits);
if(dec > 0) {
totallen = dec;
}
else {
totallen = 0;
}
/* plus 1 for decimal place */
if(dec <= 0) {
totallen += 2; /* and trailing ".0" */
}
else if(precision > 0 || flags & FLAG_HASH) {
totallen += 1;
}
/* Determine sign width (0 or 1) */
if(flags & (FLAG_SIGNED | FLAG_SIGN_PAD) || sign) {
if(sign) {
signchar = '-';
}
else if(flags & FLAG_SIGN_PAD) {
signchar = ' ';
}
else {
signchar = '+';
}
totallen++;
}
/* Determine if leading zeros required */
if(dec <= 0) {
leadingzeros = 1 - dec; /* add one for zero before decimal point (0.) */
}
if(leadingzeros - 1 > precision) {
totallen += precision;
}
else if(len - dec > 0) {
totallen += precision;
}
else {
totallen += leadingzeros;
}
/* Determine padding width */
if(totallen < width) {
pad = width - totallen;
}
totallen += pad;
if(info->nmax <= 1) {
return totallen;
}
/* Now that the length has been calculated, print as much of it
* as possible into the buffer
*/
/* Print sign now if padding with zeros */
if(flags & FLAG_ZERO_PAD && signchar != 0) {
if(info->nmax > 1) {
*(info->pinsertion) = signchar;
info->pinsertion += 1;
info->nmax -= 1;
}
}
/* Print width padding if right-aligned */
if(!(flags & FLAG_LEFT_ALIGN)) {
if(info->nmax <= 1) {
pad = 0;
}
else if((int) info->nmax - 1 < pad) {
pad = info->nmax - 1;
}
if(flags & FLAG_ZERO_PAD) {
memset(info->pinsertion, '0', pad);
}
else {
memset(info->pinsertion, ' ', pad);
}
info->pinsertion += pad;
info->nmax -= pad;
}
/* Print sign now if padding was spaces */
if(!(flags & FLAG_ZERO_PAD) && signchar != 0) {
*(info->pinsertion) = signchar;
info->pinsertion += 1;
info->nmax -= 1;
}
/* Print leading zeros */
if(leadingzeros) {
/* Print "0.", then leadingzeros - 1 */
if(info->nmax > 1) {
*(info->pinsertion) = '0';
info->pinsertion += 1;
info->nmax -= 1;
}
if(precision > 0 || flags & FLAG_HASH) {
if(info->nmax > 1) {
*(info->pinsertion) = '.';
info->pinsertion += 1;
info->nmax -= 1;
}
}
/* WARNING not rounding here!
* i.e. printf(".3f", 0.0007) gives "0.000" not "0.001"
*
* This whole function could do with a rewrite...
*/
if(leadingzeros - 1 > precision) {
leadingzeros = precision + 1;
len = 0;
}
/* END WARNING */
precision -= leadingzeros - 1;
if(info->nmax <= 1) {
leadingzeros = 0;
}
else if((int) info->nmax /* - 1 */ < leadingzeros /* -1 */) {
leadingzeros = info->nmax; /* -1 */
}
leadingzeros--;
memset(info->pinsertion, '0', leadingzeros);
info->pinsertion += leadingzeros;
info->nmax -= leadingzeros;
}
/* Print digits before decimal place */
if(dec > 0) {
if(info->nmax <= 1) {
printdigits = 0;
}
else if((int) info->nmax - 1 < dec) {
printdigits = info->nmax - 1;
}
else {
printdigits = dec;
}
memcpy(info->pinsertion, digits, printdigits);
info->pinsertion += printdigits;
info->nmax -= printdigits;
if(precision > 0 || flags & FLAG_HASH) {
/* Print decimal place */
if(info->nmax > 1) {
*(info->pinsertion) = '.';
info->pinsertion += 1;
info->nmax -= 1;
}
/* Print trailing zero if no precision but hash given */
if(precision == 0 && info->nmax > 1) {
*(info->pinsertion) = '0';
info->pinsertion += 1;
info->nmax -= 1;
}
}
