Defined lt, lte, gt, gte + misc. other updates. (#712)

Details:
- Changed invertsc operation to be a non-destructive operation; that is,
  it now takes separate input and output operands. This change applies
  to both the object and typed APIs.
- Defined an alternative square root operation, sqrtrsc, which, when
  operating on complex scalars, assumes the imaginary part of the input
  to be zero.
- Changed the semantics of addm, subm, copym, axpym, scal2m, and xpbym 
  so that when the source matrix has an implicit unit diagonal, the
  operation leaves the diagonal of the destination matrix untouched.
  Previously, the operations would interpret an implicit unit diagonal
  on the source matrix as a request to manifest the unit diagonal
  *explicitly* on output (either as something to copy in the case of
  copym, or something to compute with in the cases of addm, subm, axpym,
  scal2m, and xpbym). It turns out that this behavior was too cute by
  half and could cause unintended headaches for practical use cases.
  (This change in behavior also required small modifications to the trmv
  and trsv testsuite modules so that they would properly test matrices
  with unit diagonals.)
- Added missing dependencies for copym to gemv, ger, hemv, trmv, and
  trsv testsuite modules.
- Implemented level-0-like ltsc, ltesc, gtsc, gtesc operations in
  frame/util, which use lt, lte, gt, and gte level-0 scalar macros.
- Trivial variable rename in bli_part.c to harmonize with other
  variable naming conventions.

examples/oapi/04level0.c

@@ -166,7 +166,7 @@ int main( int argc, char** argv )
 	bli_normfsc( &zeta, &alpha );
 	bli_printm( "alpha := normf( zeta )  # normf() = complex modulus in complex domain.", &alpha, "%4.1f", "" );
 
-	bli_invertsc( &gamma );
+	bli_invertsc( &gamma, &gamma );
 	bli_printm( "gamma := 1.0 / gamma", &gamma, "%4.2f", "" );
 
 

frame/0/bli_l0_check.c

@@ -55,20 +55,8 @@ GENFRONT( copysc )
 GENFRONT( divsc )
 GENFRONT( mulsc )
 GENFRONT( sqrtsc )
+GENFRONT( sqrtrsc )
 GENFRONT( subsc )
-
-
-#undef  GENFRONT
-#define GENFRONT( opname ) \
-\
-void PASTEMAC(opname,_check) \
-     ( \
-       const obj_t* chi  \
-     ) \
-{ \
-	bli_l0_xsc_check( chi ); \
-}
-
 GENFRONT( invertsc )
 
 
@@ -357,7 +345,7 @@ void bli_l0_xxbsc_check
      (
        const obj_t* chi,
        const obj_t* psi,
-       const bool*  is_eq
+       const bool*  is
      )
 {
 	err_t e_val;

frame/0/bli_l0_check.h

@@ -51,17 +51,8 @@ GENTPROT( copysc )
 GENTPROT( divsc )
 GENTPROT( mulsc )
 GENTPROT( sqrtsc )
+GENTPROT( sqrtrsc )
 GENTPROT( subsc )
-
-
-#undef  GENTPROT
-#define GENTPROT( opname ) \
-\
-void PASTEMAC(opname,_check) \
-     ( \
-       const obj_t* chi  \
-     );
-
 GENTPROT( invertsc )
 
 
@@ -152,5 +143,5 @@ void bli_l0_xxbsc_check
      (
        const obj_t* chi,
        const obj_t* psi,
-       const bool*  is_eq
+       const bool*  is
      );

frame/0/bli_l0_fpa.c

@@ -56,6 +56,7 @@ GENFRONT( mulsc )
 GENFRONT( subsc )
 GENFRONT( invertsc )
 GENFRONT( sqrtsc )
+GENFRONT( sqrtrsc )
 GENFRONT( unzipsc )
 GENFRONT( zipsc )
 

frame/0/bli_l0_fpa.h

@@ -50,6 +50,7 @@ GENPROT( mulsc )
 GENPROT( subsc )
 GENPROT( invertsc )
 GENPROT( sqrtsc )
+GENPROT( sqrtrsc )
 GENPROT( unzipsc )
 GENPROT( zipsc )
 

frame/0/bli_l0_ft.h

@@ -37,7 +37,7 @@
 // -- Level-0 function types ---------------------------------------------------
 //
 
-// addsc, divsc, subsc
+// addsc, divsc, subsc, invertsc
 
 #undef  GENTDEF
 #define GENTDEF( ctype, ch, opname, tsuf ) \
@@ -52,18 +52,6 @@ typedef void (*PASTECH2(ch,opname,tsuf)) \
 INSERT_GENTDEF( addsc )
 INSERT_GENTDEF( divsc )
 INSERT_GENTDEF( subsc )
-
-// invertsc
-
-#undef  GENTDEF
-#define GENTDEF( ctype, ch, opname, tsuf ) \
-\
-typedef void (*PASTECH2(ch,opname,tsuf)) \
-     ( \
-       conj_t  conjchi, \
-       ctype*  chi  \
-     );
-
 INSERT_GENTDEF( invertsc )
 
