math: use SIMD to accelerate some scalar math functions on s390x

Note, most math functions are structured to use stubs, so that they can
be accelerated with assembly on any platform.
Sinh, cosh, and tanh were not structued with stubs, so this CL does
that. This set of routines was chosen as likely to produce good speedups
with assembly on any platform.

Technique used was minimax polynomial approximation using tables of
polynomial coefficients, with argument range reduction.
A table of scaling factors was also used for cosh and log10.

                     before       after      speedup
BenchmarkCos         22.1 ns/op   6.79 ns/op  3.25x
BenchmarkCosh       125   ns/op  11.7  ns/op 10.68x
BenchmarkLog10       48.4 ns/op  12.5  ns/op  3.87x
BenchmarkSin         22.2 ns/op   6.55 ns/op  3.39x
BenchmarkSinh       125   ns/op  14.2  ns/op  8.80x
BenchmarkTanh        65.0 ns/op  15.1  ns/op  4.30x

Accuracy was tested against a high precision
reference function to determine maximum error.
Approximately 4,000,000 points were tested for each function,
producing the following result.
Note: ulperr is error in "units in the last place"

       max
      ulperr
sin    1.43 (returns NaN beyond +-2^50)
cos    1.79 (returns NaN beyond +-2^50)
cosh   1.05
sinh   3.02
tanh   3.69
log10  1.75

Also includes a set of tests to test non-vector functions even
when SIMD is enabled

Change-Id: Icb45f14d00864ee19ed973d209c3af21e4df4edc
Reviewed-on: https://go-review.googlesource.com/32352
Run-TryBot: Michael Munday <munday@ca.ibm.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Michael Munday <munday@ca.ibm.com>

1 files changed, 149 insertions, 9 deletions

diff --git a/src/math/stubs_s390x.s b/src/math/stubs_s390x.s
index c3aed13e87..8da55c54ab 100644
--- a/src/math/stubs_s390x.s
+++ b/src/math/stubs_s390x.s
@@ -2,7 +2,7 @@
 // Use of this source code is governed by a BSD-style
 // license that can be found in the LICENSE file.
 
-#include "../runtime/textflag.h"
+#include "textflag.h"
 
 TEXT ·Asin(SB),NOSPLIT,$0
 	BR ·asin(SB)
@@ -34,9 +34,6 @@ TEXT ·Hypot(SB),NOSPLIT,$0
 TEXT ·Ldexp(SB),NOSPLIT,$0
 	BR ·ldexp(SB)
 
-TEXT ·Log10(SB),NOSPLIT,$0
-	BR ·log10(SB)
-
 TEXT ·Log2(SB),NOSPLIT,$0
 	BR ·log2(SB)
 
@@ -58,11 +55,154 @@ TEXT ·Remainder(SB),NOSPLIT,$0
 TEXT ·Sincos(SB),NOSPLIT,$0
 	BR ·sincos(SB)
 
-TEXT ·Sin(SB),NOSPLIT,$0
-	BR ·sin(SB)
+TEXT ·Tan(SB),NOSPLIT,$0
+	BR ·tan(SB)
+
+//if go assembly use vector instruction
+TEXT ·hasVectorFacility(SB),NOSPLIT,$24-1
+	MOVD    $x-24(SP), R1
+	XC      $24, 0(R1), 0(R1) // clear the storage
+	MOVD    $2, R0            // R0 is the number of double words stored -1
+	WORD    $0xB2B01000       // STFLE 0(R1)
+	XOR     R0, R0            // reset the value of R0
+	MOVBZ   z-8(SP), R1
+	AND     $0x40, R1
+	BEQ     novector
+vectorinstalled:
+	// check if the vector instruction has been enabled
+	VLEIB   $0, $0xF, V16
+	VLGVB   $0, V16, R1
+	CMPBNE  R1, $0xF, novector
+	MOVB    $1, ret+0(FP) // have vx
+	RET
+novector:
+	MOVB    $0, ret+0(FP) // no vx
+	RET
+
+TEXT ·Log10(SB),NOSPLIT,$0
+	MOVD    log10vectorfacility+0x00(SB),R1
+	BR      (R1)
+
+TEXT ·log10TrampolineSetup(SB),NOSPLIT, $0
+	MOVB    ·hasVX(SB), R1
+	CMPBEQ  R1, $1, vectorimpl      // vectorfacility = 1, vector supported
+	MOVD    $log10vectorfacility+0x00(SB), R1
+	MOVD    $·log10(SB), R2
+	MOVD    R2, 0(R1)
+	BR      ·log10(SB)
+vectorimpl:
+	MOVD    $log10vectorfacility+0x00(SB), R1
+	MOVD    $·log10Asm(SB), R2
+	MOVD    R2, 0(R1)
+	BR      ·log10Asm(SB)
+
+GLOBL log10vectorfacility+0x00(SB), NOPTR, $8
+DATA log10vectorfacility+0x00(SB)/8, $·log10TrampolineSetup(SB)
+
 