/* Bypass the digits we've already printed */
len -= dec;
digits += dec;
}
/* Print digits after decimal place */
if(len > precision) {
len = precision;
}
if(info->nmax <= 1) {
printdigits = 0;
}
else if((int) info->nmax - 1 < len) {
printdigits = info->nmax - 1;
}
else {
printdigits = len;
}
memcpy(info->pinsertion, digits, printdigits);
info->pinsertion += printdigits;
info->nmax -= printdigits;
/* Print left-aligned pad */
if(flags & FLAG_LEFT_ALIGN) {
if(info->nmax <= 1) {
pad = 0;
}
else if((int) info->nmax - 1 < pad) {
pad = info->nmax - 1;
}
memset(info->pinsertion, ' ', pad);
info->pinsertion += pad;
info->nmax -= pad;
}
return totallen;
}
return 0;
}
static struct fpn *
__fpu_modrem(struct fpemu *fe, int is_mod)
{
static struct fpn X, Y;
struct fpn *x, *y, *r;
uint32_t signX, signY, signQ;
int j, k, l, q;
int cmp;
if (ISNAN(&fe->fe_f1) || ISNAN(&fe->fe_f2))
return fpu_newnan(fe);
if (ISINF(&fe->fe_f1) || ISZERO(&fe->fe_f2))
return fpu_newnan(fe);
CPYFPN(&X, &fe->fe_f1);
CPYFPN(&Y, &fe->fe_f2);
x = &X;
y = &Y;
q = 0;
r = &fe->fe_f2;
/*
* Step 1
*/
signX = x->fp_sign;
signY = y->fp_sign;
signQ = (signX ^ signY);
x->fp_sign = y->fp_sign = 0;
/* Special treatment that just return input value but Q is necessary */
if (ISZERO(x) || ISINF(y)) {
r = &fe->fe_f1;
goto Step7;
}
/*
* Step 2
*/
l = x->fp_exp - y->fp_exp;
k = 0;
CPYFPN(r, x);
if (l >= 0) {
r->fp_exp -= l;
j = l;
/*
* Step 3
*/
for (;;) {
cmp = abscmp3(r, y);
/* Step 3.1 */
if (cmp == 0)
break;
/* Step 3.2 */
if (cmp > 0) {
CPYFPN(&fe->fe_f1, r);
CPYFPN(&fe->fe_f2, y);
fe->fe_f2.fp_sign = 1;
r = fpu_add(fe);
q++;
}
/* Step 3.3 */
if (j == 0)
goto Step4;
/* Step 3.4 */
k++;
j--;
q += q;
r->fp_exp++;
}
/* R == Y */
q++;
r->fp_class = FPC_ZERO;
goto Step7;
}
Step4:
r->fp_sign = signX;
/*
* Step 5
*/
if (is_mod)
goto Step7;
/*
* Step 6
*/
/* y = y / 2 */
y->fp_exp--;
/* abscmp3 ignore sign */
cmp = abscmp3(r, y);
/* revert y */
y->fp_exp++;
if (cmp > 0 || (cmp == 0 && q % 2)) {
q++;
CPYFPN(&fe->fe_f1, r);
CPYFPN(&fe->fe_f2, y);
fe->fe_f2.fp_sign = !signX;
r = fpu_add(fe);
}
/*
* Step 7
*/
Step7:
q &= 0x7f;
q |= (signQ << 7);
fe->fe_fpframe->fpf_fpsr =
fe->fe_fpsr =
(fe->fe_fpsr & ~FPSR_QTT) | (q << 16);
return r;
}
void minimize_dual(DOUBLE *Xopt, DOUBLE *Xorig, INT length, DOUBLE *SSt, DOUBLE *SXt, DOUBLE *SXtXSt, DOUBLE trXXt, \
DOUBLE c, INT N, INT K) {
DOUBLE INTERV = 0.1;
DOUBLE EXT = 3.0;
INT MAX = 20;
DOUBLE RATIO = (DOUBLE) 10;
DOUBLE SIG = 0.1;
DOUBLE RHO = SIG / (DOUBLE) 2;
INT MN = K * 1;
CHAR lamch_opt = 'U';
DOUBLE realmin = LAMCH(&lamch_opt);
DOUBLE red = 1;
INT i = 0;
INT ls_failed = 0;
DOUBLE f0;
DOUBLE *df0 = (DOUBLE *) MALLOC(MN * sizeof(DOUBLE));
DOUBLE *dftemp = (DOUBLE *) MALLOC(MN * sizeof(DOUBLE));
DOUBLE *df3 = (DOUBLE *) MALLOC(MN * sizeof(DOUBLE));
DOUBLE *s = (DOUBLE *) MALLOC(MN * sizeof(DOUBLE));
DOUBLE d0;
INT derivFlag = 1;
DOUBLE *X = (DOUBLE *) MALLOC(MN * sizeof(DOUBLE));
datacpy(X, Xorig, MN);
INT maxNK = IMAX(N, K);
DOUBLE *SStLambda = (DOUBLE *) MALLOC(maxNK * K * sizeof(DOUBLE));
DOUBLE *tempMatrix = (DOUBLE *) MALLOC(maxNK * K * sizeof(DOUBLE));