 // mulsc
@@ -119,6 +107,19 @@ typedef void (*PASTECH2(ch,opname,tsuf)) \
 
 INSERT_GENTDEF( sqrtsc )
 
+// sqrtrsc
+
+#undef  GENTDEF
+#define GENTDEF( ctype, ch, opname, tsuf ) \
+\
+typedef void (*PASTECH2(ch,opname,tsuf)) \
+     ( \
+       const ctype* chi, \
+             ctype* psi  \
+     );
+
+INSERT_GENTDEF( sqrtrsc )
+
 // getsc
 
 #undef  GENTDEF

frame/0/bli_l0_oapi.c

@@ -115,38 +115,6 @@ GENFRONT( addsc )
 GENFRONT( divsc )
 GENFRONT( mulsc )
 GENFRONT( subsc )
-
-
-#undef  GENFRONT
-#define GENFRONT( opname ) \
-\
-void PASTEMAC0(opname) \
-     ( \
-       const obj_t* chi  \
-     ) \
-{ \
-	bli_init_once(); \
-\
-	num_t     dt        = bli_obj_dt( chi ); \
-\
-	conj_t    conjchi   = bli_obj_conj_status( chi ); \
-\
-	void*     buf_chi   = bli_obj_buffer_for_1x1( dt, chi ); \
-\
-	if ( bli_error_checking_is_enabled() ) \
-		PASTEMAC(opname,_check)( chi ); \
-\
-	/* Query a type-specific function pointer, except one that uses
-	   void* for function arguments instead of typed pointers. */ \
-	PASTECH(opname,_vft) f = PASTEMAC(opname,_qfp)( dt ); \
-\
-	f \
-	( \
-	  conjchi, \
-	  buf_chi  \
-	); \
-}
-
 GENFRONT( invertsc )
 
 
@@ -181,6 +149,7 @@ void PASTEMAC0(opname) \
 }
 
 GENFRONT( sqrtsc )
+GENFRONT( sqrtrsc )
 
 
 #undef  GENFRONT

frame/0/bli_l0_oapi.h

@@ -63,17 +63,8 @@ GENPROT( addsc )
 GENPROT( divsc )
 GENPROT( mulsc )
 GENPROT( sqrtsc )
+GENPROT( sqrtrsc )
 GENPROT( subsc )
-
-
-#undef  GENPROT
-#define GENPROT( opname ) \
-\
-BLIS_EXPORT_BLIS void PASTEMAC0(opname) \
-     ( \
-       const obj_t* chi  \
-     );
-
 GENPROT( invertsc )
 
 

frame/0/bli_l0_tapi.c

@@ -66,8 +66,9 @@ INSERT_GENTFUNC_BASIC( subsc, subs )
 \
 void PASTEMAC(ch,opname) \
      ( \
-       conj_t conjchi, \
-       ctype* chi  \
+             conj_t conjchi, \
+       const ctype* chi, \
+             ctype* psi  \
      ) \
 { \
 	bli_init_once(); \
@@ -76,7 +77,7 @@ void PASTEMAC(ch,opname) \
 \
 	PASTEMAC(ch,copycjs)( conjchi, *chi, chi_conj ); \
 	PASTEMAC(ch,kername)( chi_conj ); \
-	PASTEMAC(ch,copys)( chi_conj, *chi ); \
+	PASTEMAC(ch,copys)( chi_conj, *psi ); \
 }
 
 INSERT_GENTFUNC_BASIC( invertsc, inverts )
@@ -176,6 +177,25 @@ void PASTEMAC(ch,opname) \
 INSERT_GENTFUNC_BASIC0( sqrtsc )
 
 
+#undef  GENTFUNCR
+#define GENTFUNCR( ctype, ctype_r, ch, chr, opname ) \
+\
+void PASTEMAC(ch,opname) \
+     ( \
+       const ctype* chi, \
+             ctype* psi  \
+     ) \
+{ \
+	bli_init_once(); \
+\
+	const ctype_r chi_r = PASTEMAC(ch,real)( *chi ); \
+\
+	PASTEMAC2(chr,ch,sqrt2s)( chi_r, *psi ); \
+}
+
+INSERT_GENTFUNCR_BASIC0( sqrtrsc )
+
+
 #undef  GENTFUNC
 #define GENTFUNC( ctype, ch, opname ) \
 \

frame/0/bli_l0_tapi.h

@@ -51,17 +51,6 @@ INSERT_GENTPROT_BASIC0( addsc )
 INSERT_GENTPROT_BASIC0( divsc )
 INSERT_GENTPROT_BASIC0( mulsc )
 INSERT_GENTPROT_BASIC0( subsc )
-
-
-#undef  GENTPROT
-#define GENTPROT( ctype, ch, opname ) \
-\
-BLIS_EXPORT_BLIS void PASTEMAC(ch,opname) \
-     ( \
-       conj_t conjchi, \
-       ctype* chi  \
-     );
-
 INSERT_GENTPROT_BASIC0( invertsc )
 
