[PATCH v3 14/16] MIPS: math-emu: <MADDF|MSUBF>.S: Fix accuracy (32-bit case)

[Aleksandar Markovic]

From: Douglas Leung <douglas.leung@xxxxxxxxxx>

Implement fused multiply-add with correct accuracy.

Fused multiply-add operation has better accuracy than respective
sequential execution of multiply and add operations applied on the
same inputs. This is because accuracy errors accumulate in latter
case.

This patch implements fused multiply-add with the same accuracy
as it is implemented in hardware, using 64-bit intermediate
calculations.

One test case example (raw bits) that this patch fixes:

MADDF.S fd,fs,ft:
  fd = 0x22575225
  fs = ft = 0x3727c5ac

Signed-off-by: Douglas Leung <douglas.leung@xxxxxxxxxx>
Signed-off-by: Miodrag Dinic <miodrag.dinic@xxxxxxxxxx>
Signed-off-by: Goran Ferenc <goran.ferenc@xxxxxxxxxx>
Signed-off-by: Aleksandar Markovic <aleksandar.markovic@xxxxxxxxxx>
---
 arch/mips/math-emu/ieee754sp.h |   4 ++
 arch/mips/math-emu/sp_maddf.c  | 116 ++++++++++++++++-------------------------
 2 files changed, 50 insertions(+), 70 deletions(-)

diff --git a/arch/mips/math-emu/ieee754sp.h b/arch/mips/math-emu/ieee754sp.h
index 8476067..0f63e42 100644
--- a/arch/mips/math-emu/ieee754sp.h
+++ b/arch/mips/math-emu/ieee754sp.h
@@ -45,6 +45,10 @@ static inline int ieee754sp_finite(union ieee754sp x)
 	return SPBEXP(x) != SP_EMAX + 1 + SP_EBIAS;
 }
 
+/* 64 bit right shift with rounding */
+#define XSPSRS64(v, rs)						\
+	(((rs) >= 64) ? ((v) != 0) : ((v) >> (rs)) | ((v) << (64-(rs)) != 0))
+
 /* 3bit extended single precision sticky right shift */
 #define XSPSRS(v, rs)						\
 	((rs > (SP_FBITS+3))?1:((v) >> (rs)) | ((v) << (32-(rs)) != 0))
diff --git a/arch/mips/math-emu/sp_maddf.c b/arch/mips/math-emu/sp_maddf.c
index cb8597b..b380189 100644
--- a/arch/mips/math-emu/sp_maddf.c
+++ b/arch/mips/math-emu/sp_maddf.c
@@ -24,14 +24,8 @@ static union ieee754sp _sp_maddf(union ieee754sp z, union ieee754sp x,
 	int re;
 	int rs;
 	unsigned rm;
-	unsigned short lxm;
-	unsigned short hxm;
-	unsigned short lym;
-	unsigned short hym;
-	unsigned lrm;
-	unsigned hrm;
-	unsigned t;
-	unsigned at;
+	uint64_t rm64;
+	uint64_t zm64;
 	int s;
 
 	COMPXSP;
@@ -165,108 +159,90 @@ static union ieee754sp _sp_maddf(union ieee754sp z, union ieee754sp x,
 	if (flags & maddf_negate_product)
 		rs ^= 1;
 
-	/* shunt to top of word */
-	xm <<= 32 - (SP_FBITS + 1);
-	ym <<= 32 - (SP_FBITS + 1);
+	/* Multiple 24 bit xm and ym to give 48 bit results */
+	rm64 = (uint64_t)xm * ym;
 
-	/*
-	 * Multiply 32 bits xm, ym to give high 32 bits rm with stickness.
-	 */
-	lxm = xm & 0xffff;
-	hxm = xm >> 16;
-	lym = ym & 0xffff;
-	hym = ym >> 16;
-
-	lrm = lxm * lym;	/* 16 * 16 => 32 */
-	hrm = hxm * hym;	/* 16 * 16 => 32 */
-
-	t = lxm * hym; /* 16 * 16 => 32 */
-	at = lrm + (t << 16);
-	hrm += at < lrm;
-	lrm = at;
-	hrm = hrm + (t >> 16);
-
-	t = hxm * lym; /* 16 * 16 => 32 */
-	at = lrm + (t << 16);
-	hrm += at < lrm;
-	lrm = at;
-	hrm = hrm + (t >> 16);
-
-	rm = hrm | (lrm != 0);
+	/* Shunt to top of word */
+	rm64 = rm64 << 16;
 