dual_obj_grad(&f0, df0, X, SSt, SXt, SXtXSt, trXXt, c, N, K, derivFlag, SStLambda, tempMatrix);
INT incx = 1;
INT incy = 1;
datacpy(s, df0, MN);
DOUBLE alpha = -1;
SCAL(&MN, &alpha, s, &incx);
d0 = - DOT(&MN, s, &incx, s, &incy);
DOUBLE x1;
DOUBLE x2;
DOUBLE x3;
DOUBLE x4;
DOUBLE *X0 = (DOUBLE *) MALLOC(MN * sizeof(DOUBLE));
DOUBLE *X3 = (DOUBLE *) MALLOC(MN * sizeof(DOUBLE));
DOUBLE F0;
DOUBLE *dF0 = (DOUBLE *) MALLOC(MN * sizeof(DOUBLE));
INT Mmin;
DOUBLE f1;
DOUBLE f2;
DOUBLE f3;
DOUBLE f4;
DOUBLE d1;
DOUBLE d2;
DOUBLE d3;
DOUBLE d4;
INT success;
DOUBLE A;
DOUBLE B;
DOUBLE sqrtquantity;
DOUBLE tempnorm;
DOUBLE tempinprod1;
DOUBLE tempinprod2;
DOUBLE tempscalefactor;
x3 = red / (1 - d0);
while (i++ < length) {
datacpy(X0, X, MN);
datacpy(dF0, df0, MN);
F0 = f0;
Mmin = MAX;
while (1) {
x2 = 0;
f2 = f0;
d2 = d0;
f3 = f0;
datacpy(df3, df0, MN);
success = 0;
while ((!success) && (Mmin > 0)) {
Mmin = Mmin - 1;
datacpy(X3, X, MN);
alpha = x3;
AXPY(&MN, &alpha, s, &incx, X3, &incy);
dual_obj_grad(&f3, df3, X3, SSt, SXt, SXtXSt, trXXt, c, N, K, derivFlag, SStLambda, tempMatrix);
if (ISNAN(f3) || ISINF(f3)) { /* any(isnan(df3)+isinf(df3)) */
x3 = (x2 + x3) * 0.5;
} else {
success = 1;
}
}
if (f3 < F0) {
datacpy(X0, X, MN);
alpha = x3;
AXPY(&MN, &alpha, s, &incx, X0, &incy);
datacpy(dF0, df3, MN);
F0 = f3;
}
d3 = DOT(&MN, df3, &incx, s, &incy);
if ((d3 > SIG * d0) || (f3 > f0 + x3 * RHO * d0) || (Mmin == 0)) {
break;
}
x1 = x2;
f1 = f2;
d1 = d2;
x2 = x3;
f2 = f3;
d2 = d3;
A = 6 * (f1 - f2) + 3 * (d2 + d1) * (x2 - x1);
B = 3 * (f2 - f1) - (2 * d1 + d2) * (x2 - x1);
sqrtquantity = B * B - A * d1 * (x2 - x1);
if (sqrtquantity < 0) {
x3 = x2 * EXT;
} else {
x3 = x1 - d1 * SQR(x2 - x1) / (B + SQRT(sqrtquantity));
if (ISNAN(x3) || ISINF(x3) || (x3 < 0)) {
x3 = x2 * EXT;
} else if (x3 > x2 * EXT) {
x3 = x2 * EXT;
} else if (x3 < x2 + INTERV * (x2 - x1)) {
x3 = x2 + INTERV * (x2 - x1);
}
}
}
while (((ABS(d3) > - SIG * d0) || (f3 > f0 + x3 * RHO * d0)) && (Mmin > 0)) {
if ((d3 > 0) || (f3 > f0 + x3 * RHO * d0)) {
x4 = x3;
f4 = f3;
d4 = d3;
} else {
x2 = x3;
f2 = f3;
d2 = d3;
}
if (f4 > f0) {
x3 = x2 - (0.5 * d2 * SQR(x4 - x2)) / (f4 - f2 - d2 * (x4 - x2));
} else {
A = 6 * (f2 - f4) / (x4 - x2) + 3 * (d4 + d2);
B = 3 * (f4 - f2) - (2 * d2 + d4) * (x4 - x2);
x3 = x2 + (SQRT(B * B - A * d2 * SQR(x4 - x2)) - B) / A;
}
if (ISNAN(x3) || ISINF(x3)) {
x3 = (x2 + x4) * 0.5;
}
x3 = IMAX(IMIN(x3, x4 - INTERV * (x4 - x2)), x2 + INTERV * (x4 - x2));
datacpy(X3, X, MN);
alpha = x3;
AXPY(&MN, &alpha, s, &incx, X3, &incy);
dual_obj_grad(&f3, df3, X3, SSt, SXt, SXtXSt, trXXt, c, N, K, derivFlag, SStLambda, tempMatrix);
if (f3 < F0) {
datacpy(X0, X, MN);
alpha = x3;
AXPY(&MN, &alpha, s, &incx, X0, &incy);
datacpy(dF0, df3, MN);
F0 = f3;
}
Mmin = Mmin - 1;
d3 = DOT(&MN, df3, &incx, s, &incy);
}
if ((ABS(d3) < - SIG * d0) && (f3 < f0 + x3 * RHO * d0)) {
alpha = x3;
AXPY(&MN, &alpha, s, &incx, X, &incy);
f0 = f3;
datacpy(dftemp, df3, MN);
alpha = -1;
AXPY(&MN, &alpha, df0, &incx, dftemp, &incy);
tempinprod1 = DOT(&MN, dftemp, &incx, df3, &incy);
tempnorm = NRM2(&MN, df0, &incx);
