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Merged
sigilante merged 1 commit into from
May 30, 2026
Merged

Finish rotmg to the BLAS reference (C8 part 3) #20

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3 changes: 3 additions & 0 deletions Makefile
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Original file line number Diff line number Diff line change
Expand Up @@ -57,6 +57,9 @@ BLAS_SRCS = \
$(BLAS_SRC_DIR_L1)/srotm.c \
$(BLAS_SRC_DIR_L1)/drotm.c \
$(BLAS_SRC_DIR_L1)/hrotm.c \
$(BLAS_SRC_DIR_L1)/srotmg.c \
$(BLAS_SRC_DIR_L1)/drotmg.c \
$(BLAS_SRC_DIR_L1)/hrotmg.c \
$(BLAS_SRC_DIR_L2)/sgemv.c \
$(BLAS_SRC_DIR_L2)/dgemv.c \
$(BLAS_SRC_DIR_L2)/hgemv.c \
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244 changes: 93 additions & 151 deletions src/blas/level1/drotmg.c
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@@ -1,169 +1,111 @@
#include "softblas.h"

void drotmg(float64_t *D1, float64_t *D2, float64_t *X1, const float64_t y1, float64_t *P)
{
float64_t flag = *P;
float64_t d1=(*D1), d2=(*D2), x1=(*X1);
float64_t h11, h21, h12, h22, tmp, u, p1, p2, q1, q2;
static const float64_t gam=0x40b0000000000000; // 4096.0
static const float64_t gamsq = 0x40b0000000000000 * 0x40b0000000000000;
static const float64_t rgam = SB_REAL64_ONE / 0x40b0000000000000;
static const float64_t rgamsq = SB_REAL64_ONE /
(0x40b0000000000000 * 0x40b0000000000000);
// Construct a modified Givens transformation (reference SROTMG). Given the
// diagonal scaling D1, D2, the first component X1 of the X-vector, and the
// first component y1 of the Y-vector, it computes the flag P[0] and the H
// matrix entries P[1..4] that zero the second component of the rotated
// vector, rescaling so the scale factors stay in [1/gamsq, gamsq].
void drotmg(float64_t *D1, float64_t *D2, float64_t *X1, const float64_t y1, float64_t *P, const uint_fast8_t rndMode) {
_set_rounding(rndMode);
const float64_t ZERO = { SB_REAL64_ZERO };
const float64_t ONE = { SB_REAL64_ONE };
const float64_t NEGONE = { SB_REAL64_NEGONE };
const float64_t NEGTWO = { SB_REAL64_NEGTWO };
const float64_t gam = { 0x40b0000000000000 }; // 4096
const float64_t gamsq = { 0x4170000000000000 }; // 4096^2 = 2^24
const float64_t rgam = { 0x3f30000000000000 }; // 1/4096 = 2^-12
const float64_t rgamsq = { 0x3e70000000000000 }; // 2^-24

if (f64_lt(d1, SB_REAL64_ZERO))
{
*P = SB_REAL64_NEGONE;
*D1 = *D2 = *X1 = P[1] = P[2] = P[3] = P[4] = SB_REAL64_ZERO;
return;
}
float64_t flag;
float64_t d1 = *D1, d2 = *D2, x1 = *X1;
float64_t h11 = ZERO, h21 = ZERO, h12 = ZERO, h22 = ZERO;

p2 = f64_mul(d2, y1);
if (f64_eq(p2, SB_REAL64_ZERO))
{
*P = SB_REAL64_NEGTWO;
return;
}
if (f64_lt(d1, ZERO)) {
flag = NEGONE;
d1 = ZERO; d2 = ZERO; x1 = ZERO;
h11 = ZERO; h21 = ZERO; h12 = ZERO; h22 = ZERO;
} else {
float64_t p2 = f64_mul(d2, y1);
if (f64_eq(p2, ZERO)) {
*P = NEGTWO;
return;
}
float64_t p1 = f64_mul(d1, x1);
float64_t q2 = f64_mul(p2, y1);
float64_t q1 = f64_mul(p1, x1);

