[Mesa-dev] [PATCH] gallivm: Improve lp_build_rcp_refine.

[Jose Fonseca]

Use the alternative more accurate expression from
https://en.wikipedia.org/wiki/Division_algorithm#Newton%E2%80%93Raphson_division

Tested by enabling this code path, and running gloss mesa demo.
---
 src/gallium/auxiliary/gallivm/lp_bld_arit.c | 9 +++++----
 1 file changed, 5 insertions(+), 4 deletions(-)

diff --git a/src/gallium/auxiliary/gallivm/lp_bld_arit.c b/src/gallium/auxiliary/gallivm/lp_bld_arit.c
index 02fb81afe51..8aa5931eb69 100644
--- a/src/gallium/auxiliary/gallivm/lp_bld_arit.c
+++ b/src/gallium/auxiliary/gallivm/lp_bld_arit.c
@@ -2707,11 +2707,11 @@ lp_build_sqrt(struct lp_build_context *bld,
 /**
  * Do one Newton-Raphson step to improve reciprocate precision:
  *
- *   x_{i+1} = x_i * (2 - a * x_i)
+ *   x_{i+1} = x_i + x_i * (1 - a * x_i)
  *
  * XXX: Unfortunately this won't give IEEE-754 conformant results for 0 or
  * +/-Inf, giving NaN instead.  Certain applications rely on this behavior,
- * such as Google Earth, which does RCP(RSQRT(0.0) when drawing the Earth's
+ * such as Google Earth, which does RCP(RSQRT(0.0)) when drawing the Earth's
  * halo. It would be necessary to clamp the argument to prevent this.
  *
  * See also:
@@ -2724,12 +2724,13 @@ lp_build_rcp_refine(struct lp_build_context *bld,
                     LLVMValueRef rcp_a)
 {
    LLVMBuilderRef builder = bld->gallivm->builder;
-   LLVMValueRef two = lp_build_const_vec(bld->gallivm, bld->type, 2.0);
    LLVMValueRef res;
 
    res = LLVMBuildFMul(builder, a, rcp_a, "");
-   res = LLVMBuildFSub(builder, two, res, "");
+   res = LLVMBuildFSub(builder, bld->one, res, "");
+
    res = LLVMBuildFMul(builder, rcp_a, res, "");
+   res = LLVMBuildFAdd(builder, rcp_a, res, "");
 
    return res;
 }
-- 
2.17.1