tempinprod2 = SQR(tempnorm);
tempscalefactor = tempinprod1 / tempinprod2;
alpha = tempscalefactor;
SCAL(&MN, &alpha, s, &incx);
alpha = -1;
AXPY(&MN, &alpha, df3, &incx, s, &incy);
datacpy(df0, df3, MN);
d3 = d0;
d0 = DOT(&MN, df0, &incx, s, &incy);
if (d0 > 0) {
datacpy(s, df0, MN);
alpha = -1;
SCAL(&MN, &alpha, s, &incx);
tempnorm = NRM2(&MN, s, &incx);
d0 = - SQR(tempnorm);
}
x3 = x3 * IMIN(RATIO, d3 / (d0 - realmin));
ls_failed = 0;
} else {
datacpy(X, X0, MN);
datacpy(df0, dF0, MN);
f0 = F0;
if ((ls_failed == 1) || (i > length)) {
break;
}
datacpy(s, df0, MN);
alpha = -1;
SCAL(&MN, &alpha, s, &incx);
tempnorm = NRM2(&MN, s, &incx);
d0 = - SQR(tempnorm);
x3 = 1 / (1 - d0);
ls_failed = 1;
}
}
datacpy(Xopt, X, MN);
FREE(SStLambda);
FREE(tempMatrix);
FREE(df0);
FREE(dftemp);
FREE(df3);
FREE(s);
FREE(X);
FREE(X0);
FREE(X3);
FREE(dF0);
}
/*
* sin(x):
*
* if (x < 0) {
* x = abs(x);
* sign = 1;
* }
* if (x > 2*pi) {
* x %= 2*pi;
* }
* if (x > pi) {
* x -= pi;
* sign inverse;
* }
* if (x > pi/2) {
* y = cos(x - pi/2);
* } else {
* y = sin(x);
* }
* if (sign) {
* y = -y;
* }
*/
struct fpn *
fpu_sin(struct fpemu *fe)
{
struct fpn x;
struct fpn p;
struct fpn *r;
int sign;
if (ISNAN(&fe->fe_f2))
return &fe->fe_f2;
if (ISINF(&fe->fe_f2))
return fpu_newnan(fe);
/* if x is +0/-0, return +0/-0 */
if (ISZERO(&fe->fe_f2))
return &fe->fe_f2;
CPYFPN(&x, &fe->fe_f2);
/* x = abs(input) */
sign = x.fp_sign;
x.fp_sign = 0;
/* p <- 2*pi */
fpu_const(&p, FPU_CONST_PI);
p.fp_exp++;
/*
* if (x > 2*pi*N)
* sin(x) is sin(x - 2*pi*N)
*/
CPYFPN(&fe->fe_f1, &x);
CPYFPN(&fe->fe_f2, &p);
r = fpu_cmp(fe);
if (r->fp_sign == 0) {
CPYFPN(&fe->fe_f1, &x);
CPYFPN(&fe->fe_f2, &p);
r = fpu_mod(fe);
CPYFPN(&x, r);
}
/* p <- pi */
p.fp_exp--;
/*
* if (x > pi)
* sin(x) is -sin(x - pi)
*/
CPYFPN(&fe->fe_f1, &x);
CPYFPN(&fe->fe_f2, &p);
fe->fe_f2.fp_sign = 1;
r = fpu_add(fe);
if (r->fp_sign == 0) {
CPYFPN(&x, r);
sign ^= 1;
}
/* p <- pi/2 */
p.fp_exp--;
/*
* if (x > pi/2)
* sin(x) is cos(x - pi/2)
* else
* sin(x)
*/
CPYFPN(&fe->fe_f1, &x);
CPYFPN(&fe->fe_f2, &p);
fe->fe_f2.fp_sign = 1;
r = fpu_add(fe);
if (r->fp_sign == 0) {
__fpu_sincos_cordic(fe, r);
r = &fe->fe_f2;
} else {
__fpu_sincos_cordic(fe, &x);
r = &fe->fe_f1;
}
r->fp_sign = sign;
return r;
}
int
APPEND (FUNC_PREFIX, ecvt_r) (FLOAT_TYPE value,
int ndigit,
int *decpt,
int *sign,
char *buf,
size_t len)
{
int exponent = 0;
if (!ISNAN (value) && !ISINF (value) && value != 0.0) {
FLOAT_TYPE (*log10_function) (FLOAT_TYPE) = &LOG10;
if (log10_function) {
/* Use the reasonable code if -lm is included. */
FLOAT_TYPE dexponent;
dexponent = FLOOR (LOG10 (FABS (value)));
value *= EXP (dexponent * -M_LN10);
exponent = (int) dexponent;
} else {
/* Slow code that doesn't require -lm functions. */
FLOAT_TYPE d;
if (value < 0.0)
d = -value;
else
d = value;
if (d < 1.0) {
do {
d *= 10.0;
--exponent;
} while (d < 1.0);
} else if (d >= 10.0) {
do {
d *= 0.1;
++exponent;
} while (d >= 10.0);
}
if (value < 0.0)
value = -d;
else
value = d;
}
} else if (value == 0.0)
/* SUSv2 leaves it unspecified whether *DECPT is 0 or 1 for 0.0.
