Avoid excess range in results from i386 exp, hypot, pow functions (bug 18980).

i386 exp, hypot and pow functions can return overflowing and
underflowing values with excess range and precision; ; Wilco
Dijkstra's patches to make isfinite etc. expand inline cause this
pre-existing issue to result in test failures.

This patch fixes those functions to avoid excess range and precision
in their return values.  Appropriate macros are added for the repeated
code sequences; in future I'll add more such macros and refactor
existing code forcing underflow (with or without also eliminating
excess range and precision from the return value) to use such macros.

Tested for x86.  If, after this patch, you still see x86 libm test
failures with excess range or precision, please file bugs in Bugzilla.

	[BZ #18980]
	* sysdeps/i386/fpu/i386-math-asm.h (DEFINE_FLT_MIN): New macro.
	(DEFINE_DBL_MIN): Likewise.
	(FLT_NARROW_EVAL_UFLOW_NONNEG_NAN): Likewise.
	(DBL_NARROW_EVAL_UFLOW_NONNEG_NAN): Likewise.
	(FLT_NARROW_EVAL_UFLOW_NONNEG): Likewise.
	(DBL_NARROW_EVAL_UFLOW_NONNEG): Likewise.
	* sysdeps/i386/fpu/e_exp.S: Include <i386-math-asm.h>.
	(dbl_min): Replace with use of DEFINE_DBL_MIN.
	(__ieee754_exp): Use DBL_NARROW_EVAL_UFLOW_NONNEG_NAN.
	(__exp_finite): Use DBL_NARROW_EVAL_UFLOW_NONNEG.
	* sysdeps/i386/fpu/e_exp10.S: Include <i386-math-asm.h>.
	(dbl_min): Replace with use of DEFINE_DBL_MIN.
	(__ieee754_exp10): Use DBL_NARROW_EVAL_UFLOW_NONNEG_NAN.
	* sysdeps/i386/fpu/e_exp10f.S: Include <i386-math-asm.h>.
	(flt_min): Replace with use of DEFINE_FLT_MIN.
	(__ieee754_exp10f): Use FLT_NARROW_EVAL_UFLOW_NONNEG_NAN.
	* sysdeps/i386/fpu/e_exp2.S: Include <i386-math-asm.h>.
	(dbl_min): Replace with use of DEFINE_DBL_MIN.
	(__ieee754_exp2): Use DBL_NARROW_EVAL_UFLOW_NONNEG_NAN.
	* sysdeps/i386/fpu/e_exp2f.S: Include <i386-math-asm.h>.
	(flt_min): Replace with use of DEFINE_FLT_MIN.
	(__ieee754_exp2f): Use FLT_NARROW_EVAL_UFLOW_NONNEG_NAN.
	* sysdeps/i386/fpu/e_expf.S: Include <i386-math-asm.h>.
	(flt_min): Replace with use of DEFINE_FLT_MIN.
	(__ieee754_expf): Use FLT_NARROW_EVAL_UFLOW_NONNEG_NAN.
	(__expf_finite): Use FLT_NARROW_EVAL_UFLOW_NONNEG.
	* sysdeps/i386/fpu/e_hypot.S: Include <i386-math-asm.h>.
	(__ieee754_hypot): Use DBL_NARROW_EVAL.
	* sysdeps/i386/fpu/e_hypotf.S: Include <i386-math-asm.h>.
	(__ieee754_hypotf): Use FLT_NARROW_EVAL.
	* sysdeps/i386/fpu/e_pow.S: Include <i386-math-asm.h>.
	(__ieee754_pow): Use DBL_NARROW_EVAL.
	* sysdeps/i386/fpu/e_powf.S: Include <i386-math-asm.h>.
	(__ieee754_powf): Use FLT_NARROW_EVAL.
	* sysdeps/i386/i686/fpu/multiarch/e_expf-sse2.S
	(__ieee754_expf_sse2): Convert double-precision result to single
	precision.
	* sysdeps/i386/fpu/libm-test-ulps: Update.