p1 = f64_mul(d1, x1);
q2 = f64_mul(p2, y1);
q1 = f64_mul(p1, x1);
if (f64_gt(f64_abs(q1), f64_abs(q2)))
{
h21 = f64_div(f64_mul(SB_REAL64_NEGONE, y1), x1);
h12 = f64_div(p2, p1);
u = f64_sub(SB_REAL64_ONE, f64_mul(h12, h21));
if (f64_gt(u, SB_REAL64_ZERO))
{
flag = SB_REAL64_ZERO;
if (f64_gt(f64_abs(q1), f64_abs(q2))) {
h21 = f64_div(f64_mul(NEGONE, y1), x1);
h12 = f64_div(p2, p1);
float64_t u = f64_sub(ONE, f64_mul(h12, h21));
if (f64_le(u, ZERO)) { // singular -> zero result
flag = NEGONE;
d1 = ZERO; d2 = ZERO; x1 = ZERO;
h11 = ZERO; h21 = ZERO; h12 = ZERO; h22 = ZERO;
goto store;
}
flag = ZERO;
d1 = f64_div(d1, u);
d2 = f64_div(d2, u);
x1 = f64_mul(x1, u);
} else {
if (f64_lt(q2, ZERO)) {
flag = NEGONE;
d1 = ZERO; d2 = ZERO; x1 = ZERO;
h11 = ZERO; h21 = ZERO; h12 = ZERO; h22 = ZERO;
goto store;
}
flag = ONE;
h11 = f64_div(p1, p2);
h22 = f64_div(x1, y1);
float64_t u = f64_add(ONE, f64_mul(h11, h22));
float64_t tmp = f64_div(d2, u);
d2 = f64_div(d1, u);
d1 = tmp;
x1 = f64_mul(y1, u);
}
}
else
{
if (f64_lt(q2, SB_REAL64_ZERO))
{
*P = SB_REAL64_NEGONE;
*D1 = *D2 = *X1 = P[1] = P[2] = P[3] = P[4] = SB_REAL64_ZERO;
return;
}
flag = SB_REAL64_ONE;
h11 = f64_div(p1, p2);
h22 = f64_div(x1, y1);
u = f64_add(SB_REAL64_ONE, f64_mul(h11, h22));
tmp = f64_div(d2, u);
d2 = f64_div(d1, u);
d1 = tmp;
x1 = f64_mul(y1, u);

}

if (f64_le(d1, rgamsq))
{
if (f64_ne(d1, SB_REAL64_ZERO))
{
if (f64_eq(flag, SB_REAL64_ZERO)) { flag = SB_REAL64_NEGONE; h11 = h22 = SB_REAL64_ONE; }
else { flag = h21 = SB_REAL64_NEGONE; h12 = SB_REAL64_ONE; }
while(1)
{
d1 = f64_mul(d1, gamsq);
x1 = f64_mul(x1, rgam);
h11 = f64_mul(h11, rgam);
h12 = f64_mul(h12, rgam);
if (f64_gt(d1, rgamsq))
break;
h21 = SB_REAL64_NEGONE;
h12 = SB_REAL64_ONE;
}
// Rescale D1 into [1/gamsq, gamsq].
while (f64_ne(d1, ZERO) && f64_le(d1, rgamsq)) {
if (f64_eq(flag, ZERO)) { flag = NEGONE; h11 = ONE; h22 = ONE; }
else { flag = NEGONE; h21 = NEGONE; h12 = ONE; }
d1 = f64_mul(d1, gamsq);
x1 = f64_mul(x1, rgam);
h11 = f64_mul(h11, rgam);
h12 = f64_mul(h12, rgam);
}
}
else if (f64_ge(d1, gamsq))
{
if (f64_eq(flag, SB_REAL64_ZERO)) { flag = SB_REAL64_NEGONE; h11 = h22 = SB_REAL64_ONE; }
else { flag = h21 = SB_REAL64_NEGONE; h12 = SB_REAL64_ONE; }
while (1)
{
d1 = f64_mul(d1, rgamsq);
x1 = f64_mul(x1, gam);
h11 = f64_mul(h11, gam);
h12 = f64_mul(h12, gam);
if (f64_lt(d1, gamsq))
break;
h21 = SB_REAL64_NEGONE;
h12 = SB_REAL64_ONE;
while (f64_ge(d1, gamsq)) {
if (f64_eq(flag, ZERO)) { flag = NEGONE; h11 = ONE; h22 = ONE; }
else { flag = NEGONE; h21 = NEGONE; h12 = ONE; }
d1 = f64_mul(d1, rgamsq);
x1 = f64_mul(x1, gam);
h11 = f64_mul(h11, gam);
h12 = f64_mul(h12, gam);
}
}