* This could be changed to -1 if we want to return 0. */
exponent = 0;
if (ndigit <= 0 && len > 0) {
buf[0] = '\0';
*decpt = 1;
if (!ISINF (value) && !ISNAN (value))
*sign = value < 0.0;
else
*sign = 0;
} else
if (APPEND (FUNC_PREFIX, fcvt_r) (value, ndigit - 1, decpt, sign,
buf, len))
return -1;
*decpt += exponent;
return 0;
}
struct fpn *
fpu_add(struct fpemu *fe)
{
struct fpn *x = &fe->fe_f1, *y = &fe->fe_f2, *r;
u_int r0, r1, r2, r3;
int rd;
/*
* Put the `heavier' operand on the right (see fpu_emu.h).
* Then we will have one of the following cases, taken in the
* following order:
*
* - y = NaN. Implied: if only one is a signalling NaN, y is.
* The result is y.
* - y = Inf. Implied: x != NaN (is 0, number, or Inf: the NaN
* case was taken care of earlier).
* If x = -y, the result is NaN. Otherwise the result
* is y (an Inf of whichever sign).
* - y is 0. Implied: x = 0.
* If x and y differ in sign (one positive, one negative),
* the result is +0 except when rounding to -Inf. If same:
* +0 + +0 = +0; -0 + -0 = -0.
* - x is 0. Implied: y != 0.
* Result is y.
* - other. Implied: both x and y are numbers.
* Do addition a la Hennessey & Patterson.
*/
DPRINTF(FPE_REG, ("fpu_add:\n"));
DUMPFPN(FPE_REG, x);
DUMPFPN(FPE_REG, y);
DPRINTF(FPE_REG, ("=>\n"));
ORDER(x, y);
if (ISNAN(y)) {
fe->fe_cx |= FPSCR_VXSNAN;
DUMPFPN(FPE_REG, y);
return (y);
}
if (ISINF(y)) {
if (ISINF(x) && x->fp_sign != y->fp_sign) {
fe->fe_cx |= FPSCR_VXISI;
return (fpu_newnan(fe));
}
DUMPFPN(FPE_REG, y);
return (y);
}
rd = ((fe->fe_fpscr) & FPSCR_RN);
if (ISZERO(y)) {
if (rd != FSR_RD_RM) /* only -0 + -0 gives -0 */
y->fp_sign &= x->fp_sign;
else /* any -0 operand gives -0 */
y->fp_sign |= x->fp_sign;
DUMPFPN(FPE_REG, y);
return (y);
}
if (ISZERO(x)) {
DUMPFPN(FPE_REG, y);
return (y);
}
/*
* We really have two numbers to add, although their signs may
* differ. Make the exponents match, by shifting the smaller
* number right (e.g., 1.011 => 0.1011) and increasing its
* exponent (2^3 => 2^4). Note that we do not alter the exponents
* of x and y here.
*/
r = &fe->fe_f3;
r->fp_class = FPC_NUM;
if (x->fp_exp == y->fp_exp) {
r->fp_exp = x->fp_exp;
r->fp_sticky = 0;
} else {
if (x->fp_exp < y->fp_exp) {
/*
* Try to avoid subtract case iii (see below).
* This also guarantees that x->fp_sticky = 0.