12 files changed, 244 insertions, 278 deletions

diff --git a/sysdeps/i386/fpu/e_exp.S b/sysdeps/i386/fpu/e_exp.S
index c00beedfe5..a7e7f13f6f 100644
--- a/sysdeps/i386/fpu/e_exp.S
+++ b/sysdeps/i386/fpu/e_exp.S
@@ -4,13 +4,9 @@
  */
 
 #include <machine/asm.h>
+#include <i386-math-asm.h>
 
-	.section .rodata.cst8,"aM",@progbits,8
-
-	.p2align 3
-	.type dbl_min,@object
-dbl_min:	.byte 0, 0, 0, 0, 0, 0, 0x10, 0
-	ASM_SIZE_DIRECTIVE(dbl_min)
+DEFINE_DBL_MIN
 
 #ifdef PIC
 # define MO(op) op##@GOTOFF(%ecx)
@@ -46,22 +42,8 @@ ENTRY(__ieee754_exp)
 	faddp				/* 2^(fract(x * log2(e))) */
 	fscale				/* e^x */
 	fstp	%st(1)
-	fldl	MO(dbl_min)
-	fld	%st(1)
-	fucompp
-	fnstsw
-	sahf
-	jnc 3f
-	subl	$8, %esp
-	cfi_adjust_cfa_offset (8)
-	fld	%st(0)
-	fmul	%st(0)
-	fstpl	(%esp)
-	fstpl	(%esp)
-	fldl	(%esp)
-	addl	$8, %esp
-	cfi_adjust_cfa_offset (-8)
-3:	ret
+	DBL_NARROW_EVAL_UFLOW_NONNEG_NAN
+	ret
 
 1:	testl	$0x200, %eax		/* Test sign.  */
 	jz	2f			/* If positive, jump.  */
@@ -86,20 +68,6 @@ ENTRY(__exp_finite)
 	faddp				/* 2^(fract(x * log2(e))) */
 	fscale				/* e^x */
 	fstp	%st(1)
-	fldl	MO(dbl_min)
-	fld	%st(1)
-	fucompp
-	fnstsw
-	sahf
-	jnc 4f
-	subl	$8, %esp
-	cfi_adjust_cfa_offset (8)
-	fld	%st(0)
-	fmul	%st(0)
-	fstpl	(%esp)
-	fstpl	(%esp)
-	fldl	(%esp)
-	addl	$8, %esp
-	cfi_adjust_cfa_offset (-8)
-4:	ret
+	DBL_NARROW_EVAL_UFLOW_NONNEG
+	ret
 END(__exp_finite)
diff --git a/sysdeps/i386/fpu/e_exp10.S b/sysdeps/i386/fpu/e_exp10.S
index fa54732e2a..acb5160a3f 100644
--- a/sysdeps/i386/fpu/e_exp10.S
+++ b/sysdeps/i386/fpu/e_exp10.S
@@ -3,13 +3,9 @@
  */
 
 #include <machine/asm.h>
+#include <i386-math-asm.h>
 
-	.section .rodata.cst8,"aM",@progbits,8
-
-	.p2align 3
-	.type dbl_min,@object
-dbl_min:	.byte 0, 0, 0, 0, 0, 0, 0x10, 0
-	ASM_SIZE_DIRECTIVE(dbl_min)
+DEFINE_DBL_MIN
 
 #ifdef PIC
 # define MO(op) op##@GOTOFF(%ecx)
@@ -45,22 +41,8 @@ ENTRY(__ieee754_exp10)
 	faddp				/* 2^(fract(x * log2(10))) */
 	fscale				/* e^x */
 	fstp	%st(1)
-	fldl	MO(dbl_min)
-	fld	%st(1)
-	fucompp
-	fnstsw
-	sahf
-	jnc 3f
-	subl	$8, %esp
-	cfi_adjust_cfa_offset (8)
-	fld	%st(0)
-	fmul	%st(0)
-	fstpl	(%esp)
-	fstpl	(%esp)
-	fldl	(%esp)
-	addl	$8, %esp
-	cfi_adjust_cfa_offset (-8)
-3:	ret
+	DBL_NARROW_EVAL_UFLOW_NONNEG_NAN
+	ret
 
 1:	testl	$0x200, %eax		/* Test sign.  */
 	jz	2f			/* If positive, jump.  */
diff --git a/sysdeps/i386/fpu/e_exp10f.S b/sysdeps/i386/fpu/e_exp10f.S
index a84b2ae535..1812b34398 100644
--- a/sysdeps/i386/fpu/e_exp10f.S
+++ b/sysdeps/i386/fpu/e_exp10f.S
@@ -3,13 +3,9 @@
  */
 
 #include <machine/asm.h>
+#include <i386-math-asm.h>
 
-	.section .rodata.cst4,"aM",@progbits,4
-
-	.p2align 2
-	.type flt_min,@object
-flt_min:	.byte 0, 0, 0x80, 0
-	ASM_SIZE_DIRECTIVE(flt_min)
+DEFINE_FLT_MIN
 