tmp = f64_abs(d2);
if (f64_le(tmp, rgamsq))
{
if (!f64_eq(d2, SB_REAL64_ZERO))
{
if (f64_eq(flag, SB_REAL64_ZERO)) { flag = SB_REAL64_NEGONE; h11 = h22 = SB_REAL64_ONE; }
else { flag = h21 = SB_REAL64_NEGONE; h12 = SB_REAL64_ONE; }
if (f64_ge(d2, SB_REAL64_ZERO))
while (1)
{
d2 = f64_mul(d2, gamsq);
h21 = f64_mul(h21, rgam);
h22 = f64_mul(h22, rgam);
if (f64_gt(d2, rgamsq))
break;
h21 = SB_REAL64_NEGONE;
h12 = SB_REAL64_ONE;
}
else /* d2 < SB_REAL64_ZERO */
{
tmp = f64_mul(SB_REAL64_NEGONE, rgamsq);
while (1)
{
d2 = f64_mul(d2, gamsq);
h21 = f64_mul(h21, rgam);
h22 = f64_mul(h22, rgam);
if (f64_lt(d2, tmp))
break;
h21 = SB_REAL64_NEGONE;
h12 = SB_REAL64_ONE;
}
}

// Rescale D2 into [1/gamsq, gamsq].
while (f64_ne(d2, ZERO) && f64_le(f64_abs(d2), rgamsq)) {
if (f64_eq(flag, ZERO)) { flag = NEGONE; h11 = ONE; h22 = ONE; }
else { flag = NEGONE; h21 = NEGONE; h12 = ONE; }
d2 = f64_mul(d2, gamsq);
h21 = f64_mul(h21, rgam);
h22 = f64_mul(h22, rgam);
}
}
else if f64_ge(tmp, gamsq) {
if (f64_eq(flag, SB_REAL64_ZERO)) { flag = SB_REAL64_NEGONE; h11 = h22 = SB_REAL64_ONE; }
else { flag = h21 = SB_REAL64_NEGONE; h12 = SB_REAL64_ONE; }
if (f64_ge(d2, SB_REAL64_ZERO))
while (1)
{
d2 = f64_mul(d2, rgamsq);
while (f64_ge(f64_abs(d2), gamsq)) {
if (f64_eq(flag, ZERO)) { flag = NEGONE; h11 = ONE; h22 = ONE; }
else { flag = NEGONE; h21 = NEGONE; h12 = ONE; }
d2 = f64_mul(d2, rgamsq);
h21 = f64_mul(h21, gam);
h22 = f64_mul(h22, gam);
if (f64_lt(d2, gamsq))
break;
h21 = SB_REAL64_NEGONE;
h12 = SB_REAL64_ONE;
}
else /* d2 < SB_REAL64_ZERO */
{
tmp = f64_mul(SB_REAL64_NEGONE, gamsq);
while (1)
{
d2 = f64_mul(d2, rgamsq);
h21 = f64_mul(h21, gam);
h22 = f64_mul(h22, gam);
if (f64_gt(d2, tmp))
break;
h21 = SB_REAL64_NEGONE;
h12 = SB_REAL64_ONE;
}
}
}
*D1 = d1;
*D2 = d2;
*X1 = x1;
*P = flag;
if (flag == SB_REAL64_NEGONE) { P[1] = h11; P[2] = h21; P[3] = h12; P[4] = h22; }
else if (flag == SB_REAL64_ZERO) { P[2] = h21; P[3] = h12; }
else if (flag == SB_REAL64_ONE) { P[1] = h11; P[4] = h22; }

store:
*D1 = d1;
*D2 = d2;
*X1 = x1;
P[0] = flag;
if (f64_eq(flag, NEGONE)) { P[1] = h11; P[2] = h21; P[3] = h12; P[4] = h22; }
else if (f64_eq(flag, ZERO)) { P[2] = h21; P[3] = h12; }
else { P[1] = h11; P[4] = h22; } // flag == 1
}
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