*/
SWAP(x, y);
}
/* now x->fp_exp > y->fp_exp */
r->fp_exp = x->fp_exp;
r->fp_sticky = fpu_shr(y, x->fp_exp - y->fp_exp);
}
r->fp_sign = x->fp_sign;
if (x->fp_sign == y->fp_sign) {
FPU_DECL_CARRY
/*
* The signs match, so we simply add the numbers. The result
* may be `supernormal' (as big as 1.111...1 + 1.111...1, or
* 11.111...0). If so, a single bit shift-right will fix it
* (but remember to adjust the exponent).
*/
/* r->fp_mant = x->fp_mant + y->fp_mant */
FPU_ADDS(r->fp_mant[3], x->fp_mant[3], y->fp_mant[3]);
FPU_ADDCS(r->fp_mant[2], x->fp_mant[2], y->fp_mant[2]);
FPU_ADDCS(r->fp_mant[1], x->fp_mant[1], y->fp_mant[1]);
FPU_ADDC(r0, x->fp_mant[0], y->fp_mant[0]);
if ((r->fp_mant[0] = r0) >= FP_2) {
(void) fpu_shr(r, 1);
r->fp_exp++;
}
} else {
FPU_DECL_CARRY
/*
* The signs differ, so things are rather more difficult.
* H&P would have us negate the negative operand and add;
* this is the same as subtracting the negative operand.
* This is quite a headache. Instead, we will subtract
* y from x, regardless of whether y itself is the negative
* operand. When this is done one of three conditions will
* hold, depending on the magnitudes of x and y:
* case i) |x| > |y|. The result is just x - y,
* with x's sign, but it may need to be normalized.
* case ii) |x| = |y|. The result is 0 (maybe -0)
* so must be fixed up.
* case iii) |x| < |y|. We goofed; the result should
* be (y - x), with the same sign as y.
* We could compare |x| and |y| here and avoid case iii,
* but that would take just as much work as the subtract.
* We can tell case iii has occurred by an overflow.
*
* N.B.: since x->fp_exp >= y->fp_exp, x->fp_sticky = 0.
*/
/* r->fp_mant = x->fp_mant - y->fp_mant */
FPU_SET_CARRY(y->fp_sticky);
FPU_SUBCS(r3, x->fp_mant[3], y->fp_mant[3]);
FPU_SUBCS(r2, x->fp_mant[2], y->fp_mant[2]);
FPU_SUBCS(r1, x->fp_mant[1], y->fp_mant[1]);
FPU_SUBC(r0, x->fp_mant[0], y->fp_mant[0]);
if (r0 < FP_2) {
/* cases i and ii */
if ((r0 | r1 | r2 | r3) == 0) {
/* case ii */
r->fp_class = FPC_ZERO;
r->fp_sign = rd == FSR_RD_RM;
return (r);
}
} else {
/*
* Oops, case iii. This can only occur when the
* exponents were equal, in which case neither
* x nor y have sticky bits set. Flip the sign
* (to y's sign) and negate the result to get y - x.
*/
#ifdef DIAGNOSTIC
if (x->fp_exp != y->fp_exp || r->fp_sticky)
panic("fpu_add");
#endif
r->fp_sign = y->fp_sign;
FPU_SUBS(r3, 0, r3);
FPU_SUBCS(r2, 0, r2);
FPU_SUBCS(r1, 0, r1);
FPU_SUBC(r0, 0, r0);
}
r->fp_mant[3] = r3;
r->fp_mant[2] = r2;
r->fp_mant[1] = r1;
r->fp_mant[0] = r0;
if (r0 < FP_1)
fpu_norm(r);
}
DUMPFPN(FPE_REG, r);
return (r);
}
int
APPEND (FUNC_PREFIX, fcvt_r) (FLOAT_TYPE value,
int ndigit,
int *decpt,
int *sign,
char *buf,
size_t len)
{
int n, i;
int left;
if (buf == NULL) {
__set_errno (EINVAL);
return -1;
}
left = 0;
if (!ISINF (value) && !ISNAN (value)) {
/* OK, the following is not entirely correct. -0.0 is not handled
* correctly but glibc 2.0 does not have a portable function to
* implement this test.
*/
*sign = value < 0.0;
if (*sign)
value = -value;
if (ndigit < 0) {
/* Rounding to the left of the decimal point. */
while (ndigit < 0) {
FLOAT_TYPE new_value = value * 0.1;
if (new_value < 1.0) {
ndigit = 0;
break;
}
value = new_value;
++left;
++ndigit;
}
}
} else {
/* Value is Inf or NaN. */
*sign = 0;
}
n = strx_nprint (buf, len, "%.*" FLOAT_FMT_FLAG "f", ndigit, value);
if (n < 0)
return -1;
i = 0;
while (i < n && isdigit (buf[i]))
++i;
*decpt = i;
if (i == 0)
/* Value is Inf or NaN. */
return 0;
if (i < n) {
do
++i;
while (i < n && !isdigit (buf[i]));
if (*decpt == 1 && buf[0] == '0' && value != 0.0) {
/* We must not have leading zeroes. Strip them all out and
* adjust *DECPT if necessary. */
--*decpt;
while (i < n && buf[i] == '0')
{
--*decpt;
++i;
}
}
memmove (&buf[MAX (*decpt, 0)], &buf[i], n - i);
buf[n - (i - MAX (*decpt, 0))] = '\0';
}
if (left) {
*decpt += left;
if (--len > n) {
while (left-- > 0 && n < len)
buf[n++] = '0';
buf[n] = '\0';
}
}
return 0;
}
/*
* Perform a compare instruction (with or without unordered exception).