 #ifdef PIC
 # define MO(op) op##@GOTOFF(%ecx)
@@ -45,22 +41,8 @@ ENTRY(__ieee754_exp10f)
 	faddp				/* 2^(fract(x * log2(10))) */
 	fscale				/* e^x */
 	fstp	%st(1)
-	flds	MO(flt_min)
-	fld	%st(1)
-	fucompp
-	fnstsw
-	sahf
-	jnc 3f
-	subl	$4, %esp
-	cfi_adjust_cfa_offset (4)
-	fld	%st(0)
-	fmul	%st(0)
-	fstps	(%esp)
-	fstps	(%esp)
-	flds	(%esp)
-	addl	$4, %esp
-	cfi_adjust_cfa_offset (-4)
-3:	ret
+	FLT_NARROW_EVAL_UFLOW_NONNEG_NAN
+	ret
 
 1:	testl	$0x200, %eax		/* Test sign.  */
 	jz	2f			/* If positive, jump.  */
diff --git a/sysdeps/i386/fpu/e_exp2.S b/sysdeps/i386/fpu/e_exp2.S
index b75a63a0b3..fc16a96053 100644
--- a/sysdeps/i386/fpu/e_exp2.S
+++ b/sysdeps/i386/fpu/e_exp2.S
@@ -5,13 +5,9 @@
  */
 
 #include <machine/asm.h>
+#include <i386-math-asm.h>
 
-	.section .rodata.cst8,"aM",@progbits,8
-
-	.p2align 3
-	.type dbl_min,@object
-dbl_min:	.byte 0, 0, 0, 0, 0, 0, 0x10, 0
-	ASM_SIZE_DIRECTIVE(dbl_min)
+DEFINE_DBL_MIN
 
 #ifdef PIC
 # define MO(op) op##@GOTOFF(%ecx)
@@ -44,22 +40,8 @@ ENTRY(__ieee754_exp2)
 	faddp				/* 2^(fract(x)) */
 	fscale				/* e^x */
 	fstp	%st(1)
-	fldl	MO(dbl_min)
-	fld	%st(1)
-	fucompp
-	fnstsw
-	sahf
-	jnc 3f
-	subl	$8, %esp
-	cfi_adjust_cfa_offset (8)
-	fld	%st(0)
-	fmul	%st(0)
-	fstpl	(%esp)
-	fstpl	(%esp)
-	fldl	(%esp)
-	addl	$8, %esp
-	cfi_adjust_cfa_offset (-8)
-3:	ret
+	DBL_NARROW_EVAL_UFLOW_NONNEG_NAN
+	ret
 
 1:	testl	$0x200, %eax		/* Test sign.  */
 	jz	2f			/* If positive, jump.  */
diff --git a/sysdeps/i386/fpu/e_exp2f.S b/sysdeps/i386/fpu/e_exp2f.S
index 042c83b1ef..30623cd850 100644
--- a/sysdeps/i386/fpu/e_exp2f.S
+++ b/sysdeps/i386/fpu/e_exp2f.S
@@ -5,13 +5,9 @@
  */
 
 #include <machine/asm.h>
+#include <i386-math-asm.h>
 
-	.section .rodata.cst4,"aM",@progbits,4
-
-	.p2align 2
-	.type flt_min,@object
-flt_min:	.byte 0, 0, 0x80, 0
-	ASM_SIZE_DIRECTIVE(flt_min)
+DEFINE_FLT_MIN
 
 #ifdef PIC
 # define MO(op) op##@GOTOFF(%ecx)
@@ -44,22 +40,8 @@ ENTRY(__ieee754_exp2f)
 	faddp				/* 2^(fract(x)) */
 	fscale				/* e^x */
 	fstp	%st(1)
-	flds	MO(flt_min)
-	fld	%st(1)
-	fucompp
-	fnstsw
-	sahf
-	jnc 3f
-	subl	$4, %esp
-	cfi_adjust_cfa_offset (4)
-	fld	%st(0)
-	fmul	%st(0)
-	fstps	(%esp)
-	fstps	(%esp)
-	flds	(%esp)
-	addl	$4, %esp
-	cfi_adjust_cfa_offset (-4)
-3:	ret
+	FLT_NARROW_EVAL_UFLOW_NONNEG_NAN
+	ret
 
