math: Optimize fma call on asinpif

The fma is required only for x == +/-0x1.6371e8p-4f in FE_TOWARDZERO
to provide correctly rounded results.

Checked on x86_64-linux-gnu and aarch64-linux-gnu.

Reviewed-by: Wilco Dijkstra  <Wilco.Dijkstra@arm.com>

diff --git a/math/auto-libm-test-in b/math/auto-libm-test-in
index 198dac54551688c8546bf75cd0b87ca9314d57ad..7e8cb4cef8327412b7a036cd408d9f3bde97ef9e 100644 (file)
--- a/math/auto-libm-test-in
+++ b/math/auto-libm-test-in
@@ -524,6 +524,8 @@ asinpi 0x1.f1c012p-1
 asinpi -0x1.8805060cb885cp-3
 asinpi 0x8.14d7e32b5c44642p-4
 asinpi -0xa.7ca6c96caefe80b9d757de58a578p-4
+asinpi 0x1.6371e8p-4
+asinpi -0x1.6371e8p-4
 
 atan inf
 atan -inf

diff --git a/math/auto-libm-test-out-asinpi b/math/auto-libm-test-out-asinpi
index 31fe80641168282d6bfda3e6c2740d9c484c5dcc..80f83eb6541dff8b52ce8c4e2c996a1e175a8d6e 100644 (file)
--- a/math/auto-libm-test-out-asinpi
+++ b/math/auto-libm-test-out-asinpi
@@ -2780,3 +2780,53 @@ asinpi -0xa.7ca6c96caefe80b9d757de58a578p-4
 = asinpi tonearest ibm128 -0xa.7ca6c96caefe80b9d757de58a8p-4 : -0x3.a3e55379cf8d0f73aac00cc2e5p-4 : inexact-ok
 = asinpi towardzero ibm128 -0xa.7ca6c96caefe80b9d757de58a8p-4 : -0x3.a3e55379cf8d0f73aac00cc2e4p-4 : inexact-ok
 = asinpi upward ibm128 -0xa.7ca6c96caefe80b9d757de58a8p-4 : -0x3.a3e55379cf8d0f73aac00cc2e4p-4 : inexact-ok
+asinpi 0x1.6371e8p-4
+= asinpi downward binary32 0x1.6371e8p-4 : 0x7.148bcp-8 : inexact-ok
+= asinpi tonearest binary32 0x1.6371e8p-4 : 0x7.148bc8p-8 : inexact-ok
+= asinpi towardzero binary32 0x1.6371e8p-4 : 0x7.148bcp-8 : inexact-ok
+= asinpi upward binary32 0x1.6371e8p-4 : 0x7.148bc8p-8 : inexact-ok
+= asinpi downward binary64 0x1.6371e8p-4 : 0x7.148bc7fffff78p-8 : inexact-ok
+= asinpi tonearest binary64 0x1.6371e8p-4 : 0x7.148bc7fffff7cp-8 : inexact-ok
+= asinpi towardzero binary64 0x1.6371e8p-4 : 0x7.148bc7fffff78p-8 : inexact-ok
+= asinpi upward binary64 0x1.6371e8p-4 : 0x7.148bc7fffff7cp-8 : inexact-ok
+= asinpi downward intel96 0x1.6371e8p-4 : 0x7.148bc7fffff7af9p-8 : inexact-ok
+= asinpi tonearest intel96 0x1.6371e8p-4 : 0x7.148bc7fffff7af98p-8 : inexact-ok
+= asinpi towardzero intel96 0x1.6371e8p-4 : 0x7.148bc7fffff7af9p-8 : inexact-ok
+= asinpi upward intel96 0x1.6371e8p-4 : 0x7.148bc7fffff7af98p-8 : inexact-ok
+= asinpi downward m68k96 0x1.6371e8p-4 : 0x7.148bc7fffff7af9p-8 : inexact-ok
+= asinpi tonearest m68k96 0x1.6371e8p-4 : 0x7.148bc7fffff7af98p-8 : inexact-ok
+= asinpi towardzero m68k96 0x1.6371e8p-4 : 0x7.148bc7fffff7af9p-8 : inexact-ok
+= asinpi upward m68k96 0x1.6371e8p-4 : 0x7.148bc7fffff7af98p-8 : inexact-ok
+= asinpi downward binary128 0x1.6371e8p-4 : 0x7.148bc7fffff7af94c63520731f08p-8 : inexact-ok
+= asinpi tonearest binary128 0x1.6371e8p-4 : 0x7.148bc7fffff7af94c63520731f08p-8 : inexact-ok
+= asinpi towardzero binary128 0x1.6371e8p-4 : 0x7.148bc7fffff7af94c63520731f08p-8 : inexact-ok
+= asinpi upward binary128 0x1.6371e8p-4 : 0x7.148bc7fffff7af94c63520731f0cp-8 : inexact-ok
+= asinpi downward ibm128 0x1.6371e8p-4 : 0x7.148bc7fffff7af94c63520731ep-8 : inexact-ok