* This updates the fcc field in the fsr.
*
* If either operand is NaN, the result is unordered. For ordered, this
* causes an NV exception. Everything else is ordered:
* |Inf| > |numbers| > |0|.
* We already arranged for fp_class(Inf) > fp_class(numbers) > fp_class(0),
* so we get this directly. Note, however, that two zeros compare equal
* regardless of sign, while everything else depends on sign.
*
* Incidentally, two Infs of the same sign compare equal (per the 80387
* manual---it would be nice if the SPARC documentation were more
* complete).
*/
void
fpu_compare(struct fpemu *fe, int ordered)
{
struct fpn *a, *b, *r;
int cc;
a = &fe->fe_f1;
b = &fe->fe_f2;
r = &fe->fe_f3;
if (ISNAN(a) || ISNAN(b)) {
/*
* In any case, we already got an exception for signalling
* NaNs; here we may replace that one with an identical
* exception, but so what?.
*/
cc = FPSCR_FU;
if (ISSNAN(a) || ISSNAN(b))
cc |= FPSCR_VXSNAN;
if (ordered) {
if (fe->fe_fpscr & FPSCR_VE || ISQNAN(a) || ISQNAN(b))
cc |= FPSCR_VXVC;
}
goto done;
}
/*
* Must handle both-zero early to avoid sign goofs. Otherwise,
* at most one is 0, and if the signs differ we are done.
*/
if (ISZERO(a) && ISZERO(b)) {
cc = FPSCR_FE;
goto done;
}
if (a->fp_sign) { /* a < 0 (or -0) */
if (!b->fp_sign) { /* b >= 0 (or if a = -0, b > 0) */
cc = FPSCR_FL;
goto done;
}
} else { /* a > 0 (or +0) */
if (b->fp_sign) { /* b <= -0 (or if a = +0, b < 0) */
cc = FPSCR_FG;
goto done;
}
}
/*
* Now the signs are the same (but may both be negative). All
* we have left are these cases:
*
* |a| < |b| [classes or values differ]
* |a| > |b| [classes or values differ]
* |a| == |b| [classes and values identical]
*
* We define `diff' here to expand these as:
*
* |a| < |b|, a,b >= 0: a < b => FSR_CC_LT
* |a| < |b|, a,b < 0: a > b => FSR_CC_GT
* |a| > |b|, a,b >= 0: a > b => FSR_CC_GT
* |a| > |b|, a,b < 0: a < b => FSR_CC_LT
*/
#define opposite_cc(cc) ((cc) == FPSCR_FL ? FPSCR_FG : FPSCR_FL)
#define diff(magnitude) (a->fp_sign ? opposite_cc(magnitude) : (magnitude))
if (a->fp_class < b->fp_class) { /* |a| < |b| */
cc = diff(FPSCR_FL);
goto done;
}
if (a->fp_class > b->fp_class) { /* |a| > |b| */
cc = diff(FPSCR_FG);
goto done;
}
/* now none can be 0: only Inf and numbers remain */
if (ISINF(a)) { /* |Inf| = |Inf| */
cc = FPSCR_FE;
goto done;
}
fpu_sub(fe);
if (ISZERO(r))
cc = FPSCR_FE;
else if (r->fp_sign)
cc = FPSCR_FL;
else
cc = FPSCR_FG;
done:
fe->fe_cx = cc;
}
/*
* Perform a compare instruction (with or without unordered exception).
* This updates the fcc field in the fsr.
*
* If either operand is NaN, the result is unordered. For cmpe, this
* causes an NV exception. Everything else is ordered:
* |Inf| > |numbers| > |0|.
* We already arranged for fp_class(Inf) > fp_class(numbers) > fp_class(0),
* so we get this directly. Note, however, that two zeros compare equal
* regardless of sign, while everything else depends on sign.
*
* Incidentally, two Infs of the same sign compare equal (per the 80387
* manual---it would be nice if the SPARC documentation were more
* complete).