 1:	testl	$0x200, %eax		/* Test sign.  */
 	jz	2f			/* If positive, jump.  */
diff --git a/sysdeps/i386/fpu/e_expf.S b/sysdeps/i386/fpu/e_expf.S
index 306afd1122..65cb4ec204 100644
--- a/sysdeps/i386/fpu/e_expf.S
+++ b/sysdeps/i386/fpu/e_expf.S
@@ -5,13 +5,9 @@
  */
 
 #include <machine/asm.h>
+#include <i386-math-asm.h>
 
-	.section .rodata.cst4,"aM",@progbits,4
-
-	.p2align 2
-	.type flt_min,@object
-flt_min:	.byte 0, 0, 0x80, 0
-	ASM_SIZE_DIRECTIVE(flt_min)
+DEFINE_FLT_MIN
 
 #ifdef PIC
 # define MO(op) op##@GOTOFF(%ecx)
@@ -47,22 +43,8 @@ ENTRY(__ieee754_expf)
 	faddp				/* 2^(fract(x * log2(e))) */
 	fscale				/* e^x */
 	fstp	%st(1)
-	flds	MO(flt_min)
-	fld	%st(1)
-	fucompp
-	fnstsw
-	sahf
-	jnc 3f
-	subl	$4, %esp
-	cfi_adjust_cfa_offset (4)
-	fld	%st(0)
-	fmul	%st(0)
-	fstps	(%esp)
-	fstps	(%esp)
-	flds	(%esp)
-	addl	$4, %esp
-	cfi_adjust_cfa_offset (-4)
-3:	ret
+	FLT_NARROW_EVAL_UFLOW_NONNEG_NAN
+	ret
 
 1:	testl	$0x200, %eax		/* Test sign.  */
 	jz	2f			/* If positive, jump.  */
@@ -87,20 +69,6 @@ ENTRY(__expf_finite)
 	faddp				/* 2^(fract(x * log2(e))) */
 	fscale				/* e^x */
 	fstp	%st(1)
-	flds	MO(flt_min)
-	fld	%st(1)
-	fucompp
-	fnstsw
-	sahf
-	jnc 4f
-	subl	$4, %esp
-	cfi_adjust_cfa_offset (4)
-	fld	%st(0)
-	fmul	%st(0)
-	fstps	(%esp)
-	fstps	(%esp)
-	flds	(%esp)
-	addl	$4, %esp
-	cfi_adjust_cfa_offset (-4)
-4:	ret
+	FLT_NARROW_EVAL_UFLOW_NONNEG
+	ret
 END(__expf_finite)
diff --git a/sysdeps/i386/fpu/e_hypot.S b/sysdeps/i386/fpu/e_hypot.S
index 63083ad4c9..5323fde01e 100644
--- a/sysdeps/i386/fpu/e_hypot.S
+++ b/sysdeps/i386/fpu/e_hypot.S
@@ -18,6 +18,7 @@
    <http://www.gnu.org/licenses/>.  */
 
 #include <sysdep.h>
+#include <i386-math-asm.h>
 
 	.text
 ENTRY(__ieee754_hypot)
@@ -37,6 +38,7 @@ ENTRY(__ieee754_hypot)
 	fmul	%st(0)		// x * x : y * y
 	faddp			// x * x + y * y
 	fsqrt
+	DBL_NARROW_EVAL
 2:	ret
 
 	// We have to test whether any of the parameters is Inf.
diff --git a/sysdeps/i386/fpu/e_hypotf.S b/sysdeps/i386/fpu/e_hypotf.S
index 4e22d33ebe..fd11ea7105 100644
--- a/sysdeps/i386/fpu/e_hypotf.S
+++ b/sysdeps/i386/fpu/e_hypotf.S
@@ -18,6 +18,7 @@
    <http://www.gnu.org/licenses/>.  */
 
 #include <sysdep.h>
+#include <i386-math-asm.h>
 
 	.text
 ENTRY(__ieee754_hypotf)
@@ -37,6 +38,7 @@ ENTRY(__ieee754_hypotf)
 	fmul	%st(0)		// x * x : y * y
 	faddp			// x * x + y * y
 	fsqrt
+	FLT_NARROW_EVAL
 2:	ret
 
 	// We have to test whether any of the parameters is Inf.
diff --git a/sysdeps/i386/fpu/e_pow.S b/sysdeps/i386/fpu/e_pow.S
index 40f8227fda..2903e13e59 100644
--- a/sysdeps/i386/fpu/e_pow.S
+++ b/sysdeps/i386/fpu/e_pow.S
@@ -18,6 +18,7 @@
    <http://www.gnu.org/licenses/>.  */
 