 
@@ -88,6 +77,7 @@ BLIS_EXPORT_BLIS void PASTEMAC(ch,opname) \
      );
 
 INSERT_GENTPROT_BASIC0( sqrtsc )
+INSERT_GENTPROT_BASIC0( sqrtrsc )
 
 
 #undef  GENTPROT

frame/1m/bli_l1m_tapi.c

@@ -82,6 +82,11 @@ void PASTEMAC2(ch,opname,EX_SUF) \
 \
 	/* When the diagonal of an upper- or lower-stored matrix is unit,
 	   we handle it with a separate post-processing step. */ \
+	/* NOTE: This code was disabled after I realized that when matrix A has the
+	   properties of having a unit diagonal (and being lower or upper stored),
+	   the operation should only read the strictly lower/upper triangle and
+	   leave the diagonal of B untouched. */ \
+/*
 	if ( bli_is_upper_or_lower( uplox ) && \
 	     bli_is_unit_diag( diagx ) ) \
 	{ \
@@ -98,6 +103,7 @@ void PASTEMAC2(ch,opname,EX_SUF) \
 		  rntm  \
 		); \
 	} \
+*/ \
 }
 
 INSERT_GENTFUNC_BASIC( addm, addd )
@@ -146,6 +152,11 @@ void PASTEMAC2(ch,opname,EX_SUF) \
 \
 	/* When the diagonal of an upper- or lower-stored matrix is unit,
 	   we handle it with a separate post-processing step. */ \
+	/* NOTE: This code was disabled after I realized that when matrix A has the
+	   properties of having a unit diagonal (and being lower or upper stored),
+	   the operation should only read the strictly lower/upper triangle and
+	   leave the diagonal of B untouched. */ \
+/*
 	if ( bli_is_upper_or_lower( uplox ) && \
 	     bli_is_unit_diag( diagx ) ) \
 	{ \
@@ -167,6 +178,7 @@ void PASTEMAC2(ch,opname,EX_SUF) \
 		  rntm  \
 		); \
 	} \
+*/ \
 }
 
 INSERT_GENTFUNC_BASIC0( copym )
@@ -219,6 +231,11 @@ void PASTEMAC2(ch,opname,EX_SUF) \
 \
 	/* When the diagonal of an upper- or lower-stored matrix is unit,
 	   we handle it with a separate post-processing step. */ \
+	/* NOTE: This code was disabled after I realized that when matrix A has the
+	   properties of having a unit diagonal (and being lower or upper stored),
+	   the operation should only read the strictly lower/upper triangle and
+	   leave the diagonal of B untouched. */ \
+/*
 	if ( bli_is_upper_or_lower( uplox ) && \
 	     bli_is_unit_diag( diagx ) ) \
 	{ \
@@ -236,6 +253,7 @@ void PASTEMAC2(ch,opname,EX_SUF) \
 		  rntm  \
 		); \
 	} \
+*/ \
 }
 
 INSERT_GENTFUNC_BASIC0( axpym )
@@ -307,6 +325,11 @@ void PASTEMAC2(ch,opname,EX_SUF) \
 \
 	/* When the diagonal of an upper- or lower-stored matrix is unit,
 	   we handle it with a separate post-processing step. */ \
+	/* NOTE: This code was disabled after I realized that when matrix A has the
+	   properties of having a unit diagonal (and being lower or upper stored),
+	   the operation should only read the strictly lower/upper triangle and
+	   leave the diagonal of B untouched. */ \
+/*
 	if ( bli_is_upper_or_lower( uplox ) && \
 	     bli_is_unit_diag( diagx ) ) \
 	{ \
@@ -327,6 +350,7 @@ void PASTEMAC2(ch,opname,EX_SUF) \
 		  rntm  \
 		); \
 	} \
+*/ \
 }
 
 INSERT_GENTFUNC_BASIC0( scal2m )
@@ -441,6 +465,11 @@ void PASTEMAC2(ch,opname,EX_SUF) \
 \
 	/* When the diagonal of an upper- or lower-stored matrix is unit,
 	   we handle it with a separate post-processing step. */ \
+	/* NOTE: This code was disabled after I realized that when matrix A has the
+	   properties of having a unit diagonal (and being lower or upper stored),
+	   the operation should only read the strictly lower/upper triangle and
+	   leave the diagonal of B untouched. */ \
+/*
 	if ( bli_is_upper_or_lower( uplox ) && \
 	     bli_is_unit_diag( diagx ) ) \
 	{ \
@@ -458,6 +487,7 @@ void PASTEMAC2(ch,opname,EX_SUF) \
 		  rntm  \
 		); \
 	} \
+*/ \
 }
 
 INSERT_GENTFUNC_BASIC0( xpbym )