*/
void
fpu_compare(struct fpemu *fe, int cmpe)
{
register struct fpn *a, *b;
register int cc, r3, r2, r1, r0;
FPU_DECL_CARRY
a = &fe->fe_f1;
b = &fe->fe_f2;
if (ISNAN(a) || ISNAN(b)) {
/*
* In any case, we already got an exception for signalling
* NaNs; here we may replace that one with an identical
* exception, but so what?.
*/
if (cmpe)
fe->fe_cx = FSR_NV;
cc = FSR_CC_UO;
goto done;
}
/*
* Must handle both-zero early to avoid sign goofs. Otherwise,
* at most one is 0, and if the signs differ we are done.
*/
if (ISZERO(a) && ISZERO(b)) {
cc = FSR_CC_EQ;
goto done;
}
if (a->fp_sign) { /* a < 0 (or -0) */
if (!b->fp_sign) { /* b >= 0 (or if a = -0, b > 0) */
cc = FSR_CC_LT;
goto done;
}
} else { /* a > 0 (or +0) */
if (b->fp_sign) { /* b <= -0 (or if a = +0, b < 0) */
cc = FSR_CC_GT;
goto done;
}
}
/*
* Now the signs are the same (but may both be negative). All
* we have left are these cases:
*
* |a| < |b| [classes or values differ]
* |a| > |b| [classes or values differ]
* |a| == |b| [classes and values identical]
*
* We define `diff' here to expand these as:
*
* |a| < |b|, a,b >= 0: a < b => FSR_CC_LT
* |a| < |b|, a,b < 0: a > b => FSR_CC_GT
* |a| > |b|, a,b >= 0: a > b => FSR_CC_GT
* |a| > |b|, a,b < 0: a < b => FSR_CC_LT
*/
#define opposite_cc(cc) ((cc) == FSR_CC_LT ? FSR_CC_GT : FSR_CC_LT)
#define diff(magnitude) (a->fp_sign ? opposite_cc(magnitude) : (magnitude))
if (a->fp_class < b->fp_class) { /* |a| < |b| */
cc = diff(FSR_CC_LT);
goto done;
}
if (a->fp_class > b->fp_class) { /* |a| > |b| */
cc = diff(FSR_CC_GT);
goto done;
}
/* now none can be 0: only Inf and numbers remain */
if (ISINF(a)) { /* |Inf| = |Inf| */
cc = FSR_CC_EQ;
goto done;
}
/*
* Only numbers remain. To compare two numbers in magnitude, we
* simply subtract their mantissas.
*/
FPU_SUBS(r3, a->fp_mant[0], b->fp_mant[0]);
FPU_SUBCS(r2, a->fp_mant[1], b->fp_mant[1]);
FPU_SUBCS(r1, a->fp_mant[2], b->fp_mant[2]);
FPU_SUBC(r0, a->fp_mant[3], b->fp_mant[3]);
if (r0 < 0) /* underflow: |a| < |b| */
cc = diff(FSR_CC_LT);
else if ((r0 | r1 | r2 | r3) != 0) /* |a| > |b| */
cc = diff(FSR_CC_GT);
else
cc = FSR_CC_EQ; /* |a| == |b| */
done:
fe->fe_fsr = (fe->fe_fsr & ~FSR_FCC) | (cc << FSR_FCC_SHIFT);
}
void
EditableDenseThreeDimensionalModel::setColumn(size_t index,
const Column &values)
{
QWriteLocker locker(&m_lock);
while (index >= m_data.size()) {
m_data.push_back(Column());
m_trunc.push_back(0);
}
bool allChange = false;
// if (values.size() > m_yBinCount) m_yBinCount = values.size();
for (size_t i = 0; i < values.size(); ++i) {
float value = values[i];
if (ISNAN(value) || ISINF(value)) {
continue;
}
if (!m_haveExtents || value < m_minimum) {
m_minimum = value;
allChange = true;
}
if (!m_haveExtents || value > m_maximum) {
m_maximum = value;
allChange = true;
}
m_haveExtents = true;
}
truncateAndStore(index, values);
// assert(values == expandAndRetrieve(index));
long windowStart = index;
windowStart *= m_resolution;
if (m_notifyOnAdd) {
if (allChange) {
emit modelChanged();
} else {
emit modelChanged(windowStart, windowStart + m_resolution);
}
} else {
if (allChange) {
m_sinceLastNotifyMin = -1;
m_sinceLastNotifyMax = -1;
emit modelChanged();
} else {
if (m_sinceLastNotifyMin == -1 ||
windowStart < m_sinceLastNotifyMin) {
m_sinceLastNotifyMin = windowStart;
}
if (m_sinceLastNotifyMax == -1 ||
windowStart > m_sinceLastNotifyMax) {
m_sinceLastNotifyMax = windowStart;
}
}
}
}