-	/*
-	 * Sticky shift down to normal rounding precision.
-	 */
-	if ((int) rm < 0) {
-		rm = (rm >> (32 - (SP_FBITS + 1 + 3))) |
-		    ((rm << (SP_FBITS + 1 + 3)) != 0);
+	/* Put explicit bit at bit 62 if necessary */
+	if ((int64_t) rm64 < 0) {
+		rm64 = rm64 >> 1;
 		re++;
-	} else {
-		rm = (rm >> (32 - (SP_FBITS + 1 + 3 + 1))) |
-		     ((rm << (SP_FBITS + 1 + 3 + 1)) != 0);
 	}
-	assert(rm & (SP_HIDDEN_BIT << 3));
 
-	if (zc == IEEE754_CLASS_ZERO)
-		return ieee754sp_format(rs, re, rm);
-
-	/* And now the addition */
+	assert(rm64 & (1 << 62));
 
-	assert(zm & SP_HIDDEN_BIT);
+	if (zc == IEEE754_CLASS_ZERO) {
+		/*
+		 * Move explicit bit from bit 62 to bit 26 since the
+		 * ieee754sp_format code expects the mantissa to be
+		 * 27 bits wide (24 + 3 rounding bits).
+		 */
+		rm = XSPSRS64(rm64, (62 - 26));
+		return ieee754sp_format(rs, re, rm);
+	}
 
-	/*
-	 * Provide guard,round and stick bit space.
-	 */
-	zm <<= 3;
+	/* Move explicit bit from bit 23 to bit 62 */
+	zm64 = (uint64_t)zm << (62 - 23);
+	assert(zm64 & (1 << 62));
 
+	/* Make the exponents the same */
 	if (ze > re) {
 		/*
 		 * Have to shift r fraction right to align.
 		 */
 		s = ze - re;
-		rm = XSPSRS(rm, s);
+		rm64 = XSPSRS64(rm64, s);
 		re += s;
 	} else if (re > ze) {
 		/*
 		 * Have to shift z fraction right to align.
 		 */
 		s = re - ze;
-		zm = XSPSRS(zm, s);
+		zm64 = XSPSRS64(zm64, s);
 		ze += s;
 	}
 	assert(ze == re);
 	assert(ze <= SP_EMAX);
 
+	/* Do the addition */
 	if (zs == rs) {
 		/*
-		 * Generate 28 bit result of adding two 27 bit numbers
-		 * leaving result in zm, zs and ze.
+		 * Generate 64 bit result by adding two 63 bit numbers
+		 * leaving result in zm64, zs and ze.
 		 */
-		zm = zm + rm;
-
-		if (zm >> (SP_FBITS + 1 + 3)) { /* carry out */
-			zm = XSPSRS1(zm);
+		zm64 = zm64 + rm64;
+		if ((int64_t)zm64 < 0) {	/* carry out */
+			zm64 = XSPSRS1(zm64);
 			ze++;
 		}
 	} else {
-		if (zm >= rm) {
-			zm = zm - rm;
+		if (zm64 >= rm64) {
+			zm64 = zm64 - rm64;
 		} else {
-			zm = rm - zm;
+			zm64 = rm64 - zm64;
 			zs = rs;
 		}
-		if (zm == 0)
+		if (zm64 == 0)
 			return ieee754sp_zero(ieee754_csr.rm == FPU_CSR_RD);
 
 		/*
-		 * Normalize in extended single precision
+		 * Put explicit bit at bit 62 if necessary.
 		 */
-		while ((zm >> (SP_MBITS + 3)) == 0) {
-			zm <<= 1;
+		while ((zm64 >> 62) == 0) {
+			zm64 <<= 1;
 			ze--;
 		}
-
 	}
+
+	/*
+	 * Move explicit bit from bit 62 to bit 26 since the
+	 * ieee754sp_format code expects the mantissa to be
+	 * 27 bits wide (24 + 3 rounding bits).
+	 */
+	zm = XSPSRS64(zm64, (62 - 26));
+
 	return ieee754sp_format(zs, ze, zm);
 }
 
-- 
2.7.4