 #include <machine/asm.h>
+#include <i386-math-asm.h>
 
 	.section .rodata.cst8,"aM",@progbits,8
 
@@ -165,6 +166,7 @@ ENTRY(__ieee754_pow)
 	orl	%edx, %ecx
 	jnz	6b
 	fstp	%st(0)		// ST*x
+	DBL_NARROW_EVAL
 	ret
 
 	/* y is ±NAN */
@@ -257,6 +259,7 @@ ENTRY(__ieee754_pow)
 	cfi_adjust_cfa_offset (-8)
 292:	fscale			// +/- 2^fract(y*log2(x))*2^int(y*log2(x)) : int(y*log2(x))
 	fstp	%st(1)		// +/- 2^fract(y*log2(x))*2^int(y*log2(x))
+	DBL_NARROW_EVAL
 	ret
 
 
diff --git a/sysdeps/i386/fpu/e_powf.S b/sysdeps/i386/fpu/e_powf.S
index 02338284f6..d929bdc9f1 100644
--- a/sysdeps/i386/fpu/e_powf.S
+++ b/sysdeps/i386/fpu/e_powf.S
@@ -18,6 +18,7 @@
    <http://www.gnu.org/licenses/>.  */
 
 #include <machine/asm.h>
+#include <i386-math-asm.h>
 
 	.section .rodata.cst8,"aM",@progbits,8
 
@@ -148,6 +149,7 @@ ENTRY(__ieee754_powf)
 	testl	%edx, %edx
 	jnz	6b
 	fstp	%st(0)		// ST*x
+	FLT_NARROW_EVAL
 	ret
 
 	/* y is ±NAN */
@@ -196,6 +198,7 @@ ENTRY(__ieee754_powf)
 32:	addl	$4, %esp
 	cfi_adjust_cfa_offset (-4)
 	fstp	%st(1)		// 2^fract(y*log2(x))*2^int(y*log2(x))
+	FLT_NARROW_EVAL
 	ret
 
 
diff --git a/sysdeps/i386/fpu/i386-math-asm.h b/sysdeps/i386/fpu/i386-math-asm.h
index fd4313016c..c15029d2ee 100644
--- a/sysdeps/i386/fpu/i386-math-asm.h
+++ b/sysdeps/i386/fpu/i386-math-asm.h
@@ -36,4 +36,91 @@
 	addl	$8, %esp;			\
 	cfi_adjust_cfa_offset (-8);
 
+/* Define constants for the minimum value of a floating-point
+   type.  */
+#define DEFINE_FLT_MIN				\
+	.section .rodata.cst4,"aM",@progbits,4;	\
+	.p2align 2;				\
+	.type flt_min,@object;			\
+flt_min:					\
+	.byte 0, 0, 0x80, 0;			\
+	.size flt_min, .-flt_min;
+#define DEFINE_DBL_MIN				\
+	.section .rodata.cst8,"aM",@progbits,8;	\
+	.p2align 3;				\
+	.type dbl_min,@object;			\
+dbl_min:					\
+	.byte 0, 0, 0, 0, 0, 0, 0x10, 0;	\
+	.size dbl_min, .-dbl_min;
+
+/* Remove excess range and precision by storing a value on the stack
+   and loading it back.  The value is given to be nonnegative or NaN;
+   if it is subnormal, also force an underflow exception.  The
+   relevant constant for the minimum of the type must have been
+   defined, the MO macro must have been defined for access to memory
+   operands, and, if PIC, the PIC register must have been loaded.  */
+#define FLT_NARROW_EVAL_UFLOW_NONNEG_NAN	\
+	subl	$4, %esp;			\
+	cfi_adjust_cfa_offset (4);		\
+	flds	MO(flt_min);			\
+	fld	%st(1);				\
+	fucompp;				\
+	fnstsw;					\
+	sahf;					\
+	jnc 6424f;				\
+	fld	%st(0);				\
+	fmul	%st(0);				\
+	fstps	(%esp);				\
+6424:	fstps	(%esp);				\
+	flds	(%esp);				\
+	addl	$4, %esp;			\
+	cfi_adjust_cfa_offset (-4);
+#define DBL_NARROW_EVAL_UFLOW_NONNEG_NAN	\
+	subl	$8, %esp;			\
+	cfi_adjust_cfa_offset (8);		\
+	fldl	MO(dbl_min);			\
+	fld	%st(1);				\
+	fucompp;				\
+	fnstsw;					\
+	sahf;					\
+	jnc 6453f;				\
+	fld	%st(0);				\
+	fmul	%st(0);				\
+	fstpl	(%esp);				\
+6453:	fstpl	(%esp);				\
+	fldl	(%esp);				\
+	addl	$8, %esp;			\
+	cfi_adjust_cfa_offset (-8);
+
+/* Likewise, but the argument is not a NaN (so fcom instructions,
+   which support memory operands, can be used).  */
+#define FLT_NARROW_EVAL_UFLOW_NONNEG		\
+	subl	$4, %esp;			\
+	cfi_adjust_cfa_offset (4);		\
+	fcoms	MO(flt_min);			\
+	fnstsw;					\
+	sahf;					\
+	jnc 6424f;				\
+	fld	%st(0);				\
+	fmul	%st(0);				\
+	fstps	(%esp);				\
+6424:	fstps	(%esp);				\
+	flds	(%esp);				\
+	addl	$4, %esp;			\
+	cfi_adjust_cfa_offset (-4);
+#define DBL_NARROW_EVAL_UFLOW_NONNEG		\
+	subl	$8, %esp;			\
+	cfi_adjust_cfa_offset (8);		\
+	fcoml	MO(dbl_min);			\
+	fnstsw;					\
+	sahf;					\
+	jnc 6453f;				\
+	fld	%st(0);				\
+	fmul	%st(0);				\
+	fstpl	(%esp);				\
+6453:	fstpl	(%esp);				\
+	fldl	(%esp);				\
+	addl	$8, %esp;			\
+	cfi_adjust_cfa_offset (-8);
+
 #endif /* i386-math-asm.h.  */
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index ddaa8fc93b..32f24d07a2 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -238,9 +238,9 @@ ildouble: 2
 ldouble: 2
 