+= asinpi tonearest ibm128 0x1.6371e8p-4 : 0x7.148bc7fffff7af94c63520732p-8 : inexact-ok
+= asinpi towardzero ibm128 0x1.6371e8p-4 : 0x7.148bc7fffff7af94c63520731ep-8 : inexact-ok
+= asinpi upward ibm128 0x1.6371e8p-4 : 0x7.148bc7fffff7af94c63520732p-8 : inexact-ok
+asinpi -0x1.6371e8p-4
+= asinpi downward binary32 -0x1.6371e8p-4 : -0x7.148bc8p-8 : inexact-ok
+= asinpi tonearest binary32 -0x1.6371e8p-4 : -0x7.148bc8p-8 : inexact-ok
+= asinpi towardzero binary32 -0x1.6371e8p-4 : -0x7.148bcp-8 : inexact-ok
+= asinpi upward binary32 -0x1.6371e8p-4 : -0x7.148bcp-8 : inexact-ok
+= asinpi downward binary64 -0x1.6371e8p-4 : -0x7.148bc7fffff7cp-8 : inexact-ok
+= asinpi tonearest binary64 -0x1.6371e8p-4 : -0x7.148bc7fffff7cp-8 : inexact-ok
+= asinpi towardzero binary64 -0x1.6371e8p-4 : -0x7.148bc7fffff78p-8 : inexact-ok
+= asinpi upward binary64 -0x1.6371e8p-4 : -0x7.148bc7fffff78p-8 : inexact-ok
+= asinpi downward intel96 -0x1.6371e8p-4 : -0x7.148bc7fffff7af98p-8 : inexact-ok
+= asinpi tonearest intel96 -0x1.6371e8p-4 : -0x7.148bc7fffff7af98p-8 : inexact-ok
+= asinpi towardzero intel96 -0x1.6371e8p-4 : -0x7.148bc7fffff7af9p-8 : inexact-ok
+= asinpi upward intel96 -0x1.6371e8p-4 : -0x7.148bc7fffff7af9p-8 : inexact-ok
+= asinpi downward m68k96 -0x1.6371e8p-4 : -0x7.148bc7fffff7af98p-8 : inexact-ok
+= asinpi tonearest m68k96 -0x1.6371e8p-4 : -0x7.148bc7fffff7af98p-8 : inexact-ok
+= asinpi towardzero m68k96 -0x1.6371e8p-4 : -0x7.148bc7fffff7af9p-8 : inexact-ok
+= asinpi upward m68k96 -0x1.6371e8p-4 : -0x7.148bc7fffff7af9p-8 : inexact-ok
+= asinpi downward binary128 -0x1.6371e8p-4 : -0x7.148bc7fffff7af94c63520731f0cp-8 : inexact-ok
+= asinpi tonearest binary128 -0x1.6371e8p-4 : -0x7.148bc7fffff7af94c63520731f08p-8 : inexact-ok
+= asinpi towardzero binary128 -0x1.6371e8p-4 : -0x7.148bc7fffff7af94c63520731f08p-8 : inexact-ok
+= asinpi upward binary128 -0x1.6371e8p-4 : -0x7.148bc7fffff7af94c63520731f08p-8 : inexact-ok
+= asinpi downward ibm128 -0x1.6371e8p-4 : -0x7.148bc7fffff7af94c63520732p-8 : inexact-ok
+= asinpi tonearest ibm128 -0x1.6371e8p-4 : -0x7.148bc7fffff7af94c63520732p-8 : inexact-ok
+= asinpi towardzero ibm128 -0x1.6371e8p-4 : -0x7.148bc7fffff7af94c63520731ep-8 : inexact-ok
+= asinpi upward ibm128 -0x1.6371e8p-4 : -0x7.148bc7fffff7af94c63520731ep-8 : inexact-ok

diff --git a/sysdeps/ieee754/flt-32/s_asinpif.c b/sysdeps/ieee754/flt-32/s_asinpif.c
index f9e93533d4a0b95d81caafa6fba4303a8e748553..d50de7fcd7a448570415e55d5ab34c289833b1be 100644 (file)
--- a/sysdeps/ieee754/flt-32/s_asinpif.c
+++ b/sysdeps/ieee754/flt-32/s_asinpif.c
@@ -79,8 +79,13 @@ __asinpif (float x)
       c0 += c2 * z2;
       c4 += c6 * z2;
       c0 += c4 * z4;
-      double r = fma (-c0, copysign (f, x), copysign (0.5, x));
-      return r;
+#ifndef __FP_FAST_FMA
+      /* The fma is required only for x == 0x1.6371e8p-4f in FE_TOWARDZERO
+        to provide correctly rounded results.  */
+      if (__glibc_likely (ax != 0x1.6371e8p-4f))
+       return copysign (0.5, x) - c0 * copysign (f, x);
+#endif
+      return fma (-c0, copysign (f, x), copysign (0.5, x));
     }
 }
 libm_alias_float (__asinpi, asinpi)