 TEXT ·Cos(SB),NOSPLIT,$0
-	BR ·cos(SB)
+	MOVD    cosvectorfacility+0x00(SB),R1
+	BR      (R1)
+
+TEXT ·cosTrampolineSetup(SB),NOSPLIT, $0
+	MOVB    ·hasVX(SB), R1
+	CMPBEQ  R1, $1, vectorimpl      // vectorfacility = 1, vector supported
+	MOVD    $cosvectorfacility+0x00(SB), R1
+	MOVD    $·cos(SB), R2
+	MOVD    R2, 0(R1)
+	BR      ·cos(SB)
+vectorimpl:
+	MOVD    $cosvectorfacility+0x00(SB), R1
+	MOVD    $·cosAsm(SB), R2
+	MOVD    R2, 0(R1)
+	BR      ·cosAsm(SB)
+
+GLOBL cosvectorfacility+0x00(SB), NOPTR, $8
+DATA cosvectorfacility+0x00(SB)/8, $·cosTrampolineSetup(SB)
+
+
+TEXT ·Cosh(SB),NOSPLIT,$0
+	MOVD    coshvectorfacility+0x00(SB),R1
+	BR      (R1)
+
+TEXT ·coshTrampolineSetup(SB),NOSPLIT, $0
+	MOVB    ·hasVX(SB), R1
+	CMPBEQ  R1, $1, vectorimpl      // vectorfacility = 1, vector supported
+	MOVD    $coshvectorfacility+0x00(SB), R1
+	MOVD    $·cosh(SB), R2
+	MOVD    R2, 0(R1)
+	BR      ·cosh(SB)
+vectorimpl:
+	MOVD    $coshvectorfacility+0x00(SB), R1
+	MOVD    $·coshAsm(SB), R2
+	MOVD    R2, 0(R1)
+	BR      ·coshAsm(SB)
+
+GLOBL coshvectorfacility+0x00(SB), NOPTR, $8
+DATA coshvectorfacility+0x00(SB)/8, $·coshTrampolineSetup(SB)
+
+
+TEXT ·Sin(SB),NOSPLIT,$0
+	MOVD    sinvectorfacility+0x00(SB),R1
+	BR      (R1)
+
+TEXT ·sinTrampolineSetup(SB),NOSPLIT, $0
+	MOVB    ·hasVX(SB), R1
+	CMPBEQ  R1, $1, vectorimpl      // vectorfacility = 1, vector supported
+	MOVD    $sinvectorfacility+0x00(SB), R1
+	MOVD    $·sin(SB), R2
+	MOVD    R2, 0(R1)
+	BR      ·sin(SB)
+vectorimpl:
+	MOVD    $sinvectorfacility+0x00(SB), R1
+	MOVD    $·sinAsm(SB), R2
+	MOVD    R2, 0(R1)
+	BR      ·sinAsm(SB)
+
+GLOBL sinvectorfacility+0x00(SB), NOPTR, $8
+DATA sinvectorfacility+0x00(SB)/8, $·sinTrampolineSetup(SB)
+
+
+TEXT ·Sinh(SB),NOSPLIT,$0
+	MOVD    sinhvectorfacility+0x00(SB),R1
+	BR      (R1)
+
+TEXT ·sinhTrampolineSetup(SB),NOSPLIT, $0
+	MOVB    ·hasVX(SB), R1
+	CMPBEQ  R1, $1, vectorimpl      // vectorfacility = 1, vector supported
+	MOVD    $sinhvectorfacility+0x00(SB), R1
+	MOVD    $·sinh(SB), R2
+	MOVD    R2, 0(R1)
+	BR      ·sinh(SB)
+vectorimpl:
+	MOVD    $sinhvectorfacility+0x00(SB), R1
+	MOVD    $·sinhAsm(SB), R2
+	MOVD    R2, 0(R1)
+	BR      ·sinhAsm(SB)
+
+GLOBL sinhvectorfacility+0x00(SB), NOPTR, $8
+DATA sinhvectorfacility+0x00(SB)/8, $·sinhTrampolineSetup(SB)
+
+
+
+TEXT ·Tanh(SB),NOSPLIT,$0
+	MOVD    tanhvectorfacility+0x00(SB),R1
+	BR      (R1)
+
+TEXT ·tanhTrampolineSetup(SB),NOSPLIT, $0
+	MOVB    ·hasVX(SB), R1
+	CMPBEQ  R1, $1, vectorimpl      // vectorfacility = 1, vector supported
+	MOVD    $tanhvectorfacility+0x00(SB), R1
+	MOVD    $·tanh(SB), R2
+	MOVD    R2, 0(R1)
+	BR      ·tanh(SB)
+vectorimpl:
+	MOVD    $tanhvectorfacility+0x00(SB), R1
+	MOVD    $·tanhAsm(SB), R2
+	MOVD    R2, 0(R1)
+	BR      ·tanhAsm(SB)
+
+GLOBL tanhvectorfacility+0x00(SB), NOPTR, $8
+DATA tanhvectorfacility+0x00(SB)/8, $·tanhTrampolineSetup(SB)
+
 
-TEXT ·Tan(SB),NOSPLIT,$0
-	BR ·tan(SB)