 Function: Imaginary part of "cacos_downward":
-double: 3
+double: 4
 float: 3
-idouble: 3
+idouble: 4
 ifloat: 3
 ildouble: 5
 ldouble: 5
@@ -254,9 +254,9 @@ ildouble: 2
 ldouble: 2
 
 Function: Imaginary part of "cacos_towardzero":
-double: 3
+double: 4
 float: 3
-idouble: 3
+idouble: 4
 ifloat: 3
 ildouble: 5
 ldouble: 5
@@ -294,9 +294,9 @@ ildouble: 1
 ldouble: 1
 
 Function: Real part of "cacosh_downward":
-double: 3
+double: 4
 float: 3
-idouble: 3
+idouble: 4
 ifloat: 3
 ildouble: 5
 ldouble: 5
@@ -310,9 +310,9 @@ ildouble: 2
 ldouble: 2
 
 Function: Real part of "cacosh_towardzero":
-double: 3
+double: 4
 float: 3
-idouble: 3
+idouble: 4
 ifloat: 3
 ildouble: 5
 ldouble: 5
@@ -396,9 +396,9 @@ ildouble: 2
 ldouble: 2
 
 Function: Imaginary part of "casin_downward":
-double: 3
+double: 4
 float: 3
-idouble: 3
+idouble: 4
 ifloat: 3
 ildouble: 5
 ldouble: 5
@@ -412,9 +412,9 @@ ildouble: 2
 ldouble: 2
 
 Function: Imaginary part of "casin_towardzero":
-double: 3
+double: 4
 float: 3
-idouble: 3
+idouble: 4
 ifloat: 3
 ildouble: 5
 ldouble: 5
@@ -452,9 +452,9 @@ ildouble: 1
 ldouble: 1
 
 Function: Real part of "casinh_downward":
-double: 3
+double: 4
 float: 3
-idouble: 3
+idouble: 4
 ifloat: 3
 ildouble: 5
 ldouble: 5
@@ -468,9 +468,9 @@ ildouble: 2
 ldouble: 2
 
 Function: Real part of "casinh_towardzero":
-double: 3
+double: 4
 float: 3
-idouble: 3
+idouble: 4
 ifloat: 3
 ildouble: 5
 ldouble: 5
@@ -668,10 +668,10 @@ ildouble: 3
 ldouble: 3
 
 Function: Imaginary part of "ccos_downward":
-double: 2
-float: 2
-idouble: 2
-ifloat: 2
+double: 3
+float: 3
+idouble: 3
+ifloat: 3
 ildouble: 3
 ldouble: 3
 
@@ -684,25 +684,25 @@ ildouble: 3
 ldouble: 3
 
 Function: Imaginary part of "ccos_towardzero":
-double: 2
-float: 2
-idouble: 2
-ifloat: 2
+double: 3
+float: 3
+idouble: 3
+ifloat: 3
 ildouble: 3
 ldouble: 3
 
 Function: Real part of "ccos_upward":
-double: 1
-float: 1
-idouble: 1
-ifloat: 1
+double: 2
+float: 2
+idouble: 2
+ifloat: 2
 ildouble: 2
 ldouble: 2
 
 Function: Imaginary part of "ccos_upward":
-double: 1
+double: 2
 float: 2
-idouble: 1
+idouble: 2
 ifloat: 2
 ildouble: 2
 ldouble: 2
@@ -725,77 +725,69 @@ ldouble: 1
 
 Function: Real part of "ccosh_downward":
 double: 1
-float: 1
+float: 2
 idouble: 1
-ifloat: 1
+ifloat: 2
 ildouble: 3
 ldouble: 3
 
 Function: Imaginary part of "ccosh_downward":
-double: 2
-float: 2
-idouble: 2
-ifloat: 2
+double: 3
+float: 3
+idouble: 3
+ifloat: 3
 ildouble: 3
 ldouble: 3
 
 Function: Real part of "ccosh_towardzero":
 double: 1
-float: 1
+float: 2
 idouble: 1
-ifloat: 1
+ifloat: 2
 ildouble: 3
 ldouble: 3
 
 Function: Imaginary part of "ccosh_towardzero":
-double: 2
-float: 2
-idouble: 2
-ifloat: 2
+double: 3
+float: 3
+idouble: 3
+ifloat: 3
 ildouble: 3
 ldouble: 3
 
 Function: Real part of "ccosh_upward":
-double: 1
-float: 1
-idouble: 1
-ifloat: 1
+double: 2
+float: 2
+idouble: 2
+ifloat: 2
 ildouble: 2
 ldouble: 2
 
 Function: Imaginary part of "ccosh_upward":
-double: 1
+double: 3
 float: 2
-idouble: 1
+idouble: 3
 ifloat: 2
 ildouble: 2
 ldouble: 2
 
 Function: Real part of "cexp":
-double: 1
+double: 2
 float: 1
-idouble: 1
+idouble: 2
 ifloat: 1
 ildouble: 1
 ldouble: 1
 
 Function: Imaginary part of "cexp":
 double: 1
-float: 1
+float: 2
 idouble: 1
-ifloat: 1
+ifloat: 2
 ildouble: 1
 ldouble: 1
 
 Function: Real part of "cexp_downward":
-double: 1
-float: 1
-idouble: 1
-ifloat: 1
-ildouble: 3
-ldouble: 3
-
-Function: Imaginary part of "cexp_downward":
 double: 2
 float: 2
 idouble: 2
@@ -803,15 +795,15 @@ ifloat: 2
 ildouble: 3
 ldouble: 3
 
-Function: Real part of "cexp_towardzero":
-double: 1
-float: 1
-idouble: 1
-ifloat: 1
+Function: Imaginary part of "cexp_downward":
+double: 3
+float: 3
+idouble: 3
+ifloat: 3
 ildouble: 3
 ldouble: 3
 
-Function: Imaginary part of "cexp_towardzero":
+Function: Real part of "cexp_towardzero":
 double: 2
 float: 2
 idouble: 2
@@ -819,19 +811,27 @@ ifloat: 2
 ildouble: 3
 ldouble: 3
 
+Function: Imaginary part of "cexp_towardzero":
+double: 3
+float: 3
+idouble: 3
+ifloat: 3
+ildouble: 3
+ldouble: 3
+
 Function: Real part of "cexp_upward":
 double: 1
-float: 1
+float: 2
 idouble: 1
-ifloat: 1
+ifloat: 2
 ildouble: 2
 ldouble: 2
 
 Function: Imaginary part of "cexp_upward":
-double: 1
-float: 1
-idouble: 1
-ifloat: 1
+double: 3
+float: 2
+idouble: 3
+ifloat: 2
 ildouble: 3
 ldouble: 3
 
@@ -983,27 +983,30 @@ ldouble: 2
 
 Function: "cosh":
 double: 1
+float: 1
 idouble: 1
 ildouble: 2
 ldouble: 2
 
 Function: "cosh_downward":
-double: 1
+double: 2
+float: 1
 idouble: 1
 ifloat: 1
 ildouble: 2
 ldouble: 3
 
 Function: "cosh_towardzero":
-double: 1
+double: 2
+float: 1
 idouble: 1
 ifloat: 1
 ildouble: 2
 ldouble: 2
 
 Function: "cosh_upward":
-double: 1
-float: 1
+double: 4
+float: 2
 idouble: 1
 ifloat: 1
 ildouble: 2
@@ -1019,9 +1022,9 @@ ldouble: 3
 
 Function: Imaginary part of "cpow":
 double: 1
-float: 1
+float: 2
 idouble: 1
-ifloat: 1
+ifloat: 2
 ildouble: 4
 ldouble: 4
 
@@ -1034,10 +1037,10 @@ ildouble: 7
 ldouble: 7
 
 Function: Imaginary part of "cpow_downward":
-double: 1
-float: 1
-idouble: 1
-ifloat: 1
+double: 2
+float: 2
+idouble: 2
+ifloat: 2
 ildouble: 2
 ldouble: 2
 
@@ -1050,10 +1053,10 @@ ildouble: 7
 ldouble: 7
 
 Function: Imaginary part of "cpow_towardzero":
-double: 1
-float: 1
-idouble: 1
-ifloat: 1
+double: 2
+float: 2
+idouble: 2
+ifloat: 2
 ildouble: 1
 ldouble: 1
 
@@ -1067,9 +1070,9 @@ ldouble: 2
 
 Function: Imaginary part of "cpow_upward":
 double: 1
-float: 1
+float: 2
 idouble: 1
-ifloat: 1
+ifloat: 2
 ildouble: 2
 ldouble: 2
 
@@ -1088,10 +1091,10 @@ idouble: 1
 ifloat: 1
 
 Function: Real part of "csin_downward":
-double: 2
-float: 2
-idouble: 2
-ifloat: 2
+double: 3
+float: 3
+idouble: 3
+ifloat: 3
 ildouble: 3
 ldouble: 3
 
@@ -1104,10 +1107,10 @@ ildouble: 3
 ldouble: 3
 
 Function: Real part of "csin_towardzero":
-double: 2
-float: 2
-idouble: 2
-ifloat: 2
+double: 3
+float: 3
+idouble: 3
+ifloat: 3
 ildouble: 3
 ldouble: 3
 
@@ -1120,9 +1123,9 @@ ildouble: 3
 ldouble: 3
 
 Function: Real part of "csin_upward":
-double: 1
+double: 3
 float: 2
-idouble: 1
+idouble: 3
 ifloat: 2
 ildouble: 3
 ldouble: 3
@@ -1160,10 +1163,10 @@ ildouble: 3
 ldouble: 3
 
 Function: Imaginary part of "csinh_downward":
-double: 2
-float: 2
-idouble: 2
-ifloat: 2
+double: 3
+float: 3
+idouble: 3
+ifloat: 3
 ildouble: 3
 ldouble: 3
 
@@ -1176,10 +1179,10 @@ ildouble: 3
 ldouble: 3
 
 Function: Imaginary part of "csinh_towardzero":
-double: 2
-float: 2
-idouble: 2
-ifloat: 2
+double: 3
+float: 3
+idouble: 3
+ifloat: 3
 ildouble: 3
 ldouble: 3
 
@@ -1192,9 +1195,9 @@ ildouble: 3
 ldouble: 3
 
 Function: Imaginary part of "csinh_upward":
-double: 1
+double: 3
 float: 2
-idouble: 1
+idouble: 3
 ifloat: 2
 ildouble: 3
 ldouble: 3
@@ -1207,7 +1210,9 @@ ldouble: 2
 
 Function: Imaginary part of "csqrt":
 double: 1
+float: 1
 idouble: 1
+ifloat: 1
 ildouble: 2
 ldouble: 2
 
@@ -1253,9 +1258,9 @@ ldouble: 5
 
 Function: Imaginary part of "csqrt_upward":
 double: 1
-float: 1
+float: 2
 idouble: 1
-ifloat: 1
+ifloat: 2
 ildouble: 4
 ldouble: 4
 
@@ -1429,9 +1434,9 @@ ldouble: 3
 
 Function: "erfc_downward":
 double: 2
-float: 2
+float: 3
 idouble: 2
-ifloat: 2
+ifloat: 3
 ildouble: 4
 ldouble: 4
 
@@ -1445,9 +1450,9 @@ ldouble: 4
 
 Function: "erfc_upward":
 double: 2
-float: 2
+float: 3
 idouble: 2
-ifloat: 2
+ifloat: 3
 ildouble: 5
 ldouble: 5